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Representing spatial experience and solving spatial problems in a simulated robot environment Rowat, Peter Forbes 1979

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9t  REPRESENTING  S P A T I A L E X P E R I E N C E AND S O L V I N G S P A T I A L PROBLEMS I N A S I M U L A T E D ROBOT ENVIRONMENT by PETER  M.Sc,,  University  FORBES  SOWAT  of British  Columbia,  A T H E S I S SUBMITTED IN PARTIAL THE R E Q U I R E M E N T S FOR T H E DOCTOR O F  EULF.ILLMENT D E G R E E OF  PHILOSOPHY in  THE  FACULTY  { Department  We  OF  GRADUATE  of Computer  STUDIES Science)  accept t h i s t h e s i s as conforming to the required standard- .  THE  UNIVERSITY  OF  October, ^  BRITISH  1972  COLUMBIA  1979  P e t e r Forbes Rowat , 1 9 7 9  OF  In presenting  this thesis in partial  fulfilment of the requirements for  an advanced degree at the University of B r i t i s h Columbia, I agree that the Library shall make i t freely available for reference  and study.  I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives.  It is understood that copying or publication  of this thesis f o r financial gain shall not be allowed without my written permission.  Department of  CfriAA^u^V  SCL&AICI  The University of B r i t i s h Columbia 2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5  Date  11  Abstract This t h e s i s i s concerned with s p a t i a l a s p e c t s of p e r c e p t i o n and a c t i o n i n a simple robot. To this end, the problem of designing a r o b o t - c o n t r o l l e r f o r a robot in a simulated robot-environment system i s considered* The environment i s a two-dimensional t a b l e t o p with movable p o l y g o n a l shapes on i t . The robot has an eye which 'saes' an area of the t a b l e t o p centred on itself, with a r e s o l u t i o n which decreases from the centre to the periphery. Algorithms are presented for s i m u l a t i n g the motion and c o l l i s i o n of two dimensional shapes i n t h i s environment. These a l g o r i t h m s use r e p r e s e n t a t i o n s of shape both as a sequence, of boundary p o i n t s and as a r e g i o n i n a d i g i t a l image. A method i s o u t l i n e d f o r c o n s t r u c t i n g and updating the world model of the robot as new v i s u a l i n p u t i s r e c e i v e d from the eye. I t i s proposed t h a t , i n the world model, the s p a t i a l problems o f p a t h - f i n d i n g and object-moving be based on a l g o r i t h m s t h a t f i n d the s k e l e t o n of the shape of empty space and of the shape of the moved o b j e c t . A new i t e r a t i v e a l g o r i t h m f o r f i n d i n g the s k e l e t o n , with the property that the s k e l e t o n of a connected shape i s connected, i s presented. . T h i s i s a p p l i e d to p a t h - f i n d i n g and simple object-moving problems. Fi.nally, d i r e c t i o n s f o r f u t u r e work, are o u t l i n e d .  iii TABLE OF CONTENTS I  Int rod u c t i o n .......................................... 1 1.1 Aims and motivation . . . . . . . . . . . . . . . . . . . a . . . . .!,».... .1 1.2 The a c t i o n c y c l e ............. * .............. , .6 1*3 System overview ................................. ,10 1.4 System s t a t u s ................................... 22 1.5 Reader's guide .................................. 23 XI Background Issues • • . . . . . . . . . . . . » . : < . . * > , • » . • '• . . . . i. * » • ' • • 25 II. 1 a r t i f i c i a l intelligence i s a science with g o a l s and paradigms 25 IX.1.1 The paradigms of A r t i f i c i a l I n t e l l i g e n c e ...26 IX. 1,. 2 AI has p o t e n t i a l l y rich relationships with many other f i e l d s 29 II.1.3 Understanding the world i s a p r e r e q u i s i t e to doing mathematics 4 . . . . . . . . . . . . . . . . . . . . . 34 IX. 1.4 A theory of intelligence w i l l be p r i m a r i l y concerned with representations of t h e world .............................. 36 II.1.5 A theory o f i n t e l l i g e n c e w i l l describe intelligent systems a t many different l e v e l s ,. . .. ....... . . . . . . . ...... ....... ......... .39 I I . 2 Simulating a robot i s a promising approach to A r t i f i c i a l Intelligence ........................ 41 11*3 The c u r r e n t AI t r a d i t i o n f o r t h e design of planning and problem s o l v i n g ' systems i s not e a s i l y adaptable t o my purpose . 4 . . . . 45 II.3. 1 An exegesis of some AI p l a n n i n g and problem-solving systems ................... .45 11.3.2 C r i t i c i s m s of the Fregean t r a d i t i o n i n planning and problem-solving ............... .55 I I . 4 A survey of c l o s e l y r e l a t e d t o p i c s ............. 58 II*4.1 Previous robot s i m u l a t i o n s ................ 59 IX. 4'. 2 Three a n a l y s e s of simple organisms ......... 62 11.4.3 S i m u l a t i o n s based on animal behaviour . .... 65 IX. 4*4 Robot s i m u l a t i o n s based on decision theory .................................... 67 11.4.5 C o g n i t i v e maps ............................ 69 11.4.6 S p a t i a l planning systems .................. 71 11*4.7 Systems f o r s i m u l a t i n g . the motion of r i g i d o b j e c t s ............................. 72 IX. 4. 8 Imagery ............ 76 I I . 4.9 B e h a v i o u r a l t h e o r i e s ...................... 77 III The s i m u l a t e d organism-environment system ........... 83 I I I . 1 The simulated environment, TABLETOP ............ 87 I I I . 1.1 An overview of the s i m u l a t i o n method ..... 87 III.1*2 The algorithms used i n the s i m u l a t i o n .... 97 III-1.2.1 The o v e r l a y problem 117 III.1.3 An example of TABLETOP performance 122 I I I . 2 The simulated organism Utak and h i s t a s k s 128 III.2.1 Design c o n s i d e r a t i o n s ......... .,128  iv  III.2.2 III,. 2.3  IV  V  The s e n s o r y - m o t o r c a p a b i l i t i e s o f Otak ..130 Examples of Utak's sensory-motor experience ... , , . .... , ..... ... ... .» ... . 132 I I I , 2. 4 Examples o f t a s k s f o r Utak 134 I I I . 3 An extension and two generalizations of TABLETOP ...... 135 Towards t h e d e s i g n o f a r o b o t - c o n t r o l l e r »I * . . . . . . . . 143 IV. 1 An a n a l o g y i . 143 IV,2 The p a r t s o f an o r g a n i s m - c o n t r o l l e r ...... .. ... 147 IV, 3 The g o a l b e h a v i o u r f o r an o r g a n i s m - c o n t r o l l e r .149 IV.4 A f i r s t approach t o implementation ............175 IV. 4.1 D e f i n i t i o n o f t h e w o r l d model ,.,.,......,..176 IV;l4>2 P e r c e p t i o n : accommodation to the first r e t i n a l impression . . . ^ , 1 7 8 IV, 4.2,1 Edge and r e g i o n f i n d i n g .............179 IV.4;2.2 Interpreting the first retinal impression . . . . . . . . . . . . . . . . . . . . . . . . . . 181 IV. 4.2.3 Accommodating the default world model to the first retinal impression 185 IV,4.3 P e r c e p t i o n : accommodation t o subsequent r e t i n a l impressions . . . . . . . . . . . . . . . . . . . . . . 187 IV;. 4.4 accommodation, a n o t h e r a p p r o a c h ..........190 IV. 4,5 The s p a t i a l p l a n n e r .,.,,.,.,,..,....,,.,,,192 IV.5 An a l t e r n a t i v e a p p r o a c h t o i m p l e m e n t a t i o n i . . . . . 1 9 3 IV. 6 Summary .................................194 P a t h - f i n d i n g and t h e s k e l e t o n o f a p l a n a r shape i..,,,196 V. I Introduction to path-finding algorithms . . . . . . . . 196 V.2 The s k e l e t o n 202 V, 2, 1 D e f i n i t i o n and p r o p e r t i e s ............. 203 V.2.2 Approximating the E u c l i d e a n plane ......... 206 V.2.3 Montanari's algorithm .....................210 V. 2. 4 The new a l g o r i t h m 214 V.2,5 Ridge-following .V, i . ^ > i .->. . 219 V.2.6 D s i n g p a r a l l e l i s m t o compute t h e s k e l e t o n .224 V,2.7 Paths between objects and superfluous branches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 V.3 Using the skeleton f o r p a t h - f i n d i n g . . . . . . . . . . . . 226 V,3-1 D e s c r i b i n g a s k e l e t a l path . . . . . . . . . . . . . . . . 228 V, 3. 2 O p t i m i z i n g a s k e l e t a l p a t h . . . . . . . . . . . •» . .. 230 V.3.3 C o m p a r i s o n o f s k e l e t a l and A* p a t h f i n d i n g 233 V.4 Other a p p l i c a t i o n s of the skeleton . . . . . . . . . . . . . 233 V, 4. 1 O b j e c t moving i . . . . . . . . . . . . 234 V. 4.1.1 C i r c u l a r s h a p e d o b j e c t o f r a d i u s r ... 234 V,4,1.2 Other o b j e c t shapes i , , ... . 234 V.4,1.3 An L - s h a p e d o b j e c t . . . . . . . . . . . . . . . . . . . 235 V.4.2 F i n d i n g empty s p a c e . . . . . . . . . . . . . . . . . . . . . . . 236 V.4.3 Finding t h e s h o r t e s t d i s t a n c e between two shapes 2 36 V,4.4 F i n d i n g nearest neighbourhood r e g i o n s ,.,..237 V. 5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238  V  VI  Summary, c o n c l u s i o n ^ and f u t u r e work . . . . . . . . . . . . . . . 240 VI. 1 Summary ... .. ......... ............ . . 240 VI. 2 Conclusion 243 VI.3 Research problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 a p p e n d i c e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....... . ......... .246 a.1 T a B L E T O P u s e r ' s manual .... . . ^ 2 4 6 A.2 A c o m b i n a t o r i a l lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 A.3 On F u n t ' s r i g i d shape r o t a t i o n a l g o r i t h m . . . . . . . . . 251 R e f e r e n c e s ........... . . . . . . . . . . . . . . . . . . ... .-M . . . . . . . . . . . . . . 258 v  vi L I S T OF FIGURES Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure  1.1 . . . . . . . . . . . . . 9 1.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.3 13 I. 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.5 . . . . . . . . , . . . ; , . » . . . . . . . . , . . . , , . , . . . , , . , . . , . . . . ; . . . 20 1.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 III. 1 , ....... 91 III.2 93 III.3 , 96 III.4 99 I I I . 5 ...... .... . 103 III.6 105 III.7 107 111*8 109 III.9 110 III.10 112 III.11 116 III.12 120 III.13 121 I I I . 14 123 III.15 .................................... * ...133 IV.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 IV.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 IV. 3 . 178 IV.4 ..,.,.,,.....,...184 IV.5 185 V.I ,.. ,. 198 V.2 201 V.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...... ....... 207 V.4 , 208 V.5 .,. 210 V.6 211 V.7 , 214 V. 8 .....................218 V. 9 . . . . . . . . . . . . . . . . . . . . . . . . . ,., 221 V.10 223 V.11 ........ 227 V.12 . . . . ....... 229 V.13 231 A3.1 , 252  vii  Oh t h e mind, mind h a s m o u n t a i n s ; c l i f f s F r i g h t f u l * sheer, no-man-fathomed.  of f a l l Gerard  Manley H o p k i n s  ££k£2£i e l e m e n t s  I would l i k e t o acknowledge my enormous debt to Richard Rosenberg, who h a s s u p e r v i s e d me, and who has g i v e n me a d v i c e , encouragement and s u p p o r t beyond a l l expectations of duty throughout t h e many y e a r s I h a v e s p e n t on t h e Ph.D program. I w i s h t o t h a n k A l a n Mackworth f o r s e r v i n g on my t h e s i s committee and f o r a l w a y s b e i n g r e a d y t o l i s t e n and t o g i v e me a d v i c e and e n c o u r a g e m e n t ; H a r v e y Abramson* Ray R e i t e r , Bob Wpodham, and John Y u i l l e f o r s e r v i n g on my t h e s i s c o m m i t t e e ; Gordon M c C a l l a , B i l l Havens, R a c h e l G e l b a r t , B r i a n Funt, Mike • K u t t n e r , • Roger Browse, Jan Mulder, and Randy G o e b e l f o r many helpful d i s c u s s i o n s ; Nona and Gwen f o r d r a w i n g t h e d i a g r a m s ; and above all Nona, w i t h Ruby, L e n a and Taku, f o r s t a n d i n g by me t h r o u g h a l l t h e s e y e a r s , s u p p o r t i n g ma i n e v e r y i m a g i n a b l e way, and f o r b e i n g t h a i r own d e l i g h t f u l s e l v e s . .  1  CHAPTER I INTRODUCTION  1.1. Aims and  motivation  This t h e s i s i s animated connection simple  by  between p e r c e p t i o n  things  a  and  desire action.  to  understand  Every day  we  do  the such  as  a v o i d i n g a l l o b s t a c l e s i n c r o s s i n g a c l u t t e r e d room n a v i g a t i n g through an u n f a m i l i a r house making  and  executing  a mental plan to go to the. l o c a l shop  or c r o s s a campus moving an awkward piece of f u r n i t u r e around a house. Likewise  our pet dogs and  their spatial  c a t s are good  so  easily,  processes  which may The  navigating  through  world. For an organism to do  Here you  at  are  what  such  tasks -  computational  required?  w i l l f i n d the beginnings of an answer to t h i s be r e f i n e d i n any question  as  one  stated  question,  of a dozen d i r e c t i o n s ; is  too  meaningful answer; to d e l i n e a t e i t more  nebulous precisely  to be given I  opted  a to  Inlntroduction  2 proceed 1.  as f o l l o w s :  Design and implement a simulated robot world  which  reflects  to a c e r t a i n extent the s p a t i a l aspects of a c l u t t e r e d room or the f l o o r p l a n of a house. . 2.  Specify  a  class  of  tasks  of a s p a t i a l nature which the  robot might reasonably be expected 3..  Design handle  computational  processes  The a  simulated robot world  non-trivial  and a c t i o n .  treatment  The  world.  which enable the robot t o  these t a s k s i n a reasonably  T h i s , i n summary, has been my  t o solve i n t h i s  i n t e l l i g e n t manner.  research program. i s c a r e f u l l y designed to  enforce  of the i n t e r a c t i o n between p e r c e p t i o n  robot's sensory input from d i s t a n t p a r t s of the  environment i s e i t h e r non-existent or very i n e x a c t and f u z z y , i n accord with r e a l world organisms; actions  executed.  I  yet p l a n s have t o be made  am thus s q u a r e l y c o n f r o n t e d , a l b e i t  c r u d e l y , with the problem of a c t i n g i n the. face and  inexact  knowledge.  In  the  simulated  of  and very  incomplete  robot world i t i s  p o s s i b l e f o r the executed  a c t i o n s t o be inexact i n  fuzzy  i n the r e a l world.. So f a r , however, I  manner,  have suppressed of  the  just  as  t h i s f e a t u r e , i n order to ease  overriding  concern:  the  creation  of  a  similarly  the  achievement  a  functioning  robot-controller.  This t h e s i s i s a l s o animated by the b e l i e f t h a t fundamental importance  to understand  i n v o l v e d i n s p a t i a l problem s o l v i n g .  the computational  it  is  of  processes  There are s e v e r a l l i n e s of Inlntroduction  3 argument t o e n c o u r a g e t h i s First  of a l l , s p a t i a l  fundamental a b i l i t y and  i f we  bumping  couldn't into  instance, or and  solve  we c o n t r o l  since  spatial We  large  must be  we i n h a b i t  problems  are  also  rectangular  one  we  of  would  superbly  of a small  round  spatial  [Marr,1976]  object  reasoning  with  world  at i t .  winding  be For  roads  the v e l o c i t y  precision.  satisfies  to guide the choice  most  always  good  s h a p e s on  fine  the  a spatial  l o t mazes, and a b a l l - p l a y e r c o n t r o l s  Second* by  reasoning  we p o s s e s s ,  things!  i n parking spin  belief.  the c r i t e r i a  of a research  proposed  problem  i n AI.,  "If one b e l i e v e s t h a t t h e aim o f information-processing studies i s to formulate and understand particular information-processing problems, then i t i s the s t r u c t u r e o f those problems t h a t i s central, not the mechanisms through which they are implemented* T h e r e f o r e , t h e f i r s t t h i n g t o do i s to find problems that we c a n s o l v e w e l l , f i n d o u t how t o s o l v e them, and examine o u r performance in the light of that understanding* The most fruitful source of such p r o b l e m s i s o p e r a t i o n s t h a t we p e r f o r m well, fluently, reliably, (and hence unconsciously) , since i t is d i f f i c u l t t o s e e how r e l i a b i l i t y c o u l d be achieved i f t h e r e . w e r e no sound u n d e r l y i n g method." Spatial  reasoning  reliably"  and  worthwhile  branches; touching  largely  research  Third, crayfish  i s a problem  there  runs an  we  solve  unconsciously;  "well,  therefore  fluently, i t'i s  a  objective. i s  an  mazes; b i r d s orca  that  whale  evolutionary don't races  a s t a l k ; a mouse w i l l  bump  argument.  into  through  a  rarely f a i l  or  a dog i t s bone; t h e monkey s w i n g s from  as  "ontegeny  r e c a p i t u l a t e s phylogeny",  forest  simple  leaves  and  kelp  bed w i t h o u t  to reach  i t s cheese  branch  one  The  t o b r a n c h . . So,  might  well  expect  Ialntroduction  4 s p a t i a l reasoning t o underly our higher mental f a c u l t i e s . aside,  the  minuscule  devastating flowers,  of  the  hummingbird  solves  an a  s p a t i a l problem: given a meadow with a p r o f u s i o n of  each  variety  propertias,  the  i n p u t while  foraging  expended  brain  As  having  humming  [Sass  bird  and  et  different appears  to maximize net energy  simultaneously  a l , , 1976/].  A  nectar-producing  minimizes  truly  the  amazing  piece  time of  computation by a very s m a l l brains Fourth,  there i s a developmental  argument.  Young c h i l d r e n  s o l v e s p a t i a l problems such as the c l a s s i c a l monkey and problem hours  before old,  flinching  they can t a l k , and the newborn babe, only a  will if  bananas  it  react  appropriately  comes  dangerously  to  a  close,  f o l l o w i t with eye-movements i f i t passes  moving and  behind  few  object,  c o n t i n u i n g to a  stationary  spatial  metaphors.  o b j e c t [ Bower, 1974 ]. Fifth, Consider  our language  the  word  is  permeated  "permeate"  by  j u s t used.  Does i t not evoke a  v i s u a l image c o n s i s t i n g of " s p a t i a l metaphors", "permeating", a  very p h y s i c a l sense, "our language"?  accompany every sentence type  of  language  uses  one u t t e r s ? spatial  in  Does not a v i s u a l image Even  metaphors.  the  most  abstract  For i n s t a n c e , one  " b u i l d s " an argument "on" a f i r m "foundation"; one  "arrives  at"  a conclusion; S i x t h , there are spatial  reasoning  scientific  many  and  discoveries.  anecdotes  visual For  imagery instance,  concerning in the  the  use  of  making fundamental paper  models  of  I•Introduction  5 Pauling f o r t h e a l p h a - h e l i x , and of Watson and C r i c k f o r the DNA molecule; Faraday's v i s u a l i z a t i o n o f magnetic l i n e s of f o r c e narrow  tubes  curving  as  through space; Kekule's d i s c o v e r y of the  s t r u c t u r e of the benzene molecule by h i s v i s u a l i z a t i o n of a r i n g of  snake-like,  tail;  writhing,  chains, each s e i z i n g i t s neighbour's  and i n mathematics, Hadamard has documented many i n s t a n c e s  where a problem was apparently These arguments i n favour lead  solved by v i s u a l imagery.. of s p a t i a l  one to propose the hypothesis  f o r s p a t i a l reasoning developed  reasoning  t h a t the mechanisms r e q u i r e d  may well underly  other a b i l i t i e s t h a t have  l a t e r i n e v o l u t i o n , f o r i n s t a n c e the use of language..  The o v e r a l l s t r u c t u r e of my t h e s i s may now I  functioning  summarized..  The o v e r a l l implementation g o a l i s t o  robot-controller  f o r the  simulated  implemented p a r t s are d e s c r i b e d i n d e t a i l . implemented,  their  theory  only  be  build  robot..  For those  parts  cases,  further  Intelligence,  intellectual disciplines:  feature  that  a The  not  i n some progress  made through an attempt a t implementation.  a l l i s s a i d and done, t h i s i s the Artificial  made on  and design i s sketched  depth, to the point a t which, i n some can  be  l a y o u t a r e s e a r c h program and d e s c r i b e the progress  several fronts.  yet  inexorably  After  distinguishes  as a c t u a l l y p r a c t i s e d , from a l l other the  development  of  theory  through  program implementation.  Iaintroduction  6  1,2  The a c t i o n  The  cycle  information-processing  p h y s i c a l l y i n t e r a c t s with the three  distinct  interest  of  p a r t s : sensory r e c e p t o r s , a c t i o n e f f e c t o r s ,  and  which  in  is  outside  world  r e l a t e s the senses  must  and  the  this  thesis  will  be  referred  in  intermediary, requirement behaviour;  to  as  My  the  The i n t e r m e d i a r y could of course be n u l l  t h a t r e s u l t s i n a very u n i n t e r e s t i n g organism survive  actions..  i n a s u f f i c i e n t design f o r the i n t e r m e d i a r y ,  robot-controller.  long  that  consist  an i n t e r m e d i a r y t h a t main  component of any organism  its  the  world.  In  my  robot-controller,  that  the  organism  which  not  case, the design of the is  constrained  e x h i b i t reasonably  ( I n t e l l i g e n t behaviour  could  but  by  the  intelligent  w i l l be taken as a  primitive  judgment and analyzed no f u r t h e r . ) The the  major task of a r o b o t - c o n t r o l l e r , i n order  organism's  survival  chances,  to  improve  i s to b u i l d a world model: a  model of the o u t s i d e world.. In i n f o r m a t i o n - p r o c e s s i n g terms, world  model  interpretive sensory  is  a  data  procedures,  input.  base  of  enables  Eguivalently,  it  facts the  procedures f o r making p r e d i c t i o n s about good  world  The purpose plans and  model  makes  which, together with  prediction  is  a the  a  data  of  future  structure  outside  world*  and A  c o r r e c t p r e d i c t i o n s most of the time.  of a world model i s to  allow  the  thus to b e t t e r achieve the organism's  construction goals.  of  Building  a world model i s an i n d u c t i v e task, using sensory i n p u t s as  the  I•Introduction  7  primitive organism  items  evidence.  i s a f u n c t i o n of  furthermore o f the  of  can  outside  n e v e r be world  organisms  octopus,  for instance,  surface  texture  by  effectors, as  an  one  may  the  and  argue  whereas  there  design  of  receptors,  As  true  a  world  an and  nature  consequence, models.  To  only  an  touch  can  smooth  perspex sphere i s  o r g a n i s m and sensory  fact,  a  certainly  the  case of the i n a l a r g e or  an  may  the  a t any  signal  be  outside  amount o f  world  unbounded  potentially world*  n a t u r a l sensory  of  may  the  be  sense-able  of  by  outside  that  a  side finite  i f  one  world  are  or both,  finite  neither contain  information  nor  available  argument: by  receptors,  input  is  then  This i s  small  A more p r a c t i c a l a l l  the  information  information.  could  taken  information,  moreover,  the  is  action  sensory  of  is infinite,  fact  world  the  amount  and  sense-able  more g e n e r a l  On  and  supported  amount  time  features  This  world  moment i n t i m e a  unbounded  one  outside  receptors  or  finite  a t any  that  infinite  outside  First,  receive  detected  r e c e i v e a l l the the  of  smooth p e r s p e x c y l i n d e r h a v i n g  obvious  or t h a t the  i s an  organism  is  either  continuous*  a special  of  a small  organism's  follows.  only  which c o u l d be believes  model  c o r r e c t - the  i s n e c e s s a r i l y always sloppy.  as  can  from  a long  its  i n f o r m a t i o n - t h e o r e t i c arguments.  organism  there  curvature,  intuitively  following  of  different  whose s e n s e  from  world  unknowable.  very  i n t e r f a c e between an  defined  design  assumed t o be  build  and  the  [Wells,1978].  same c u r v a t u r e The  the  i s forever  different  indistinguishable  Thus  the  very  digitized,  Inlntreduction  8  hence i s an a p p r o x i m a t i o n to  be  the  statement  action  that  side,  the r e s u l t  implies  the  standard  of comparison  existence  points  percent  here* .  supposing  But  taken,  so  First,  so  mistakes  discussion  repetition perception,  While introduce  is  p l a n n i n g , and  taken  they  am  following  i n the  world  model which  incorrect,  may  be  very  or sloppy,  was  model i s n e v e r  outcome  used  as a  There  are  one  hundred  simply  wrong.  model i s e x a c t , t h e : c o m p u t a t i o n  of  require  of  life  an  unbounded  goes on and  in  amount  actions  must  amount  be of  I n our  in serial  are presumably  performed in  in  three  parts:  in  these most  parallel.  general,  i n p u t a t any  tactile*  the p e r p e t u a l  o r d e r , whereas  organisms  Our  robot-controller  terminology: the t o t a l  (visual,  by  a loop containing  action.  1.1.  figure  a t the top l e v e l *  a u d i t o r y , .,.)  a sensory,  summary,  was  world  cycle,  discussing  olfactory,  impression,  position  I  action  The  inevitable.  performed  the f o l l o w i n g  called  In  are  of t h e : a c t i o n  as f o l l o w s . .  must be c u t o f f i n a f i x e d  functions,  organisms  tactile,  may  argue  s o f a r i s summarized  p r o c e s s e s are  living  a  the world  may  outcome o f the a c t i o n .  predicted  the computation  robot-controller  three  a  i n the o u t s i d e world  - and The  o f an of  t h e outcome o f an a c t i o n time..  one  f o r the  e x a c t , so t h e  Second,  time  that are generally  continuous. On  two  to q u a n t i t i e s  sensory instant  let  me  (visual, of  time  olfactory,, auditory,,...)  D a v i d Hume*  then, the a c t i o n  cycle  information-processing  of  occupies a any  fundamental  organism.. ImIntroduction  The  PLAN MODEL  -MOTZG&_ OUTPUT  S L 0 P I N  P  r tr k r  y ACE  fe I Gr-LLfLE EJL  THE ACTION CYC  10  elucidation main t a s k chapters  I-3  o f my r e s e a r c h  The  the outside  is  i s the  described  in  world;  main p r o g r a m s : TABLETOP,  OTAK, t h a t  simulates  that  t h e r o b o t ; and  t h e r o b o t - c o n t r o l l i n g program.  restraining the  boundary later.  that  some  the o b j e c t s will  There  this  a frictionless  b o u n d a r y ; . T h e r e may  tabletop,  constitute  be  of  the  outside  another  object  standstill  t o a s t h e verc[e t o a v o i d  confusion  i n a fixed  offending  obstruction.  a  small  The c o n c e p t s  so.  Consequently there  times  associated  object  collides  with with  robot an  object.  laws o f p h y s i c s  remains i n v a r i a n t  gap  during  comes  between  o f mass and  to  an  have  difficulty in "slow  down"  movements, and when a wide  moving  obstacle  near  up" o r  by  i t and t h e  momentum  would be l i t t l e  a r e no " s t a r t  hold:  i s obstructed  t h e moving o b j e c t  been i m p l e m e n t e d , t h o u g h t h e r e  doing  o r movable  o f a moving o b j e c t  with  shapes  tabletop  or t h e verge then  immediate  shapes  These  world*  t a b l e t o p the everyday  path  polygonal  The  a r e n e v e r any h o l e s  i f the  a  polygonal  and some movable.  i s t o s a y , t h e shape o f an o b j e c t and  t a b l e t o p with  be a r b i t r a r y  fixed  referred  simulated  motion,  not  robot,  overview  TABLETOP s i m u l a t e s  On  My p r o g r e s s  program  system c o n s i s t s of t h r e e  simulates  on  the simulated  I V and V.  System  PPA,  i t s structure, for  of  one: o f  its  lateral  Inlntroduction  11  extremities  no  t e r m i n a l r o t a t i o n of any kind i s s i m u l a t e d : t h e  o b j e c t simply comes t o an immediate UTAK  simulates  dimensionless space.  the  robot, Utak*, who i s r e p r e s e n t e d  p o i n t and i s f r e e t o move anywhere t h e r e i s  Though  dimensionless,  adjacent o b j e c t s which have edge-to-edge  halt.  contact*  and can move with  he: cannot  point-to-point,  slip  as a empty  between  point-to-edge,  two or  He can grasp an a d j a c e n t movable o b j e c t ,  and r e l e a s e such a o b j e c t .  An  example,  task  environment i n c l u d i n g Utak i s shown i n f i g u r e 1.2... Utak senses h i s environment with an eye field  of  view  centre  (the "fovea")  periphery,* . at  having and  a  progressively  sticking  pointing directly  limited  a v a r i a b l e r e s o l u t i o n : f i n e i n the coarser  towards  The eye may be thought of as a TV camera,  the top of a s t a l k  camera of  and  having  the  suspended  v e r t i c a l l y up from Utak, with the  downwards a t the t a b l e t o p and i t s f i e l d  view c e n t e r e d on Utak.. Thus the eye gets  a  two-dimensional  view o f p a r t o f the t a b l e t o p and an image of Utak always appears at  the c e n t r e of the f i e l d The  r e t i n a l geometry  Each l i t t l e certain  of view* of the eye i s shown i n f i g u r e I * 3 ( a ) .  square c o n s t i t u t e s a r e t i n a l  area  of  the  task  environment  field*  a  n  ^  covers  a  depending upon Utak's  iRather than always r e f e r r i n g t o the "robot" and using the pronoun " i t " , I w i l l u s u a l l y r e f e r to "Utak", who may be l i k e n e d to a semi-intelligent dog, and use the pronoun "him". Of course, no s e x u a l discrimination i s intended.^ Likewise no p h y l o g e n e t i c d i s c r i m i n a t i o n i s intended e i t h e r : "Utak" and "him" are simply more pleasant ways t o r e f e r t o what i s merely an abstract device embodied i n a computer program used to probe very g i n g e r l y i n t o the p r i n c i p l e s o f c o g n i t i v e s c i e n c e . I«Introduction  12  Fix  ED  PART  ITION  MOVABLE 08J-6CT  U T A K  A  Fl&VRE  I.Z.  A  TASK  ENVIRONMENT.  FIGURE 1.3  (a) The r e t i n a l  geometry.  0  o  O  o o  O  O  6  0  o  O  o  O  o  6  1  6 6 6  7  /  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  o  X  o  %  2,  V  ©  o  O  o o  o  o  O  o  o o  o  O  O  o o  ©  • • • • E D E E • • • • • • B E • • • • F J E E E E G 1 E O E E O E  • • • • • • E E • • • • • • • • O  o  o  o  o  o  O  o  O  ©  ©  o  o  o  o  o  o  6  (o  (o  (o  6  FIGURE 1.3  2,  z  I  o  1  0  O  O  O  o  »•>  4  (b) The i n t e g e r s i n t h e squares form the r e i t i n a l i m p r e s s i o n c o r r e s p o n d i n g to, Utak's p o s i t i o n i n F i g u r e 1.2.  14  position. retinal range  Corresponding cell,  which  to  each  registers  retinal  field  there  a gray_level, or i n t e g e r i n the  0 - 7 , t h a t depends on the r a t i o of o b j e c t t o  of the task environment  total  covered by the r e t i n a l f i e l d .  retinal  cells  at  one  particular  r e t i n a l impression r e c e i v e d by Utak when figure  1.2  "tactile"  i s shown  i n figure  r e c e p t o r s , one i n each  directions,  which  immediately  adjacent  structured  allow  s e t of  him  object.. eight  i n time* .. The  i n the  situation  of  the  to  sense  colors  by a l l  instant  1.3(b).  A  area  A retinal  impression i s the s t r u c t u r e d s e t of g r a y l e v e l s r e g i s t e r e d the  is a  of  Utak a l s o has e i g h t eight  basic  the  tactile-  compass  colour  impression  registered  by  of  an  i s the  the  tactile  r e c e p t o r s at one p a r t i c u l a r i n s t a n t of time*'. In  sum,  then, Utak i n h a b i t s an o u t s i d e world which may be  l i k e n e d t o a t a b l e t o p with c o n f i n i n g verges, where he can wander around  and move o b j e c t s , and where h i s sensory c o n t a c t with  world c o n s i s t s of a s e r i e s of r e t i n a l and It  i s h i s problem  (James' "blooming, model"  to  make  buzzing  f o r planning  sense  impressions.  of a l l t h i s sensory i n p u t  confusion")  purposes.  tactile  this  That  and  create  a  "world  i s a major problem f o r  Utak's b r a i n , the r o b o t - c o n t r o l l i n g program. The  class  of t a s k s given to Utak c o n s i s t s of path  ("Go t o t h e n o r t h - e a s t corner") and o b j e c t moving the  square  of a task may model.,  tasks  finding ("Push  movable o b j e c t i n t o the next room").. The statement require  Consider,  considerable  f o r instance,  changes  the  to  Utak's  object-moving  task  world just  Inlntroduction  15  mentioned. has  only  his  world  a  room  I f Otak has so f a r seen a square explored  one  "understanding" an  but  what he t h i n k s i s one end of a s i n g l e room,  model before t h e task statement with  movable o b j e c t  square  movable  the task statement  w i l l simply c o n s i s t of  object  i n i t ; but  h i s world model w i l l  after  include  e x t r a room with a doorway which connects i t t o the room he's  currently  i n at  a  position  consistent  with  h i s accumulated  sensory experience t o date. PPA, ACCOM, act;  the r o b o t - c o n t r o l l e r , i s d i v i d e d  SPLAN,  and  ACT.  the three p a r t s o f  the a c t i o n  cycle..  to  ACCOM  accepts  SPLAN  i s the  task  a  spatial  i s r e s p o n s i b l e f o r always maintaining a v a l i d  achieve the c u r r e n t  updating  parts:  (accommodates) the c u r r e n t world  model i n the l i g h t of t h i s new evidence; and  three  PPA i s an acronym f o r p_erceive, p_lan,  r e t i n a l impression and m o d i f i e s  planner  into  by  creating  a  new  plan  plan  or by  an o l d one; while ACT simply computes from the c u r r e n t  plan t h e next a c t i o n t o be executed. . A in  world  model, a t a s k , and a plan a r e d e f i n e d at a l l times  PPA, whatever Utak's a c t u a l s i t u a t i o n ,  before  Utak  "opens  h i s eye" and  including  the moment  receives his f i r s t  retinal  impression. . So far,; the f o l l o w i n g d e f a u l t s have been used. world  model  i s taken  Utak's i n i t i a l assumed  world,  to  position. which  be  a l a r g e empty square  The d e f a u l t task means  "collect  input) t o confirm the c u r r e n t world results  i n the s p e c i f i c  task  i s to  evidence:  The  centred on  explore  the  ( i ; e . sensory  model".. I f the d e f a u l t task  o f , say, "go t o t h e . n o r t h - e a s t Ialntroduction  16  c o r n e r " , then the c u r r e n t plan would c o n s i s t of walk a c t i o n s the  hypothesized  position  of  the  north-east  p o s s i b l e d e f a u l t s are " s l e e p " o r " f i n d I  have  not  considered  These are c l e a r l y rewards. for  The a r c h e t y p a l problem  food i n an environment  are  partly  known.  is  a  involve  decision-making  whose f o o d - s u p p l y i n g  i s the  There  of motivation or d r i v e .  c o n s i s t s of an organism  The organism  running low); what organism?  and  survival  large s c i e n t i f i c  hunting  (food or f u e l  strategy  for  me,  these problems are secondary  sensory  ACC-INIT  the very f i r s t  all  problems.  program, r e s p o n s i b l e f o r understanding  impressions,  ACC-SOB. to  ACCOM  theory.  to the b a s i c q u e s t i o n s of  r e p r e s e n t i n g the s p a t i a l world and s o l v i n q s p a t i a l The  subsequent  divides  into  this  l i t e r a t u r e devoted to  such problems i n the f i e l d s of d e c i s i o n theory and game For  and  characteristics  i s g e t t i n g hungry  best  Other  food". ,  problems  important  corner.  to  two  parts,  incoming  ACC-INIT  and  accomodates the i n i t i a l d e f a u l t world model  r e t i n a l impression while ACC-SOB accomodations  of  the  carries  out  world model to incominq  sensory i m p r e s s i o n s . The  spatial  planner  SPL&N  depends on a subsystem  SHAPE to solve p a t h - f i n d i n g and object-moving makes is of  extensive  maintained Cartesian  the C a r t e s i a n SHAPE  use of the world model.  problems...  world  functions  model  SHAPE  The:basic world model  i n a format o f p o i n t s and l i n e s s p e c i f i e d coordinates  called  by means  and w i l l sometimes be r e f e r r e d t o as or  the  Cartesian  represent a t i o n .  by p r o j e c t i n g and r e - p r o j e c t i n g a l l or p a r t o f I«Introduction  17  the  Cartesian  world  Path-finding c a s e s from require  and  one  p r o j e c t i o n on  representation to  The  as  most  algorithms  an  this  image  important  shape.  i t i s the of  what  the  was  reasons  algorithms  totally the all  is of  of  will  of  the  the  Cartesian  sometimes  be  collection  of  object-moving  the  skeleton  of  for  devised in  which I  a  two  more cumbersome  term  a shape l o o k s  chapter  was  V,  i t .  the  to  an  examine  the  found  that  problems  derive  that,  skeleton  these a  would  out  published of  the  provided  I t turned  L u c k i l y , one  able  get  p r o b l e m s , and  object^moving t o compute  To  like,  I  for path-finding  problems., of  a shape;  drawn i n f i g u r e 1.4.  a  nice  mathematical  Consider  the  shape  is  then defined  maximal c i r c l e s has  very  a shape;;  within  skeleton  skeleton  cases  provided  satisfactory  algorithm.  There skeleton  of  were u n s a t i s f a c t o r y .  a good b a s e from skeleton  be  given  more i n t e r e s t i n g  is  and  axis transform  heuristic  could  simple  array  SHAPE  concept  a useful tool  useful  algorithms for  of  skeleton  skeleton  solved  projection  digital  part  symmetric  i t s skeleton  a  A  screen). in  A more d e s c r i p t i v e b u t  shape and  be  screen;  are  (the  representation.  b a s e d upon the  dimensional  idea  the  projections. onto  array  problems  for solving path-finding  These are  for  digital  object-moving  several  referred  model onto a  and  in this  associated  with  the  set of a l l c i r c l e s  partially  set.  t o be In  i t the  definition  order the  them  locus  by  of  radius  the  that l i e  inclusion;  the  a d d i t i o n , each  of  centre  point  of t h e : m a x i m a l  of  of the  circle  I•Introduction  F.I  &UR  £  X.4-,  _/_We_4.K.£4ETOH  OF  A SHAPE.  19  with c e n t r e at that p o i n t ; t h i s i s known as the guench f u n c t i o n . However,  the  skeleton  algorithm  that  e x a c t l y the s k e l e t o n as I have j u s t the  metric  points  in  a plane,  metric  to  approximate  quasi-Euclidean "local"  d e f i n e d i t . . . T h i s i s because  Euclidean The planner. solve  between  and  the  I t has  the s k e l e t o n can I  two  Dsing  this  be computed i n a very  shall,  computed  two  can  by  than  when . necessary,  can  also  be  as  and  can  the be  spatial  following  find§E§S§  problem  shape t h a t you  s u r f a c e , where do you  to  problems.  s o l v e . the  the  the 1.5.  used  object-moving  to  dimensional  want  place i t ?  to The  concerned with the s k e l e t o n of a shape are V.  To complete t h i s overview ACT,  used  known  cluttered  algorithms  is  idea behind  and The  on the d i g i t a l s k e l e t o n of f i g u r e  Given a two a  algorithm*.  be observed by o v e r l a y i n g  j u s t p a t h - f i n d i n g and  otherwise  on  my  a very i n t u i t i v e appeal  worked out i n chapter  component  between  distance. .  s k e l e t o n of a shape i s the key  [Sussman,1973J.  theory  Euclidean  as  s k e l e t o n of 1.4  For i n s t a n c e , i t  down  distance  a l g o r i t h m uses a q u a s i - E u c l i d e a n  Consequently  skeleton,  more  problem,  the  the  using  between a E u c l i d e a n s k e l e t o n , as d e f i n e d above,  digital  difference  for  whereas my  metric,  manner.  distinguish  put  compute  c i r c l e s used i n the mathematical d e f i n i t i o n are drawn  the.familiar Euclidean  the  I use does not  of  PPA,  the  third  and  the e x e c u t i v e program that computes the  a c t i o n f o r Utak from a completed p l a n .  This  is  not  final next  entirely  t r i v i a l because the s i z e of the next a c t i o n has to be a f u n c t i o n I«Introduction  pi  lc h i  ;  »  (A \  X I  P! 2 .  *  *  21  of  t h e c o n f i d e n c e Otak has  the  vicinity  which he  can  of  i n the d e t a i l s  h i s current position  execute  an  action*  through  a room c l u t t e r e d  one  can  register  can  c o n t r o l o n e ' s movements.  the  To summarize  shape. stage of  elaboration  I.4  design,  of the  items  and  have  outlined  and  on  figure  1*6,  be  cycle  with  one on  how  runs  how  well  well  one  the  major  I have p r e s e n t e d  of f i g u r e  as  an  dimensional  which i l l u s t r a t e s  regarded  in  a  first  this order  1.1.  System s t a t u s All  degrees  parts of  produce and  the and  system  and  some p a r t s have  retinal  described  in  in f u l l  ACC-SOB h a s  major  A full  SHAPE  IV.  while  but is  the  The  ACCOM,  implemented.,  been  SPLAN,  Of t h e two  of the  overall  complete*,  to varying The  a c t i o n s and implemented  current status of  ACC-INIT has  implementation  been a t t e m p t e d , subpart  namely  i n chapter  been d e s i g n e d  implemented. not  been  i m p r e s s i o n s , have  chapter I I I .  o t h e r p a r t s o f the system, described  h a v e been d e s i g n e d ,  OTAK s i m u l a t i o n p r o g r a m s , which e x e c u t e  tactile  are  of  detail,  TABLETOP and  has  which  t h e s k e l e t o n o f a two  may  action  at  model  accuracy  depends b o t h  the r o b o t - c o n t r o l l e r ,  accompanying  PPA's  I  world  of t h e  speed  of the  section:  u n d e r l y i n g concept, The  and  furniture  positions  this  components o f PPA, important  with  The  of the  and  ACT,  the is  s u b p a r t s o f ACCOM, been  spatial  design SHAPE'S  designed planner  of SPLAN and most  and SPLAN its  fundamental  ^Introduction  22  TlirT/NAL.  Ac c o ^  UTAK  SPLAN  T*€  O 0 T S \ & £  WORL\>  /  j  V / STRUCTURE  f«\oTtof\ O OTPyT  ACT  PLAN  F l GURE  I. 6  23  o p e r a t i o n , the s k e l e t o n - f i n d i n g computation, implemented;  that  is  complete  and  i s the main a l g o r i t h m i c c o n t r i b u t i o n of t h i s  thesis. Taking  the  engineering  view  towards  Al,  contributions in this thesis.  One  i s an  s i m u l a t i n g the motion of r i g i d  two  dimensional  i s the design and p a r t i a l implementation that  finds  I  efficient  of  make  two  system  for  shapes, the other  a  spatial  paths and produces plans f o r moving two  planner  dimensional  shapes around on a f l a t s u r f a c e .  1.5 Reader's guide Chapter background  I I , c o n s i s t i n g of issues.  The  two  first  parts,  is  numerous  pieces  of  work  from  d i s c i p l i n e s t h a t are c l o s e l y r e l a t e d to describes  the  the  Al  my  second  and  own.,  robot-controller  part sister  Chapter  design.,  I  IV  covers  III  to  be.  able  theory and a l g o r i t h m s  for  the  whole  i n c l u d e i n chapter IV a number of  task s c e n a r i o s t h a t my r o b o t - c o n t r o l l e r , when f u l l y designed  its  an  design c o n s i d e r a t i o n s and a l g o r i t h m i c d e t a i l s of  the simulated robot world, while chapter  is  with  p a r t concentrates on g i v i n g  o v e r a l l view of the whole A l e n t e r p r i s e : w h i l e reviews  concerned  to execute. . Chapter computing  the  implemented,  V d e s c r i b e s the  skeleton  of  a  two  dimensional shape, and i t s u s e f u l n e s s f o r p a t h f i n d i n g and o b j e c t moving problems. foregoing,  The  discusses  c o n c l u d i n g chapter my  VI  recapitulates  the  c o n t r i b u t i o n t o the A l e n t e r p r i s e , and I"Introduction  24 d e s c r i b e s f u t u r e d i r e c t i o n s of The  appendices  research.  include  a  user's manual f o r the TABLETOP  s i m u l a t i o n , a c o m b i n a t o r i a l lemma r e q u i r e d some  proofs  concerning  the  in  simulation  chapter  V,  and  system of Funt [1976]  r e q u i r e d i n s e c t i o n 11*4.7* If  you want to see a new  i t e r a t i v e a l g o r i t h m f o r computing  the s k e l e t o n read s e c t i o n V.2.4.  For a new  application  skeleton,  to p a t h f i n d i n g , read s e c t i o n 7,3.  I f you  algorithms  f o r s i m u l a t i n g the TABLETOP world read  of  want to  the see  section III.1.  The.  o v e r a l l design of a r o b o t - c o n t r o l l e r i s o u t l i n e d i n chapter  IV.  Finally,  Intelligence,  if  you  want  read the f i r s t  a  general  review  of  three s e c t i o n s of chapter  Artificial I I . . The  l a s t s e c t i o n of chapter I I contains a l i t e r a t u r e review.„  I"Introduction  25  CHAPTER-II BACKGROUND-ISSUES  In of  this  chapter  Artificial  Artificial  II.J  my p u r p o s e  Intelligence  Intelligence  Artificial  i s to briefly  and t h e n  and o t h e r  Intelligence^  t o review  sketch the nature related  work  in  fields.  i s a s c i e n c e - w i t h g o a l s and  para diqms Artificial man's  eternal  urge,  Less p o e t i c a l l y , to  Intelligence to  i s t h e computer age  understand  i t i s a scientific  make c o m p u t e r s more u s e f u l  computational intelligence, displayed  by man, a n i m a l ,  schizophrenic engineering  discipline  h i s mind and c o n s c i o u s n e s s . discipline.whose  of  and  here: -  principles  whether  o r computer.  tendency  of  goals  are  and t o d i s c o v e r and u n d e r s t a n d i n  terms t h e t h e o r i e s irrespective  expression  on  [Michie,1978]  underly  the: intelligence  The r e a d e r the  that  will  one: hand defines  is  note  a  i t is  an  i t as  "the  !The name i s u n f o r t u n a t e , f o r i t i s n o t t h e c u r r e n t e n d - p o i n t i n a p r o g r e s s i o n t h a t g o e s a n i m a l i n t e l l i g e n c e * human i n t e l l i g e n c e , a r t i f i c i a l i n t e l l i g e n c e , ...!*! .... as many a layman seems t o think on f i r s t h e a r i n g t h e name. N e i t h e r i s i t concerned with c o m p u t e r based s u p p o r t s y s t e m s f o r men i n s p a c e , a s one s c h o l a r seemed to think. (How about computer c o g n o l o g y ? ) Also, since one cannot denote a practitioner by t h e u s u a l scheme o f appending "-ist" t o t h e s u b j e c t ' s name, one i s f o r c e d t o u s e cumbersome terms such as "researcher in Artificial Intelligence". IlaBackground  Issues  26  pursuit  of  engineering  goals  through  machine  p r o c e s s i n g of  complex i n f o r m a t i o n i n t e r m s o f human c o n c e p t s " -  while  on  the  other  concerned  with  hand  i t  understanding is  areas of  study.  The  If  used  more  the  as  a  word  "paradigm"  a social  sense*  subject what  psychology  the  than  what  i n many d i f f e r e n t  senses,  h a r d l y one  understanding computational  of  we  Intelligence  held  on  the  has  shall  been  around  workers s i n c e a  subject  i s a young s c i e n c e and  except  for  intelligence  Symbol  System H y p o t h e s i s  symbol  system  the  Kuhn  in  10  1955. .  perhaps  So  still  a  result.  studies.,  has  its  necessary.  in scientific  at a l l  other  are  so  existence of a g e n e r a l l y accepted  overthrown  so  [ Masterman, 1970 i] p o i n t e d o u t ,  view o f  the  these  are  ( m e t a p h y s i c a l paradigms or "Weltanschauung";  get  and  Intelligence :  d e f i n e d group o f communicating  Intelligence  for  As  terms,  i s a s c i e n c e then  Artificial  s e l f - c o n s c i o u s as a As  was  as  summer s c h o o l was  Artificial bit  computational  Intelligence  sense  discipline,  t o p h i l o s o p h y and  J. Kuhn, 1962 i]?  clearly  person  in  paradigms of A r t i f i c i a l  i n t r o d u c e : each In  intellectual  akin  Artificial  paradigms  an  intelligence  perhaps  I I . J..J.  is  T h i s has  the  basic  would now  by [ N e w e l l  necessary  revolutions) i n i t i a l l y  and  be  belief  and  that  achieved  been s t a t e d  there an  through  as t h e  Physical  Simon* 1 976 i}: "a  physical  sufficient  means f o r g e n e r a l  II«Background  Issues  27 i n t e l l i g e n t action". was  Very  soon the c e n t r a l importance  g e n e r a l l y accepted, and  Newell  and  Simon  as  this  the  too  has  Heuristic  been  Search  symbol  problem-solving progressively  system by  search  modifying  solution structure." Artificial  exercises  Now  Intelligence  -  that  symbol  its is,  enshrined  Hypothesis:  s o l u t i o n s to problems are represented as symbol physical  of s e a r c h by "The  structures.  A  intelligence  in  by • generating  and  s t r u c t u r e s u n t i l i t produces a  the g e n e r a l l y accepted core t o p i c s can  be  of  summarized as [Nilsson,1974 ]:  r e p r e s e n t a t i o n of knowledge, s e a r c h , common-sense:reasoning deduction,  and  computer  languages and systems a p p r o p r i a t e f o r  i n v e s t i g a t i n g the f i r s t three Going  down  paradigms,  one  or  Intelligence?  some  more  t o o l k i t . . One design.  A  what are some of the i n s t r u m e n t a l accepted  computer  course, the s i n e g j i a npn however  topics..  level*  generally The  and  tools  of  Artificial  programming languages are, of  of A r t i f i c i a l  specific,  Intelligence*  There  are  widely used, t o o l s i n the A l ' e r s  such i s the p r o d u c t i o n production  and  system  system  consists  style  of  a  s i t u a t i o n - a c t i o n r u l e s p l u s a scheme f o r choosing  of  program  collection  of  which r u l e  to  ( apply  next.  Any|  g e n e r a l i z a t i o n of Another as a data together  a  production  behaviouristic  i s the semantic structure with  system  of  can  be  vxewed  stimulus-response  as  a  system.  net approach; here a system i s designed labelled  arc-traversal  nodes  algorithms.  h i s t o r i c a l l y , d i r e c t l y d e r i v e d from  and  connecting  This  approach  arcs is,  a s s o c i a tHaBackground ionist psychology. Issues  28  The  last  tool  we w i l l mention i s the most w e l l e s t a b l i s h e d of  them a l l , with a long i n t e l l e c t u a l h i s t o r y behind object  of  some  controversy:  first  i t , and t h e  order p r e d i c a t e  calculus,  which i s taken d i r e c t l y from t r a d i t i o n a l mathematical l o g i c . . What  are  Intelligence? attempting  As  or  Artificial What  of  the  examples,  defining anyone  problems  who  uses  of A r t i f i c i a l a  computer  in  t o : understand n a t u r a l language, play games such as  chess, c o n t r o l scene,  some  a robot, understand a TV image o f  understand  speech,  is  a  real  world  considered t o be working i n  Intelligence. are  Intelligence?  some  of  the c u r r e n t hot problems i n A r t i f i c i a l  Here i s a l i s t ,  culled  from  [ M c C a r t h y , 1 9 7 7 3 and  [ Simon, 1977 J . •  the problem  of c o o p e r a t i n g with others* or  opposition  -  this  overcoming  their  i s a task which even the youngest  infant  handles very w e l l [Donaldson,1978 ] . . •  the a c q u i s i t i o n of knowledge [ Winston, 1970 i], [ Winston* 1 978 g.  •  r e a s o n i n g about concurrent events and a c t i o n s . ,  B  expressing  knowledge  about space, and the l o c a t i o n s ,  shapes  and l a y o u t s of o b j e c t s i n space. a  the  r e l a t i o n between a scene and i t s two d i m e n s i o n a l image -  t h i s i s the v i s i o n  problem, c u r r e n t l y being attacked by  many  workers, f o r i n s t a n c e , [Barrow and Tenenbaum,1 9 7 8 J . . B  r e a s o n i n g with concepts of cause and can*  a  finally,  the  problem  of  representation  -  what knowledge  enables a system to c r e a t e a r e p r e s e n t a t i o n and o p e r a t o r s f o r IlaBackground Issues  29 a  new  is  to  and be  unfamiliar  problem?  distinguished  from  This  representation  knowledge  of  how  knowledge  to  solve  a  problem. In  summary, I h a v e o u t l i n e d  "Artificial  Intelligence"  by  this scientific  describing  field  i t from  known  several  as  Kuhnian  viewpoints*  I I . J_. 2 AI  has  potentially rich - relationships  with  many, o t h e r  fields There are and  other  work on  many r e l a t i o n s  fields  getting  subfield  of  research  has  study.  a  acrimonious  have  This  debate  advocates  to  Intelligence [ M i n s k y and community  research  i s of  simply  reasons f o r t h i s schism methodology  In  relationship i s the  example research  and  whereas  ignored seem t o  order  of  Artificial  an  programs.  relationship.  most  of  competing  Artificial  believe  with  topic  of  Intelligence The  more  that  monumental i m p o r t a n c e  [Miller,1978J  paradigms.  of  Intelligence  Papert,1972J, has  whereas i n f a c t t h i s f i e l d  differing  a somewhat l o p s i d e d  of A r t i f i c i a l  a  an  would  that  form  relationship -  Intelligence  might e x p e c t  language  contentious  a n o t h e r example, p s y c h o l o g y  enjoyed  research  example, one  proper,  linguistics*  Artificial  understand  somewhat  p a r a d i g m s , a l a Kuhn, due As  For  a machine t o  linguistics  traditional enduring,  of  between  the  vocal  Artificial  for  psychology  psychological  Intelligence* .  stem l a r g e l y f r o m  differences  -  another  example:  of  to  keep h i s  science  well  The in  competing  IIoBackground  founded Issues  30  on  f a c t s , and hence s c i e n t i f i c a l l y  is  concerned  with  t o produce f a l s i f i a b l e  demonstrably  true  hand, t h e A r t i f i c i a l produce  computations with  empirical are of  i s that  the latter  taken  as i n t u i t i v e l y  computation.  For  a  intolerably  obvious,  instance  unacceptable.  on  Thus  any  concerned  and  e m p i r i c a l consequences.  The  which  by  proposed  after  To c o n c l u d e :  explosion  actual  Artificial  a l l - i t i s grounded  and  large  or that  facts  mechanism  or  which  otherwise  potential  runs  computer  i s exponentially  domain o f i n t e r e s t i s u n l i k e l y t o be a c c e p t a b l e  run..  with t h e  but with t h e e m p i r i c a l  any  an a l g o r i t h m  to  mechanisms  i s n o t s o much c o n c e r n e d  combinatorial  slowly  theories  On t h e o t h e r  is  theories,  f a c t s o f human m e n t a l a b i l i t i e s ,  encounters  the  researcher  true  is,  consequences.  comp_utational  demonstrably  the psychologist  theories, that  empirical  Intelligence  falsifiable  difference  respectable,  is  slow i n  i n the  long  I n t e l l i g e n c e i s n o t so a r t i f i c i a l  on t h e e m p i r i c a l , n a t u r a l ,  facts  of  computation. One might  expect  behaviour  studies  reasons.  First  therefore to  is B  and  the  behaviour  i t should  of B d u p l i c a t e s  no s i g n i f i c a n t of  A,  operationalisra.)  t o be some  and A r t i f i c i a l  the c o n s t r u c t i o n  duplicate  behaviour  there  contact  animal  I n t e l l i g e n c e , f o r a t l e a s t two of  animals  of computational be  between  easier..  is  simpler  processes  (When  I  say  and  sufficient that  t h e b e h a v i o u r o f A, I mean t h a t  the there  o b s e r v a b l e d i f f e r e n c e between t h e b e h a v i o u r o f as  in  the  Turing  Second, t h e e v o l u t i o n  test  or  in  Bridgeman's  o f human b e h a v i o u r ( i * e . IIsBackground  Issues  31 intelligence)  can  be  traced  J e r i s o n , 1973 3-  behaviour subsystems  that  had  through  Consequently  a l r e a d y been  many one  grades might  shown t o d u p l i c a t e  behaviour occurring  earlier  could  be  blocks i n the c o n s t r u c t i o n  that  duplicate  a v e r y few contact  between t h e  A  animal  hungry  two  problem  monkey  later,  fields;  is and  get  his  T h i s problem  a box  typically  i n t h e c o r n e r ; how was  way  outdated  from  Artificial  More  algorithms;  facts  "Intrinsic  similar  t o the  bananas  problem.  does  about  the  visual  chimpanzees  and  or  four  have  are simply  into  also,  a t present.„  another  based  on  off  automata t h e o r y .  is clearly  the  the  branched  related aspects  Tenenbaum, 1978 ] a r e  of the columns i n  To  work on n e u r a l  c o r t e x , w h i l e some  Images" o f [ B a r r o w structure  vision  monkey  bananas.  which was  developed  hanging  the  up t h r e e  M c C u l i o c h - P i t t s model o f t h e n e u r o n , I n t e l l i g e n c e and  a  does come  Some v e r y e a r l y  [ M o o r e , 1956 ],  no  that  relationship  r e c e n t work by [ M a r r , 1976 fj on  the.known the  no  from  describe  neurophysiology  r e s e a r c h e r s , neurons  n e t s by [ K l e e n e , 1956 j} and now  piled  t o get the  and  almost  Intelligence  of implementing  systems  essentially  s o l v e d by K o h l e r ' s  t h e chimpanzee  Intelligence  surprisingly,  Artificial  monkey and  of  apart  In p a s s i n g , l e t me  boxes i n a m a r g i n a l l y s t a b l e p i l e  perhaps  been  record  i n a room w i t h a bunch o f b a n a n a s  the c e i l i n g  Artificial  t h e r e has  s t u d i e s - the  from  [ K o h l e r , 1 9 2 5 ];  In f a c t ,  that  aspects of  evolutionary  f o r p r o b l e m - s o l v i n g systems  behaviour  food?  the  a s p e c t s o f human b e h a v i o u r . .  s t u d i e s reviewed  traditional from  as b u i l d i n g  in  animal  expect  animal  used  of  visual  IlaBackground  to of  very  cortex. Issues  32 The  n e u r a l net  idea  has  been d e v e l o p e d  [ B r i n d l e y , 1969 ij  and  lErmentrout  Cowan, 1 9 7 8 .  also  and  paragraph  with neurophysiology On  a  deeper  relationship its  very  vision,  then  is  is  example,  is It  the  the  human  a r e found  CNS  decrease  has  in  being  computing  a  t o be  out  system  in  the  i s found  Artificial  for and  CNS?"  Intelligence As  another  Habituation i s  or p r o b a b i l i t y  of a  stimulus.  response  Habituation  i s the s i m p l e s t type of o t h e r k i n d s of  of  t o compute  these f u n c t i o n s ? "  i n the amplitude  and  the case  sufficient  phenomenon of h a b i t u a t i o n .  nature  two-way  neurophysiology  Take  carried  visual  f e a t u r e s i n common w i t h  sometimes  rich  n e u r o p h y s i o l o g y i s "Where  r e p e a t e d p r e s e n t a t i o n of a p a r t i c u l a r ubiquitous  word f o r word,  a  and  neurobiology.  in  throughout.  expect  Intelligence  the question f a c i n g  consider the  a gradual to  i f  over almost  might  computations  functions,  "Why  the  of behaviour  level  computations  e.g.  evolution  f o r behaviour  cousin,  physiologist  has  taken  one  a  S i n c e human n e u r o p h y s i o l o g y  the q u e s t i o n f a c i n g  are these  certain  be  by  biologists,  substituted  close  If certain  Conversely,  can  between A r t i f i c i a l  vision.  how  mathematical  e v o l v e d , t h e comments a b o u t  preceeding  or  by  further  learning.  learning  component o f more complex l e a r n i n g . ,  and  is  Consequently,  an  u n d e r s t a n d i n g o f t h e mechanisms of h a b i t u a t i o n  c o u l d be  to  build  Its biological  mechanisms f o r o t h e r t y p e s o f l e a r n i n g .  mechanisms  are  I K a n d e l , 1 978 i]. Intelligence  being On  slowly  t h e one  teased  out  hand, i t i s e a s y  viewpoint t o propose  by  neurobiologists  from  many methods  used  of  the  Artificial  implementing  II*Background  Issues  33 habituation;  the  obverse  of  I n t e l l i g e n c e one should p r e f e r some  this  i s that  a learning  in  Artificial  mechanism  which,  at  l e v e l o f d e s c r i p t i o n , i s consonant with the known f a c t s o f  habituation. There and  i s a strong  philosophy.  Artificial  This  r e l a t i o n between A r t i f i c i a l  i s not s u r p r i s i n g i n view of the f a c t  Intelligence  has  t r a d i t i o n a l problems of Artificial the  Intelligence  to  consider  philosphy.,  In  some, of  designing  the major  almost  any  I n t e l l i g e n c e system commitments have t o be made about  nature of knowledge, how knowledge i s o b t a i n e d ,  represented action.  that  and  The  used,  and  connection  how  i t is  the r e l a t i o n between knowledge and  between  philosophy  and  Artificial  Intelligence  i s considered  [Burks,1978J,  and o t h e r s * . [McCarthy e t al.,1978] have  a  f o r e x p r e s s i n g "knowing t h a t " and used i t t o s o l v e  formalism  two  riddles involving  some  recent  philosophy problems  papers by  knowledge : about knowledge. [McCarthy,1977a,b,c],  approaching  from  by [ Sloman, 1 978 s], [Dennett,1978a],  the  many  an  the  Artificial  enormous i n f l u e n c e I  have  sketched  between A r t i f i c i a l animal  Intelligence  philosophical viewpoint. . In  of  philosophy  is  viewpoint promises t o have  on p h i l o s o p h y . the  actual  Intelligence  or  and  potential  interactions  linguistics,  psychology,  behaviour* the n e u r o s c i e n c e s , and philosophy.  Artificial  in  has made i n r o a d s on  Intelligence  summary, i t seems t h a t whereas the i n f l u e n c e slight,  McCarthy,  traditional  Artificial  described  I n t e l l i g e n c e tread  i t s own w e l l - d e f i n e d  path  Thus does through  !!•Background Issues  34  the  maze o f modern s c i e n c e ,  being  enriched  by  with  many o t h e r  II> 1> 3 Oa der s t and i n g the  the  fields  world  potential for enriching o f the  scientific  i s a - p r e r e q u i s i t e -to  and  endeavour.  doing  mathematics An to  e a r l y dream o f  prove  significant  seemed, a p e r f e c t calculus, and  i n which p r o o f s  and the  run! i t  rules. The  ensuing  is  now  traditional  failure. to  Intelligence  mathematical  tool  a formal  deduction it  Artificial  just  system proceed  by  Put  formal  the  the  combinatorial  c l e a r t h a t any manner  M o r a l - a new  of tool  theorems;  waiting  which can  researchers  to  be.  There used:  express a l l of mechanical  system  use  mathematical i s useless  was,  was  mathematics,  application  until  one  of let  uncontrollable,  of a f o r m a l logic  it  predicate  i n a c o m p u t e r , and  explosion  direct  was  system  in  is  doomed  to  has  learnt  how  use i t . In  t o expect Hilbert,  retrospect,  one  s u c h a scheme who  formalizations  was  can to  say  that  succeed..  personally  i t was  quite  Consider  responsible  unreasonable  the  words  for  of  several  of m a t h e m a t i c s [ H i l b e r t , 1927 ij:  No more than any o t h e r s c i e n c e can m a t h e m a t i c s be f o u n d e d by l o q i c a l o n e ; r a t h e r , a s a condition for t h e use o f l o g i c a l i n f e r e n c e s and t h e p e r f o r m a n c e o f l o g i c a l o p e r a t i o n s , s o m e t h i n g must a l r e a d y be given to us in our faculty of r e p r e s e n t a t i o n , c e r t a i n e x t r a l o g i c a l concrete objects that are: i n t u i t i v e l y present as immediate experience prior to a l l thought. I f l o g i c a l i n f e r e n c e i s t o be r e l i a b l e , i t must be p o s s i b l e t o s u r v e y t h e s e o b j e c t s c o m p l e t e l y i n a l l t h e i r p a r t s , and t h e f a c t that they differ from one a n o t h e r * and t h a t t h e y f o l l o w e a c h o t h e r , IIoBackground  Issues  35  or are concatenated, is immediately given i n t u i t i v e l y , together with the o b j e c t s * as something t h a t can n e i t h e r be reduced to anything e l s e nor requires reduction. C l e a r l y H i l b e r t had no i l l u s i o n s system  about  the  use: of  a  formal  f o r d i s c o v e r i n q mathematical theorems., My own i n t u i t i o n  i s that the o b j e c t s o f one's thought - noesgs - which a r e "surveyed"  when proving a mathematical theorem, are e s s e n t i a l l y  the same as the noeses i n v o l v e d i n manipulating o b j e c t s external world.  being  world,  or  in  i n the  making mundane plans f o r a c t i o n i n the  T h i s i s s a i d by [Kleene,1952, p.51, using a  quote  from  Heyting j]: "There remains f o r mathematics no other source than an intuition, which places i t s concepts and i n f e r e n c e s before our eyes as immediately clear.. T h i s i n t u i t i o n i s nothing other than the f a c u l t y of considering separately particular concepts and inferences which occur regularly i n ordinary thinking." Consequently my guess i s that no r e a l l y i n mechanical theorem how t o get machines  system  achievements  proving a r e l i k e l y to occur u n t i l we  to  model  there  are  problems  with  truth*  One  mathematical  approach might be t o use two f o r m a l systems, each of r e f e r to and hence leads to problem  a  approximate the other.  reconsideration  fMinsky,1969,p.4263,  proposals  f o r representation  suggests  how  an  know  t o handle the r e a l world.  I t i s w e l l known that formal  significant  of  using  a  possible which  can  In o n e . d i r e c t i o n  this  Minsky's  "models  of  models"  i n another d i r e c t i o n t o p r a c t i c a l theory.,  approximating  [McCarthy,1977a,p.5 ]  formal  system  might  II»Background  be  Issues  36  constructed.  II..1.4 A theory o f i n t e l l i g e n c e w i l l be p r i m a r i l y - concerned  with  r e p r e s e n t a t i o n s of the-world As i s a l r e a d y c l e a r , any theory all  be  concerned with r e p r e s e n t a t i o n s .  [McCarthy and Hayes,1969$ c l a s s i f y by  their  adequacy.  facts  of  the  a  giant  aspect  quantum  book  is  of  reality  mechanical  metaphysically  t h a t i n t e r e s t us. For  wave  red".  A  a  First  order  epistemologically propositional knowledge,  as  practical  But  fact  but  notions  of  h e u r i s t i c a l l y adequate are I n t e l l i g e n c e , and henceforth The  practical  facts  about  fails  on  of  cause  It  some  can  on  the  express  other  and  kinds  of  ability.^  A  adequate i f i t represents the  the of  world  direct  that interest  I consider only  are to  problems. potentially Artificial  these.  amount o f search i n v o l v e d i n s o l v i n g a problem  critically  as  i s epistemologically.  representation*  i s heuristically  representations  such a  such  p r a c t i c a l f a c t s and can be used t o compute answers t o Only  i t  - a formal system - i s a candidate  adequate  knowledqe  such  representation  logic  represent  equation..  representation  adequate i f i t can express a l l the world.  world  could have t h a t form without c o n t r a d i c t i n g  r e p r e s e n t a t i o n cannot even express "this  level,  r e p r e s e n t a t i o n s of the  i n s t a n c e , a quantum t h e o r i s t c o u l d , i n p r i n c i p l e , by  above  At a very gross  A representation i s called  adequate i f the world the  of i n t e l l i g e n c e w i l l  depends  the r e p r e s e n t a t i o n of t h a t problem.. For example II»Background  Issues  37 [ A m a r e l , 1 968 (J c o n s i d e r e d [MSG]  t h e M i s s i o n a r i e s and C a n n i b a l s  and worked t h r o u g h s e v e r a l d i f f e r e n t  most p o w e r f u l . r e p r e s e n t a t i o n general  problem  the  simplest  at  a l l .  to find  M&C  new  solution  will  problem  that  finding  this  a  is  solution  with  only  eons-long Any  of  an  problem  world  be as  problem  many  T h i s i s what I t could  to  different  many  repairing  a  through  parts  cortex  devoted  f o r these  be  us:  the  other  viewpoints  as  f o r the  result  have a c c e s s  f o r a p r o b l e m . , J. Minsky , 19751] c i t e s  of  a  good r e p r e s e n t a t i o n  solver will  outside  evidence  to  applicable  surrounding  of the  representations  the  of  an  search.  endowed,  the  search?  which  However, t h e a d v a n t a g e o f a good  i t may  representations of  in  good  auto-mechanic  also  be programmed  finding  the  c a r , who  m e c h a n i c a l , and v i s u a l r e p r e s e n t a t i o n s are  search  of  evolutionary  representations  problem,  no  from  develop  competent  a system  a little  Humans have a r e m a r k a b l y  three-dimensional  a  almost  of the search  i s that  possible*  more  m e r e l y moving t h e f o c u s  representation  -  considerably  the s o l u t i o n t o a problem.  o f t h e problem._  Moral  The  p r o b l e m , and t h e s o l u t i o n t o  for  representation  problems;.  a  how c o u l d  representation be f o u n d  representations._  dropped o u t o f i t with arises,  h a p p e n s when one " s e e s " said  solve  than the o r i g i n a l  The q u e s t i o n  a  could  problem  the  world*  multiple  to solve  a  witness  to visual, There  the  uses  evolution,  world,  to several example  electrical,  problem.,  We  with  several  the  different  a u d i t o r y , and t a c t i l e  is  also  representations.  psychological For instance,  !!•Background  Issues  38 I Posner,1 972g  presents  evidence  experiments  f o r the  existence  corresponding  to d i f f e r e n t  that  an  infant  distinct  the: q u e s t i o n different  of  i s born  reaction  distinct  time  representations  [Bower,1974]  suggests  with an w h o l i s t i c , multimodal o b j e c t of development  representations. i s , what  on  modalities..  concept which i n the course many  based  into  For a problem s o l v i n g system,  interactions  representations?  differentiates  This  should  is  occur  largely  an  between unexplored  question* Minsky suggested t h a t an i n t e l l i g e n t system be organized as a c o l l e c t i o n o f i n t e r a c t i n g schemata ., A schema c o n s i s t s 2  bundle  of  "slots , 1 1  one  closely related features.  f o r each  member  In the absence  of  a  of a c o l l e c t i o n o f  of  evidence  to the  c o n t r a r y , the s l o t s of a schema assume d e f a u l t v a l u e s . . A schema i s a l s o l i k e n e d t o a mini-theory If  one  f o r a s m a l l p a r t of the  wishes t o handle schema theory  in f i r s t  world.  order l o g i c , i t  might be worth p o i n t i n g out t h a t the r e l a t i o n between  a  and  between a  i t s default  values  i s s i m i l a r to the r e l a t i o n  formal system and i t s standard integers  are  the  standard  model model  in  logic,  f o r any  just  schema  as t h e  formalization  of  arithmetic* In  view of the requirement of m u l t i p l e r e p r e s e n t a t i o n s f o r  zMinsky used 'frame', but I p r e f e r to f o l l o w [ Simon, 19771], who pointed out t h a t 'schema' i s a more a p p r o p r i a t e term, l o r two s u b s t a n t i a l reasons. . F i r s t , the term has been widely used i n the A l and p s y c h o l o g i c a l l i t e r a t u r e i n the sense with which i t was i n t r o d u c e d by B a r t l e t t i n 1932; second, 'frame' already has a w e l l - d e f i n e d t e c h n i c a l meaning i n the A l l i t e r a t u r e . II»Background  Issues  39 a problem s o l v e r , augmented  by  allowing  representations* aspect  Ninsky's  schema  every  schema  T h i s might be done  o f the world  schema,  to as  may have d i s t i n c t  t a c t i l e o r o l f a c t o r y schema. verbal  theory  between  There  visual  have  perhaps  Each  verbal, visual, are  be  many d i f f e r e n t  follows.  schema,  v e r b a l schema f o r one s m a l l aspect  should  small  auditory,  associations  between  e t c . ; i n a d d i t i o n the  of the world  may  evoke i t s  v i s u a l schema, which may evoke i t s a u d i t o r y schema, e t c . To summarize t h i s s e c t i o n : any f u n c t i o n i n g r o b o t - c o n t r o l l e r must  use  a heuristically  adequate r e p r e s e n t a t i o n  t h a t i s , a world model which reduces to time  required  to  produce  a plan  a  of the world,  minimum  the  or to s o l v e other  search  frequently  encountered problems.  I I . 1> 5 A theory  of i n t e l l i g e n c e w i l l d e s c r i b e  intelligent  systems at many d i f f e r e n t l e v e l s  A  c l o s e l y r e l a t e d i s s u e concerns how t o d e s c r i b e  information the  processinq  information  system.  processing  a complex  Marr and Poggio[1976] argue that of  a  system  such as the c e n t r a l  nervous system needs t o be understood a t four n e a r l y  independent  l e v e l s of d e s c r i p t i o n : (1)  that  (2)  that are  (3)  that  at which the nature of a computation i s expressed; at  which the algorithms  t h a t implement a computation  characterized; at  which  an  algorithm  i s committed t o p a r t i c u l a r HaBackground  Issues  40 mechanisms; and (4)  that  at which the mechanisms are r e a l i z e d  In g e n e r a l , the nature of a computation problem  to  i s determined  by the  be s o l v e d , the mechanisms t h a t are used depend upon  the a v a i l a b l e hardware, depend  i n hardware.  upon  both  and  the  the  nature  particular of  the  algorithms  chosen  computation and on the  a v a i l a b l e mechanisms; For example, c o n s i d e r the F o u r i e r transform.. The theory of the F o u r i e r t r a n s f o r m independently One it.  of  i s well  the  understood,  particular  and  i s expressed  way i n which i t i s computed.  l e v e l down, there are s e v e r a l  algorithms  f o r implementing  F o r i n s t a n c e , the Fast F o u r i e r Transform* which i s a s e r i a l  algorithm based upon the mechanisms of the d i g i t a l computer, and the  algorithms  of  holography,  which  are p a r a l l e l a l g o r i t h m s  based on the mechanisms of l a s e r o p t i c s , can implement  the  Fourier  about d e s c r i b i n g a details the  of  transform.,  complex  algorithms  essential  thing  system,  The  both  be  used  to  meta p o i n t to be made  i s that  while  the  gory  and mechanisms are of great importance,  i s to  understand  computation enforced by the problem  +  +  the  nature  of  the  t h a t i s being s o l v e d . .  +  To summarize t h i s s e c t i o n , I have: briefly  outlined  Artificial  I n t e l l i g e n c e by examining i t from l i s Background  Issues  41  s e v e r a l Kuhnian •  argued world  that  viewpoints;  i t i s necessary  before  one  can  hope  t o know how t o understand t h e to  know  how  to  do  more  s o p h i s t i c a t e d t a s k s such as mathematics; •  pointed out that any theory concerned  of i n t e l l i g e n c e  must be p r i m a r i l y  with r e p r e s e n t a t i o n s of the world, and s e c o n d a r i l y  w i l l d e s c r i b e any i n t e l l i g e n t system i n many d i f f e r e n t  I I . 2 S i m u l a t i n g a robot i s a promising  ways.  aEjiroach t o A r t i f i c i a l  Intelligence A l o t of work i n A r t i f i c i a l problems  which people f i n d  problems  which  reasoning  require  i s devoted  to  i n t e l l e c t u a l l y challenging* that i s ,  extensive  by  one's  are  t h a t people s o l v e e a s i l y and unconsciously  the  s o l u t i o n of these  has  the  problems  that  conscious  of i n t e l l i g e n c e .  paradoxical  c o n c l u s i o n t h a t only  are: intellectually  uninteresting . to  awareness  Intelligence* then  somewhat  are  lying  "easy" problems which are of most  fundamental i n t e r e s t t o any budding theory  for  every  - and t h e r e f o r e s o l v e well - and i t i s the p r i n c i p l e s  behind  one  definition  conscious  problems t h a t people are not i n g e n e r a l good a t . . But there  day  almost  of  are  problems  Thus  use  they  many  abilities.  Intelligence  So those one's  of fundamental i n t e r e s t to A r t i f i c i a l  But t h e r e i n l i e s the g r e a t e s t hope f o r optimism,  i t i s much e a s i e r t o be o b j e c t i v e about the s u b j e c t !!•Background  Issues  42 matter and not be functioning source  of  led  astray  one's  of guidance.  own  about  which are now Since  the.greatest s c i e n t i f i c  progress  examples  matter.  human  mind  Vision  been  devoted  how  is  such  an impressive  Intelligence  involved  the v a r i o u s aspects, e*g.„perception, memory, p l a n n i n g ,  reasonably  be expected  together..  Further*  these  Thus the complete s i m u l a t i o n of some very simple  would  be  instance,  a  worthwhile,  study  is  a  put  crayfish,  together  many  different  notably  investigated  A p l y s i a , or sea hare, by  turtle.  organisms,  a l l the i n f o r m a t i o n about one  organism.. I t should be added that there are most  or  problem here, i n t h a t even though a great  d e a l i s known about many aspects of has  organism  in A r t i f i c i a l Intelligence, for  a s i m u l a t i o n of a s t a r f i s h , or there  might  t o appear i n s i m p l e r organisms i n s i m p l e r  form.  no-one  and  to some s m a l l aspect of i t . , But i t i s q u i t e  a c t i o n , or speech, are woven  However  and  Intelligence.  l i k e l y t h a t there are b a s i c p r i n c i p l e s of i n t e l l i g e n c e in  be  of " u n i n t e r e s t i n g " problems  unfathomable a phenomenon, most work i n A r t i f i c i a l has  the  fallible  subject  are  whole  about  a devilishly  major s u b f i e l d s of A r t i f i c i a l  the  ideas  s c i e n c e s , where i t i s very easy to  the  speech-understanding  intuitive  consciousness,  After a l l *  has occurred i n the "hard" objective  by  neurobiologists  simple  single  creatures,  which have been e x t e n s i v e l y [Kandel,1976 ]  and  would  t h e r e f o r e be good candidates f o r the f i r s t s e r i o u s s i m u l a t i o n of a complete l i v i n g c r e a t u r e . some  s i m p l e r world  The  other suggestion  and organism and  is  to  invent  work out a l l the d e t a i l s of IlaBackground  Issues  43 the  organism-controlling  from  the  psychologist's  Dennettf1978J  suggested  critique  of  Artificial  followed,  with  point  make  simulation  Intelligence.  satisfy  and  the  the  on  and  cheap  the  other  the  and  of  analysis in  animal  from  provided  introspection,  the by to  robot  "naturalness"  extensive  while  program  and  should  from  on  criteria  of  of  on  actual  both  the  In  the  on t h e one hand  "animal-like-ness", feasible  t o simulate  c a n be  bug  done  using  design the  one hand  creatures,  the  intuition other  based  hand i t c a n n o t  used t o c o n s t r u c t  f o r the robot  reflect  and  based  proceed  on  with  the  studies  one's avoid  own being  i t ; namely  be c o m p u t a t i o n a l l y  world  the  from  on  to  various of  t h e . most one c a n do i s t o s e t t l e  "naturalness"  but  One has t o  o f t h e machine i n which t h e : p r o g r a m  fact  design  should  The  the concern that i t , t o o , should  arbitrary  control  program.  or  the  programs.  by t h e m a t e r i a l b e i n g  In  I have  b y p s y c h o l o g y , as f a r a s i t g o e s , f r o m  architecture  run.  recently  philosphical  constructing  experimentation of  observation  behaviour,  constrained  the  performance  organism-controlling derived  in  organism-controlling  organism-controlling  ideas  a  problems*  hand be c o m p u t a t i o n a l l y  enough t h a t  observe  of  more  out  representation.  decisions  world  some c r i t e r i a  and  and  this  T h i s i s the path  involves methodological  arbitrary  simulation,  view,  e m p h a s i s n o t so much on p r o b l e m s o f  approach  many  of  t h i s i n the context  r a t h e r on p r o b l e m s o f s p a t i a l This  TodaJ. 1 9 6 2 3 c a r r i e d  program.  r u n s , and feasible upon  some  some  unstated  the design  of the  HaBackground  Issues  44 controlling And  when  judged? world  program.  Again, this  nothing  that  is  given  an  is*  of  position  would be  the an  the  robot  world  performance  And  of  made.  seriously  finally,  even  in  always  the  i f  course  programs the  principle  some  of  used  human/environment  are  that  to the  and  much  t h a t no  o f the  a  with  road t o  a  designs  with  an  compared  potholes;  are of there  simulated  the  whole  principle worlds  robot but  the  discontinuity  human/environment via  then  with  worlds,  than  robot  actual  series  t h a t the  interesting  least  principles  robot  simpler  at  for  above, f o r  whole  roughly  This  better i f the  qualitative:  methodological  p r o m i s e s t o l e a d t o new  even  c o u l d be  knowledge  intuitive  f o r then  proposed  simulated  h i g h l y complex  In c o n c l u s i o n , t h e s t u d i e s i s strewn  so  system  of complexity  t o c a r r y over  Or  f o r various simulated  possibility  on  compared  building  robot  "elegance".  interesting  i s a t work which would say  worlds  level  the: c o n t r o l l e r organism*  controlling  obvious  be  or  be  since there i s  rely  were b u i l t *  c o u l d be  could  simulated  task  to  i s i t to  o r more d i f f e r e n t  program  of a r e a l  uncovered  robot  has  "interest", i f two  how  designed  i n i t s n a t u r a l environment, as  behaviour  the  improved  built,;  impossible One  "naturalness",  i n t e r - d e s i g n comparison  organism  an  with.  organism-controlling  simulated  is  it  and  arbitrarily  strictly,  t o compare  notions  designed  true  is  at  going  system. simulation  the  route  is  vistas!  IlaBackground  Issues  45 II.3  The  current Al t r a d i t i o n  f o r the d e s i g n of p l a n n i n g  problem s o l v i n g - systems i s not  easily  adaptable  and  to  my  purpose  My  research i s , i n part, a reaction  approach  to the d e s i g n of p l a n n i n g  T h i s a p p r o a c h i s so w i d e s p r e a d a  tradition.  call  i t the  [Newell,  Extending Freqean  Shaw,  &  and  the  Simon,1957]  [ Sussman, 1975 i]  Sussman,1977] epitomizes  The -  series  GPS  s y s t e m s say  about a c t i o n , section  is  remedy, and  I I , 3 . J An  nothing  amplify  show why,  exegesis  of  [Newell  systems. be  called we  programs  LT  & Simon,1963] -  H a r t , & N i l s s o n * 1972 ]  One's  t o one's o n g o i n g  -  a  everyday  p e r c e p t i o n and  and  plan. ,  justify  The  this  of some A l p l a n n i n g and  behaviour  is  actions,  yet  o n l y very purpose  complaint,  t e m p o r a r i l y , I shun t h i s  S  [ D o y l e , 1 978 i]  TMS  a b o u t p e r c e p t i o n and  i . e .. executing to  Al  of i S l o m a n , 1 9 7 1 g ,  [ McDermott, 1 978 ]  tradition..  related  usual  - NOAH [ S a c e r d o t i , 1977 9 - EL [ S t a l l m a n  DESI  this  intimately these  -  justifiably  terminology  tradition.  the  problem-solving  t h a t i t may  BLOCKS [ W i n o g r a d , 1 9 7 2 ] - STRIPS [ F i k e s , HACKER  against  little  of  this  suggest  a  tradition..  problem-solving  systems LT, first  52  the l o g i c  theorist,  theorems  was  given  i n the P r i n c i p j a  Russell.  A l l these  generate  subproblems  the t a s k  used  proving  the  M a t h e m a t i c a - o f Whitehead  are theorems i n the i t  of  sentential  substitutions,  calculus.,  detachment*  IlaBackground  & To  and  Issues  46  forward size  and b a c k w a r d c h a i n i n g , and t o r e d u c e  i t used  matching  and s i m i l a r i t y  52 t h e o r e m s and f a i l e d to  time  and space  on 1 4 .  Al  space  38 o f t h e  I t proved  Most o f t h e s e f a i l u r e s  very  important  i n L T a r e w i d e l y used  most modern  tests.  search  were  programming  i n A l . . The  techniques  i n A l and a r e i n c o r p o r a t e d i n t o  languages.  Its  importance  lies,  however, n o t s o much i n t h e t e c h n i q u e s i n v e n t e d by N e w e l l , and  Simon,  -  contributions in  t h e type  terms, followed which  verbally  and be  constructing airport. learning  believe system. being advice  which  shadow  accept  to  considered  a p l a n t o g e t from  something like  idea  i t must f i r s t  i t i s not q u i t e t h e r i g h t One o f t e n  about  i t .  To  illustrate type  i n one's  be c a p a b l e o f  was and  way t o d e v e l o p  i t i n words o r b e i n g  problem home  to  being  of the  told i t .  are reasons t o an  intelligent  a t some s k i l l able t o accept  Verbal expression of a s k i l l  i t s  t o be c a p a b l e o f  but there  becomes v e r y c o m p e t e n t  able t o express  of a decade,  f o r a program  a respectable basis,  which  was t o be a b l e t o r e a s o n  everyday  t h e desk  was t h a t  Kuhnian  published a proposal f o r  advice*  the  In  and  i n the c u r r e n t A l scene* .  year [McCarthy,1958J  able  technical  a paradigm  A l f o r the greater part  Shaw,  attempted,  acceptable*  established  T h i s program  he  important  o f problem  was f o u n d  program.  The b a s i c  may seem  i n the type  a significant  following Taker  undeniably  Shaw, and Simon  casts  functioning  That  - but r a t h e r  by m a i n s t r e a m  Advice  are  of s o l u t i o n  still The  an  these  Newell*  due  limitations.,  LT i s , h i s t o r i c a l l y , introduced  the  without verbal  comes a f t e r , n o t  II«Background  Issues  47 b e f o r e , t h e a c q u i s i t i o n of competence at the s k i l l .  To  give  a  very personal example^ I have two daughters aged 6 and 8 who can now s k i p r o f i c i e n t l y  -  yet they  nothing about technique; having  have  been  told,  verbally,  t h e i r only i n s t r u c t i o n has c o n s i s t e d o f  t h e i r hands held f o r s e v e r a l hours on beginners'  The  Advice  programs.  Taker  The program  proposal  of  influenced  [ Black, 1964 3,  the  slopes.  several program  later QA3  of  [ Green, 19 6 9 §, the MICROPLANNER language of [ Sussman, Winograd, & Charniak,1971J, and STRIPS a l l Taker.  Indeed  leaned  heavily  on  the  Advice  the f u n c t i o n i n g of MICROPLANNER c l o s e l y  follows  the o u t l i n e on pp. 406-409 o f [ McCarthy, 1 9583. GPS,  another  landmark  i n A r t i f i c i a l I n t e l l i g e n c e [Newell  and Simon,1963], i s a program whose design goal was t o human thought. as  the  I t handled  missionaries  problems,  proving  and  simulate  a v a r i e t y of i n t e l l e c t u a l t a s k s , such cannibals  theorems  in  task, the  some  integration  first-order  predicate  c a l c u l u s , and the monkey and bananas problem*. GPS deals with task  environment c o n s i s t i n g o f o b j e c t s which can be transformed  by v a r i o u s operators; and  i t detects  differences  between  objects;  i t o r g a n i z e s the i n f o r m a t i o n about the task environment i n t o  goals. what  a  Each g o a l i s a c o l l e c t i o n o f constitutes  goal  attainment,  information  that  defines  makes a v a i l a b l e the v a r i o u s  kinds of i n f o r m a t i o n r e l e v a n t to a t t a i n i n g t h e : g o a l , and r e l a t e s the i n f o r m a t i o n t o other g o a l s . . There are three types of g o a l s :  IIoBackground  Issues  48  Transform  object  A into object  B,  Reduce d i f f e r e n c e between o b j e c t Apply - o p e r a t o r Basically,  GPS  Q to  achieved  to  recursively  the  attainment  of the  Meanwhile  there  studies  in  set  the  a goal  up  initial was  principle  says  deduce BvC.  BvC  resolution principle  this  example  and  predicate  calculus,  arguments  of  algorithm  the  so  variables  such  become i d e n t i c a l  with  the  this  the  resolution principle,  formed  contributions  from  may  [ D a v i s , 1 9 6 3 ],  order  formula  This  and  was  two  logic,  clauses  others, a l l  consolidated  resolvent be  of  and  AvB  and  by  i t  by  that  variables  free  A,  B,  arguments  of  arguments of  can  may The  i n terms  allowing  may  order  appear  as  matching  substitutions  A i n the  A i n the  first  second  for  clause clause,  The  r e s u l t i n g r u l e of deduction  can  be  is  be:  complete  for  c a l c u l u s - t h a t i s , any  provable  well  be  proved to  of  extra  first  Introduce a  - t o compute  one  -iAvC.  i t t o the  C,....  resolution -IAVC  s u c c i n t l y described  lift  and  the  AvB  s y m b o l s and  predicate (wff)  effort  Generalize  i s possible.at a l l .  first  to  The  the  the  if  the  lead  logic.,  unification  that  would  from  symbols  - known as  heuristic  o f work e m a n a t i n g  follows.  predicate  means-ends  line  from t h e  full  disjunction  a  propositional  i s called  as  using  of I R o b i n s o n , 1 965 i ] .  in  that  A.  another  mechanize mathematics*  i t s simplest,  B,  goal. .  [ P r a w i t z , 1 9 6 0 ],  resolution principle At  by  object  s u b g o a l s whose a t t a i n m e n t  mathematical  [ G i l m o r e , 1960 ] , aimed t o  object  A and  deduced  by  sufficiently IIsBackground  many Issues  49 a p p l i c a t i o n s o f the r e s o l u t i o n The  resolution  theorem-proving mathematically matching,  principle.  principle  thus  reduces  to one r u l e o f i n f e r e n c e which subsumes, by the elegant u n i f i c a t i o n a l g o r i t h m , the s u b s t i t u t i o n s ,  and  similarity  t e s t s of LT.  However,  c o n s i d e r a b l e c h o i c e i n d e c i d i n g what p a i r of pair  of  predicate  together.  The  symbols  question  [Kowalski,1969]..  He  that  the  generalized  Raphael,19683,  and  of  derived A*  independent  of  search  strategies. search  reduced  of  QA4  that,  semantics  under  trying  this f a c i l i t y  the search. prover  to  by  which  In to  &  these  However, h i s s t r a t e g i e s  of the c l a u s e s and l i t e r a l s the search  control  these*  space  the: s i z e  i s not of the o f the  MICRO-PLANNER,  it is  possible  prove a wff of a c e r t a i n  other f a c t s of c e r t a i n r e s t r i c t e d type should However  studied  d e s p i t e the mathematical elegance  appeared. in  what  Nilsson,  rose when the programming languages  CONNIVER, and recommend  was  [Hart,  conditions  Hopes o f being a b l e t o  space  and  search s t r a t e g i e s f o r r e s o l u t i o n  under c o n s i d e r a t i o n * and conseguently significantly  clauses  strategy  algorithm  stated  the  there:remains  (technically, l i t e r a l s ) to resolve  s t r a t e g i e s were a d m i s s i b l e and optimal. are  mechanical  be  tried  does not* i n g e n e r a l , s u f f i c i e n t l y  to  type, first. reduce  [ R e i t e r , 1 9 7 2 J proposed the use of models i n theorem help  c o n t r o l the search, basing h i s approach on the  theorem  proving  machine  proposal  was  present  to the theorem prover a model of the  axiomatic  system i n v o l v e d .  to  of  I G e l e r n t e r , 1959t]. ,. H i s  geometry  In a d d i t i o n he  proposed  a  HaBackground  set of Issues  50 procedures required  for by  interface  extracting  the  theorem  between  such  syntactic  l o g i c a l system.  startling  breakthrough.  accepted way search  space  p r i n c i p l e may exposing in  information prover,  a  There  of using semantics in  and  semantic So f a r ,  about a  still  model when  flexible,  subsystem  this  to  the  has  general,  and the p u r e l y  not  led  to  any  seems t o be no g e n e r a l l y  control  the  size  of  the.  a theorem prover., In summary, the r e s o l u t i o n  be somewhat n e g a t i v e l y c h a r a c t e r i z e d  as  elegantly  the c o m b i n a t o r i a l e x p l o s i o n which seems t o be i n h e r e n t  any s t r a i g h t - f o r w a r d attempt  to  do  mechanical  mathematics  based on Fregean formalisms. The frame - problem a r i s e s whenever a theorem to the a  reason about a c t i o n s . QA3 program, system  This was f i r s t  a r e s o l u t i o n theorem  For  example,  (ON A B) and  (ABOVE A C ) .  some  facts  i f A, B, and C are b l o c k s , two  (ON B C ) ,  and  an  obvious  this axioms  deduction  is  I f the e f f e c t of an a c t i o n i s modelled by changing  which  which are now  of  false.  the previous deductions are s t i l l One  seems  c e r t a i n f a c t s remain unchanged modelled.  have  about  system of axioms then a f t e r the a c t i o n one cannot  formally,  an  Suppose you  of axioms that d e s c r i b e s a s i t u a t i o n i n the world - a  situation..  the  used  done by [Green,1969] i n  prover.  world model - and perhaps have deduced  might be  prover i s  to  need  axioms  be  sure,  t r u e and  saying  that  when the e f f e c t s of an a c t i o n are  T h i s i s e x a c t l y what Green d i d .  Every p r e d i c a t e  had  e x t r a argument p o s i t i o n f o r a s t a t e - v a r i a b l e - a s i t u a t i o n a l  f l u e n t i n the terminology of [McCarthy  &  Hayes,1969]  -  II«Background  which Issues  51  assumed a new value whenever an a c t i o n  was executed i n the world  model;  least  An a c t i o n was modelled by  axiom  described  said,  loosely,  objects  that  those  action, are s t i l l  true  multiplicity  axioms  the  was only the  of  axioms  able  most  languages.  describing  t o handle the s i m p l e s t  trivial  tasks,  attributes  However,  between  in  us c a l l  of each a c t i o n *  and  of problems..  In  any but  MICROPLANNEE, CONNIVER, and QA4 the p r o c e d u r a l  They r e p r e s e n t an advance over QA3 as follows._  as  describes  They  I n CONNIVER and QA4 each c o l l e c t i o n  a p a r t i c u l a r s i t u a t i o n i n the world  is  a c o n t e x t , and whenever the e f f e c t s of an a c t i o n So f a r ,  d e v i c e s used f o r modellinq the e f f e c t s of an a c t i o n -  other words, f o r s p r o u t i n g  addition  the  the world model, the axioms  are modelled, a new context i s sprouted from the o l d * . only  by t h e  explosion.  of axioms that  the  of  i t would be q u i c k l y overcome by t h e  do not use s t a t e v a r i a b l e s .  maintained  and the others  are not d i r e c t l y a f f e c t e d  a f t e r the action*  One  i n e f f i c i e n c i e s o f a r e s o l u t i o n theorem prover, QA3  combinatorial Let  axioms.  describing  both the e f f e c t s and n o n - e f f e c t s  inherent  two  the d i r e c t e f f e c t s of an a c t i o n  o f the world model that  describing  at  and  deletion  of  a new facts  though more powerful methods are  context  -  have  been  the  (axioms) from a context, even available  in  the  procedural  languages. STRIPS [ F i k e s and N i l s s o n * 1971g can successful The  marriage  of  GPS  be  described  as the  and the theorem proving approach.  problem space c o n s i s t s of an i n i t i a l world model, a HaBackground  s e t of Issues  52  operators  which  STRIPS attempts  affect to f i n d  transform  the i n i t i a l  statement  i s true.  wffs  the  in  the world a  sequence  of  operators  A world model i s represented  first-order  predicate was  initially  a  which must be s a t i s f i e d  wff,  world.  An  operator  the o p e r a t o r t o be a p p l i c a b l e , and a world  will  set  model  is  to  be  an  operator  This function i s s p e c i f i e d  and  delete  The  changes  consists  of  i n a world model f o r  function  which  describes  by two  effect  lists,  the add  list  of a p p l y i n g an a p p l i c a b l e  operator t o a given world model i s t o d e l e t e from the model those  a  changed when the operator i s  applied.  list.  of  the robot  t o an a c t i o n r o u t i n e whose execution causes  precondition  the  which  In  applied,  real  the  statement.  as  calculus*  i n the surrounding  how  a goal  world model i n t o a model i n which the g o a l  problems to which STRIPS corresponds  model, and  c l a u s e s s p e c i f i e d by the d e l e t e l i s t  all  and to add a l l those  c l a u s e s s p e c i f i e d by the add l i s t . , STRIPS attempt  begins  a p p l y i n g a r e s o l u t i o n theorem prover to  t o prove t h a t the goal wff GO  world model MO. in  by  the i n i t a l  f o l l o w s from  I f the proof succeeds  world model.  Otherwise  then GO  the  is trivially  the uncompleted  taken to be the " d i f f e r e n c e " between MO  and GO.  initial  proof  are  the . o p e r a t o r s  allow the proof t o  whose  continue.  a p p l i e d r e c u r s i v e l y t o these.  sought.  e f f e c t s on world models would  The  precondition  r e l e v a n t o p e r a t o r s are then taken to be new is  is  Next, o p e r a t o r s  t h a t might be r e l e v a n t t o " r e d u c i n g " t h i s d i f f e r e n c e are These  true  wffs  of  subgoals, and  A search s t r a t e g y i s  STRIPS  used  !!•Background  the  to  Issues  53 control  the  order  in  which  relevant  o p e r a t o r s are a p p l i e d .  STRIPS t e r m i n a t e s when a sequence o f o p e r a t o r s  has  been  found  which t r a n s f o r m s MO i n t o a world model i n which GO i s t r u e . STRIPS was l a t e r extended triangle in  by s t o r i n g g e n e r a l i z e d plans i n a  t a b l e format { F i k e s , Hart, N i l s s o n , 1972 [J. . T h i s was used  two ways: t o allow s i m i l a r  re-planning,  and  to  problems  assist  to  be. s o l v e d  without  i n monitoring the progress o f the  robot i n the course of e x e c u t i n g the plan. in  i n t e r e s t i n g guestion a r i s e s concerning t h e a b i l i t i e s of  STRIPS.  There a r e problems STRIPS can s o l v e and there are  similar  problems  has  a  STRIPS  perspicuous  very  cannot s o l v e ; at the.same time STRIPS  structure.  This  naturally  suggests  the  q u e s t i o n : i s there an i n t e r e s t i n g and u s e f u l way t o c h a r a c t e r i z e those problems - world model p l u s goal wff -  actually  solvable  by STRIPS? HACKER [Sussman,1975J  is  also  concerned  plans but works by a process of debugging skill  almost  One  contains  a l l the  BLOCKS  right plans, or  world  r e q u i r e d i n the course of s o l v i n g a BLOCKS type  of  producing  a c q u i s i t i o n . . HACKER i s endowed with s e v e r a l databases  assertions.  others  with  contain  bugs,  i n f o r m a t i o n about  types  summarizing  of  bugs.  patches HACKER  knowledge  problem,  starts  with  and a  techniques  for  dumb i n i t i a l  trial  procedure  f o r the t a s k .  fails  "process model" of t h e s t a t e o f the computation  a  point of f a i l u r e  i s constructed.  while  programming techniques, types  f o r bugs,  The t r i a l  of  procedure executes, and i f i t  HACKER then examines  a t the  this  IIoBackground  to  Issues  54  discover  why  the  procedure. f a i l e d .  attempts  to classify  If  attempt  the  about  bug-types  procedure; repeated,  i s used  If  process  an  procedure  that  until  a  a  known  and  to  patch  knowledge the  a bug f a i l s ,  of  i s then  then  is  HACKER  debugged  any o f a c e r t a i n  L o o s e l y s p e a k i n g , HACKER  database  trial  procedure  HACKER ends w i t h a f u l l y solve  types.  bug"  satisfactory  can s u c c e s s f u l l y  from  several  a modification  to c l a s s i f y  tasks.  i s t o s a y , HACKER  t h e n HACKER*s b u i l t - i n  "trial  Otherwise,  o f b l o c k s world  procedure  of  attempt  resigns;  one o f  t o propose  iteratively*  basically  a  i s successful  The  obtained.  class  t h e bug i n t o  That  general compiles  a l l t h e n e c e s s a r y f a c t s and  advice. The ability was  important  - i t wasn't good  of  a  retaining a  contribution  distinctly the reasons  o f HACKER was n o t i t s p l a n n i n g  - n o r even new  type  -  why a c e r t a i n  EL  of  [ Stallman  the  TMS s y s t e m Neither  and  which  the t e c h n i c a l  idea of  action  was p e r f o r m e d  or  why  This i s the idea  back-tracking of  the  & Sussman,1977], and was d e v e l o p e d  STRIPS n o r HACKER  and  -  system  further i n  of [Doyle,1978J.  the f o l l o w i n g  tabletop  ability  but  new p i e c e o f c o d e was added t o a p r o c e d u r e . .  underlying the dependency-directed  to  i t s learning  problem  three  C l i e s on A,  C  on  the table.  as  (AND (ON A B)  in  could the  obtain  BLOCKS  b l o c k s A, B, C.  The g o a l i s t o b u i l d These  systems  fail  the o p t i m a l world..  A and B r e s t a tower because  solution  There  is  a  on t h e t a b l e  A on B on C, w i t h the goal i s stated  (ON B C) ) , and b o t h STRIPS and  HACKER  IIoBackground  proceed Issues  55  to  attack  each subgoal independently.  Achieving e i t h e r o f the  ON subgoals  i n t e r f e r e s with a c h i e v i n g the other;  put A on B  you can't put B on C; i f you f i r s t  r  i s on A), you interacting  can't  put  to  Sacerdoti's subgoals*  on  B.  This  handle  r  put B on C  (which  i s an  example  [ T a t e 1 975 ], and [Warren,1975 ] a l l  of  system..  problems; I w i l l b r i e f l y  NOAH  builds  as  a  a  i s imposed  network  only  in a  when  sketch NOAH,  of  p r o c e d u r a l network.  r e g u i r e d t o achieve a goal are s t o r e d order  wrote  r  such  represented  temporal  first  subgoals;  [Sacerdoti*1975 J systems  A  I f you  goals  The subgoals  partial  necessary  order;  a  to resolve a  conflict  between brother subgoals.,  achieve  a g o a l i n a l a y e r e d f a s h i o n by expanding one subgoal at  a time* keeping primitive  NOAH c o n s t r u c t s  and  a  plan  a c a r e f u l watch f o r p o s s i b l e i n t e r a c t i o n s ,  actions  are reached*  In t h i s way a f u l l y  re-planning  to  achieve t h e f a i l e d  handled  subgoal and p a t c h i n g the  new plan i n t o the o r i g i n a l p r o c e d u r a l net. is  until  detailed  plan i s c o n s t r u c t e d before e x e c u t i o n begins; e r r o r s are by  to  To  summarize:  NOAH  a very e l e g a n t system which r e p r e s e n t s a c u r r e n t peak i n the  technology  of p l a n n i n g systems f o r a BLOCKS type  world*  II*3.2 C r i t i c i s m s of - the Fregean t r a d i t i o n - i n p l a n n i n g and problem-solving The  AI t r a d i t i o n , based upon  criticised  on two l e v e l s :  Fregean  formalisms,  can be  one i s p u r e l y t e c h n i c a l , the other i s  p h i l o s o p h i c a l . . On the t e c h n i c a l l e v e l there a r e a t l e a s t II"Background  three Issues  56 criticisms. reasoning  First,  about  previously.. handling facts,  actions*  Second,  a continual  an  ability  i n p u t from the  there  there  a changing  apply  to  static  interested  stream  axiom  well  numbers. trying  Lastly, to  knowledge On Fregean  more  formula  concerned  with  "dimension"  of  about  demands t h a t  well  accommodate  sensory  be  termed  a database  the  of  perpetually  Tarski-Kripke: In  addition*  the n a t u r a l  capture many  semantics  numbers  t o automate  the  i f  one  is  which  is  mathematics  that  concept  difficulties  only  no  Fregean  of the  natural  encountered  and  --  knowledge  in  about  formalism.  of  an the  action  and  attempt  as  in  the act of w r i t i n g to  yet  change., formula  - just  the dimension  level,  world;  Fregean  being tackled  to  contradictory  receives  might  causes, a b i l i t i e s *  implies  a  This  that  in  t h e r e i s no known s e m a n t i c s f o r  -  philosophical  aspect  organism  in  described  encountered  possibly  the well-known f a c t  fully  i n a Fregean a  of  i s trying  there are  reason  actionless  problem  to r e c a l l can  difficulty  systems*  it  encountered  problem,  o f e v i d e n c e about  o f axioms  t h e c a s e i f one  system  stream  Third,  presumably  formal  the  how  i n r e a s o n i n g about  would be  i s the frame  of any  problem:  database  difficulty  outside world.  o u t s i d e world.  a changing  the  is  incoming  a x i o m s t o an i n c o m i n g changing  This  required  accommodation  is  capture i n A l one  It's  as  a  by  timeless,  i s above a l l though  the  i s o f the wrong t y p e f o r t h e physics,  dimension  t y p e o f a f o r m u l a match t h e  t y p e o f t h e phenomenon d e s c r i b e d  down a  the  theory  dimension  formula. IlnBackground  Issues  57 At  this  p o i n t I must c a l l a h a l t .  l i n e of argument l e a d s t o deeper w a t e r s t h i s p o i n t , and,  developing  concerned  a  evidence;  than I care to e n t e r at  the  about  world  and  thesis.  r o b o t - c o n t r o l l e r one  with reasoning  accommodating  this  to do i t j u s t i c e , would t a k e . f a r more space  time than can be a f f o r d e d i n t h i s In  3  A c o n t i n u a t i o n of  actions  model  and  is, with  primarily, continually  t o the sensory i n p u t stream  s e c o n d a r i l y one d e s i r e s computationally  efficient,  at l e a s t t r a c t a b l e , algorithms f o r c a r r y i n g out these  of or  processes.  Throughout the exegesis I pointed out t h a t , i n e f f e c t ,  the  c o m b i n a t o r i a l e x p l o s i o n has not been brought under c o n t r o l .  For  some  and  special  proof  [Tseitin,1968J  procedures,  have  given  Without i n t r o d u c i n g any theorem  10  in  J.Cook  this  special &  "Cook a  &  Reckow, 1974 ij  more  precise  terminology,  Reckow, 1974 ] -  statement.  their  can  result  be r e - s t a t e d as  follows: For  infinitely  many n, there e x i s t s a theorem with n  c l a u s e s f o r which the number of steps i n i t s proof i s at l e a s t e x p o n e n t i a l i n (log(n) Thus one  may  complexity  conclude suqgests  shortest  squared).  t h a t the evidence, so f a r , from s t u d i e s of that  the  computational  reguirements  of  ^Because i t l e a d s to the c o n c l u s i o n t h a t the metaphysics of Platonism, as found i n the p h i l o s o p h i c a l t r a d i t i o n which s t a r t s with P l a t o and continues with Descartes, Kant* Frege, Russell, and modern a n a l y t i c p h i l o s o p h e r s , i s suspect. A new metaphysics can be based on the notion of " p r o c e s s " as i n Whitehead's Process and reality: T h i s i s part of another great t r a d i t i o n , l a r g e l y i g n o r e d by modern p h i l o s o p h e r s , which can be t r a c e d from Aristotle through medieval p h i l o s o p h e r s to Bergson, Whitehead, H u s s e r l , and o t h e r s . II«Background  Issues  58 r e s o l u t i o n theorem-proving There already  is,  however,  an  important  i Kowalski, 1969 jj  mentioned,  algorithms  are of an i n t r a c t a b l e nature.  f o r theorem-proving  open problem  derived  it  was  open  improvement  case  n**2, a s i g n i f i c a n t  question  of  A*  be  is:  can  carried  of  improvement;  to  A*. A*,  a l g o r i t h m B whose  Martelli's  over  As  search  behaviour  2**n, and r e p l a c e d A* by a new  worst case behaviour was obvious  heuristic  t h a t were g e n e r a l i z a t i o n s of  But [ Mart e l l i , 19771] analyzed the worst found  here.  The  analysis  Kowalski's  and  search  algorithms? In c o n c l u s i o n , I hope t h a t some  notion  of  why  I  feel  the  knowledgeable  and  have chosen  consequently can understand to take another  has  t h a t the Fregean t r a d i t i o n i n Al  planning and problem-solving systems i s , perhaps, tracks,  reader  why,  on  the  wrong  i n my r e s e a r c h , I  approach.  II.4 A survey of c l o s e l y r e l a t e d t o p i c s The  purpose  comprehensive description  of  this  survey of  two  of  section closely  related  is  to  provide  related  topics,  work,  namely  a  and  fairly a brief  imagery  and  behavioural theories.. I s t a r t with the l i t e r a t u r e on a n a l y s e s and s i m u l a t i o n s organisms.  There  independent,  and each with i t s own  have  are  many  such  studies, particular  of  a l l more or l e s s orientation.  I  t r i e d to c l a s s i f y them a c c o r d i n g to t h e i r emphasis, but no IIoBackground  Issues  59 mutually e x c l u s i v e c l a s s i f i c a t i o n seems p o s s i b l e .  The  headings  I have chosen a r e : •  f u n c t i o n i n g robot  •  analyses  *  s t u d i e s based on animal behaviour;  •  a p p l i c a t i o n s of d e c i s i o n  •  c o g n i t i v e maps.  The  simulations;  o f simple organisms, without  inclusion  of  theory;  c o g n i t i v e maps here may seem a l i t t l e  p l a c e , but a moment's c o n s i d e r a t i o n * studies  are  simulation;  concerned  of the f a c t t h a t  reasoning*  •  s p a t i a l planners and  •  representation  T h i s f a l l s e a s i l y i n t o two c l a s s i f i c a t i o n s : conceived  as p o t e n t i a l t o o l s f o r a r c h i t e c t s  others;  systems f o r s i m u l a t i n g the motion of r i g i d  There  appropriate.  then proceed t o the . l i t e r a t u r e on s p a t i a l  and  a l l such  with how an animal or man f i n d s i t s way  around i t s environment, shows that i t i s q u i t e I  out o f  i s , in  addition,  one p u b l i s h e d  system f o r p a t h - f i n d i n g  [ Thomson, 1977i], which I do not i n c l u d e here appropriately Similarly  covered  in  my  bodies.  section  since  V.I  I do not review the l i t e r a t u r e on  on  the  i t is  more  path-finding. skeleton  here  s i n c e t h a t i s done i n s e c t i o n V. 1.  I i * 4 . 1 Previous [Nilsson environment  robot &  simulations  Raphael, 19671]  i n order  simulated  a  robot  and  its  to study the key problems i n designing and II«Background  Issues  60 controlling robot,  a robot.  was  simulated  based  robot  containing  Their l a t e r on  r e s i d e s on  both  the  simulated  features  that  system  any r e a l  f o roverall  by u s i n g  immediately  and  sensory  information. by  The  pushing  contained  robot  problem-solving  " g o t o " and " p u s h t o " p r o b l e m s .  of l o c a t i o n s .  i t s  Plans  front  could  richer  model o f i t s  f o r communicating  program, and a r o b o t The t a s k s  to solve  Moore's m a z e - s o l v i n g  The r o b o t  in  control.  several  i n a much  These i n c l u d e t h e r o b o t ' s  a heuristic  program  constructed  uses  a p r o b l e m - s p e c i f i c a t i o n language  the robot,  executive  the: location  changes to i t s environment  the  would n e e d .  environment, with  of  basic  environment  about  into"  movable o b j e c t s .  design  important  information  c o r r e c t , or update t h i s  c a n make s p e c i f i e d  The  Their  and s e n s e when i t "bumps  i n i t s e n v i r o n m e n t and  establish,  appropriate  arbitrarily  or l e f t ,  stores  properties of objects  robot  exploration.  SHI  The r o b o t c a n  It  an  the  movable and nonmovable o b j e c t s . .  an  to  preliminary  Shakey,  checkerboard  turn r i g h t  inputs  of  large  move f o r w a r d , object.,  this  design  these  algorithm  sense the contents  consisted of tasks  were  on t h e a r r a y  o f the  square  o f i t , and use t h i s t o c o r r e c t t h e w o r l d  model* Of closest my  the  published  studies  that  t o mine i n t e r m s o f o v e r a l l  simulated  world,  robot-controller corresponding  are  Utak's a l l  parts of their  I know o f , t h e i r s  a i m s and  sensory more:  design..  equipment,  sophisticated  i s the  However,  and than  Utak's the  system* II^Background  Issues  61 Becker and Merriam I Merriam, 1975 fj) world  ([ Becker, 1972 ], [Becker  simulated  a  robot  cart  which used a s o p h i s t i c a t e d eye with  information  about  i t s surroundings.  This  eye  i n a two a  fovea  a "Martian"  could e i t h e r gather  coarse  eye for  a  landscape  detailed  and f o c u s s i n g down on one.object  information..  eye-controlling  This  conflict  scene.  a The  unfortunately  natural-looking design not  o b j e c t when the environment  took  of  robot  the  into  a ' lookout t o get more  resolved  by  the  and  which  when l o o k i n g at a s t r e e t program  was  The eye could a l s o track a f i x e d  the v i s u a l  by Martian  path  effort...,  eye-controlling  acount  The  later  the  finite  occlusion  mountains.  simulation size  of the  of the robot  of, f o r instance,  A long term memory was used  information.  i s a more s o p h i s t i c a t e d s i m u l a t i o n of the world and  a d i f f e r e n t eye, but no design of  scan  moved*  which s t o r e d no s p a t i a l Theirs  progress,  specified.  c h a s s i s and simulated Martian h i l l s  Thus the  program which took i n t o account such f a c t o r s as  d r i v e , s a l i e n c e of an o b j e c t , produced  was  was  information  small area, and could change i t s f o c a l p o i n t .  objects,  up  i n f o r m a t i o n from a  could be used f o r two c o n f l i c t i n g t a s k s : keeping new  pick  a city street  l a r g e area or could "zoom" down and o b t a i n d e t a i l e d from  dimensional  to  Initially  environment was used but subsequently used.  & Merriam,1973],  the simulated  of the robot executive*  robot executing  or r e p o r t  a goto o r pushto task, appears  to have been p u b l i s h e d .  IlaBackground  Issues  62 II.4.2 Three analyses of simple organisms Each organism  of  these  from  theoretic  analyses  a distinct  analysis  approach  environment;  of  the  Toda's  survival  paper  d e c i s i o n theory; while Becker a  representation  should develop  for  over  of  is  in  of  events  organism relating  the  i s concerned  external  an  equation  an  in  an  organism  same vein but  uses  with the s t r u c t u r e of and how  this structure  time.  [Simon,1956] considered a s i m p l i f i e d v i s i o n , with a s i n g l e need - food activity:  behaviour  point of view.. Simon's paper i s a game  environment i n which he d e r i v e s one to  the  resting,  organism  and  only  with  three  e x p l o r a t i o n , and o b t a i n i n g food.  of  I t has to  point  derived  the chances of s u r v i v a l of the  organism  depended  environment organism that  equation showinq how  and  on two  four  parameters,  describinq  the  two  of  kinds  s u r v i v e on a plane with i s o l a t e d an  sources  circular  orqanism,  organism  and  extended could  to  assure  be. s a t i s f i e d  decision  achieved  theory.  a  behaviour  found  i t s several  high p r o b a b i l i t y of i t s s u r v i v a l He a l s o  showed  how  multiple  with a very simple choice mechanism.  over qoals This  without the use of u t i l i t y f u n c t i o n s as i n  Simon's a n a l y s i s c a s t s e r i o u s doubts upon the  u s e f u l n e s s of then c u r r e n t economic and rational  he  the  i n i t s n a t u r a l environment r e q u i r e s only very  p e r i o d s of time.  a n a l y s i s was  the  assuming  behaved i n the obvious " r a t i o n a l " way.„ Thus  an  He  describinq  simple p e r c e p t u a l and choice mechanisms t o s a t i s f y needs  food*  s t a t i s t i c a l theories  as bases f o r e x p l a i n i n g the  of  characteristics  IIoBackground  Issues  63 o f human and  other  dissatisfaction As views  sprang  a device to man  planet. distributed eating  a  u n i f y the  s t u d i e d the The on  surface*  The  program  were  amount of  job  design*  to t r a v e l  uranium The  are  representation  i n at  collected effect  also  ]  terms.  then  to induce,  such  function  a  distant  uranium  obtains  randomly  energy  program,  each moment* ,  i n the  of p r o c e s s e s experience world  b l o c k s may  given  and  and  from  a  the  to  Extending on  The  Simon's  choice  robot  choose  maximizing  choice  the  strategy  strategy  uses  the  choice  c o u l d reduce the c o m p u t a t i o n a l  a simple  robot  be  future,.  (My  style.),  He  by  which the  i t gained  c o n s i s t s of placed  and  world  events  i n t r u e Baconian  a system  e n v i r o n m e n t . . The  on  c h o i c e program has  robot observes  "Popperian"  coloured  robot  psychology  no  and  effort stored  environment.  The  events  the  this  emotion, . . . ) ,  robot  collect  o f o b s t a c l e s on  in  manipulate  The  is  analyzed  "Baconian"  predict  the  considered.  of t h e  [ B e c k e r , 1973  tries  to  perceiving  a l l considered.  various approximations  required  motivation,  of a s o l i t a r y is  which  a d e c i s i o n - t h e o r e t i c a n a l y s i s based  specified.  and  design  from  f u n g u s t h a t grows a t random l o c a t i o n s on  bodily  what d i r e c t i o n approach,  v a r i o u s ways i n  s u r f a c e , and  certain  (And  & GPS?)  learning,  robot's the  rationality. .  f o r t h LT  (perception,  [ T o d a , 1 9 6 2J  how  organismic  a  as they  style,  call  happen  and  r e p r e s e n t a t i o n s to  system proposed robot  through  i n what I  may  be  said  a representation could  store  interacting  smooth  manipulated,  to  shelf  and  with i t s on  a simple  li«Background  which movable Issues  64  square eye with 9 square in  the  eye  retinal  A h i s t o r y i s kept  commands  with the  their  robot  representation,  and a hand t h a t  a 1 X 1 r e d s q u a r e . . The w o r l d  as  physics.  record  fields,  of  sensory tries  which  motor  to  obeys t h e laws o f  commands  answers.  and  From  induce  appears  of  this  a  query  historical  semantic-net-like  i t u s e s t o p r e d i c t t h e outcome o f f u t u r e  actions. Becker's followed so  approach  is  A i n the past,  that  the  Becker's  with  a Baconian  his  analysis.  i tclearly approach*  input),  deciding  which  attempted  a t t o o low a l e v e l  are  B e c k e r d o e s , i t e n d s up b e i n g as a h y p o t h e t i c a l  observations must  decide  supposing problem relation part  in  a  by  which  the  'event'. large  there  is  on g u i t e  that  kernel  of  the  start  problem  one and s h o u l d  as,  I  claim,  criteria.  make a  million  i s not f e a s i b l e , Second,  have  therefore  a  i s the causal  be s t o r e d  What i f two c a u s a l l y r e l a t e d k e r n e l s periods  o f t i m e , a s might  of  decision i s  interest.)  may  of  of kernels  has been c h o s e n , t h e r e kernels  fact,  associated  arbitrary  but since are  i fB  succeeds,  the  If this  could  ones  i t  stream  scientist  how many n e a r b y chosen  continual  representation,  based  Baconian  significant  of deciding to  of  that  the d i f f i c u l t i e s  significant.  situation,  somehow  of t h i s  separated  a  the  that  A i n the future.  These a p p e a r r i g h t a t given  kernels  remember  B to follow  illustrates  First,  idea:  i n t e r e s t i n g n o t because  (motor commands and s e n s o r y  (Just  should  can expect  approach i s very  because  on one s i m p l e  an o r q a n i s m  organism  but  based  as are  occur i n object  II«Background  Issues  65  occlusion  problems?  problem,  which  might  several numerical hoc  basis  etc.,  B e c k e r has be  are  generalized,  termed  used t o e n a b l e  or  numerical  feature;  In  sum,  a very  its  and  not  Simulations  simulate  based  aphid  alternations e.g. model  is  based  reciprocal is  on  a separate  centre  sufficiently  strong  the at  centre a time  active system persist  This  is  a  be  These  mainly  of  for  even  of  with  behaviour,  wingspreading.  The and  For each  activity  there  each  other.  inhibition  one  several  When  from  equally stimulated  a system only  a  concerned  drives,  the  such  designed  centres,  active  such  was  types  flying,  i t i s possible for  period  but  model i s o n l y  inhibit  centre  i t  rival;  a is but  i s active to  be  configuration i s unstable)..  The  e x h i b i t s h y s t e r e s i s : once an for  to  unsatisfactory  proposal,  centres  t o s u p p r e s s an  concurrently,  ad  cost  subrules.  a very  different  concepts  The  f a t i g u e s ; . In (although  s c a l e s are  between c e n t r e s . .  centre*  particular  into distinct  probing,  the  inhibition  an  confidence,  a model a n i m a l which  several  feeding,  on  on a n i m a l - b e h a v i o u r  behaviour.  between  walking,  manipulated  successes.  [Ludlow,1976J d e s c r i b e s to  and  this  Third,  ( d e r i v e d from events)  interesting  for i t s  s o l u t i o n to  'windowing' p r o b l e m .  rules  differentiated  arbitrary  I I . 4._3  a  measures o f c r i t i c a l i t y ,  apparently  faults  satisfactory  s c a l e s are introduced  to provide  which  no  activity  when t h e  centres  i s started i t  drive l e v e l  will  necessary  IlaBackground  to  Issues  66  e l i c i t the a c t i v i t y has been reduced would  seem  t o be a necessary  execute many d i f f e r e n t approach  might  controlling  by the  f e a t u r e of any organism  behaviours, to prevent  usefully  be  several different  incorporated  Releaser  Mechanisms"  with  an  a  control  program  the e x e c u t i v e c o n t r o l h i e r a r c h y .  The  (ADROIT) t h a t moves  The  along  the  in  a  programmed,  lines  of  the  ADROIT avoids o b s t a c l e s when en route  a goal by r e a d i n g the angles  cylinders.  system  of  designed  theory, .  AI  the Lorenz - Tinbergen  with a small number of c i r c u l a r o b s t a c l e s was  afore-mentioned to  in  This  "Selection  computer s i m u l a t i o n of a small animal plane  which can  thrashing.  animal behaviour by adding to  This  behaviours.  [ F r i e d m a n , 1 9 6 7 J analyzes and extends theory of i n s t i n c t i v e  performance..  and  ranges  to  the  edges  of  s t r u c t u r e of the " B e h a v i o u r a l U n i t " to c a r r y out  a "go t o " command was  exhibited.  No r e p r e s e n t a t i o n of the world  was i n v o l v e d . [ A r b i b & L i e b l i c h , 19771] are concerned  to  bridge  the  gap  between human memory s t u d i e s and the p s y c h o l o g i c a l l i t e r a t u r e animal l e a r n i n g and c o n d i t i o n i n g . . The research  effort  on  Pavlov - Bitterman learning  are  animal theory  the  that  same  They propose  major reason f o r the huge  behaviour has been the Thorndike the  in  [ Bitterman, 1975 ]; consequently research..  this  underlying  a l l animals,  processes including  i s an important d i r e c t i o n  a theory of how  an orqanism  in  its  spatial  environment  of  man of  couples i t s  memory s t r u c t u r e to i t s s p e c i f i c a c t i o n r o u t i n e s so t h a t i t operate  on  may  i n an i n t e l l i g e n t manner. II»Background Issues  67  They  adopt a world  model i n t h e  containing  drive-related  sensorimotor  features.  dynamics,  the  theory  learning  •LI'H'H  The t h e o r y  of  environment, An  approach  from  particular  robot  where e a c h  decision  edges  nodes  containing  general  drive  in  the  world.  results that relate r a t  that  d e c i s i o n - theory consider  operates  t h e . decision-making  in  i s  a  poorly  known  a c t i o n may have many p o s s i b l e o u t c o m e s .  b a s e d on m a x i m i z i n g t h e e x p e c t e d  each  with  behaviour*  Kiefer,1973]  a  and  where t o move n e x t  Robot - s i m u l a t i o n s based - on &  graph  model i s u p d a t e d , and t h e  e x p l a i n s some e x p e r i m e n t a l  [Jacobs  a  specifies the  way i n which t h e w o r l d  and s p a t i a l  component  of  information  way i n which t h e r a t d e c i d e s Their  form  developed.  utility  resulting  The d e c i s i o n t o e x e c u t e  a c t i o n i s viewed as a move  in  a  game  against  a  the  environment;  t h e outcome o f an a c t i o n i s t h e e n v i r o n m e n t ' s move  in  t h e game*  The e s t i m a t e d  by  backing  that  the u t i l i t y  expected the  up from  value  expected  task  assigned of their  utility  to  f o r a nest,  i s to build  the robot  eating,  is  utilities.  evaluated  using  the f a c t  The d e c i s i o n t h a t  chosen,  insect-like  This  robot  and may be s t u n g  a nest.  of a plan,  i s  t o a s e t o f u n c e r t a i n outcomes i s t h e  The t a s k  but i s s p e c i f i e d  adding  of a d e c i s i o n  the t e r m i n a l stages  c o n t r o l a simulated material  utility  approach  which s e e k s  i s  by an enemy.  m a t e r i a l t o the nest,  the u t i l i t y finding  used  food, The  i s not e x p l i c i t l y  through  maximizes to  collects robot's  represented  functions  for  m a t e r i a l , and b e i n g IlaBackground  Issues  68  stung.  Likewise,  through eating  its will  exceeds  a  utility  No  decision  (negative)  et  a  positive  and  false  the  tradeoffs  goals,  taking of  It i s also acguire  w o r t h w h i l e , and Feldman  not  of  &  among  used t o a  i n the  whether v e r i f i c a t i o n  Sproull  discuss  and  provided  give  a  are  the  -  have  used  utility function for  and  function is  used  achieving  value  be  of  problems  much p l a n n i n g  possible  to  reliability,  the  t e s t s should  false  of  suitability  s o l u t i o n s t o the  many o t h e r  the  actions  strategies  how  under  distance.  may  theory  strategy,  model,  this  a  such f a c t o r s a s  formulate  world  from  a  In  monkey i s  utility  as  problem.  the  apply  stated  the  sensing  various  starve.  respective  pushed  using  The  ever  represented  be  decision  i n t o account steps  be  bananas  All  strategy,  not  can  reliable  answers.  will  S p r o u l l , 19771]  "suitability"  is  technigues  robot  used  meal  solving.. Their  to  pushing, climbing,  solution  complexity  to  sensinq  except  utility  previous  is  &  s u i t a b l e , and  i n t e r m s of e n e r g y c o s t .  reveal  goal.  are  goal  environment i s used.  and  available  negative  The  best  problem  monkey and  device  - walking*  various  how  for the  energy c o s t s .  the  all  the  equivalent  the  the  starvation of  a  with the  poor  [Feldman  symbolic  of  not  Unfortunately  defined  and  s e v e r a l boxes are  device  to  to  version  with  of  the  representation  essentially  but  find  -  goal  a l . , 19753  bananas  monkey  bound  as  in fact  so  examples are  version  and  certain  theory  modified  function  represented  time s i n c e  stored  [Coles  i s not  never o c c u r i f the  However, t h e either.  eating  effort  the of is  performed.  applications  IIsBackground  of  Issues  69 d e c i s i o n theory i n robot problem s o l v e r s . Feldman and S p r o u l l ' s paper supports t h e i r c l a i m t h a t "a combination  of  d e c i s i o n - t h e o r e t i c and  symbolic  artificial  i n t e l l i g e n c e paradigms o f f e r s advantages not a v a i l a b l e to e i t h e r individually".  However,  although  I  can't  yet pinpoint i t  e x a c t l y , I confess t o a gueasy f e e l i n g when a p p l y i n g p r o b a b i l i t y theory to symbolic theory  reasoning.  The  basic  i s the p r o b a b i l i t y of an event,  value o f the r e l a t i v e frequency  definition  of the  defined as "the l i m i t i n g  of occurrence  o f the event  in a  long sequence of o b s e r v a t i o n s of randomly s e l e c t e d s i t u a t i o n s i n which the event is  very  may occur" [ Parzen, 1960 i]. . P h i l o s o p h i c a l l y  u n s a t i s f a c t o r y . . Bayes' theorem, an important  computing  conditional  unsatisfactory..  The  probabilities, task  of  clearly  difficulties  and proposing a new d e f i n i t i o n  beyond  scope o f t h i s t h e s i s .  the  is  rule:for  even  delineating of  this  more these  probability  is  A l l t h a t can be s a i d i s t h a t  t h e r e are many i n k l i n g s around, and i n chapter  IV  I  will  give  These s i m u l a t i o n s serve to confirm Simon's c o n c l u s i o n  that  some i n d i c a t i o n o f the d i r e c t i o n r e q u i r e d *  traditional of  decision  theory i s not a p p r o p r i a t e t o the a n a l y s i s  b e h a v i o u r a l systems.  I I . 4. 5_ C o g n i t i v e maps  A  traditional  cognitive  maps  field  of  psychology  ([ Trowbridge , 1913 ],  i s concerned  [ Tolman, 1948 ],  with  [Moore  IIsBackground  &  Issues  70 Golledge, 1976 ], j_ K u i p e r s , 19781]) . the  knowledge  a  person  l a r g e - s c a l e space.  has  A person's about  cognitive  map i s  the s p a t i a l s t r u c t u r e of  Thus the t o p i c of cognitive:maps  i s relevant  to my work. The  f u n c t i o n s of a c o g n i t i v e  information position,  about  and  problems.. through  to  map  assimilate  new  the environment, t o r e p r e s e n t one's c u r r e n t answer  route-finding  and  relative-position  I t i s b u i l t up from o b s e r v a t i o n s made:as one t r a v e l s the  environment.  computational  model  [ K u i p e r s , 1978 ]  presents  a  (the TOUR model) of the c o g n i t i v e map t h a t  uses m u l t i p l e (5) r e p r e s e n t a t i o n s f o r builds  are t o  the c o g n i t i v e  map,  and  up knowledge by o b s e r v a t i o n s and by i n t e r a c t i o n s between  the separate r e p r e s e n t a t i o n s .  Whereas TODR gains new  knowledge  by d i s c r e t e o b s e r v a t i o n s at a s m a l l number of f i x e d p l a c e s , Utak gains new knowledge by r e c e i v i n g a new r e t i n a l impression new  position  impression  and  r e s o l v i n g the d i f f e r e n c e s between the a c t u a l  and the p r e d i c t e d r e t i n a l impression by modifying the  hypothesized  shape  environmental  empty space i s very s i m i l a r t o K u i p e r ' s  map  when regarded  concerned PPA  at a  of the environment*  as a network of r o u t e s .  Utak's s k e l e t o n o f the  Whereas TOUR i s only  with c i t y - s t r e e t networks and not at a l l  explicitly  environmental  represents space.  In  the two sum,  dimensional  Kuiper's  cognitive  work  with  shape,  shape o f the is  somewhat  complementary t o mine.  IIsBackground  Issues  71 II.4.6  Spatial  planning  systems  [ Eastman, 1973 i] r e v i e w s c u r r e n t program, tasks.  GSP,  for  rectangular  computer),  edge-adjacency  overall  the design  Various  the  proposer  DDs i n  consistent in are  which  S which  satisfies  are  described  S,  which,  proposes  with the arrangement  several  DDs  (e.g..an  reguirement f o r the of  the  a l lthe S-relations. depth-first improve  a  made;  t h e s i d e s o f t h e DUs a r e a l i g n e d  with  search.  o f GSP  new  The  the search,  an a r r a n g e m e n t  for  already  room),  the  An i m p o r t a n t p a r t  locations  arrangement  an a r r a n g e m e n t  which  when g i v e n  a new  (e.g. the p a r t s o f a  between  i s to f i n d  i s the  o f some o f  DU  which  are  Only  arrangements  the  sides  of  S  considered. f P f e f f e r k o r n , 1975 |J d e s c r i b e d  which  relaxed  the r e s t r i c t i o n  a l l o w i n g non-convex p o l y g o n a l type of s p a t i a l  constraint  which  a l l t h e empty  says that  connected. arrangement are  (DOs)  or a sight-line  from t h e S - r e l a t i o n s .  location  rectangular  o f GSP i s as a b a c k t r a c k i n g  heuristics  derived  S-relations  t h e problem  space  a large units  reguirement  operator's desk), in  design  and s e v e r a l  and d e s c r i b e s  two d i m e n s i o n a l s p a t i a l  Given a space S (e.g.  smaller  DUs  solving  programs  marked  DPS  that  convex and  planner,  DPS,  a l l s h a p e s b e : r e c t a n g u l a r by  s h a p e s , and which  on an a r r a n g e m e n t :  allowed  a path  a  must  o f space occupancy  polygons are the  primitives;  some a r e marked o c c u p i e d .  new  constraint,  space i n the arrangement  uses a representation  i n which empty  another s p a t i a l  be  o f an Some  These  convex  IlnBackground  Issues  72  polygons are c a l l e d represented  Each space block  as a set of s i d e s , and  When a new  by  a  side  of  space b l o c k s and  location  the  in  turn  new  every  space  block  shape i s broken i n t o  the occupancy marked a c c o r d i n g l y .  proposer e s s e n t i a l l y  space b l o c k s . . As i n GSP  is  each s i d e as a set of p o i n t s .  shape i s added t o an arrangement  intersected separate  space b l o c k s .  proposes a l l the c o r n e r s  the c o n s t r a i n t s are used to  two The  of empty  guide-  the  search* . Both systems explore the  branching  proposer and try  concerned  where  f a c t o r at each node i s c o n t r o l l e d by the l o c a t i o n  new  shapes.. The  convex polygon represented fault  t r e e of space . l a y o u t s  by other h e u r i s t i c s which decide  fitting  main  a search  from  my  order  to  p r i m i t i v e shape concept used i s a  as a l i s t  point  i n what  of  of boundary p o i n t s .  Their  view i s that these systems are  only with o b j e c t placement, not  with  path-finding  or  o b j e c t moving,.  II.4.7  Systems f o r s i m u l a t i n g the motion of r i g i d  [Baker,1973J, spatial  dissatified  simulation,  desired  with one  objects  conventional in  r e l a t i o n s h i p s of p o i n t s were e x p l i c i t . .  which To t h i s end  methods f o r the  spatial  he  presented  the design  of an i t e r a t i v e array of l o g i c c i r c u i t s  which  simulate  the  or  rotation  of  this  arbitrary The  continuous  shapes, and  rigid  translation  implemented a s i m u l a t i o n  system c o n s i s t s of a r e c t a n g u l a r a r r a y of l o g i c a l  could of  array.  circuits,  II«Background  Issues  73  each  representing  coordinate  a unit  system  the  square.  On  reaching  t o keep t r a c k  the  side  of the point  An  is  object  greater  than  of  stability  o f a s q u a r e , c o n t r o l and m o d i f i e d  local  are passed t o the neighbouring as a c o l l e c t i o n  root  of  of points  between  square. (where f o r  points  2 (root2)) ,  from  that  a  must  be  and i t s m o t i o n points.  can  derive  t h e u s e o f a n a l o g u e s i n t h e same way t h a t  people  e n d , he i m p l e m e n t e d  system  was  to  computer  a system  solve  two  program  WHISPER.. The  dimensional  comment  on  h i s arguments c o n c e r n i n g  from  my p o i n t  o f view WHISPER was i n t e n d e d  f o r simulating  rigid  object  motion  the:use t o be  purpose  blocks  p r o b l e m s by t h e use o f a s o - c a l l e d a n a l o g u e .  not  system  as i t c r o s s e s  was n o t d e v e l o p e d t o h a n d l e c o l l i s i o n s . „  To t h i s this  local  arc.  square  [Funt,1976] argues  do..  a  or a c i r c u l a r  represented  the  has  by f o l l o w i n g t h e p a t h s o f a l l t h e c o n s t i t u e n t  system  benefits  circuit  of a single point  r e a s o n s t h e minimum d i s t a n c e  simulated The  Each  I t s p a t h may be a s t r a i g h t l i n e  coordinates  technical  square.  I  world will  of analogues; a  performance  under t h e i n f l u e n c e o f  gravity. The  input  t o WHISPER i s a two d i m e n s i o n a l  s q u a r e s on which t h e s i d e view coloured, the  arbitrarily  corresponding  instabilities immediately interactions:  and  of a configuration  shaped, b l o c k s real  world  under  collapse, i n  the a  array  rotation, collision,  has been drawn. situation  influence  flurry  of  of  sliding,  of  block  of colored distinctly Typically  contains  many  gravity  would  motions  and f r e e  and  fall*  II»Background  Issues  74  WHISPER s i m u l a t e s produces  as  output  this  t h e same a r r a y  updated t o d i s p l a y t h e i r simulation  makes  human r e t i n a program  in  which  collapse  predicted  extensive some  the  retina,  contacts  about  symmetry;  The  non-overlapping size  circular  increases  with  parallel Funt's array  of  as  a  fixed  retina  is  o f automata.  similar  in this  properties  r e s i d e i n t h e diagram;  simulated  program,  movement  motions t h e  disintegrates  into  a  while  an  conclusion  the s i m u l a t i o n  WHISPER i s n o t s u i t a b l e f o r my H Howden, 1969 i]  considers  fact  and  finding finding array  an  c e n t r e . . Each  neighbours. iterative  becomes known t o shape  and  other  and a f t e r on  small i s o l a t e d  a few  the  array  pieces.  a p p e a r s i n a p p e n d i x A.3. of r i g i d  is  operating i n  to Baker's  object  of  The b u b b l e  immediate  are simple  of  of t h i s  that  circular  object's  of  multitude  area,  processors  their  primitives  depiction  main  operations  or bubbles.  respect  precise demonstration is  a  O n l y t h e c o l o r o f an o b j e c t  main  the  motions  the r e t i n a l  of  with  WHISPER'S  WHISPER'S  block  of  The  s o t h a t t h e whole r e t i n a  number only  of  o f r o t a t i o n , and  fields,  processor,  positions  resembles t h e  control  of  and  places..  which  centre  consists  and c o m m u n i c a t i n g  the block  the  d i s t a n c e . from  b u b b l e h a s an a s s o c i a t e d conceived  finding  retinal  array  t h e use o f s e v e r a l  visualization  retina  input  resting  Under  gravity,  including  between b l o c k s ,  but with  use of a r e t i n a  i n t e r a c t i o n s a r e computed t h r o u g h on  the  final  respects.  knows  on  motion p r o v i d e d  A The by  purpose.. the  sofa-moving  task;  that i s ,  II*Background  Issues  75 produce a plan f o r moving a two  dimensional  to  to  another  when  surrounding, The  and  constrained  shape from one.place  remain w i t h i n the w a l l s of a  i n general non-convex, two  edges of the w a l l s and  of the  of p o i n t s using chain-encoding i s easy t o simulate  dimensional  s o f a are represented  [Freeman,1974];  r i g i d o b j e c t motion.  used  In a pre-execution an  be extended to do so.  such an extension*  array  since.he  the  walls.  Presumably the  reported  I am  on a running  f o r every point on the perimeter  2 *  of the  program. into  must  sofa* ,  At  any  (integral)  point  within  plan the  i s a s m a l l number of p o s s i b l e a c t i o n s of t r a n s l a t i o n  or r o t a t i o n which may actions  So  (length of s o f a perimeter)  produced as f o l l o w s .  w a l l s there  be  referenced  times f o r every i n t e r s e c t i o n t e s t performed*. A sofa-moving is  will  author  step, the p o i n t s of the wall are sorted  the w a l l array i s u s u a l l y  it  i n t h i s paper  of buckets, which, i n the extended a l g o r i t h m ,  probed twice  lists  I t i s not, however, so  that the a l g o r i t h m as described  work, though i t can  as  conseguently  easy to detect the i n t e r s e c t i o n of the s o f a and not convinced  shape.  are  those  be a p p l i e d to the f o r which the  sofa;  the  permissible  intersection test f a i l s .  The  plan i s produced by executing  an u n d i r e c t e d , l o o k i n g  heuristic  s t a t e space e n t a i l e d by the s e t of  search through the  p e r m i s s i b l e a c t i o n s at each p o i n t . , That t h i s at  all  is  somewhat  surprising  -  scheme  apparently  backwards,  performed  i t d i d , on some  poorly s p e c i f i e d examples.  I t would perform p a r t i c u l a r l y  in  a  the  simplest  case  -  small  sofa  badly  w i t h i n a l a r g e empty II«Background  Issues  76 containing  space.  I I . 4; 8 Imagery  Mental imagery i s r e l e v a n t PPA  because the SHAPE  subsystem  of  can be viewed as a model of mental imagery even though t h a t  was not t h e goal of SHAPE'S design., discussed  in  the  [Piaget,1954 §,  This  Shepard,  presents  the c u r r e n t  imagery  has  been  p s y c h o l o g i c a l l i t e r a t u r e by \_ B a r t l e t t , 1932 i ] ,  [ Hebb, 196 8 ], i s how  Mental  iShepard,19783  iii the c o n c l u s i o n  and  many  of h i s recent  others. review,  s t a t u s of mental imagery i n psychology:  I submit t h a t there are both l o g i c a l and a n a l o g i c a l processes o f thought, and t h a t processes of the l a t t e r type, though often neglected i n p s y c h o l o g i c a l r e s e a r c h , may be comparable i n importance to the former. By an a n a l o g i c a l or analog process I mean j u s t t h i s : a process i n which the i n t e r n a l s t a t e s have . a natural one-to-one correspondence to appropriate intermediate states i n the e x t e r n a l world. . Thus, t o imagine an o b j e c t such as a complex molecule r o t a t e d i n t o a d i f f e r e n t o r i e n t a t i o n i s to perform an analog process i n t h a t h a l f way through the process, the i n t e r n a l s t a t e corresponds t o the external object i n an o r i e n t a t i o n h a l f way between the initial and f i n a l orientations. And this correspondence has the very r e a l meaning t h a t , a t t h i s half-way p o i n t * the. person c a r r y i n g out the process w i l l be e s p e c i a l l y f a s t i n d i s c r i m i n a t i v e l y responding t o the e x t e r n a l presentation of the corresponding external structure i n e x a c t l y that s p a t i a l o r i e n t a t i o n . The i n t e r m e d i a t e s t a t e s of a logical computation do not i n g e n e r a l have t h i s property. Thus, a d i g i t a l computer may c a l c u l a t e the c o o r d i n a t e s of a r o t a t e d s t r u c t u r e by performing a matrix multiplication. But the intermediate states of t h i s row-into-column c a l c u l a t i o n w i l l at no point correspond t o - o r p l a c e t h e . machine i n readiness f o r - an intermediate o r i e n t a t i o n o f the external object. !!•Background  Issues  77 To  summarize: thanks to the s e a r c h i n g r e a c t i o n time experiments  of Shepard and process now  h i s c o l l e a g u e s , the n o t i o n of a n a l o g i c a l  has  a f i r m p i e c e o f evidence  I have already imagery  in  could  34)  as v i s u a l  justifiably  and  i n t e r p r e t H i l b e r t ' s "concrete  can  be  used  construct.  [ Pylyshynj 1 9 7 3 , 1976?}  The  and  review, i s provided  Behavioural  In  The  others. He  to  a scientifically  main  protagonists  of  been  latest  design  of  a t t e n t i o n and  neurology.  "tridimensional  respectable have  been  Pomerantz, 1977 ij.  This  word i n t h i s debate, and  a  a  robot  controller  Hebb  one  is,  a b e h a v i o u r a l theory* . Thus i t i s worth  extended  I t i s intended  of  and  area.  developed a c e l l - a s s e m b l y theory  approaches h i s theory  facts  notion  the  [Anderson,1978J.  developing  [Hebb,1949]  whether  as  t a k i n g a b r i e f look at work i n t h i s  which has  (p.  theories  attempting  essentially,  by  over  [Kosslyn  cannot be d i s c u s s e d here..  II.4.9  objects"  imagery.  imagery  explanatory  mental  mathematical d i s c o v e r y ; i n a d d i t i o n  There i s c u r r e n t l y a debate mental  on.  mentioned the apparent importance of  scientific  one  to rest  thought  by  [Good, 1965 ],  of  [ B i n d r a , 1976 ],  t o be a p h y s i o l o g i c a l theory from two  and  of thought.  d i r e c t i o n s : the: p s y c h o l o g i c a l  o r i e n t a t i o n , and describes  lattice-like  behaviour,  a  assembly  the then  current  cell-assembly of  cells,  supposed to be the b a s i s of p e r c e p t u a l i n t e g r a t i o n . "  facts as  a  that I have Again,  HaBackground  he  Issues  78  writes,  assemblies  structures that only  by  may e n t e r any be  "diffuse,  function briefly  virtue  constituent  are  of  cells...  the  time  theory  and  underlies  the  relation  a  to  (subjective stimulus theory  a  new  stimulus  entity."  fault  as  described  Though  of  the  unit  times...,  At to  cell-assembly A pexgo  distinctive  neural  well  r e s p o n s e made i n  as  the  the  awareness  o r image) o f t h a t cell-assembly/pexgo  p r e c i s e stage  directly  s t r u c t u r e , which  SHRDLU d i r e c t l y  of d e v e l o p m e n t t o  wonderful  i s perhaps t h i s : i t  i n terms o f (the p o o r l y  might be l i k e n e d t o t r y i n g t o  such  a s an  operating  i n t e r m s o f machine c o d e ,  m e n t i o n o f PLANNER, PROGRAMMER,  LISP, stacks,  descriptive  In other  words, t h e d i f f e r e n c e i n  the  between n e u r o n and t h o u g h t , i s t o o g r e a t reductionist  theory.  system  by-passing  o f computer  descriptive  Artificial  or  a s s e m b l e r s and  vocabulary  science*  one s i n g l e  of  pexgp.  t h e Hebb-Bindra theory  a b i g c o m p u t e r program  by  firing  benefit.  explain  gap  so  considered  the  as p e r c e p t  suggestive,  neuronal  other  may be  identifying  entity,  known)  the  do  transmission  diversifies  the  t o e x p l a i n human t h o u g h t  Winograd's  and  the  at d i f f e r e n t  concept,  i s a t an i n s u f f i c i e n t l y  The  all  or  excited,  underlies  experience  o f any d i r e c t  tries  and  "currently  that  in  irregular  b a s i s " [ p. 196-7iJ. .  introduces  organization  all  cell  one moment, t h e a c t i o n o f an a s s e m b l y on an a l l - o r - n o n e  systems,  relations  one a s s e m b l y ,  [ Bindra,1976J extends  be  as c l o s e d  An i n d i v i d u a l  i n t o more t h a n  anatomically  level,  t o be b r i d g e d Intelligence,  IIsBackground  Issues  79 using to  the  build  language  of computer  the r e q u i s i t e  [Miller, i d e a s on  of  "TOTE"  executing  plans.  The  (fixed  describe  action  animal  most  units  specific  (test;  TOTE c o n c e p t p_attern) ,  behaviour  sketched  suggestion  operate,  i s related  which  and  ideal  position  theories.  P r i b r a m , 1960 ] a l s o  their  importance  FAP  intermediate  G a l a n t e r and  behaviour;  s c i e n c e , i s i n an  t o the  i s used  to  trace  test,  by  the  out  some  was  the  exit)  in  notion of  a  ethologists  to  evolution  of  behaviour. In p o n d e r i n g carrying  out  concluded,  best  c o m p u t e r s have had  that  theory  the  of the  direction  of M i l l e r ' s  reason  physical  I will  start  positive  can  world.  second  direction.  look s u p e r f i c i a l l y content  from  "don't"s..  success  in  our  First  viewpoint*  My  there  a theory  is  no  second,  that  to handle  the  work i s a s m a l l s t e p i n  +  the  +  from  negative  similar  Here t h e y  because  conclusion.  I conclude  with the  is  i s to develop  +  what  little  o f c o g n i t i v e o r g a n i z a t i o n , and  hope f o r p r o g r e s s  structure  So  so  human i n f o r m a t i o n p r o c e s s i n g t a s k s , [ M i l l e r , 1 9 7 4 ]  first,  satisfactory the  why  of  our  survey  conclusions all,  t o our The  though  project,  of the  literature?  and  proceed  in  many o f  these  studies  few  l e s s o n s t o be  have any learnt  a  positive  are  mainly  HaBackground  Issues  are.  80  • Hebb - Bindra  -  • Jacobs & K i e f e r  don't t r y t o do too much with one theory -  don't  try to  apply  decision  theory  d i r e c t l y to behaviour a C o l e s , Feldman & S p r o u l l decision  theory  I n t e l l i g e n c e don't • Ludlow, Friedman  -  irrelevant  and really  Artificial  mesh together  because they model  behaviour  without a world model a Becker  & Merriam  -  they  get  bogged  down  d e t a i l s ; no f u n c t i o n a l  i n simulation robot-controller  designed or implemented, a "Baconian"  Becker  * Simon* Toda  -  -  don't  use  the  Baconian  representing  experience.  interesting  high  rational  level  behaviour,  but  approach  to  analyses  of  irrelevant at  our l e v e l o f s y n t h e s i s * m Imagery  -  this of  i s an acceptable n o t i o n ; any model  i t i s of i n t e r e s t . .  arises  as  designed Of Baker's  the  three  studies  i s promising  simulation  but  side  tool.  model  effect  of a system  on the s i m u l a t i o n o f r i g i d not  of i t  f o r s p a t i a l reasoning.  carried  f a r enough,  i s not s a t i s f a c t o r y a f t e r the f i r s t  Howden's i s c o m p u t a t i o n a l l y experimental  a  My  rather  expensive  motion. Funt's  few moves, while f o r use  as  an  When i t comes t o s p a t i a l planning, Eastman  and P f e f f e r k o r n get bogged  down  in  heuristic  search  HaBackground  because Issues  81  their  underlying  representation  Howden's approach r e s u l t s i n a positively, precursor  Nilsson  of my  common-sense Lieblich,  own  &  Kuipers  space  combinatorial  work.  of  large-scale  model a r a t ' s c o g n i t i v e showed how  space,  The  model and  a r e s u l t of i n n a t e d r i v e s and  of a graph i s a promising of PPA  and  in  the  More  models Arbib  &  about  course  of  Arbib & L i e b l i c h  showed how  l e s s o n to be l e a r n t here i s t h a t a world  design  and  map.  to form a g r a p h - l i k e c o g n i t i v e map..  as  who  fragmentary p i e c e s of i n f o r m a t i o n  used a graph f o r t h e i r world modified  explosion.  T h i s leaves only K u i p e r s ,  one's s p a t i a l environment can be i n t e g r a t e d experience  i s inadeguate,  Raphael's i s i n t e r e s t i n g , but only as a  knowledge  who  of  it  could  be  of e x t e r n a l rewards. model i n  the  form  idea* * T h i s i s not i n c o r p o r a t e d i n the  but o b v i o u s l y  should  be  taken  up  as  soon  as  possible*  I will first  now  summarize t h i s chapter  delineated  Intelligence; interaction  the nature  then  I  of t h i s modern s c i e n c e .  described  next  the  between, r e p r e s e n t a t i o n and  i n t e l l i g e n c e ; then I presented The  on background i s s u e s . ,  section  my own  sketched  I n t e l l i g e n c e approach t o planning  importance search i n any  approach to  the  the  traditional  and  problem-solving,  I  Artificial of,  and  theory  of  subject. Artificial and  II«Background  found Issues  82  it  to  be  reviewed be  a  wanting f o r my  purposes;  while i n the l a s t s e c t i o n I  the l i t e r a t u r e on s i m i l a r p r o j e c t s but found  notable  A l l told, background  to  l a c k of p o s i t i v e content, only c a u t i o n a r y t a l e s .  the reader should now to  there  my  work;  let  have me  a now  good  feeling  advance  to  for  the  the  first  IlaBackground  Issues  embattlement.  83 CHAPTER I I I THE SIMULATED ORGANISM-ENVIRONMENT SYSTEM  T h i s system i s the b a s i c experimental It  provides  simulated  sensory input f o r , and accepts organism  that  I  call  input-output  characteristics  relevant  to  the  only read  t h e . r e s t of  this  111*2.2,  and  the  III.2.3,  The aim o f t h i s chapter  this  peruse  examples  planar  that  object  an  in  section  shapes.  competent  (a)  section  III.1.3 the  and  simulated  organism  controlling  be expected t o s o l v e . . I t simulates  the  physical  which have the form of  The t a b l e t o p i s bounded by a verge  can never f a l l o f f .  The p h y s i c s  and  sections  An o b j e c t moves only  Utak i s both h o l d i n g t h i s o b j e c t and executing command*  directly  For t h i s purpose you need  smooth t a b l e t o p o f o b j e c t s  polygonal  the f u n c t i o n a l are  i s to d e s c r i b e  system i s c a l l e d TABLETOP. a  Only  a  system and to d e s c r i b e the t a s k s t h a t such  program, might reasonably  on  research.  motor output from,  system  introductory  an organism, i f endowed with a  motion  of  r e s t o f my t h e s i s .  organism-environment  The  Utak.  t o o l f o r my  involved i s e s s e n t i a l l y  a pushto or  so when turn  trivial:  The shape of an o b j e c t i s i n v a r i a n t under t r a n s l a t i o n  and  rotation. (b)  I f a motor command  t o go a c e r t a i n d i s t a n c e : i n  d i r e c t i o n would r e s u l t i n Utak c o l l i d i n g the  with  a  an o b j e c t or  verge, then he h a l t s a s h o r t d i s t a n c e before IIIaThe simulated  certain  the f i r s t  organism-environment system  84 i n t e r s e c t i o n of h i s path with such an o b s t a c l e * (c)  S i m i l a r l y , i f Utak i s g r a s p i n g a  push  command  colliding  with  come  an  to  that  an o b j e c t and  would r e s u l t  some o b s t a c l e , then immediate  halt  When  Utak  is  temporarily, (e)  Utak  can  grasping  considered  minimum  as one  new  the  occurred.  the o b j e c t  are,  object..  neighbouring  o b j e c t s only i f the  between them i s greater  than  a  certain  experimental  the;  permanence  and  of the shape.of p h y s i c a l o b j e c t s .  In b u i l d i n g the TABLETOP tool  that  system  was  I  aimed  inexpensive  to  concerned to f i n d exact s o l u t i o n s to c o l l i s i o n approximate  solutions  to  collision  III.3.1  I  sketch  one  way  to  produce  an  I was  not  use.  problems.  problems  TABLETOP system computes are q u i t e s u f f i c i e n t section  object  value.  impermeability  In  the  would have  To put i t i n a n u t s h e l l , TABLETOP s i m u l a t e s  the  object or Utak  and  an o b j e c t he and  go between two  width of the gap  Utak  executing  a s m a l l d i s t a n c e before  p o i n t at which the t h i s c o l l i s i o n (d)  i n the  is  for  my  Thus,  that  the  purposes.  that TABLETOP c o u l d  be  extended to compute exact s o l u t i o n s * Previous shapes  simulations  (reviewed  incorrect, TABLETOP  or system  of  the  p h y s i c s of p l a n a r  i n 11*4.7 above) have e i t h e r computationally is  complete,  expensive correct'  l i m i t a t i o n s which I s p e c i f y l a t e r , and mean that both motion and  to to  been  whereas  within  c o l l i s i o n s are handled* _  III«The simulated  incomplete,  use,  efficient.  polygonal  my  certain  By complete I TABLETOP  is  organism-environment system  85  cheap  to use,  has  been used e x t e n s i v e l y , and has  v i a b l e experimental The  design  tool*  of  TABLETOP  is  based  on  the  r e p r e s e n t a t i o n s f o r o b j e c t s , the C a r t e s i a n and Cartesian  on the  two  r e p r e s e n t a t i o n of an o b j e c t s p e c i f i e s the shape of  the  of p o i n t s where each p o i n t i s s p e c i f i e d by  r e a l numbers. boundary  of of  himself  position,  consisting  a d d i t i o n , Utak has to  the  p o i n t s are t h e . p o i n t s  shape.,  An  edge  in  has  of  a  a  Cartesian  two  of  inflection  the  Cartesian  an o b j e c t i s a p a i r of consecutive  Utak  referring  The  the  the l i s t .  points in  representation*  or  s i n g l e p a i r of p o s i t i v e r e a l s . ,  an absolute  orientation*  Note that I am  In  here  s i m u l a t i o n of Utak, not the r o b o t - c o n t r o l l e r  Utak. The  TABLE  is  a  two  dimensional  corresponds t o a square i n a two  an a s s o c i a t e d c o l o u r , one objects colour  may  the  grid  tabletop.  letters  have the same c o l o u r , and  of  entry  squares  Each o b j e c t  A,B,  ...  Z.  the verge always has  has Two the  'B'.  Now colour  of  array where each  dimensional  c o v e r i n g the s u r f a c e of the:simulated  imagine t h e . C a r t e s i a n c  superimposed  representation  on  the  representation TABLE  of the o b j e c t i s defined  of an o b j e c t  grid.. to be the  of TABLE t h a t l i e w i t h i n , or are i n t e r s e c t e d by the  of  The  representation  for  use  the d i g i t a l . .  o b j e c t by a l i s t positive  proved to be a  Cartesian representation  of the o b j e c t .  d i g i t a l r e p r e s e n t a t i o n of an o b j e c t are IIIaThe simulated  The  with  digital  set of squares the  edges  of,  A l l sguares i n the  assigned  the  object's  organism-environment system  86  colour  c.  The  digital  representation  of  an o b j e c t i s a l s o  c a l l e d the p r o j e c t i o n of the o b j e c t onto the TABLE. digital  r e p r e s e n t a t i o n , or p r o j e c t i o n ; c o n s i s t i n g of the  of TABLE t h a t c o n t a i n s h i s p o s i t i o n . this  square  TABLE.  is  His  the  of  position  all  p r o j e c t i o n , a l s o , i s outside  of  all  lies  outside  a l l the d i g i t a l  currently  be d i s p l a y e d on a screen Utak  described This  the  does  not  "see"  i n subsection  the  Cartesian Normally  representations the  or  has  onto  the  TABLE array  can  chapter  is  this  to  organized  of  as  follows.  system.  and  shown t h a t an  Section I I I . 2  III.1  Section  This  includes  discusses  and  includes  In  the  final  the  examples  section  design of  adapted  part  of  the  TABLETOP  f o r p a r a l l e l computation, and  method g e n e r a l i z e s to three  an  It is  simulation  is  that the TABLETOP  (or more) dimensions.  III«The simulated  his  (III.3)  g e n e r a l i z a t i o n s of TABLETOP are c o n s i d e r e d . . important  the  t h e . s p e c i f i c a t i o n of  Dtak,  sensory-motor experience. extension  Remember  display; h i s v i s u a l input i s  used* the problems encountered, and  capabilities  watch.  III.2.2.  the r e q u i s i t e algorithms..  easily  d i s p l a y of  verge are p r o j e c t e d  f o r a human user  d e s c r i b e s the TABLETOP s i m u l a t i o n  and  to  CRT  grasping  array when TABLETOP i s i n o p e r a t i o n . . The  method  assigned  letgo.  Utak, a l l the o b j e c t s , and  that  a  square  o b j e c t s , but i t can happen that i t l i e s w i t h i n  p r o j e c t i o n of an o b j e c t t h a t he i s recently  colour  the o b j e c t s on the t a b l e t o p .  his  the  The  BUGMARK, an a s t e r i s k on the  Cartesian  representations  TABLE  Utak has  Also,  it  is  organism-environment system  87  shown  how  answers  to  This i s an independent system that simulates the e f f e c t  of  collision  III.1  to  extend  TABLETOP  to  obtain  exact  problems.  The simulated environment, TABLETOP -  motor  commands i s s u e d by Utak.  It i s instructive  s i t down with TABLETOP and attempt a task such an 'L* shaped o b j e c t through a narrow The L-shaped o b j e c t problem Otak.  Indeed,  in  Kuhnian  as  or  i f ,  is  the  archetypal  terminology,  progress  organism-controlling where  Otak  is  program  able  in  the  task  intelligence.  construction  of  to the  t o s o l v e t h i s problem autonomously will  for  t h i s i s the paradigm  f o r Otak has advanced  b e l i e v e t h a t n o n - t r i v i a l advances been  manipulating  doorway..  problem f o r t h i s approach to understanding s p a t i a l When,  f o r a user to  almost  the point then I  certainly  have  made towards understanding the nature of some computations  t h a t are o f fundamental importance f o r s u c c e s s f u l organisms., At that  point  i t w i l l be o f great i n t e r e s t  facts  about b i o l o g i c a l b r a i n s i n terms of  to i n t e r p r e t  the known  these„computations.  111*1^1 A.D. overview of the - s i m u l a t i o n - method A  slide  is  the  simplest  movement of Otak along a sequentially  checking  i n t e r s e c t e d by Otak's  line each  action segment,  square  position  as  of he  of It  Otak. is  T h i s i s the simulated  by  the TABLE g r i d t h a t i s moves  along  the  III«The simulated organism-environment  line system  88  segment.  If  a  non-empty  (coloured)  sguare  of  encountered before the end of the l i n e segment, then point  of  intersection  with  the  from  this  point.  first  This  by  backing  neighbouring lies  If  the  Cartesian  point  representations  of  of two  o b j e c t s are so c l o s e t h a t no empty sguare o f  between  off  i s done by t a k i n g a p o i n t a  s m a l l d i s t a n c e € back along the l i n e segment from the intersection.  the  o b s t r u c t i n g sguare i s found,  second the h a l t i n g p o s i t i o n of Utak i s obtained slightly  TABLE i s  TABLE  t h e i r d i g i t a l r e p r e s e n t a t i o n s then Utak i s unable  t o s l i d e between the two objects* When  Utak  i s not g r a s p i n g  an o b j e c t he can only execute a  s l i d e a c t i o n o r a grasp a c t i o n . is  not  already  representation  grasping  i s adjacent  representation.  Two  Utak can grasp an o b j e c t i f  some  object  t o a square i n the  squares  are  horizontally,  v e r t i c a l l y , or d i a q o n a l l y  are:  TABLE  eight  and  squares  adjacent  i f his object's  adjacent  to  digital digital  i f they  adjacent.  Thus  Utak's  he  are there  diqital  representation* When Utak i s qrasping t u r n , or l e t g o a c t i o n s . Utak's  Cartesian  representation pushto  In t h i s s t a t e the r e l a t i v e p o s i t i o n  representation  and  the o b j e c t ' s  remains i n v a r i a n t under t r a n s l a t i o n —  actions  However, whereas single  an o b j e c t he can only execute pushto,  —  and  Utak's  rotations digital  --  of  Cartesian caused  by  caused by turn a c t i o n s .  representation  i s always  a  sguare, an o b j e c t ' s d i g i t a l r e p r e s e n t a t i o n may appear t o  change r a t h e r d r a s t i c a l l y i f the s i z e of the TABLE squares i s o f IIIaThe simulated  orqanism-environment system  89  the  same  simplest  order  of  magnitude  as the s i z e of the object*  example of t h i s e f f e c t i s  Cartesian  given  by  an  object  The whose  r e p r e s e n t a t i o n i s a square of e x a c t l y the same s i z e  as  the TABLE squares.  I f t h i s object's Cartesian representation i s  exactly  with  aligned  representation moved  TABLE  square  then  its  i s j u s t t h a t TABLE square, but i f the  diagonally  representation  a  a  small  distance  then  diqital  object  its  is  digital  becomes a l a r g e r square c o n s i s t i n g of f o u r  TABLE  squares. Suppose t h a t the user of TABLETOP requests whose  intent  is  from  some  if  the achieved of  any,  d»  occurs,  distance.  actually  d i s the  9  is  measured  f o l l o w i n g method i s traversed  intended  before  The  d i s t a n c e to the nearest  determines the achieved  area  object  are erased.  representations  Then the achieved The  for  as  the  grasped  object  o b s t a c l e found, i f  distance.  computed, j u s t as f o r the s l i d e a c t i o n . is  computed  of  Dtak  and  the  normal has  edges  of  the  a direction  Cartesian in  the  achieved follows*  distance First  the  These  r e p r e s e n t a t i o n whose outward  range  III»The simulated  of  d i s t a n c e f o r Utak i s  l e a d i n g edges r e l a t i v e t o the d i r e c t i o n 9 are determined. are  a  d i s t a n c e , d' i s  B a s i c a l l y the method i s t o scan the  F i r s t the c u r r e n t d i g i t a l the  angle  line  TABLE t h a t would be swept out by the o b j e c t i n the course of  the t r a n s l a t i o n . any,  The  f i x e d d i r e c t i o n * , The  used to compute the d i s t a n c e collision,  action  t o move the grasped object i n a s t r a i g h t  through d i s t a n c e d i n d i r e c t i o n 8. clockwise  a pushto  (6-90°, e+ 9 0 ° ) . .  As  the  organism-environment system  90 object  is  moved,  each,  l e a d i n g edge sweeps out  shape of a parallelogram* . Each imagined for  such  are  parallelogram  as superimposed on the TABLE g r i d .  an L-shaped o b j e c t subjected shown  in figure:III*1.  any  or  intersect  to a p a r t i c u l a r  distance  non-empty  or e l s e to be the minimum over the square.  The  lie  PE generated by E.  For  TABLE  the  minimum  point of the subpart of Then  the o b j e c t *  distance  i s returned  distances  DE  Utak  and  distances  is  scan,  for  each  f o r each l e a d i n g edge  as the  F i n a l l y the o v e r a l l achieved  minimum o f the a c h i e v a b l e both  minimum  minimum of the DE's  E, l e s s a small q u a n t i t y 6,  Then  action  to be d, i f no non-empty squares are found i n the  scanned  be  that  the square l y i n g w i t h i n PE i s computed*  for  pushto  (coloured),  from the edge E to the nearest  defined  to  For each leading edge E a scanning  the p a r a l l e l o g r a m  scanned square t h a t i s  is  the  The:parallelograms  process i s s t a r t e d t h a t scans those squares of within  an area i n  achieved  distance  d i s t a n c e d' i s the  f o r the o b j e c t and  the o b j e c t are r e - p r o j e c t e d  f o r Otak.  onto the  TABLE  g r i d at the computed f i n a l p o s i t i o n * . By c o n s t r u c t i o n , these p r o j e c t i o n s never o v e r l a p Now whose  the p r o j e c t i o n of an  is  to  rotate  the  radians about Utak's p o s i t i o n U. for if  computing the angle any,  obstacle.  suppose that the TABLETOP user requests intent  occurs.  rotation.  Both  Two  would be swept out by the  a turn  scan  methods w i l l  £  be  described  a  collision,  r o t a t i o n , <J>' i s the  for  action,  grasped by Utak by  a c t u a l l y r o t a t e d before  (J> i s the intended methods  object  new  achieved  o b s t a c l e s i n the area  that  o b j e c t i n the course of r o t a t i o n *  The  IIIaThe simulated  organism-environment system  FIGURE T I I . 1  91  Direction of movement  6  The four parallelograms form an L-shaped object subject to a p a r t i c u l a r PUSHTO action. Also shown are the Cartesian and d i g i t a l representations of the L-shape. Left constrainin edge Destination edge  Original leading edge  Right constraining edge  b)  Features of a p a r a l l e l o gram generated by an edge during a PUSHTO action.  92 angle  to  the nearest  rotation.. second one the  The  may  i f any,  miss a small one.,  method  the  Since  motion  computation. object,  for  obstacles  method, s i n c e i t and  may  be  the  parallels  of independent  of Utak and  the grasped o b j e c t  Utak's p o s i t i o n does not change: i n not  directly  Then the l e a d i n g  relative  whereas  first.  projections  does  achieved  Although the second method i s the  translation  i s described  First erased;  used  determines the  method f i n d s a l l the  c u r r e n t l y implemented, the f i r s t  interest,  his  first  obstacle,  to  the  contribute  segments  a  rotation,  the  collision  the  edges  of  rotation  U,  must  be  r o t a t i o n of an o b j e c t about U,  the  centre  of  to  are  of  the  determined. Definition.  For  a clockwise  l e a d i n g segment of an edge E i s found as f o l l o w s . . line  L  collinear  with  point N t o the centre to  E.  Compute on the  of r o t a t i o n U and  E at the p o i n t N.  Now  l i n e L the  draw an  of  it  may  normal  take the s e m i - i n f i n i t e h a l f - l i n e of L  with E.  l e a d i n g segment of E.  the  nearest  outward  t h a t l i e s t o the l e f t of the outward normal at N, intersection  Consider  The  and  form  the  r e s u l t i n g segment of E i s the  Note that the l e a d i n g segment of an  c o n s i s t of a l l or p a r t of the edge, or be n u l l .  segments f o r a s p e c i f i c t r i a n g l e  and  points  of  The  edge  leading  rotation  are  shown i n f i g u r e I I I . 2 . Lemma.  For  a clockwise  rotation  of  an  l e a d i n g segment of an edge E of the o b j e c t any  point  x on the i n t e r i o r of the  object has  the  about  the  property:  l e a d i n g segment, there  IIIaThe simulated  U,  is  for a  organism-environment system  FIGURE I I I . 2  Outward normal  6 AN^, = l e a d i n g segment of edge AB. BNp = l e a d i n g segment of edge BC. CNg = l e a d i n g segment of edge CA. Thus f o r r o t a t i o n c l o c k w i s e about P t h e r e a r e 3 l e a d i n g segments. CLOCKWISE ROTATION  For c l o c k w i s e r o t a t i o n about Q t h e r e i s o n l y 1 l e a d i n g segment: BC.  T h i s f i g u r e shows t h e l e a d i n g segments o f t h e t r i a n g l e ABC f o r two p o i n t s o f r o t a t i o n . I f a c l o c k w i s e r o t a t i o n about P i s i n t e n d e d , then t h e l e a d i n g segments a r e AN , BN^, CN^. I f an a n t i - c l o c k w i s e r o t a t i o n about P i s i n t e n d e d , then t h e l e a d i n g segments a r e N^B, N^C, and N^A. I f a c l o c k w i s e r o t a t i o n about Q i s i n t e n d e d , t h e r e i s o n l y one l e a d i n g segment: BC. I f an a n t i - c l o c k w i s e r o t a t i o n about Q i s i n t e n d e d , t h e r e a r e two l e a d i n g segments: CA and AB.  94  rotation  about  U such t h a t i f x* i s the new  p o s i t i o n of x, the  arc xx' l i e s i n the e x t e r i o r of the o b j e c t . Proof. other  Pick a disc centre  x, small enough that i t i n t e r s e c t s no  edge of the o b j e c t , and so t h a t i t does not c o n t a i n  p o i n t of the l e a d i n g segment* the new  Consider a r o t a t i o n so small  p o s i t i o n x' of x l i e s w i t h i n  Because  x  lies  to  the  left  the  of  disc  exterior  of  the  shape.  centred  that  on  x.  the outward normal to E the  d i r e c t i o n of motion of x i s p e r p e n d i c u l a r the  an end  Thus,  to Ox and p o i n t s  into  t h e . a r c xx' l i e s i n the  e x t e r i o r of the object* . QED. In  other  words  out  a new  area of  Depending  on  Cartesian  shape  considerable  the l e a d i n g segment of an edge E always sweeps t h e . TABLE  the  angle of  overlap  in  of  the  the  course: of  rotation  object,  and  there:  a  rotation.  the. exact o v e r a l l  will  in  general  be  between the areas swept out by each l e a d i n g  segment., I have ignored  the  problem  of  eliminating  multiple  scanning o f areas o f TABLE i n a turn a c t i o n . As t h e o b j e c t r o t a t e s each l e a d i n g four-sided  area  of space,  The s i d e s d i s t a l  point of r o t a t i o n are c i r c u l a r straight lines. that i f A  #  B are  segment  and  A',  0.  a r c s , the  sweeps  the  original  other  end-positions  B' are the f i n a l  two  Each doughnut  upon the TABLE g r i d *  slice  of  end-positions  and A'B'O  differ  out  a  and proximal to the  Hence I c a l l t h i s shape a doughnut  segment, then t r i a n g l e s ABO about  segment  only  sides  are  slice.,  Note  the  leading  of the l e a d i n g by a  rotation  i s t o be imagined as superimposed  The doughnut  s l i c e s f o r the r o t a t i o n of an  III»The simulated  organism-environment system  9 5  L-shaped  o b j e c t subjected  i n figure III*3. that  lie  of  For each l e a d i n g segment S the  within  are scanned;  to a p a r t i c u l a r t u r n a c t i o n are shown  between the l e a d i n g  {This i s  not  a  trivial  For each l e a d i n g segment S, the minimum i s taken  over the angles computed f o r each o b s t r u c t i n g square, minimum  slice  square the.minimum angle  r o t a t i o n s u f f i c i e n t t o cause a c o l l i s i o n  segment S and the square i s computed,  the  squares  or i n t e r s e c t the corresponding doughnut  For any non-empty scanned  computation;}  TABLE  of  a l l these  minimums,  taken  and  then  over a l l l e a d i n g  segments, g i v e s the achieved r o t a t i o n <>'•  Finally,  and  onto the TABLE g r i d .  the  rotated  object  are r e - p r o j e c t e d  That* i n o u t l i n e , i s the s i m u l a t i o n The  basic  problems  faced  both  Utak  method used i n TABLETOP.,  in  an  implementation  of this  s i m u l a t i o n method are as f o l l o w s . . •Tracing  a line  -- the intended path i n a s l i d e a c t —  the s i d e s of a p a r a l l e l o g r a m  in a  pushto  action —  the  straight  and  curved  sides  of  a  of  an  doughnut s l i c e i n a t u r n a c t i o n  •Scanning  a shape  -- the  Cartesian  object, f o r  representation  projecting  object's d i g i t a l  or  erasing  the  representation  the p a r a l l e l o g r a m  swept out by a  leading  edge i n a pushto a c t i o n -- the doughnut s l i c e  swept out by a l e a d i n g  IIInThe s i m u l a t e d organism-environment  system  FIGURE III.3  6  Rotation about U.  An L-shaped object showing i t s Cartesian and d i g i t a l representations. For the centre of r o t a t i o n , U, there are 5 leading segments (CB, BA, AN, FE, EM) and 5 doughnut s l i c e s swept out during the action (BCC'B', ABB'A', NAA'N', EFF'E', MEE'M'). N i s the point on AF closest to U, M i s the point on ED closest to U.  leading segment outer constraining arc  6' destination segment Features of the doughnut s l i c e generated by rotating the leading segment AB about the centre of rotation U by angle 0 .  97  segment i n a t u r n a c t i o n  •Computing  minimum  distance  from a l e a d i n g edge t o (a subpart  of) an o b s t r u c t i n g sguare  •Computing minimum angle  from a l e a d i n g segment  to  (a  subpart  of) an o b s t r u c t i n g sguare.  III>1.2 The a l g o r i t h m s  used i n - the  simulation  In t h i s s u b s e c t i o n I d e s c r i b e the:algorithms the. problems two  specified  line-tracing  circular  arcs.  i n the previous  subsection.  a l g o r i t h m s , one f o r s t r a i g h t I first  qrid  containing  the  squares  process  correctly.  This  as  has  tracing  seemingly innocuous reguirement i s a  alignment  c o i n c i d e n c e of the l i n e with tracing  o f the  the  t r i c k y t o program because of the s p e c i a l cases such  line.  i n i t i a l and t e r m i n a l p o i n t s of the  l i n e i n order t o i n i t i a l i z e and terminate  occur  There a r e  d e s c r i b e how t o t r a c e a s t r a i g h t  straight  little  solve  l i n e s and one f o r  As a p r e r e q u i s i t e f o r t h i s one has t o know the TABLE  used to  of  the  the  grid  t o handle four cases, I  can and  with  the  axes  lines..  The  code f o r  one f o r each guadrant of the  direction  o f the  line;  guadrant  case.  L e t the c u r r e n t sguare-be the square c u r r e n t l y  under c o n s i d e r a t i o n i n the c u r r e n t sguare can e i t h e r and  right  from the c u r r e n t  will  line  that  only  describe  line-tracing  the  procedure.  northeast  The  next  be one up, one r i g h t ; or d i a g o n a l l y up square.  IIInThe simulated  This  choice  i s made  by  organism-environment system  98 computing  whether the northeast corner of the c u r r e n t square i s k comparison of  l e f t o f , r i g h t o f , or on the l i n e . of  SP and SD,  suffices A  the  i n v o l v i n g two m u l t i p l i c a t i o n s and one  slopes  comparison,  ( f i g u r e I I I . 4). circular  arc i s t r a c e d i n a s i m i l a r manner.  I f the a r c  t r a v e r s e s more than one quadrant i t i s broken i n t o subarcs traversing subarc  a l l or  traverses  procedure  is  part of a s i n g l e quadrant; the  northwest  next  When the a r c or  almost  the  current  (figure III.4).  square  is  As f o r the l i n e case,  e i t h e r one up, one r i g h t , or one  d i a g o n a l l y up and r i g h t from the c u r r e n t square, and t h i s is  same  used as f o r the case:of a l i n e whose d i r e c t i o n i s  in the northeast quadrant the  quadrant  each  made by computing  choice  whether the northeast c o r n e r of the c u r r e n t  square i s i n s i d e , o u t s i d e , or on the  arc.  This  requires  two  m u l t i p l i c a t i o n s , an a d d i t i o n , and a comparison; There are s e v e r a l o p e r a t i o n s which may squares  t h a t a l i n e passes through.  be added to a scan t a b l e f o r square  is  non-empty  and  a  i n t e r s e c t i o n computation may  applied  to  The square c o o r d i n a t e s  scanninq  hence  be  routine  or,  if  the may the  r e p r e s e n t s an o b s t r u c t i o n , an  be -executed  and  the  line-tracinq  procedure.abandoned. For the purpose of p r o j e c t i n g the C a r t e s i a n  representation  of a concave o b j e c t i n t o i t s d i g i t a l r e p r e s e n t a t i o n on the TABLE (briefly,  drawing  the  Cartesian  representation  object), is  and  erasing  decomposed  i t  later,  the  i n t o convex subparts.  T h i s i s done manually when the o b j e c t i s f i r s t  specified.  When  III«The simulated organism-environment  system  FIGURE  III.4  T r a c i n g an a r c i n the north-west quadrant.  100  the  object  erased  is  drawn or erased  each convex subpart i s drawn or  separately.  The  digital  representation  object i s constructed Cartesian  row  representation  by  of  a  row..  convex  First  are t r a c e d , and  (subpart  the  edges  of in  the c o o r d i n a t e s  the c o o r d i n a t e s o f each row.  of the squares at the l e f t  Since  cover only the  the s i z e of the  v e r t i c a l extent  p a i r of  ( l e f t and  row  I f the o b j e c t  I f the o b j e c t for  turn action.  of TABLE t h a t corresponds  digital  The  representation  scan t a b l e s and  when, or i f , the A new  scan t a b l e i s s u f f i c i e n t  to  to scan  row  by  i s f i x e d the scan t a b l e s are then, d i s c a r d e d .  i s movable, the  l a t e r use  records  extremities  r i g h t ) scan t a b l e e n t r i e s .  t a b l e i s then used to draw the row.  right  the  of the convex shape, an o f f s e t i s  a l s o s t o r e d t h a t s p e c i f i e s the the f i r s t  and  the  of  squares encountered are used t o update a scan t a b l e t h a t  an)  o f f s e t s are  o b j e c t i s erased  scan t a b l e has  to be  stored  f o r a pushto or  constructed  for  each  convex subpart every time the o b j e c t i s redrawn. The action  parallelogram is  III.1).  scanned  The  sequence:  swept out by  in  almost  a l e a d i n g edge i n  identical  fashion  edges of such a p a r a l l e l o g r a m  leading  edge  AB,  left  are  d e s t i n a t i o n edge: A' B'.,  square can  the edge AB.  encountered* distance nearest  in  while  tracing  the  the  direction  e  p a r t of the  obstructing  (see f i g u r e  traced  in  No  the right  obstructing  I f an o b s t r u c t i n g square i s  edge  AA',  from the square  IIInThe simulated  pushto  c o n s t r a i n i n g edge AA',  c o n s t r a i n i n g edge BB', occur along  a  then  the  minimum  l e a d i n g edge AB to that  lies  within  the the  organism-environment system  101 parallelogram  i s computed.  T h i s i s taken as the new  the amount of the t r a n s l a t i o n . , encountered while t r a c i n g BB'.,  Similarly  if  an  value  of  obstacle  d, is  I f e i t h e r or both of these cases  occur then the  p o s i t i o n of the d e s t i n a t i o n edge  is  effectively  moved  to the  the  destination  closer  o r i g i n a l p o s i t i o n AB.  edge, at i t s p o s s i b l y new  p o s i t i o n , i s traced and  f o r the p a r a l l e l o g r a m  i s complete.. The  parallelogram  scanned and  found  the  distance  to the nearest The  one  obstructing  is  of the o b s t a c l e i s computed. a l e a d i n g segment i n a turn  concave bounding l i n e —  figure  the  the  arc does not c r o s s  p o i n t of r o t a t i o n .  doughnut s l i c e  inner  constraining  III.3)  i s cut along t h i s and  segment  AN,  the  vertical  vertical  in  each part formed i s scanned s e p a r a t e l y . .  The  the  inner c o n s t r a i n i n g arc NN',  (line  the  UU'  d e s t i n a t i o n segment A'N'.  line  no  line  I f t h i s c o n d i t i o n holds then  edges of a doughnut s l i c e are t r a c e d i n  sequence:  leading  outer c o n s t r a i n i n g  No o b s t r u c t i n g  square can  arc  occur  AN. . I f an o b s t r u c t i n g square i s encountered while t r a c i n g  the arc NN* nearest  then the  p a r t of the  i s computed. rotation., AA'.  square  However, s i n c e : a shape i s scanned row-by-row t h i s i s of  through the  along  the  from the l e a d i n g edge AB i n the d i r e c t i o n 9  corner  consequence provided  AA',  the scan t a b l e  TABLE sguares within  i f an  doughnut s l i c e swept out by  a c t i o n has arc.  are now  Now  minimum angle of r o t a t i o n about obstructing  square within the  T h i s i s taken as the new  S i m i l a r l y i f an o b s t a c l e  value of  to  doughnut the  the slice  intended  i s encountered while t r a c i n g  I f e i t h e r or both of these cases occur then III»The simulated  0*  the  position  organism-environment system  102  o f the d e s t i n a t i o n segment i s e f f e c t i v e l y r o t a t e d the o r i g i n a l p o s i t i o n AN. possibly  new  position  doughnut s l i c e doughnut out  Now the d e s t i n a t i o n i s traced  i s complete.  slice  are  and  The  back c l o s e r t o  segment  at i t s  the scan t a b l e f o r the  TABLE  squares  within  the  scanned and c o l l i s i o n computations c a r r i e d  i f any o b s t r u c t i n g squares are found. F i n a l l y I must s p e c i f y the c o l l i s i o n computations.. F i r s t I  d e s c r i b e them f o r a pushto a c t i o n , then f o r a t u r n The  simplest  swept out by  a  case i s t h i s :  leading  edge  encountered.  The  amount  c o l l i d e s with  the  nearest  calculated  (figure  f o r t h i s edge. corners  of  The nearest  o f the square.  when scanning the p a r a l l e l o g r a m AB,  an  obstructing  square  movement of the o b j e c t before  point  III.5).  action.  P  of  the  square  i t * . For  p o i n t of a  T h i s nearest  instance, corner  southeast  Let  the outward normal to direction  of  motion,  be  square  corner  is  one  of the  depends only  on the  i s used to  f o r a l e a d i n g edge.in the northeast  guadrant the nearest corner.  AB  This i s the d i s t a n c e to c o l l i s i o n  quadrant of the l e a d i n g edge so a simple t a b l e . l o o k u p find  must  is  of  an  obstructing  sguare  i s the  n be a u n i t v e c t o r i n the d i r e c t i o n o f  AB, and  let d let p  d i s t a n c e t o c o l l i s i o n i s given  (E-n)  be  a  unit  vector  be the vector  AP.  i n the Then the  by the formula  / (i-n)  If an o b s t r u c t i n g sguare i s encountered III»The simulated  <M  while  tracing  a  organism-environment system  103 FIGURE I I I . 5 - A formula f o r the d i s t a n c e from a l e a d i n g edge to the n e a r e s t p o i n t of an o b s t r u c t i n g square.  AB i s a l e a d i n g edge PB = p e r p e n d i c u l a r d i s t a n c e |r = cos*  d  f  l  I L. i- > 0 from AB to P = p_.n  l  C  <  = (£.n) / (d.n)  n = coj  > O  104 constraining  edge  of a p a r a l l e l o g r a m ,  f i n d the d i s t a n c e to obstructing  collision.  square may  The  the  cases a r i s e  (1)  left (figure  c o n s t r a i n i n g edge of the p a r a l l e l o g r a m ,  four  between  and  the  left  of  collision  of  the  leading  the  obstructing  right is  square  constraining  the  same  as  edges.  before,  corner  lies  The  corner  c o n s t r a i n i n g edge* from  lies  The  s i d e of the  The  nearest  the  to  the  distance  to  left  of  collision  the  left  is  the  c o n s t r a i n i n g edge: i n t e r s e c t s  the the  square.  corner  c o n s t r a i n i n g edge. distance  to  A along the l e f t c o n s t r a i n i n g edge to  p o i n t P where the l e f t  (4)  using  corner.  nearest  distance  The  on the l e f t c o n s t r a i n i n g edge.  The d i s t a n c e t o c o l l i s i o n i s the d i s t a n c e from A  (3)  lies  (A) .  nearest  nearest  the  When  P  The  of  III.6).  distance to  (2)  corner  edge. ,  The nearest corner  equation  nearest  to  l i e o u t s i d e the p a r a l l e l o g r a m or even on  the o p p o s i t e s i d e of an extension tracing  more c a r e : i s r e q u i r e d  lies The  to  the  distance  right to  of  collision  the is  right the  from B along the r i g h t c o n s t r a i n i n g edge to the  p o i n t Q where the r i g h t c o n s t r a i n i n g edge i n t e r s e c t s III»The simulated  the  organism-environment system  105  FIGURE I I I . 6  ,3'  Cases i n computing d i s t a n c e t o c o l l i s i o n a l o n g a c o n s t r a i n i n g edge. AB = l e a d i n g edge. NC = n e a r e s t c o r n e r of o b s t r u c t i n g square. P = n e a r e s t p o i n t of o b s t r u c t i n g square.  106 side  of  the  square.  There  are  really  i n v o l v e d here depending on whether P and  l i e on  the  edges of the square.. However, i t i s not  necessary to go  to  BQ  the  since  trouble  of  figuring  s u f f i c e s t o return the distance Notice (4)  out the  t h i s w i l l be computed under case (3)  when the r i g h t c o n s t r a i n i n g edge i s being  traced.  So i t  AP.  t h a t , when t r a c i n g the r i g h t c o n s t r a i n i n g edge [with  right  ( f i g u r e 111.6(5)). been  Q  same or adjacent  distance  case  two subcases  returned  and  left  transposed]  T h i s i s because the d i s t a n c e  from  an occurrence of case  BB',  could not occur AP  would  have  (3) when t r a c i n g the  l e f t c o n s t r a i n i n g edge, and so the r i g h t c o n s t r a i n i n g edge would only be t r a c e d  as f a r as B''.  There are four cases when edge*  tracing  the  left  constraining  t h r e e cases when t r a c i n g the r i g h t c o n s t r a i n i n g edge, and  these are a l l repeated f o r each of the other three which  the  l e a d i n g edge may l i e .  by one 2 x 4 x 4  decision  table  quadrants  in  These 28 cases can be handled with  one  row  of  four  null  for a  turn  entries. Now I action.  describe  the  collision  computations  Suppose t h a t an o b s t r u c t i n g square i s encountered when  scanning the doughnut s l i c e swept out by a l e a d i n g segment.. The amount  of  r o t a t i o n of the object  before  of an edge AB c o l l i d e s with some point of calculated  (figure  III.7).  t h i s edge.  The p o i n t of  the  the l e a d i n g segment AN the  square  T h i s i s the angle-to square  IIIaThe simulated  at  which  must  be  collision for the  collision  organism-environment system  107  FIGURE I I I . 7  AB  = object's  edge.  AN = l e a d i n g segment. U  = centre  of r o t a t i o n .  P  = obstructing  point.  P' = p o i n t which c o i n c i d e s w i t h P a t the n e a r e s t moment of collision.  (-o)  = UP = UP' .  of  = angle t o c o l l i s i o n .  _ n — = - u n i t outward normal to AB.  u cos  r  x  = d i s t a n c e UN.  -- - C P. •«.)/£  cos V s * / r  « j - cos"'  FIGURE I I I . 7 .  -  cs'  [*/r}  The diagram shows the p o i n t P', on the edge AB, which c o i n c i d e s w i t h the p o i n t P a t the moment of c o l l i s i o n . The formula shows how to compute PUP', the angle t o c o l l i s i o n .  108  occurs  is  the c o l l i s i o n p o i n t .  I a l s o c a l l t h i s the  corner s i n c e i t i s c l e a r that the corner  of  the  obstructing  t r i v i a l t o determine  collision  square.  point  collision  must  Unfortunately  which" corner of the square; i s the  be  a  i t i s not collision  c o r n e r . . For i n s t a n c e , as the o b s t r u c t i n g square v a r i e s over  the  squares w i t h i n a doughnut s l i c e the c o l l i s i o n c o r n e r v a r i e s too. I f the r o t a t i o n i s c l o c k w i s e and the o b s t r u c t i n g square i s moved c l o c k w i s e then the c o l l i s i o n c o r n e r of moves  in  a  clockwise  o b s t r u c t i n q square.. collision  collision  c o n t a i n s e i t h e r two centre  d i r e c t i o n r e l a t i v e to the centre of the  the  collision  obstructing  corners  for  a  or three c o r n e r s .  sguare*.  specific  corners  instance,  if  and  the if  axes  there  0  lies  in  corners,  and i f 0 l i e s on the south v e r t i c a l  collision  corners III.9  determined  are  shows  the  southwest  occurrences  to  collision  with  of  and  of  each  an  at  grid  candidate  between the axes  ( f i g u r e 111*8).  northwest,  c o r n e r s , f o r 0 i n the southwest anqle  two  the southwest guadrant  c o r n e r s are the southwest,  The  set  l e a d i n g segment  are  U i s i n a quadrant  collision  collision  The  Suppose axes are taken  there are t h r e e candidate c o l l i s i o n c o r n e r s  ,  s e t s of candidate  of the o b s t r u c t i n g square and a l i q n e d with the  I f 0 i s on one of  Figure  square  c o r n e r s as a f u n c t i o n of the p o s i t i o n of the c e n t r e of  candidate  lines.  obstructinq  I t i s possible to specify  r o t a t i o n 0 r e l a t i v e to  the  the  the and  For  candidate northeast  a x i s the  candidate  northwest  corners.  of  the  candidate  guadrant. obstructing  by f i n d i n g the angle to c o l l i s i o n with  each  sguare i s of  the  III«The simulated organism-environment system  109  FIGURE I I I . 8  MW.Nt.SE.  —p w  S6.  This shows, for a clockwise rotation, how the set of candidate c o l l i s i o n corners of an obstructing square varies as a function of the p o s i t i o n of the centre of rotation r e l a t i v e to the axes of the square. This i s the set of c o l l i s i o n corners that must be considered i f the obstructing square i s encountered during the scan of the doughnut s l i c e . Along the arcs are shown the edges or corner that may be involved i f the obstructing square i s encountered when tracing a constraining arc.  FIGURE III.9  For a clockwise rotation about the point U i n the southwest quadrant r e l a t i v e to the axes of an obstructing square, this shows how each of the candidate c o l l i s i o n corners could actually occur. Leading segment AB c o l l i d e s with the southwest corner, CD c o l l i d e s with the northwest corner, and EF c o l l i d e s with the northeast corner. A'B', C'D', and E'F' are the positions of AB, CD, and EF, respectively, at the moment of c o l l i s i o n .  111  collision (or  corners  two) angles.  i s the corner  s e p a r a t e l y and t a k i n g the minimum of the three The c o l l i s i o n  corner  an  edge  a p o i n t U, the angle to c o l l i s i o n  as f o l l o w s .  L e t n be the u n i t vector  AB  being  i n the  direction  collision  on  of the from 0"  distance  to AB, l e t r be the r a d i u s UP, l e t £ be the v e c t o r point  rotated  with a p o i n t P i s found  outward normal to AB, l e t x be the p e r p e n d i c u l a r  the  square  with the s m a l l e s t a n q l e - t o - c o l l i s i o n .  Given a l e a d i n q segment AN of about  of the o b s t r u c t i n g  UP, l e t P' be  AN which c o i n c i d e s with P at t h e moment when the  occurs,  (figure I I I . 8 ) .  and  l e t alpha  be  to  collision  alpha = arcos[ - (p. n ) / r ] - a r c o s [ x / r ]  (B)  Then the f o l l o w i n g alpha = /PUN  -  the  angle  holds. /P«UN  cos (/PUN) = (p_/r) . (-n) = - ( p . n ) / r cos(/P«UN) = x/r  I f an o b s t r u c t i n g square i s encountered while inner  or  slightly corner  oufter  simpler.  Instead  of r o t a t i n g the  the  computation i s  candidate  collision  backwards to whe^re i t s a r c i n t e r s e c t s t h e l e a d i n g segment  as i n the:usual leading the  c o n s t r a i n i n g a r c , the c o l l i s i o n  tracinq  segment  case, here one has to r o t a t e the endpoint o f the forwards to where i t s a r c i n t e r s e c t s a s i d e o f  o b s t r u c t i n g square.  The computation i s simpler  s i d e s o f the square are a l i g n e d with the c o o r d i n a t e I describe t h i s c o l l i s i o n involving the p o i n t  the  outer  because  the  axes..  computation only f o r an  example  constraining arc (figure I I I . 1 0 ) . .  Suppose  of r o t a t i o n U l i e s i n the southwest guadrant IIIoThe simulated  relative  organism-environment system  FIGURE I I I . 1 0  112  AB = o b j e c t ' s  edge.  AN = l e a d i n g segment. U  = centre  of r o t a t i o n .  A' = p o i n t of c o l l i s i o n w i t h o b s t r u c t i n g r  = UA = UA'.  a.  ' vector  °f  = angle t o c o l l i s i o n = ^ A  square,  UA.  UW = p e r p e n d i c u l a r  UA'.  from U t o c o l l i s i o n  ri  = u n i t outward normal from c o l l i s i o n  x  = distance  s i d e of square, side,  UV^  COSft:(SL).(-rs)* , t o i ,  (-Vr)/l.)  FIGURE I I I . 1 0 - The diagram shows the i n t e r s e c t i o n A' o f an outer c o n s t r a i n i n g a r c w i t h an o b s t r u c t i n g square. The formula shows how t o compute the angle of c o l l i s i o n . '  113 to  the  axes of symmetry of the square, and the endpoint A of a  l e a d i n g segment AN c o l l i d e s with a s i d e of the square. involved  is  the  collision  tracinq routine. west  side  of  from 0 to AN, from  0  to  side,  collision  one  drops  s i d e , meeting  p e r p e n d i c u l a r p r o j e c t i o n of A onto OW.. collision,  s i d e i s the  Instead of dropping a p e r p e n d i c u l a r  f o r t h i s computation the  side  and i s s p e c i f i e d by the a r c  In the example shown the c o l l i s i o n the square.  The  a  perpendicular  i t at W.  Let V be the  Then alpha, the angle to  i s given by alpha = arcos[-UV/r] - arcos[ UW/r]  The  arc  tracing  routine  may,  instead,  s p e c i f y that the a r c  e n t e r s the o b s t r u c t i n g square at the c o r n e r P., are  known so the angle t o c o l l i s i o n  (C)  The coords of  i s then simply given by  alpha = 2 * arcosj AP/ (2*r) i] When most  tracing  two  found.  routine  squares is  are  abandoned  encountered, as  soon  with  different  the.square.  ways  four  distinct  A  4x3  in  which  the  arc  may  Each of these twelve cases reduces  to one or other of the computations (D).  an  p o s i t i o n s of the c e n t r e of r o t a t i o n 0, and f o r each of  these t h e r e are t h r e e intersect  since  as an o b s t a c l e i s  For such an o b s t r u c t i n g square t h e r e are  relative  and  (D)  the c o n s t r a i n i n g a r c s of a doughnut s l i c e at  obstructing  arc-tracing  P  decision  s p e c i f i e d by  table  specifies  equations the  procedure.  (C)  correct .,  +  +  +  IIIaThe s i m u l a t e d organism-environment  system  ,11 4  To  sum  up t h i s s e c t i o n so f a r , I have guided you  c o l l e c t i o n of algorithms involved  in  algorithms  an  sufficient  implementation  f o r scanning an  parallelograms pushto and  and  turn actions  the exact  d i s t a n c e to c o l l i s i o n *  these two  basic  former  inverse  scanning  algorithms  c i r c u l a r a r c s , and  cosines  not  or  and  for  algorithms  angle  to  time-consuming  quicker*  but d i r t i e r  and  implementation;  cheap*  coding.  10°,  This  is  i s erased, the  and  obstructing  its  squares  representation). i s encountered  the  the  new  latter  This or  the  requires I  used  more expensive,  is  to  Cartesian  projection  (without  TABLETOP  be  rotated  the The  representation onto  actually  TABLE  drawing  on  turn  digital rotated  scanned the  a  method  second method r e f e r r e d t o  for  digital  i s repeated u n t i l an o b s t r u c t i n g  square  intended  If  anqle  o b s t r u c t i n g square i s found, a b i n a r y the  for  a n a l y s i s . . The  procedure: a c t u a l l y implemented does the f o l l o w i n g .  by  tracing  f o r computing  Conseguently  computationally  Namely, when an o b j e c t  representation  the  collision*  extensive . case  computationally  and  page 92.  for  include  given above f o r the t u r n a c t i o n i n  careful  of  shape,  These  actions.  algorithms  are  TABLETOP..  respectively,  lines  requires  of  problems  s l i c e s swept out i n the course of  straight  The  and  to solve the b a s i c  object's  doughnut  through a  is  achieved.  search i s c a r r i e d out  l a s t sub-angle of r o t a t i o n u n t i l the  achieved  an over  position  is  l o c a t e d t o w i t h i n 2° accuracy. This  method l e a v e s open the  possibility  III«The simulated  that  some  small  organism-environment system  115 obstacle  may  be  jumped  over  between the 10° t e s t p o s i t i o n s .  T h i s has not y e t happened i n p r a c t i c e , p a r t l y because only simple  TABLETOP environments have been used t h a t do not c o n t a i n  s m a l l i s o l a t e d o b s t a c l e s , and p a r t l y because movable  o b j e c t s has not been s u f f i c i e n t l y  the  which  such an i n c i d e n t could  occur  size  configuration  digital  representation  occupies  an  obstacle  a s i n g l e sguare of TABLE  at a d i s t a n c e of about 13.5 from Utak, and Utak executing a c t i o n of more than 10° towards the o b s t a c l e An important implementation many  pushto  o b j e c t , the deformed  and  Cartesian  due  to  what was o r i g i n a l l y  turn  in  would have Utak grasping the  narrow edge o f a 1 x 14 movable o b j e c t or " s t i c k " , whose  of the  l a r g e f o r an o b s t a c l e  to be missed i n a 10° r o t a t i o n * . The simplest  When  very  problem  actions  a turn  (figure III.11).  arises  i n practice.  are a p p l i e d t o a movable  representation  of  the  object  becomes  cumulative f l o a t i n g point i n a c c u r a c i e s . a sguare may a t some l a t e r  time  look  Thus like  the end view o f a squashed cardboard box. To  overcome  representations  this  problem  three  Cartesian  are used f o r an o b j e c t , not j u s t  one;  style When the  o b j e c t i s f i r s t s p e c i f i e d a base r e p r e s e n t a t i o n i s s e t up.. T h i s is  i t s o r i g i n a l Cartesian representation.  sequence o f a c t i o n s the c u r r e n t  Cartesian  always  rotation  applied  be to  relatively  represented  as  one  t h e base  representation.  uncommon*  and  A f t e r any a r b i t r a r y representation and  Since  a r e computationally  r o t a t e d base r e p r e s e n t a t i o n i s a l s o used. III»The simulated  can  one t r a n s l a t i o n rotations  are  expensive,  a  This c o n s i s t s of the  orqanism-environment system  FIGURE I I I . 1 1  A T h i s shows the s i m p l e s t k i n d of s i t u a t i o n i n which a p o t e n t i a l o b s t a c l e (marked 'B') c o u l d be missed by the a l g o r i t h m a c t u a l l y implemented. Utak i s h o l d i n g a long s t i c k and when he executes a t u r n a c t i o n t o the r i g h t of a t l e a s t 10°, the o b s t a c l e i s missed by the a l g o r i t h m .  117  base  representation  current  Cartesian  rotated  by  the angle between i t and the  representation;  During  a  sequence  t r a n s l a t i o n s between two r o t a t i o n s , the C a r t e s i a n at  the end o f each t r a n s l a t i o n  representation  that  i s derived  r o t a t i o n occurs a new r o t a t e d base directly  from  representation from  base  r o t a t i o n . . When a  representation  the base r e p r e s e n t a t i o n .  i s computed  The c u r r e n t  Cartesian  a t t h i s point i s then obtained by one t r a n s l a t i o n  the new  rotated  base  representation.  implemented the C a r t e s i a n r e p r e s e n t a t i o n cannot  representation  from the r o t a t e d  was computed at t h e l a s t  of  of  With t h i s scheme a  movable  object  deform* however many pushto and t u r n a c t i o n s are a p p l i e d  to the o b j e c t . One  final  problem remains t o be c o n s i d e r e d .  I l l * ! . 2; 1. The o v e r l a y problem  A digital  problem  involving  representations  the crops  h o l d i n g and moving an o b j e c t .  interaction up  occasionally  contiguous  with  representation  and  when  and  Otak i s  formed  When he f i r s t  i s necessarily  the o b j e c t ' s d i g i t a l  time, the E u c l i d e a n  Cartesian  I r e f e r t o the system  Utak and a held o b j e c t as a sum o b j e c t . object h i s d i g i t a l  of  grasps an  outside  representation;  by  and  At t h a t  d i s t a n c e d between h i s C a r t e s i a n p o s i t i o n  the n e a r e s t point N on the o b j e c t ' s C a r t e s i a n  U  representation  must have a value s t r i c t l y between 0 and 2 * r o o t 2 . . The  distance  III«The s i m u l a t e d organism-environment system  118  d remains until  i n v a r i a n t over  Utak e x e c u t e s  When d < r o o t 2 such that lie  in  i ti sclearly  the d i g i t a l  in  the  held  concern while not  affect  U and N i n  representation object's  Utak  go o f t h e o b j e c t . .  to execute a s l i d e point  representation are  empty  procedure  situation  action.  within  o f an o b s t a c l e ,  representations  Consequently  the object  i ti s possible with  a square  This  i s o f no  since  i t does  i n p u s h t o and t u r n occurs  routine  a square  before  go and t h e n f i n d s that  belonging  and t h e r e f o r e  actions.  immediately  Suppose he l e t s  a c t i o n , . . The s l i d e  lies  Cartesian  representation..  the computations involved arises i fthis  starting  the  t o hold  The-problem lets  slide  o f Utak t o c o i n c i d e  digital  Utak c o n t i n u e s  by a  p o s s i b l e t o p o s i t i o n t h e sum o b j e c t  same s q u a r e o f TABLE.  for  movements o f t h e sum o b j e c t  a letgo action followed  the points the  a l l further  Utak's  to the d i g i t a l  fails!  TABLE s q u a r e s n e x t t o U t a k ' s s q u a r e t h e n  tries  If  there  the f o l l o w i n g  h a n d l e s the problem.  1.  L e t t h e v a l u e o f BUGSQUARE be t h e c o o r d i n a t e s o f t h e TABLE s q u a r e c u r r e n t l y o c c u p i e d by U t a k , l e t OLDBUGSQUARE be t h e value o f BUGSQUARE a t Utak's previous position* l e t BUG MARK be the colour assigned t o Utak's digital r e p r e s e n t a t i o n on TABLE, and l e t OVERLAY be t h e o v e r l y i n g colour o f t h e BUGSQUARE. The v a l u e o f OVERLAY i s t h e c o l o u r empty e x c e p t when t h e BUGSQUARE i s w i t h i n t h e h e l d object's d i g i t a l representation.,  2.  After a pushto o r turn a c t i o n , f i r s t draw t h e g r a s p e d object, then s e t OVERLAY = COLOUR-OF (BUGSQUARE) COLOUR-OF (BUGSQUARE) = BUGMARK  3.  I f Utak is about to execute, a slide OVERLAY y* empty, t h e n d o : COLOUR-OF(BUGSQUARE) = empty OLDBUGSQUARE = BUGSQUARE Compute t h e r e s u l t o f t h e s l i d e * III«The s i m u l a t e d  and  organism-environment  i f  system  119  I f achieved p o s i t i o n s t i l l l i e s w i t h i n OLDBUGSQUARE then COLOUR-OF(OLDBUGSQU ARE) = BUGMARK else COLOUR-OF(OLDBUGSQUARE) = OVERLAY This procedure has proved s u f f i c i e n t not  solve  the  problem  r e p r e s e n t a t i o n of digital  Utak  in can  representation  of  general.  i n practice In  fact  l i e arbitrarily  but  the  digital  f a r within  the h e l d o b j e c t .  does  the  T h i s can a r i s e i f  there i s a l o n g s t r a i g h t " c a n a l " of width s t r i c t l y  between 1 and  2 u n i t s i n the o b j e c t ' s C a r t e s i a n r e p r e s e n t a t i o n . . L e t the c a n a l have l e n g t h n+1. lie  astride  In one p o s i t i o n of the o b j e c t  a column of squares.  head of t h e c a n a l  and  position  object  of  the  grasp  the  the  the  canal  Then Utak c o u l d s l i d e to the object  there* .  In  the f i r s t of  type of p o s i t i o n and has l e t i t go i n t h e second  position;  representation  When  One  he with  wants n  to  squares  execute of  a  the  solution  slide,  Utak i s  object's  digital  i n figure III.12. that  immediately s p r i n g s t o mind and can be  e a s i l y implemented w i t h i n the c u r r e n t TABLETOP philosophy following.  Before  next  closest  d i g i t a l representation; ensures  i s the  a grasp a c t i o n can be executed the 20 c l o s e s t  sguares t o Utak's square must be empty and some 24  type  between him and the empty TABLE squares o u t s i d e .  This i s i l l u s t r a t e d  of  digital  Now suppose t h a t Utak has grasped the o b j e c t i n  h o p e l e s s l y trapped  rinq  another  c a n a l may not s t r a d d l e any whole  TABLE squares, so t h a t the c a n a l does not appear i n the representation;  may  square  i n the  squares must belong t o the o b j e c t ' s  This i s shown i n f i g u r e  III.13.  This  t h a t no p o i n t of the subseguent held o b j e c t l i e s  within  III«The simulated  organism-environment system  120  FIGURE III.12  FIGURE III.12 - (a) The C a r t e s i a n r e p r e s e n t a t i o n o f an o b j e c t , w i t h a c a n a l of w i d t h 1.5. (b) The o b j e c t p o s i t i o n e d so t h a t the c a n a l i s open i n the d i g i t a l r e p r e s e n t a t i o n . Utak i s able to s l i d e t o the head of the c a n a l and grasp the o b j e c t t h e r e . (c) The o b j e c t p o s i t i o n e d so t h a t the c a n a l i s closed. I f Utak now l e t s go the o b j e c t , no s l i d e a c t i o n can get Utak beyond the b o r d e r s of h i s c u r r e n t d i g i t a l r e p r e s e n t a t i o n . He i s trapped.  121  •K  4  •  ___________  FIGURE III.13  - One s o l u t i o n to the o v e r l a y problem i s shown.here. Before Utak can s u c c e s s f u l l y ' grasp an o b j e c t , two c o n d i t i o n s must h o l d . (1) The 20 squares of TABLE c l o s e s t to Utak must be empty. (2) At l e a s t one of the 24 squares forming a r i n g around the 20 c l o s e s t squares must belong t o the o b j e c t ' s d i g i t a l representation.  122 root2  units  "overlay"  of  Utak's  position,  thus  that  the  above  problem cannot a r i s e *  Another s o l u t i o n representation  of  would  require  coordinates,  require  that,  in  the  Cartesian  Utak and the o b j e c t t o be h e l d , Utak was  w i t h i n root2 u n i t s of any would  and  edge  closest  of  edge  the  object.  calculations  This in  not  however Cartesian  a type of c a l c u l a t i o n t h a t I wish to t r y and  avoid  as much as p o s s i b l e . Now  I shall  show some examples of the TABLETOP  program  in  action.  I I I . 1.3  An example of TABLETOP p_erf or ma nee ;  The:following session  with  slightly  edited.  human  user  pages, f i g u r e 1 1 1 * 1 4 , show  TABLETOP  recorded  during  the  L-shaped  from  UBC s Open House  I t shows the s t a t e of the  solved  excerpts  object  TABLE problem*  array The  snapshot i n c l u d e s a statement of the t a s k , which i s read by user, not  Utak!  The  an a c t i o n command i s s u e d by the  •  the '*•  a  B  the  state  a  first the  of the nine Utak.  (Thus  the BUGMARK  representation TABLE squares i n the  centred  on  contents  of the OVERLAY variable.),  the typed  as  user  of the TABLE a r r a y , with  showing Utak's d i g i t a l contents  1979,  subseguent snapshots show:  •  resulting  a  the  centre  square  3x3 shows  array the  response from TABLETOP.  {I have added comments w i t h i n braces l i k e IIIaThe simulated  this.j  organism-environment system  1  •  TRANSLATE B B B B B B B B B B B B B B B B B B B B B B B B B B * B B B B B B B B B B B B B B B  >  A  BY  (-10  0)  I.  E.  HOVE  IT  DP  BY  10  UNITS  B B B B B B B B B B B B B B B B B B B B B B B B B  B  B  A A A A A A  A  B  B B B B B B B B B B B B  B B  B B B B  B B B B B B B B B B B B B B B B B B B B B B B B B  OK  Fi£UKE  III.IA-  B B B B B B B B B B B B B B B B B B B B B B B B B B B B  12V  (GBASP) B B B B B B B B B B B B B B B B B B B B B B B B B B * B A B A B A B A B A B A A B B B B B B B B B B B B B B B B BBB m * c»  >  GOT  IT!  B B B B B B B B B B B B B B ,  B B B B B B B B B B  B  B B B B B B B B B B B B B B B B B B B  A  B B B B B B B B B B B B B B B B B B B B B  B B B B B B .  B B B B B B B B B  B B B B B B B B B B B B  (PUSHTO  6.0  125  N)  B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B , B ' B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B  B B B B B B B B  B B B B * A A  A A  A A A A A A A A A  & A  A A  :  BAA  .4A >  HIT!  B B B B B B B B  B B B B B B B B B B B B B B B B B B B B B B B B B B B B  (PUSHTO 1.0  B)  B B B B B B B B B B 5 B B B B B B B B B B B B B B B B B B B B B B B B B B ^ B B B B \ B B B B B B B B B B A . ^ B B * A A B B A A A B B B B B B B B B B B B B B B B B B B B B B B B B B A A A B B A A A A B B A A A A B B A A A B IB A A B B B B B B B B * B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B ..A .AA ..A  >  HIT! i  126  (PDSHTO 5-0 N ) B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B ,. _ : B B B B B B A A ft A B B * A A A B B A A B B A A B B A A B B A A B B A A B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B. B B B B B B B B B B: B B B B B B B B B B B B B B B B B B B B B B B S B B B B B B B B B o AA . AA  >  OK  127  128 I I I . 2 The simulated organism Otak and h i s tasks  III.2.1 Design  considerations  Now t h a t I have described the simulated  environment,  what  k i n d of organism should be b u i l t t o l i v e there, and what k i n d o f t a s k s should the organism be r e q u i r e d questions  are  expect a  colour  closely blind  linked  since,  human  to  execute?  These  two  f o r example, you cannot  respond  to  traffic  correctly  unless  cues  such  as  light  available.  More p r e c i s e l y , what  kind  of  actions  organism  other  to  lights  position  are  should  the  be capable o f executing and what kind of sensory  should the organism r e c e i v e from i t s environment?  input  The kinds  of  i n p u t / o u t p u t allowed t o the organism, and the kind of task he i s r e q u i r e d t o s o l v e , both mould t o a c e r t a i n extent t h e design the  mediating  mechanism,  or  organism-controller,  that  of lies  between i n p u t and output; Asking  these  questions  f a c t u a l and methodological the  organism be?  o f design immediately  questions.  I f so, what animal?  are the design d e c i s i o n s to be made? is  to  How  r a i s e s many  animal-like  should  I f not, by what c r i t e r i a I f the simulated  organism  be l i k e some s p e c i f i c animal, e x a c t l y what sensory  and motor output messages does t h a t animal's  brain  input  receive  and  behaviour  of  definitely  be  send? Since I am i n t e r e s t e d i n the animals  and  humans,  the  principles  organism  of  should  III-The simulated organism-environment system  129 animal-like. are,  The subsequent q u e s t i o n s  unfortunately,  virtually  about  sensory-motor  unanswerable; i n no case a r e a l l  the r e l e v a n t f a c t s f o r one i n t e r e s t i n g animal known. instead, again,  fall  back  I/O  One might,  upon the gross behaviour of an animal, but  i n almost no case are a l l the r e l e v a n t f a c t s known!  This collected behaviour published simpler  situation a wealth of  the  has  of  recently  information  octopus  improved.  M.J.Wells  has  about  the  physiology  and  [ W e l l s , 1978 ],  and  E.R.Kandel  has  a comparable c o l l e c t i o n o f i n f o r m a t i o n about  an  even  c r e a t u r e , the marine s n a i l A p l a s i a [Kandel,1978].  With  a view t o r e c e p t o r d e s i g n , I have perused  various  known  facts  about r e c e p t o r s i n mammals, i n c l u d i n g v i s u a l r e c e p t o r d e n s i t i e s , receptive f i e l d  s i z e s , and m a g n i f i c a t i o n f a c t o r s i n the b r a i n .  One has t o r e s o r t to c r i t e r i a  o f elegance,  f i n a l l y , i n the AI approach, on the c r i t e r i o n feasibility. sciences, My  This  i s in  n a t u r a l n e s s , and of  computational  c o n t r a s t t o most o t h e r  experimental  where the f i n a l a r b i t e r i s experimental  feasibility..  a t t i t u d e was w e l l put by the philosopher  D a n i e l Dennett  when he wrote [Dennett,1978,p.104] 11  one does not want t o get bogged down with t e c h n i c a l problems i n modeling t h e : c o g n i t i v e e c c e n t r i c i t i e s of turtles i f the p o i n t o f the e x e r c i s e i s t o uncover very g e n e r a l , very abstract principles that will apply as w e l l t o the c o g n i t i v e o r g a n i z a t i o n of the most s o p h i s t i c a t e d human beings. So why not then make up a whole c o g n i t i v e c r e a t u r e , a Martian three-wheeled iguana, say, and an environmental niche f o r i t to cope with? I t h i n k such a p r o j e c t could teach us a great d e a l about the deep principles o f human c o g n i t i v e psychology, but i f i t could n o t , I am g u i t e sure t h a t most of c u r r e n t A.I. modeling o f f a m i l i a r human mini-tasks could not III«The simulated  organism-environment system  130 either.  11  Utak i s my  three-wheeled  Martian iguana and TABLETOP i s h i s  niche.  I l l * 2 . 2 The  sensory-motor  c a p a b i l i t i e s - of-Utak  Utak can move i n a s t r a i g h t l i n e , he can object,  and he can push*  grasp  design  of  h i s motor output immediately  the obvious f e a t u r e s of the This  is  the  fact  design  of  when  a  once.  biological  system  c o u l d be d e s c r i b e d  that  a  motor  never-ending  of  acts. as  a  series  an  pattern of  course, i s very d i f f e r e n t from a  never-ending  typical  are alert  transducer  i n p u t p a t t e r n s on  l a r g e number of output l i n e s .  on a s i m i l a r l y  another  Indeed,  patterns  series  present-day  I t seems u n l i k e l y t h a t  to understanding the computations  of  T h i s , of computer  a l l i n f o r m a t i o n through a b o t t l e n e c k formed  the s i n g l e high-speed CPU. close  output.  lines  into  channels  Thus  output  m i l l i o n s of i n p u t l i n e s  which  has  t h a t e x a c t l y one output has to be a c t i v e t o  b i o l o g i c a l system transforms  He  c o n t r a d i c t s one of  natural  execute an a c t i o n , whereas l a r g e numbers active  movable  t u r n , and l e t g o a h e l d o b j e c t .  f i v e motor outputs, only one o f which i s a c t i v e a t the  a  we  can  by get  occurring i n b i o l o g i c a l  systems i f we allow the " b o t t l e n e c k " design of c u r r e n t computers to i n f l u e n c e our t h i n k i n g . The consisting  visual  sensory  input  is  of 160 input l i n e s from  somewhat  more  realistic,  160 r e t i n a l r e c e p t o r s . , Utak  IIIaThe s i m u l a t e d organism-environment  system  131 gets  a  bird's  environment  eye  as  though  f i e l d s are arranged each  view  directly  his  eye  down  immediate The  48 f i e l d s each 16 times the s i z e of a  i n an outer, p e r i p h e r a l , zone.  the  ratio  t a b l e t o p covered of  an  object  Each r e t i n a l  by the c e l l ' s i s ignored.  impression,  adjacent squares The  Utak  impression  Utak's  which  ( f i g u r e 1.3).  a set of 160  consists  computes  the  array  comes  can of  The.  colour  graylevels constitutes be  the  representation* the  from  TABLE  reflected  by a change i n the representation  a  to  new  sensed  via  a  c o l o u r s of the 8  a  r e t i n a l and  halt.  of r e t i n a l f i e l d s on  directly  digital  that  to Utaki simulation  digital  field  Object c o l o u r s  each time. Utak  superimposes  0-7,  cell  of o b j e c t to t o t a l area i n the p a r t of the  one r e t i n a l i m p r e s s i o n . tactile  fields  i n an i n t e r m e d i a t e zone  r e g i s t e r s a 3 - b i t g r a y l e v e l , or i n t e g e r i n the range reflects  retinal  as f o l l o w s : 64 i n a c e n t r a l f o v e a , 48  surrounding the f o v e a , and field  his  were on a s t a l k .  4 times the s i z e of a f o v e a l f i e l d  foveal  on  of  and  array.  Utak  or  TaBLE,  computes an  retinal  To  action impression of  the  do  tactile so  it  c e n t r e d on graylevels  by Utak w i l l only  if  be the  an o b j e c t held by  him  changes;  More s o p h i s t i c a t e d v i s u a l sensory systems are easy  to  propose,  but t h i s one i s c o m p u t a t i o n a l l y cheap and has  sufficed  so far,; The  concepts  of  speed,  mass, a c c e l e r a t i o n , and momentum  have not been implemented., a s the reader w i l l see, the to design an o r g a n i s m - c o n t r o l l e r f o r t h i s simple world  attempt r a i s e s an  IIIaThe simulated organism-environment system  132 ample  range  perception  of and  features.  interesting action  and  without  fundamental the  addition  problems of  these e x t r a  Nonetheless, the d i s t a n c e between s u c c e s s i v e  impressions  may  in  retinal  be viewed as a measure of speed i f one assumes  t h a t r e t i n a l i m p r e s s i o n s are r e c e i v e d at a c o n s t a n t r a t e .  I l l . 2.3 Examples Figure  of Utak^s sensory-motor experience  III.15  shows  the  r e t i n a l and t a c t i l e i m p r e s s i o n s  r e c e i v e d by Utak immediately p r i o r t o the f i r s t few  actions  in  the performance of s e c t i o n I I I . 1.3.  I l l - 2 . U Examples  of t a s k s f o r Utak  Here:I present a l i s t expect handle..  a  competent Their  of t a s k s , i n E n g l i s h , which  I  would  o r g a n i s m - c o n t r o l l e r f o r Utak to be a b l e to method  of  presentation  to  Utak's  o r g a n i s m - c o n t r o l l e r w i l l be d e s c r i b e d i n s e c t i o n IV.2.  "Go t o the.northeast  corner"  "Go t o the next room" "Go t o the square" "Go  round the square and  return"  "Push the square i n t o the northeast c o r n e r " "Push the square i n t o the next room" "Push the b r i c k through the door" "Push the b r i c k around the c o r n e r " "Push the L-shaped o b j e c t i n t o the next room" IIInThe simulated organism-environment system  FIGURE III.15  16151413121 1 109  8 7 6 5 1 . 3  2 1 0 1 2 3 4 5 6 7  c  c  ( c c c  c c  7|7  c  7|0 7 1 7  7I 7  7 I 7 71 0 01 0 OJ 0 7 j 7 71 0 0 ( 0  (  c c  7(7  7| 0 01 0 0 ( 7  7|7  7| 0 710  71 7 7J 0 7 | 7 7|  c  0(7  01  0I 7  0 OJ 7  0 0]0 0)7  7J7 71 0 0)0 017 0  c c (  .('  c (  * > *  (ROLL 5.0 HE) ( 4 . 2 4 1 6 4 0.735398) (THLOOK)  9  10 111213141516 . 16  134. 161511*13121  1109  8  7  6  5  4  3  2  1  0  1  2  3  4  5  6  7  8  9  1 0 1 1 1 2 1 3 1 '11516 16  15  14  if  13  12  f  11  f  10 9  (  -  c c  — 1  1  •  1 1  0  •  1  0  0  1  0  0  8 7  I I 6 1  0  4 1  j 7 i o '  iv  (  c  0 | 0 | 0 1 0  (*  0 j 0  3  01  jo" 0 | 0 | 0 1 0  | 7 I 0 '  5  1  0: 2  OJ0|0| 0  0 1 0| 1  i 7 | o ' 7 | . 7 | 7 j 7* 7 1 7 * 1  c  I  7 1 0 J0 | 0 | 7 |  0  0  0 I 01  |7|0  0 J 0 | 0 | 7 0 | 01  17J0J  0 | 0 | 0  |7|0  01 0 | 0 | 7  1  (  c  j  70  j  2 0(  3 0 1 0 |  4  c  1 "»  1  0  |  (J  1  0  .1  5  i  c  6 0  I 2  7 8  c  9  c  10 11  c c  12 13 14 15  c .  c  c (  B B B . * _ . - & >  * >  *  N i l .  (ROLL ( 1 .  1 . 0 E) 1 . 5 7 0 7 9 6 )  (THLOOK)  16  135 When a compass d i r e c t i o n appears i n the task refers  to  Utak's  own l o c a l o r i e n t a t i o n system, which need not  c o i n c i d e with the TABLETOP o r i e n t a t i o n . the  first  r e t i n a l impression  not  It i s initialized  i s received.  f a c i n g at that time becomes north do  when  Whatever d i r e c t i o n he  i n h i s o r i e n t a t i o n system.  I  claim to have a system or even the o u t l i n e s of a system  t h a t can handle a l l these t a s k s ; I am p r e s e n t i n g to  statement t h i s  show  the  ultimate  design  this l i s t  here  goals f o r a r o b o t ^ c o n t r o l l e r f o r  Utak.  I I I . 3 An extension The from  and two g e n e r a l i z a t i o n s of TABLETOP  purpose of t h i s s e c t i o n i s t o d i s c u s s i s s u e s that a r i s e  the design  of TABLETOP.  These a r e not germane t o the main  argument o f my t h e s i s but are of right.  They  are  also  some . i n t e r e s t  relevant  to  questions  in  their  in  own  automatic  assembly. The  first  issue  TABLETOP s i m u l a t i o n , achieve  exactness?  concerns exactness.  How accurate  and how, i f at a l l , could For  the  moment  I  i t be extended to  will  assume t h a t the  r e f e r e n t f o r the terms "accuracy" and "exactness" i s Cartesian  representation  represented  t o a l i m i t e d p r e c i s i o n i n some computer.  of  an  object  of  shapes,  i s the  using  the  real  usual  numbers  The motion  may, i n the worst case behaviour of TABLETOP, be  h a l t e d i f a p o i n t o f the moving o b j e c t comes w i t h i n root2 p o t e n t i a l o b s t r u c t i o n , whether or not a c o l l i s i o n Ilt«The simulated  of  a  would occur i n  organism-environment system  1 36 the  Cartesian  obstacle corner  representation.  intersects  and  i f the  intersects  the  a  path  TABLE of  same  This  Otak, or  opposite  c o r n e r * . The  arbitrarily  far  the  the  Cartesian  approach of potential How the  Otak, or  can  this  (Otak) The  onto the  by  edge  that is  stored  as  an  coordinates standard  line  The  an  i s  each  TABLETOP c o l l i s i o n  point  may  collision  may  the  intersection cure  i s  be  not  point,  or  correspond  arise  remedied?  attention to  In  the be even  to  a  i f the  line  of  angle  with  a  In  the  describing  case  of  the  course  of  whenever a TABLE s q u a r e the  a  moving  by  Then  square e d g e (s) (are)  projecting i s  entered  t r a v e r s i n g edge i s s t o r e d  i s entered  collision  s e v e r a l edqes a  each  on  the  which  time the TABLE,  caused  retrieved.  point*  this  are  the  idea  of  Otak  Cartesian  sguare  Then the  i f any,  pointer  path  the  at  to  be  Cartesian  computed  by  any  algorithm. based  on  Cartesian  representations  and  scales  magnification,  of  object, to  projecting higher  one  to  close  this.,  obstruction i s  second  close  object.,  edge..  of  the  the  held  makes a n e a r - z e r o  back to  obstructing  of  a  edge o f  arbitrarily  affairs  TABLE a r r a y ,  representation(s) marked  of  I f a square  an  of  These cases can  restrict  cure  for  encounters  I  a pointer  square.  i f an  edge.  approaching  first  but  point  object,  state  cures  objects an  an  obstructing  possible  point  point*  point  Cartesian  TABLETOP c o l l i s i o n collision  a  TABLE s q u a r e  from  occur  square : a r b i t r a r i l y  diagonally  worse,  can  III»The s i m u l a t e d  onto  the  each time  of  TABLE  repeatedly at  higher  re-determining  organism-environment  the  system  137  obstructing  squares.  point,  i f  a n y , h a s been f o u n d  I call  this  the  The  focus  process  halts  when  the  collision  t o w i t h i n the r e q u i r e d  method.  To  explain  i t  I  R  of  accuracy. need  some  terminology. . A C-representation representations coordinate  operations  or  more  A coordinate  t o some  fixed  distinct  with  Say t h a t  respect  a  line  replaced  segment by a l i n e  translation,  of  by  some the  and s c a l i n g  c o o r d i n a t e : system.  Let  a  (R,C) be a r e c t a n g l e o f any s i z e (R,C)  has  been  window W i f  A l l p a r t s o f R that l i e wholly any  objects, using  C-representation  to a given  Cartesian  system C i s o b t a i n e d  initial  W on a C - r e p r e s e n t a t i o n  tabled  collection  of a sequence of r o t a t i o n ,  or o r i e n t a t i o n .  a)  one  s y s t e m C.  application  window  of  (R,C) i s a  R  outside W are  that intersects  segment t h a t t e r m i n a t e s  removed  and  an edge o f W i s at  that  edge*  In computer g r a p h i c s terms, R i s c l i p p e d * . b)  The c o o r d i n a t e  system C i s t r a n s f o r m e d  into  a  new  system  by •  rotating  i t into  a  moving t h e o r i g i n  •  applying  scale  direction,  so  alignment  with  to the centre factors,  that  one  t h e e d g e s o f W, o f W, in  each  coordinate  t h e s i d e s of W c o i n c i d e with t h e  s i d e s o f TABLE. c)  The C - r e p r e s e n t a t i o n  Suppose  the  (R,C) i s p r o j e c t e d o n t o  coordinate IIIaThe  system  simulated  TABLE.  C* i s t h e r e s u l t  of a p p l y i n g  organism-environment  system  138 to  a  coordinate  translation,  system  and  C  scaling  a  operations  s e r i e s can always be reduced and  two  series  to one  as  i n b)  rotation,  the  by a p p l y i n g  above.  one  to  rotation,  is  Such a  translation, Let Q' be  Q,  in  i n v e r s e s of the o p e r a t i o n s i n t h e . s e r i e s .  r e s o l u t i o n of the c o o r d i n a t e system C maximum  several  s c a l i n g s . , L e t Q be a u n i t square i n C'.  r e c t a n g l e i n C t h a t i s obtained order,  of  defined  the  reverse Then the  to  be  of the lengths of the s i d e s of Q i n the o r i g i n a l  the  system  C, I  c an  now  describe  p r e c i s e l y the focus meth od f o r  more  f i n d i n g a s a c c u r a t e l y as d e s i r e d the c o l l i s i o n between  Otak's  c o l l e c t i o n EO the.  obje c t s  intended  path  and  s i d e s of TABLE.  CP2,.  T able  the  verge  the  Let E be the  an o b s t a c l e .  of  all  in  the environment, l e t C be the  and  l e t W c o i n c i d e with  C-representation Let  Find  potential  all  (R ,C) ,  Otak's intended messaqe  path..  "no  r e s o l u t i o n of C of  any,  the  WO r  Let 6 be the r e s o l u t i o n r e q u i r e d .  window W.  the  if  of the o r i g i n a l C a r t e s i a n r e p r e s e n t a t i o n s  o r i g i n a l c o o r d i n a t e system CO,  CP1.  and  point.  collision  be the new obstructing  collision  the  with  r e s p e c t to the  C-representation* TABLE  squares  I f there are none then e x i t  i s l e s s than of  (R,C)  found".  o b s t r u c t i n g square encountered.  path  with  Otherwise, i f the  6, then compute the  intended  alonq  with  the  point first  Find t h e . c o o r d i n a t e s  t h i s p o i n t i n the o r i g i n a l c o o r d i n a t e system CO  and  of  exit  III«The simulated organism-environment system  139  with these  coordinates  Otherwise, CP3,.  for  the  point  of  collision.  continue..  Take the s m a l l e s t r e c t a n g l e W  1  direction  of  motion  t h a t i s a l i g n e d with  the  of Otak and that c o n t a i n s a l l the  p o t e n t i a l o b s t r u c t i n g squares found i n  step  CP2.  Let  (R,C)= (R« ,C) , the window W=W«, and go to step C P l .  A m a g n i f i c a t i o n always occurs at step CP1 w"' i s s m a l l e r than the p r e v i o u s window W.  i f the new  window  The r e c t a n g l e W  will  1  always be a l i g n e d with the c o o r d i n a t e axes except, p o s s i b l y , first  time t h a t CP3  step CP1  i s executed*  Thus a r o t a t i o n  i s executed i n  at most once.  This r o t a t i o n , permitted by a l l o w i n g the window W» not  to  be  aligned  with  s p e c i a l type of case* obstructing  squares  corner-to-corner  be  in  Namely,  the  case  where  the  form a d i a g o n a l across the TABLE a r r a y , as  and  than  one  potential  both  approximately  l i e approximately p a r a l l e l to each  A window a l i g n e d with the axes would not, i n t h i s  smaller  CP3  the axes, i s necessary to handle  can happen i f an edge and Otak's path both extend  other.  the  the  current  m a g n i f i c a t i o n could occur.  window,  and  case,  consequently  As a r e s u l t of t h i s s i n g l e  no  rotation,  the intended path of Otak i s always p a r a l l e l to one of the  axes,  say the v e r t i c a l . Suppose  the TABLE g r i d has n u n i t squares along each  Then the r e c t a n g l e W  of CP3  every  CP3  execution  of  w i l l have h o r i z o n t a l width  a f t e r the f i r s t ,  side..  one  in  s i n c e a l l the  squares  IIIoThe simulated organism-environment  system  140 i n t e r s e c t e d by a v e r t i c a l l i n e l i e  in  horizontal  w i l l t h e r e f o r e be n i n every  scale  execution of CP1 greater  than  use*  One  after  1,  execution of CP1 This  factor  may  a  CP1  t h e . second. . horizontal  Since  n  column.,  is  magnification  seem  an  integer  occurs i n every  it  out  is  because,  if  the  c o n s i s t s only of convex shapes, the p r o j e c t i o n  onto TABLE can be done such  very  fast  hardware was  method might become f e a s i b l e . .  with  some  simple  available, this  i n any dimension.  parallel  magnification  Another reason i s t h a t t h i s  method* i n s i m p l e r form, can be used to solve l i n e a r problems  The  l i k e a c o m p u t a t i o n a l l y expensive method to  reason I have sketched  If  single  a f t e r the second.  C-representation  hardware.  in  a  A f i n a l reason i s t h a t an  same  programming extension  of the f o c u s method i s used i n SHAPE, the s p a t i a l planner i n the o r g a n i s m - c o n t r o l l e r of Utak. The  parallel  hardware  f o r each TABLE sguare. broadcast  to  r e g u i r e d c o n s i s t s of one component  Given a  every component.  line  L,  its  coordinates  are  Each component computes whether  i t s corresponding TABLE sguare l i e s to the r i g h t o f , to the  left  of, or i s i n t e r s e c t e d  take  one time u n i t . by for  L e t t h i s computation  Then the p r o j e c t i o n o f a convex shape S  m l i n e s takes m time u n i t s , one f o r each l i n e , one  operation is  by, the l i n e L.  extra is  intersected  corresponding  AND this. by,  operation  by  each  bounded  plus the time  component.  The  AND  I f a TABLE square l i e s to the r i g h t of* or every  component  line signals  of  t h e . shape. S,  "inside  S";  then  the  otherwise  the  III«The simulated organism-environment  system  141  component s i g n a l s " o u t s i d e S". . One  other  question  naturally  TABLETOP be g e n e r a l i z e d t o  three  answer  the  is  yes,  provided  arises.  or  Can the design of  higher  projection  dimensions?  The  of an n-diraensional  convex polytope onto a g e n e r a l i z e d TABLE array can be  computed.  The g e n e r a l i z e d TABLE c o n s i s t s of an n-dimensional array o f u n i t hyper-cubes. projecting  The s c a n - t a b l e a  convex  technigue  polygon  onto  used  the  must  be  easy  passes through.  to  compute  TABLETOP  TABLE does not  g e n e r a l i z e to n dimensions.. To apply the it  in  scan-table  which hyper-cubes  In t h r e e dimensions  this  is  face i n t e r s e c t s . axes  there  is  no  simple  does  not  seem  algorithm  to  sketched above f o r computing convex  polygon  onto  hyper-plane one simply hyper-cube  of  the  l i e s t o the l e f t hyper-plane. completes This swept  translation,  of  u n i t cubes the  corresponding  generalize.  in parallel  TABLE computes  in  final  AND  scan-table  projection easily..  parallel,  operation  the  However, the method  the  generalizes  the  to  for  for  each  of  a  For  each  each  unit  hyper-cube  of, to the r i g h t o f , or i s i n t e r s e c t e d  by,  the  hyper-cube  computation,.  method  out  problem  n-dimensional a r r a y , whether the  One  the  technique  When the face i s o b l i g u e to a l l the c o o r d i n a t e  l i n e - t r a c i n g a l g o r i t h m i n two dimensions., Thus technique  easily  a hyper-plane  the  d e t e r m i n i n g , f o r each face of a polyhedron, which  for  by  a or  can  also  leading to  be  used t o compute.the  hyper-plane  compute  the  in  segment  the of  hypercubes  course a  of  a  hyper-sphere  IIIaThe s i m u l a t e d organism-environment  system  142  ( g e n e r a l i z a t i o n of a doughnut s l i c e ) swept out by hyper-plane one  in  the  course  of a r o t a t i o n ;  (a p a r t of)  In t h i s l a t t e r  has t o compute whether a hyper-cube i s i n s i d e ,  intersected  by  the  TABLETOP method can  surface of a hyper-sphere; be g e n e r a l i z e d to higher  +  +  In t h i s chapter  +  case  outside, Thus the  a  or  basic  dimensions.  +  +  I have d e s c r i b e d the design of the TABLETOP  s i m u l a t i o n system, and  gone  into  sufficient  detail  that  the  e s s e n t i a l problems t o be handled i n an implementation are  clear.  I have a l s o shown how  obtain  more  accurate  t h i s design could be  collision  points,  and  extended  how  the two  t a b l e t o p could be g e n e r a l i z e d t o three or more particular  I  introduced  the  accurate c o l l i s i o n p o i n t s .  focus  This  design of SHAPE, the s p a t i a l  to  dimensional  dimensions..  method f o r o b t a i n i n g more  will  reappear  later  simulate  an  environment  advantages of such a  system  as are  simple that  as some  a of  a s s o c i a t e d with r e a l world  s l o p p i n e s s are avoided,  hardware i s r e q u i r e d , and  the  prototype  organism-controller  next chapter  sensory-motor is  the  required  tabletop.. the  The  problems  no a d d i t i o n a l  experience  easily reproducible.  I d e s c r i b e a c l a s s of algorithms  f u n c t i o n i n g of the  in  planner.  In c o n c l u s i o n , c o n s i d e r a b l e programming e f f o r t i s to  In  of In  a the  fundamental to the  organism-controller. III»The simulated  organism-environment system  143 CHAPTER IV TOWARDS THE DESIGN OF A ROBOT-CONTROLLER  The the  purpose of t h i s chapter i s to present  design  and  implementation  an  reguire  two  parts,  a  design  seems  data p a r t c a l l e d the world model or  c o g n i t i v e map and a process p a r t c a l l e d the a c t i o n c y c l e . latter  consists  to  of a r o b o t - c o n t r o l l e r f o r Utak.  As d e s c r i b e d i n the i n t r o d u c t o r y chapter, any such to  approach  This  of a loop c o n t a i n i n g the three subprocesses o f  p e r c e p t i o n , p l a n n i n g , and a c t i o n . The chapter i s s t r u c t u r e d as f o l l o w s . I present In  the  an analogy second  In the f i r s t  t h a t i s u s e f u l i n approaching  section  I  present  the  which  any  made  scenario  o f the  complete r o b o t - c o n t r o l l e r f o r Utak should  d i s p l a y t o be a c c e p t a b l e . progress  problem.  p a r t s r e q u i r e d of any  r o b o t - c o n t r o l l e r and i n the t h i r d I present a behaviour  the  section  In the f o u r t h s e c t i o n I d e s c r i b e  i n one approach to the design and  of a r o b o t - c o n t r o l l e r , and i n the l a s t  section  I  the  implementation describe  an  a l t e r n a t i v e approach t o t h i s problem.  IV.1  An analogy  I s t a r t with a thumbnail between  the  scientific  sketch of t h e  method  and  well-known  analogy  the process of p e r c e p t i o n  IVnTowards the design of a r o b o t - c o n t r o l l e r  144  since  this  was  the  organism-controller* some phenomenon. and  an  hypothesis i s used are  experiment almost  point  Consider  an  f o r my  hypothesis. to p r e d i c t  done  -  exactly  as  To  test  what w i l l  an experiment.  and makes  design  experimenter  He o r she wants t o understand  proposes  actions  starting  of  the  ;  investigating the  phenomenon  i t s validity  be observed  if  this  certain  He or she c a r r i e s out the  observations.  If  the  observations  p r e d i c t e d then the experimenter's  are  degree of  confidence or b e l i e f i n the hypothesis i n c r e a s e s . . One then that  the  hypothesis  explains  the  observations.  If  o b s e r v a t i o n s are not as p r e d i c t e d but the hypothesis can be  an  improved  predicted  and  adjustment  hypothesis. cannot  then  be  there  is  still  an  currently  explain  otherwise:  ignored.  higher  experiment  hypothesis  observation by  an  easily  principle,  before  but  o b s e r v a t i o n s are not as by  simple  parameter  makes a s t r u c t u r a l change, i f to  accommodate  them..  which the experimenter  hypothesis  then  i t is  If  cannot  noted  but  With t h i s new h y p o t h e s i s , or o l d hypothesis  confidence, and  the  accommodated  makes  the more  h y p o t h e s i s t o these, and so on* in  If  the experimenter  p o s s i b l e , t o enable the  with  the  modified t o accommodate the o b s e r v a t i o n s , e.g. by changing a  parameter* then the degree of confidence remains as in  says  experimenter  designs  another  observations,  accommodates  E v e n t u a l l y the hypothesis  the will,  be so w e l l adjusted t o the o b s e r v a t i o n s t h a t the  hypothesis w i l l be g e n e r a l l y accepted as a u s e f u l d e s c r i p t i o n o f one  aspect  of  Nature.  The hypothesis w i l l be c o n s i s t e n t with  IVaTowards the design of a r o b o t - c o n t r o l l e r  145  a l l the o b s e r v a t i o n s so f a r , or i n other words may  be  regarded  as the t r u t h a t t h a t p a r t i c u l a r time and p l a c e ; . Note the :pragmatic most  satisfactory  action.  at  nature of s c i e n c e :  whatever  a p a r t i c u l a r time i s used  For i n s t a n c e , Newtonian mechanics was  immensely  successful  theory  even  theory  is  as a b a s i s f o r  an a c c e p t a b l e and  though i t was  known t h a t i t  could not e x p l a i n the p r e c e s s i o n of the p e r i h e l i o n of Mercury., Now  return  to  Otak i n h i s simulated world. . At a l l times  Utak maintains an h y p o t h e s i s about  the world, c a l l e d  the  world  model.. Each p a r t of the world model has an a s s o c i a t e d degree c o n f i d e n c e , and these degrees of confidence may to  time*  In general the degree  vary  from  time  of confidence a s s o c i a t e d with a  p a r t i c u l a r p a r t w i l l i n c r e a s e with time; only the occurrence some  guite  experimenter external  unusual  event  will  cause  i s Utak; the phenomenon  world;  the  of  observations,  to  it  to  decrease.  be  explained  of The  is  the  or p i e c e s of evidence, are  provided by the s e r i e s of sensory impressions impinging on Utak; and  any hypothesis or world model must be c o n s i s t e n t , as f a r as  possible, least,  with the s e r i e s of sensory impressions.. At  the  very  the c u r r e n t world model must be c o n s i s t e n t with the most  recent sensory impression. In  t h i s analogy, £§_rception i s the a c t of accommodating the  world model to e x p l a i n the  current  sensory  impression*  while  m a i n t a i n i n g c o n s i s t e n c y as f a r as p o s s i b l e with p r e v i o u s sensory impressions.  When there i s no e x t e r n a l l y imposed task, p l a n n i n g  is  on  deciding  an  experiment  to  gather  more  evidence  to  IV«Towards the design of a r o b o t - c o n t r o l l e r  146 c o r r o b o r a t e the  c u r r e n t world  out  actions.  the  planned  dependent  on  the  the c u r r e n t  If  a l l p a r t s of the  world  world,  considerable  hypothesis  even  s t a t e o f TABLETOP.  i t may  though  in  perform  then  minimal  degree  accomplish sensory  accommodated perception* cycle* world  of  model* t h e n  impression.  He  passes  control  accomplish first  the  few  retinal  the  Utak  the  the  basis  and is  given  interprets  still  task  speed  the  parts  particular to a  and be  act. high  knows  the  may the  be  current  mistaken  which  to the  planner  task.  An the  and  even  this  cycle  the  sensory  accommodate  it* world  on  i s r e c e i v e d , i n t e r p r e t e d and  by  retinal  Then  and he  model, and  initial  executed.  design  of<  assumes a d e f a u l t  impression  and  Any  action  first  an  to  must,be  first  i s decided  IV«Towards the  plan  course,  first  w h i c h makes  plan,  plan  continual  of  he  a  overall  hypothesis.  i n terms of t h i s  act  some  must  r e c e i v e s the  model t o  statement  this  This  a task  has  Utak  construct  of  is,  this  task  impression  a  there  c a r r y i n g out  acting  o p e n s h i s eye  a c t i o n s of  may  will  hypothesis.  m o d i f i e s the d e f a u l t world interprets  fact  imposed  received while  Utak  with  seem t o Utak t h a t he  the c u r r e n t hypothesis  on  planning,  When  with  been c o r r o b o r a t e d  words he  belief,  task  by  carrying  otherwise.  provided  impression  executed  associated  actual  i s an e x t e r n a l l y  the  be  between h i s h y p o t h e s i s  In o t h e r  when he seems t o know there  have  then  difference  If  act w i l l  model most r e l e v a n t t o t h i s  of confidence  whole  Each  Acting, i s simply  degrees of c o n f i d e n c e  of  degree  model.  plan  to  examining  the  Then  another  accommodated  by  of a r o b o t - c o n t r o l l e r  j  147 the world act  model, the plan modified i f necessary,  and  the  next  produced and executed. This  analogy  with  Map-in-the-Head d e s i g n . structure occurs  science  In t h i s , s p a t i a l  isomorphic t o a  when  the  constrasts  printed  map  with  and  spatial  analogy with t h e s c i e n t i f i c assumption  and  reasoning  "mind's eye" examines t h i s s t r u c t u r e .  i s , perhaps: Who draws the map?  Such a  important  of  This i s answered by t h e  method: By a process  modification*  naive  knowledge r e s i d e s i n a  proposal begs answers t o many q u e s t i o n s , the most which  a  of  hypothesis  using p a r t i a l evidence  presented  through t h e senses.  IV.2 The p a r t s of an o r g a n i s m - c o n t r o l l e r Any complete o r g a n i s m - c o n t r o l l e r f o r Otak must least  the  following  program  steps.  A l l that  i s a world model, a way to r e c e i v e a r e t i n a l  and an a c t i o n  at  These can be s t a t e d here  without s p e c i f y i n g data s t r u c t u r e s or processes. needed  contain  is  impression,  effector.  INITIALIZATION STEPS • 1.  Set the c u r r e n t world model equal  to  some  default  world  model. 2.  Receive the f i r s t r e t i n a l  3.  Analyze the r e t i n a l impression i n t o r e g i o n s and borders..  4.  Interpret identify  the  regions  impression.  in  the  retinal  impression  the image of Otak i n the r e t i n a l  impression.  and  IVaTowards the design of a r o b o t - c o n t r o l l e r  148  5.  Modify  the d e f a u l t world model to be  interpreted r e t i n a l 6.  Accept This  a task and may  consistent  i n t e r p r e t i t i n terms of the world model.,  require  in  substantial  the  current r e t i n a l  the  impression.  modification  model, f o r i n s t a n c e the a d d i t i o n of an mentioned  with  task  of the  object  if  world  one  is  but no o b j e c t i s " v i s i b l e " i n the  impression.  PLAN 7.  C o n s t r u c t a plan to achieve the  task,  usinq  the  spatial  planner. THE  ACTION CYCLE ACT • 8.  Test whether the task i s complete*, I f so, STOP.  9.  Decide  on  initial  portions  the  confidence  next a c t i o n to take, by examining the of  the  associated  plan  with  and  the  degrees  those p a r t s of the  of  world  model c l o s e to the planned a c t i o n s . 10.  Execute  the  next a c t i o n and  r e c e i v e the next  retinal  impression. PERCEIVE 11.  I n t e r p r e t the new  retinal  impression  the c u r r e n t world model, and necessary retinal  12.  to  make  it  on the  basis  of  modify the world model as  consistent  with  the: c u r r e n t  impression.,  Is the plan s t i l l  viable?  I f so go t o 8.  IVsTowards the design of a r o b o t - c o n t r o l l e r  149  13.,  O t h e r w i s e , re-compute a l l o r p a r t of the p l a n * step  The  parts  as  in  7 , and go t o 8.  of the action  cycle  correlate  with  figure  1.6  as  follows. Steps  8, 9 , 6 10 a r e c a r r i e d 11, "perceive",  Step  A  task  presented  task  two  statement  as two  g o a l world the  i s carried  12 & 13 a r e c a r r i e d  Steps  as  required world  F o r example  difference  a square  object,  between t h e s t a r t  and g o a l  of  reconcile  t h e c u r r e n t l y assumed  model  assumption  implied  behaviour  The i n t e n d e d  the  by  t o circumvent  IV. 3 The g o a l  III.2.4  sguare  (page  intended  134)  the  f o r an  world  executing  a task.  task  of  a s he c a r r i e s  starting  t o be and  models c o r r e s p o n d i n g  t h e next  world  room"  will  doorway,  statement,;  I  have only  in  the  i n step model  to  the  models b e i n g  world  a  6 i s to  with  the  make  of n a t u r a l language  this input.  organism-controller  o f some  of  the  of  task  in figure  and a f t e r  model  A detailed  models, a  default  the  s i t u a t i o n s before  how  6 i s assumed  The p r o b l e m  is illustrated  indicate  Utak  object.  the h a n d l i n g  meaning  i n step  and a c o n n e c t i n g  position  world  the  SPLAN.  the world  "Push t h e s q u a r e o b j e c t i n t o  rooms,  ACT.  o u t by ACCOM. .  o u t by  parameterized  model;  o u t by  each  Utak  statements  IV. 1. task  might  change  appears i n f i g u r e  IV«Towards the d e s i g n  shows  b u t does  s c e n a r i o of the intended  o u t one t a s k  This  of  not while  behaviour IV.2.,  It  of a r o b o t - c o n t r o l l e r  I  FIGURE IV.1  A  The meaning o f t a s k statements.  i t  "GO TO NORTH EAST CORNER"  "GO ROUND SQUARE AND RETURN"  "PUSH SQUARE OBJECT TO NORTH EAST CORNER"  "PUSH L-SHAPED OBJECT INTO NEXT ROOM"  150  151  s t a r t s with a summary on the f i r s t many  pages  of  this  page  (a),  showing  how  f i g u r e r e l a t e to executions of the  the  action  cycle* In in  the i n i t i a l TABLETOP s i t u a t i o n S-1  (b), Otak i s l o c a t e d  the area of the southwest c o r n e r , a square o b j e c t l i e s  i n the  northeast c o r n e r , and two t h i n h o r i z o n t a l o b s t a c l e s separated a s m a l l gap are i n the east h a l f of the t a b l e t o p or "room" dimensions  tabletop.  The  actual  are 40X40.  The d e f a u l t world model assumed by Otak b e f o r e opening eye  is  a  The f i r s t  sguare  room of dimensions  superimposed  on  preferred  i t . . When  this  i n t e r p r e t a t i o n i s r e c o n c i l e d with the d e f a u l t world model,  WM-1  i s obtained  interpretation  his  36X36 c e n t r e d on him ( c ) .  r e t i n a l impression i s shown i n (d) with the  line-segment  by  (e), containing a s i n g l e small object o b j e c t l .  Then  the task statement  i s r e c e i v e d ( f ) , which r e a l l y c o n s i s t s of  subtasks..  there a l r e a d y i s a square o b j e c t , o b j e c t l , i n  Since  the c u r r e n t world model WM-1, the to  square WM-1  t h i s i s immediately  o b j e c t o f the task statement*  i s r e q u i r e d by the task statement.  included,  identified  I f the statement  f o r i n s t a n c e , "go between the square.and  beyond  the  area  covered  planned i n the world model and a f i r s t The  size  by  which  had  the L-shape" in  a  the r e t i n a . . A path i s  action  decided  on  (g).  of the a c t i o n * or e q u i v a l e n t l y the d i s t a n c e t r a v e l l e d  between r e t i n a l impressions, i s p r o p o r t i o n a l t o with  as  Thus no m o d i f i c a t i o n  then an L-shaped o b j e c t would have had t o be hypothesized position  two  the  structure  of  the world  the  confidence  model i s known.. T h i s  IV«Towards the design of a r o b o t - c o n t r o l l e r  I FIGURE IV.2{a)  Executions  of the a c t i o n  cycle.  (b) I n i t i a l s i t u a t i o n S-1. (c) D e f a u l t w o r l d model ¥M-0 (d) F i r s t r e t i n a l i m p r e s s i o n RTI-1 . {e) F i r s t w o r l d model WM-1 {£•) Task s t a t e m e n t (g) F i r s t p l a n , PLAN-1, and f i r s t a c t ACT-1 (h) (i) (j)  New s i t u a t i o n S-2 Next r e t i n a l i m p r e s s i o n RTI-2 World model WM-2, p l a n PLAN-2 , a c t ACT-2  <k) S i t u a t i o n S-3 (1) R e t i n a l i m p r e s s i o n RTI-3 ,(m) World modal WH-3, completely  new  p l a n PLAN-3, a c t ACT  <.n) S i t u a t i o n S-4 (p) R e t i n a l i m p r e s s i o n RTI-4 <g) World model WM-4, p l a n PLAN-4, a c t ACT-4 (r) <s) (t)  S i t u a t i o n S-5 R e t i n a l i m p r e s s i o n RTI-5 World model WM-5, p l a n PLAN-5, a c t ACT-5  (u) iv) (w)  S i t u a t i o n S-6 R e t i n a l i m p r e s s i o n RTI-6 W o r l d modal WM-6, p l a n PL AN-6 , a c t ACT-6  '53  >  30  RO'JND THE SQOARE  OBJECT  TO  THE  SE  CORNER  > * (TA.BLETOP) * B B B B B B B B B B B B B B B B 3 B 3 B B B B B B B B B B B B B B B B B B B B 3 3 8 * B 3 * B 3 * B B * B 3 *B C C C C B * B C C C C 3 * B C C C C B * B C C C C B * 3 B * B B * B B * B B * B B * B * B * B B. * B B * B B * B B B B B B B B B B B B B B B B B B * B B * B B * B * B B * B B * B ' 3 * B * B B * B * B B * B B * B * B * B * ' . '3 * B B * B 3 * B B * B B * B B * B 3 * B * B B B B B B 3 B B B B B B B B B B B B B B B B B B B B . B B B B B B B B B B B B B B 3 0  B  8  B  B  3  B  3  FIGURE I V . 2  (c)  The d e f a u l t w o r l d m o d e l WM-O.  a  A FIGURE I V . 2  (e)  The w o r l d m o d e l WM-1 a f t e r t h e f i r s t r e t i n a l impression RTI-1 received.  FIGURE IV.2 (d)  Retinal  i  7  O o o O O SB O o o O o O  7 o  7 i  /  7  i  i m p r e s s i o n RTI-1.  o  o  o  o  ©  o  o  ©  ©  o  o  ©  o  o  O o cnnnnnan o o •••••••• o o o •••••••• 0 o •••••••E o o •••nnnnc o o o• • • • • • c n o  o o  o o o  1  i V u  7  7  7  7  7  7  7  7  7  7  7  y  7  7  7  7  i  #»»  o o  .9  ©  ©  o  o  to o  p.  o  o  © _ •  T h i s shows the gray l e v e l s r e c e i v e d by Utak's r e t i n a from the TABLETOP w o r l d . The c e n t r a l '7' i s the image o f Utak. The o v e r l a i d dashed l i n e s show the line-segment i n t e r p r e t a t i o n .  FIGURE IV.2  T h i s may  (f)  Task statement "Go round the square o b j e c t to the south-east c o r n e r " .  be t r a n s l a t e d as: " F i n d a square o b j e c t . " "Keeping the square o b j e c t on your r i g h t , to t o a p o i n t near the square o b j e c t on the s i d e away from your c u r r e n t p o s i t i o n " S t i l l keeping the square o b j e c t on your r i g h t , go from t h i s p o i n t to the s o u t h east c o r n e r . "  •  •  A  FIGURE IV.2  (g)  PLAN-1, ACT-1, superimposed on  WM-1.  The t h i c k e n e d l i n e s correspond t o the l i n e segment i n t e r p r e t a t i o n of RTI-1. The o t h e r segments forming the boundary of the t a b l e t o p a r e h y p o t h e s i z e d .  * (BOLL 9.0 E) ( T A B L E T O P ) (THLOOK) * B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B * B '* B * B * B * 3 C * B C * B * B C * B * B * B * B * B * B * B * B * B * B « 3 B B B B B B B B B * B * fl * B * B * B * * B * B * B * B * B * B * B " " * B * B * B * B * B * B * B * B * B • B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B  F I G U R E  |  V .  a (4.)  ScWfcc-n  B B B B 3 B B 3 B B B B B B C C C B C C C B C C C C B C C C B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B 3 B B 3 B B B  S-A  FIGURE IV.2 ( i ) R e t i n a l i m p r e s s i o n RTI-2  «  6  4-  i I J  4-  0 4  r i i  4 1  b  o 6  o  0  o.  o 0  *  0 '& ' -1  0  0 d « » 0 0' 0 0 0 0  o' 0 0 0° 0 !thi * 0 0 • • n n n n n n d d 0* d 0° • • • • • • a n 0° o° 0 e d d 0 0° b d 0° •••••••• d 0 6 0 6 0° 0° o 0 a 0-® 0 o 0 0° 0' 0° d d 0 d 0  0 0  ©  n  *  0  0  0 0  4  0 The p r e d i c t e d  o  O  0 0' d  0  i  o  o  0  0  A  a  0  0  6  0 0° 0 o  6  0 ©  0  i  0 0 0° 0* 0 0 0 0 6  0  o  0  g r a y l e v e l s are i n s c r i b e d i n the top r i g h t  hand c o r n e r of a l l but the f o v e a l r e t i n a l f i e l d s . The predicted  l i n e segment i n t e r p r e t a t i o n i s shown by the  o v e r l a i d dashed l i n e s a t the l e f t hand s i d e and a t r e t i n a l f i e l d ( ( o f ) . The o n l y d i f f e r e n c e between p r e d i c t e d g r a y l e v e l s occurs at  (yfl);  t h i s r e s u l t s i n a new  segment i n t e r p r e t a t i o n o v e r l a y i n g  both f i e l d s  and a c t u a l  line  (*) and (G) .  FIGURE IV.2 ( j )  World model WM-2,  w i t h PLAN-2 and ACT-2.  The p o s i t i o n and shape of o b j e c t 1 have been updated - i t i s no l o n g e r a square o b j e c t . The p r e v i o u s p l a n , PLAN-1, had t o be m o d i f i e d s l i g h t l y .  • * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  B B B B B B B B B B B B B B B B 3 B 3 B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B C C C C B B C C C C B B C C C C B B C C C C B B B B B B B B B B B B B B B B B B * B B B B B B B B B B B B B B B B 3 B B B B B B B B B B B B B B B B B B B 8 B B B B B B B B B B B " B B B B B B B B B B B  *  3  * * * * B  * B B B B 3  B B  3 B D - B B 3 B B B B B B 3 B B B B B B B B B 3 B B 3 B B 3 3 3 8 B B 3 B B  FIGURE. IV.2  o  7  (1)  o o  o e  Retinal impression RTI-3.  7  o  O  6  o 0  o o  o  o *  o a  o  o  ©  o B  o  o to  e  o  o• o  ©  ©  o  a  O  o C? a  o  o  2l  • •  O  o« o  • o  •••aaooQ •••••••• ••••••33 • • • • • • • a  e  o  o'  o  o o  o  o  o  O  o  o  «  t>  o  O  0  1  ¥• • o*>  a  t  of  • • • • • • E W o CCCC3EEn e « o o o *> c « a o o •  o  7 to  o  o  -*  o  o  6  6  o  o e  ©  o  o  O  7  o  o o  r  o o o o oo •••••••• O o«  • o  7  o  o o  o  •  ©  o  o  «  «  o  O  o  o  7  r  o  o  O  o  •  The actual gray levels d i f f e r i n several places from the predicted gray levels (in the RH corner of each f i e l d ) . The row of O's across the top forces the north verge out by four units. The 2 and 6 i n the top RH corner forces the introduction of a new object. F i n a l l y , the several differences at middle right force another change in the shape of object 1.  FIGURE IV.2 (m)  World model WM-3,  with PLAN-3 and ACT-3.  OBJECT  PLAN - *5  The north verge moved out by four units; object 2 i s new and i s square while the old object 1 can no longer be considered square; therefore, object 2 i s assumed to be the square object of the task.  Z  * >  (BOLL 3.0 2) (T&BLETOP) (THLOOK) ( 3 . 1. 570796)  • B B ' B B B B B B B B . B B B B B B B B B B B * B  - B B B B B B B B B B B B B B B B B B B B B B  * B *  B  B  B B B B B B B B B B  * B * B * B * B * B * B * B *'B * B  C C C C  '  * B *  C C C C  C C C C C C C C  •  *  B  B  B B  * B * * * *  B B B B  B  B B  * 3 * B  B B B B B B B B B B  B B B  B  * B * B * B  * * * *  3 B B B  * * *  B B B  B -B B B B B B B B B B  * 3 * B * B * B *B * B * B * B *  B B  B .  B  B B B B  B  * B B B B . B B B B B B B B B B B B B B B B B B B  F I G U R E  B B B B B  j\f.  a  gnD  B B B B B B B B B B B  ^*u.a+t*n  S-(5&  B. 3 3 B B B B B  FIGURE IV.2 (p)  7  7  1  7  e>  0  r  T  7  7  7  7  0  o  o  o  o  0  0  0  CF  a  0  •  o 0"  o  O •*  o  o  o  *  D  o  o o  O  *>  o  o o e>O • • • • • • • • o o d o« o O o 0 « o« o cf o  a  t>  O a  o  o  o  o  o  o  o  o  O  o  o  O e  o  «  o  o  o  V  •  a  •  O  7  y  o  O  o  R e t i n a l impression RTI-4.  ••: 7*  e  o  «  0  o  ao*> »> o o o  7 L 9  o o  0"  o 9  a  O  The gray l e v e l d i f f e r e n c e s on the r i g h t - h a n d s i d e f o r c e the east verge to be moved out by two u n i t s , and a new o b j e c t , o b j e c t 3, to be i n t r o d u c e d .  FIGURE IV.2 (q) World model WM-4,  w i t h PLAN-4 and ACT-4.  The e a s t verge moved out by two u n i t s ; new obj e c t 3  *  ( 1 -  * *  0  S )  3 . 1 4 1 5 9 3 )  ( T A B L E T O P ) B  *  B  *  B  *  B  B  *  B .  *  B  *  1.  ( R O L L  >  B  B  B  B  B  B  B  B  B  B  B  B  B  "  B  B  B  B  B  B  B  B  B  B  B  B  B  B  B  B  B  B  B  B  B  B  B  B  B  B  B B B  *  B B C  B  C C  C  C  C  C  B B  B  *  B  *  B  B  *  B  B  *  B  B  *  B  B  *  B  B  *  B  B  *  B  B  *  B  B  *  B  B  *  C  C  *  *  C  C  C  C  B C  C  C  B  B B  B B  B  B  B  B  B  B  B  B  B  B  B  B  B  B  B  B  *  B  B  *  B  B  *  B  B  *  B  B B  *  B  *  B  B  *  B  B  *  B  B  * 3  B  *  B  B  *  B  B  * 3  B  *  B  B  *  B  B  * 3  B  * B * B  B B  * 3  * a  *  B  * 3 • B B B B B B B B B B B B 3 B 3 B 3 3 3 B 3 B B B B B B B B B B B B B B B B B B B B B  B B  B B •  FIGURE IV.2 (s)  7  7 7  7  7  R e t i n a l i m p r e s s i o n RTI-5.  7  7  7  7  t  7  7 7* 7  ¥  7  r  7'  V  /  e  •  o  «  e  c (9  o ©  O  •  o  7  7  7  *  7  7  7  / 7 7' y 7  r  7  7 7 f » •» * 7 7 77 7  aaaEODDB  •  •  ©  o  o e o ©  o\ «  o  o  *  e  O  O  0  o  o  T  7  o  • o*  'f  «  o 0  o  7  «  •  —f~.—i  7  * 7  7 —J  7  T  i  oft i  ;o  7  \ 7  «  o  •  7  7  y  6 o  o —- • o O  7  •»  . z_ H E E E S I E O E 7« 7 « • angEnaaa o  « o  o  7  7  7*  o  b  7  7  7 7  7  7 7  Once a g a i n , the gray l e v e l d i f f e r e n c e s on the r i g h t hand s i d e f o r c e the east verge out by two u n i t s and a change i n the p o s i t i o n and shape of o b j e c t 3. The gray l e v e l s f o r o b j e c t 2 ( j u s t below c e n t r e ) were e x a c t l y as p r e d i c t e d .  FIGURE IV.2  (t)  World model WM-5,  w i t h PLAN-5  A  0  OQ36CT  i  PLAM-5  The east verge moved out by two u n i t s ; shape of o b j e c t s changed.  n o B B B B B B B B B B B B B B B B 3 B B B B B B B B B B B B B B B B B 3 B B B  * C C C C C C C C C C C C  * *  c c c. c  *  B B B B B B B B B B B B  *  *  * *  •  B  B  B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B  B  B B B 33 B B BB 077 DR = 0 3. 20, T = 0. *  PICTURE  3 B B B B BB 3 28T  B  B B B B B 3 B B B B B B B B B B B B B 3 B B B  iv\a(V) S t ^ a f t o n £-6  FIGURE I V . 2 (v) R e t i n a l i m p r e s s i o n  o o 0  o  0  o  0  o  o  2  0  o  o o 0  o  0 o  RTI-6.  O  4|  7  7  ! e • O  4j  7  7  7  7  7  7  /  7  7  -i l  7  7  7  7  Z  0 0 0 o o 0  0 0 0 7 o o o 0 7 o o o 7 •••EIHEOE 0 7 o o • • • • • • • • •44- 4- • • • • • • • • 7 • • • • • • • • 0 o •••••••• 0 7 o o o o 0 0 0 7 o o o o o 0 0 7 o  0  O  O  o  O  O  A  4 ii  The p r e d i c t e d gray l e v e l s a r e n o t shown h e r e because o n l y one d i f f e r e n c e between p r e d i c t e d and a c t u a l occurs: i n t h e Fovea a t t h e l e f t hand end o f o b j e c t 3. T h i s f o r c e s a v e r y s m a l l change i n o b j e c t 3.  FIGURE IV.2  (w)  World model  WM-6.  i V c = i t I  »  \ v \  V  The shape of o b j e c t 3 changed v e r y  slightly.  x  173 d i s t a n c e can a l s o be regarded Utak  travels,  impressions  if  one  as a measure of speed  makes  the  are r e c e i v e d at a constant  The TABLETOP s i t u a t i o n S-2  assumption  with that  which retinal  rate.  a f t e r the e x e c u t i o n of the  a c t i o n i s shown i n (h) and the new  retinal  received  g r a y l e v e l values of 2 i n the  ( i ) . The two  neighbouring  impression*  first  upper r i g h t hand s i d e are.not as p r e d i c t e d by WM-1; the  position  and  shape  of  objectl  must  be  RTI-2,  consequently changed  to  be  c o n s i s t e n t with RTI-2, while m a i n t a i n i n g c o n s i s t e n c y with RTI-1. As a r e s u l t of t h i s change o b j e c t l  i s no longer square  i s some doubt as to whether i t should s t i l l the  square o b j e c t of the task statement..  other v i s i b l e , p o t e n t i a l l y square, square  there  identified  with  There i s , however, no  o b j e c t with which the  task's  o b j e c t could be i d e n t i f e d , short of h y p o t h e s i z i n g one i n  an a r b i t r a r y p o s i t i o n beyond covered  by the r e t i n a .  the  (j).  The  original  a c t i o n i s decided The  new  s i t u a t i o n S-3  predicted  to  has been found objectl  turns  object.  plan  is  or  has  been  The  remains  new  world model i s  unchanged and  another  i s shown i n (k) and the next  retinal  (1).  retinal  o b t a i n WM-3 and the  shape  T h i s d i f f e r s c o n s i d e r a b l y from  impression.  i n t e r p r e t a t i o n s are d e r i v e d and accordingly  that  on.  i m p r e s s i o n , RTI-3, obtained the  area  Thus the known o b j e c t l i s r e t a i n e d , f o r  the moment, as the t a s k ' s square WM-2  be  and  the world  (m). of  A new the  New model  square supposed  out to be f a r from square.  line-segment WM-2  modified  object, object2, square  object  Thus the new  object2  IVnTowards the design of a r o b o t - c o n t r o l l e r  174  is  assumed to be the square  the: p o s i t i o n  of  o b j e c t of the task statement.,  the edge of the "room" i s not as expected  has t o be moved out by f o u r u n i t s . new and  plan from  Also,  The  planner i s c a l l e d  the c u r r e n t p o s i t i o n of Utak going  and  and  a  around o b j e c t 2  back to the southeast corner i s c o n s t r u c t e d . . Since t h e r e i s  a gap  between o b j e c t l  and the s i d e of the room, and  s i n c e a path  going v i a the gap should be s h o r t e r than going on the other s i d e of o b j e c t l , the new  plan goes through  Another a c t i o n i s decided situation  S-4  (n)  and  on  and  retinal  by two  results  u n i t s . . The  object  object3  presented  g r a y l e v e l of one the  it),  model  is  Wti-4  decided on and The ETI-5 of  new  (s) *  the  embedded  fours  be  in  From  consistent  as  a  were  the to  evidence assume  t o the edge of the with  the  the line-^segment  small  (q) ;  a  retina;  evidence  from  interpretation  so i n s t e a d object3 i s assumed., The new the plan remains unchanqed, and  an  world action  executed. s i t u a t i o n i s S-5  has  to  ( r ) , with new  be moved out by two  shape of o b j e c t 3 changed* (t) ,  The  retinal  impression  Again t h i s i s not q u i t e as p r e d i c t e d ; the east  room  in  (p) . .  where  side.  t h i s i n t e r p r e t a t i o n i s not c o n s i s t e n t  obtained from  RTI-4  i s interpreted  east  i n BTI-4 alone i t would  is  resulting  i n the east s i d e of the room being moved out  against  (which  executed,  hand s i d e  s m a l l t h i n o b j e c t not q u i t e extendinq  RTI-3  gap.  impression  g r a y l e v e l s of zero along the r i g h t predicted  this  and the p o s i t i o n  In the accommodated  the . plan remains the same.  The  side  world model  next s i t u a t i o n S-6  and WM-5  (u)  and  IVaTowards the design of a r o b o t - c o n t r o l l e r  175  r e t i n a l impression RTI-6 are obtained actions*  RTI-6  (v)  o b j e c t 3 which was and  the  occur*  IV.4  S-6,.  shows c l e a r l y the gap between o b j e c t l  only deduced from p r e v i o u s r e t i n a l  current  situation  after several intermediate  world  model  WM-6  (w)  impressions  correctly  Thus i n t h i s example no more  The  approach to  idea  statements  The  about  world model c o n s i s t s  the  shape  of  the  of  evidence  correctly.  between s c i e n c e  a  verge,  o b j e c t s on the t a b l e t o p , and the shapes of statement  collection  the  objects..  help determine when  to  new  what  of  a  extent  evidence  p o s i t i o n s of end-points terms  Each  i s t o have an a s s o c i a t e d degree of confidence based on c o l l e c t e d from a s e r i e s of r e t i n a l  modified  of  the p o s i t i o n s of  impressions.  degree of confidence i s to be used i n the . accommodation to  can  implementation  i s to take s e r i o u s l y the analogy  and p e r c e p t i o n *  reflects  accommodation  so the remainder of the plan w i l l be executed  A first  and  Cartesian  old  statements  i s r e c e i v e d . . The  of l i n e s  and  coordinate  other system  This process,  should  statements  spatial  be give  facts  in  c e n t r e d on Utak.  A  s p a t i a l problem i s to be solved by p r o j e c t i n g a l l or part of the world  model  onto  a  screen  —  Utak's map-in-the-head --  s o l v i n g the problem there and t r a n s l a t i n g the. s o l u t i o n plan —  back i n t o the C a r t e s i a n c o o r d i n a t e system.  there i s a world model and may  a p l a n , even though  --  then the  At a l l times  initially  these  be simple d e f a u l t s * IV«Towards the design of a r o b o t - c o n t r o l l e r  176 The'implementation of these i d e a s order  given  by  the  list  of  r e c o n c i l i n g a world model with ignored  on  the  basis  models.  a task statement,  that  Steps 1-5  I  could  for  my  purposes and a  in  the  get  was by  6,  initially  with  simple  r e g u i r e r e c o n c i l i a t i o n of  two  were accomplished and then step 7,  the  implementation of a s p a t i a l planner* c u r r e n t techniques  approached  program p a r t s i n IV.2. . Step  p a t h - f i n d i n g problems t h a t did not world  was  was  tackled.  I found  that  f o r p a t h - f i n d i n g were not r e a l l y s a t i s f a c t o r y t h a t an approach based on  skeleton  of  shape  promised  described  i n the next chapter. .  to  be  the  use  u s e f u l . ..  of  the  T h i s work i s  F i r s t I w i l l d e s c r i b e the world model.  IV. 4._1  D e f i n i t i o n of the  The nodes  data s t r u c t u r e f o r a world model c o n s i s t s of a t r e e  linked  corresponding  the  by  relations.  The  root  of the  t o the f l o o r s p a c e . . The  isolated  corresponding  objects  on  to an o b j e c t may  the o b j e c t i s complex and  the  of  t r e e i s a node  to Otak, c a l l e d $org, which has one  corresponding to  world model  son,  $floor,  sons of $ f l o o r correspond  tabletop.,  The  node  N  i n t u r n have sons i f the shape of  i s best d e s c r i b e d  in  a  hierarchical  manner. . A node corresponds to a shape on the t a b l e t o p and consisting  of  the c o n t a i n i n g r e c t a n g l e  a l i g n e d with the axes  that  contains  boundary shape as a c i r c u l a r l i s t  (the s m a l l e s t  the  shape),  is a  rectangle  the  actual  of s t r a i g h t - l i n e segments,  IV«Towards the design  list  the  of a r o b o t - c o n t r o l l e r  177  shapes of any relations any.  holes i f present, and  between t h i s node and  Each node has  between  two  i t s own  objects  a s u b l i s t c o n s i s t i n g of  i t s descendants i n the t r e e , i f  c o o r d i n a t e system,  specifies  the  and  translation  r e q u i r e d to get from the c o o r d i n a t e system of one a  other. .  r e l a t i o n i s simply  a list  the  rotation  node2's.  to  get  from  In the implementation  a  relation  and  rotation  node  to  (nodel node2 o f f s e t )  the o f f s e t i s a t r i p l e c o n s i s t i n g of the and  the  x-  nodeVs  and  the where  y-translation  c o o r d i n a t e system to  so f a r , the r o t a t i o n has  always  been zero, By s p e c i f y i n g the world model i n t h i s manner i t i s easy modify  the  world  model  motion of an o b j e c t caused to  to  r e f l e c t the motion of Utak or the  by the motion of Utak.. M l  be done i s t o modify one r e l a t i o n * .  of d e t a i l .  tabletop  shape  in  F i g u r e IV. 3 shows the world model t r e e f o r a  situation*  When  a  retinal  impression  has  r e p r e s e n t o b j e c t s or verge.  be d i s t i n g u i s h e d from so  accommodate  that  the verge  finally  (explain)  world  them.  The:  d e s c r i b e these o p e r a t i o n s  and  those  Then the o b j e c t r e g i o n s must  regions  the  impression  been r e c e i v e d i t must be  analyzed to f i n d those r e g i o n s which r e p r e s e n t space  stage  has  increasing  IV.4.2 P e r c e p t i o n : accommodation to the f i r s t r e t i n a l  which  that  This tree representation  can a l s o be used to s p e c i f y a complicated levels  to  in  model next  (steps 3,4,5  an  interpretation  can  be modified to  three:  sub-sections  of IV.2) .  IVeTowards the design of a r o b o t - c o n t r o l l e r  FIGURE IV.3  VERGE  "A  (a) A w o r l d model, drawn on the E u c l i d e a n plane.  o f f s e t - Ri\  Shape of v e r g e , w i t h c o o r d i n a t e o r i g i n A  Shape of OBI, with coordinate o r i g i n B.  Shape of 0B2, with coordinate o r i g i n C.  (b) Tree c o r r e s p o n d i n g to the world model of ( a ) .  179  2. J. Edge and r e g i o n A  region  finding  i n the r e t i n a l impression i s a connected  set of  r e t i n a l c e l l s where a l l the c e l l s have a zero g r a y l e v e l , o r e l s e a connected  a l l have a non-zero g r a y l e v e l . d e f i n e d u s i n g edge-adjacency.  s e t on the r e t i n a i s  Two c e l l s are edge  adjacent  i f  they have:an edge o r part of an edge i n common., Thus d i a g o n a l l y adjacent c e l l s are not edge adjacent. for  any  two  edge-adjacent cells  retinal  c e l l s i n t h e r e g i o n , there i s a c h a i n o f  r e t i n a l c e l l s which s t a r t s a t  and f i n i s h e s at the other.  the  border  in this  one  with  a  non-zero  direction,  would  of  given  graylevel  would  crawling  always f i n d the boundary  of a  be t r a v e r s e d by the  t u r t l e i n a clockwise d i r e c t i o n and any other boundary hole)  the  such t h a t a t u r t l e ,  non-zero r e g i o n on i t s r i g h t . , Thus the (outer) region  of  The border between two r e g i o n s  has a d i r e c t i o n a s s o c i a t e d with i t , along  a r e g i o n i s connected i f ,  (i.e. a  the r e g i o n would be t r a v e r s e d i n a c o u n t e r - c l o c k w i s e  direction* The  b a s i c b u i l d i n g block f o r f i n d i n g the edges of a r e g i o n  i s the " i n t e r - c e l l - e d g e " of  retinal  cells  (ICE) which i s created between any p a i r  where  the  g r a y l e v e l of one i s zero and the  g r a y l e v e l of the other i s non-zero* , a f i r s t impression  produces  a l l the  connected  scan  of the r e t i n a l  r e g i o n s and marks the  p o s i t i o n of each ICE with a data s t r u c t u r e l i n k e d t o each member c e l l of t h e ICE. The next o p e r a t i o n l i n k s the ICEs of one r e g i o n i n t o one or more  disjoint  circuits..  Since more i n f o r m a t i o n i s needed f o r  IV«Towards the design of a r o b o t - c o n t r o l l e r  180 l a t e r grouping  operations,  when  an  ICE  i s being,  traversed  several  e x t r a p i e c e s of i n f o r m a t i o n are added: the d i r e c t i o n of  traverse  (N E S W), the g r a y l e v e l s of the c e l l s of the ICE, and  the  s i z e s of these c e l l s , the r e s u l t being c a l l e d a chunk.  l a s t two items the world  are needed l a t e r as evidence  model.  The  f o r t h e segments  of  Some ICEs l i e along the edge of the r e t i n a and  s p e c i a l chunks have to be used. The  linking  i s done by t a k i n g one ICE a s s o c i a t e d with the  r e g i o n i n question and i t e r a t i v e l y  f i n d i n g i t s successors  using  the geometry of the r e t i n a l impression u n t i l a c l o s e d c i r c u i t i s formed.  I f an ICE a s s o c i a t e d  with  the  region  still  remains  c i r c u i t i s started.  This i s  unlinked  i n a c i r c u i t then another  continued  u n t i l a l l the ICEs are exhausted.  Next,  a grouping  o p e r a t o r t r a v e r s e s each c h u n k - c i r c u i t and  groups c o n s e c u t i v e chunks having a segment,  pt2 d i r n l e n type  evidence)  p t 1 , p t 2 , d i r n , l e n , s p e c i f y the endpts,  t o t a l l e n g t h r e s p e c t i v e l y of a s t r a i g h t EXTERIOR  d i r e c t i o n , and  l i n e segment.  "Evidence"  is  the a  retina  list  or  of pairs  i s interior  the  retina.  (graylevels cell-sizes)  derived  from the component chunks, shortened The  to  by grouping  identical  is  intended  pairs  meaning of "evidence" here i s how well the l i n e  segment was defined by the g r a y l e v e l s i n the r e t i n a l It  "Type" i s  or INTERIOR depending on whether the segment c o i n c i d e s  with an edge o f  together;  into  A segment i s a l i s t (pt1  where  the same compass-direction  to  provide  restrictions  on  how  impression. much  the  IVaTowards the design of a r o b o t - c o n t r o l l e r  181 parameters of t h i s l i n e segment could be changed t o subsequent the  retinal  current  operation  impressions  retinal  is a  without  impression..  accommodate  losing consistency  The  end  result  every  lines  that  right-handed  This  is  also  turtle  known  turns  r e t i n a i s found.  list  regions,  for  a  f o r every  left-handed  counter-clockwise  At  traverse. In  one  i s t r a v e r s e d once and the  the  same time, the maximum  segments t h a t c o i n c i d e with  an edge of the  T h i s i s c a l l e d "max-resegs" below. of the edge and  where . each  borders.  a  border  is  segment-circuit, turtle-turns,  corresponds t o f l o o r s p a c e * and  has  on  i t s p-list  a b o r d e r - l i s t of one p-list  with  max-resegs, and  IV.4.2.2 I n t e r p r e t i n g the f i r s t the fovea of the eye  r e g i o n f i n d i n g stage i s  region  and  In  of  counts 1 f o r  as the T o t a l T u r t l e T r i p theorem;.  g r l - c l a s s , number of sguares, Each  circuit  i t s e l f and  counts -1  computed.  f i n a l output  of  crosses  each s e g m e n t - c i r c u i t  number of consecutive  The  this  of the t r i p the t o t a l w i l l be e i t h e r 4 f o r  t r a v e r s e or -4  f i n a l operation* total  nowhere  90° t u r n and  90° t u r n . . At the end a clockwise  of  segment-circuit.  Suppose a t u r t l e t r a v e r s e s an a r b i t r a r y c l o s e d straight  with  or  properties their  a the  more name,  values..  r e t i n a l impression -  a r e t i n a l c e l l with a cell  with  zero g r a y l e v e l  non-zero  graylevel,  n e c e s s a r i l y 7, corresponds to e i t h e r an o b j e c t , the verge, or to Utak h i m s e l f . with  zero  r  In the p e r i p h e r a l p a r t s of the eye  graylevel  may  correspond  a retinal  to an area of the  cell  tabletop  IV«Towards the design of a r o b o t - c o n t r o l l e r  182 which i s not e n t i r e l y graylevel  of  7 may  floorspace, correspond  and  similarly  one  with  a  to an area of t h e ; t a b l e t o p which  i s not e n t i r e l y o b j e c t or boundary. „ In any are  one r e t i n a l impression  interpreted  connected,  as  i f two  the r e g i o n s of zero g r a y l e v e l  floorspace;.  Since  or more disconnected  all  floorspace  is  regions of zero g r a y l e v e l  appear i n the r e t i n a l impression the i n t e r p r e t a t i o n must p r o v i d e that  these are connected*  I f a l l the f l o o r s p a c e r e g i o n s have a  segment c o i n c i d e n t with an edge of the needs  to be done; i t i s assumed t h a t they are  the area of the t a b l e t o p covered one  retina  of  the  surrounded passage  two  or  more  no  action  connected.outside  by the r e t i n a l i m p r e s s i o n .  floorspace  regions  is  If  completely  i n the r e t i n a l impression by a non-zero r e g i o n then a  must  be hypothesized  r e g i o n and the  nearest  natural  to  place  i t s l e n g t h to a between  then  two  between the surrounded  neighbouring  hypothesize  minimum,  is  region.  The  such a passage, i n order to keep the  floorspace regions.  can e a s i l y be found  floorspace  floorspace  line  of  shortest  distance  T h i s l i n e of s h o r t e s t d i s t a n c e  from the s k e l e t o n of the complement  of  the  f l o o r s p a c e r e g i o n s ; t h i s w i l l be d e s c r i b e d i n s e c t i o n V.4.2.. The  non-zero r e g i o n s are  objects  or  verge.  the  surrounded  verge  surrounds  as  either  T h i s i s s t r a i g h t f o r w a r d i n two  non-zero r e g i o n completely itself  interpreted  surrounds  isolated  cases.. I f a  a zero r e g i o n , and  is  not  by a zero r e g i o n , then t h i s i s i n t e r p r e t e d as  of  the  tabletop,;  a  non-zero  region  If  a  zero  region  completely  then  this  latter  region  is  IVaTowards the design of a r o b o t - c o n t r o l l e r  183 interpreted  as  an  isolated  object  with  a  high  degree  of  I f n e i t h e r of these two cases holds then the max-resegs  of  certainty.  the  outer  boundary  of  the non-zero r e g i o n  with t u r t l e - t u r n s = 4 ) i s examined.  (the unigue  Remember  that  border  "max-resegs"  records the maximum number of c o n s e c u t i v e segments of the border of  the r e g i o n t h a t c o i n c i d e with edges of the  value  is  If i t s  z e r o , one or two then the r e g i o n i s i n t e r p r e t e d as an  i s o l a t e d o b j e c t , otherwise  as p a r t of the  i l l u s t r a t e s t h i s i n t e r p r e t a t i o n scheme. in  retina..  t h i s way i s s u b j e c t  to  revision  subseguent r e t i n a l impressions  or  verge..  Figure  IV.4  Any i n t e r p r e t a t i o n made a  are r e c e i v e d .  "double-take" A region  when  initially  i n t e r p r e t e d as an i s o l a t e d o b j e c t may l a t e r t u r n out t o be correctly  i n t e r p r e t e d as boundary, and v i c e versa.  i l l u s t r a t e s a p o s s i b l e double  more  F i g u r e IV.5  take.  IV.4.2.3 Accommodating the d e f a u l t world model to the f i r s t retinal  impression  The d e f a u l t world model with which Otak "wakes up" simplest  p o s s i b l e : a square  has  must be m o d i f i e d retinal  After  the  first  retinal  been r e c e i v e d and i n t e r p r e t e d , t h i s world (accommodated)  to  be  consistent  with  model this  impression.  F i r s t the i n t e r p r e t e d r e t i n a l impression what  the  f l o o r s p a c e centred on h i s p o s i t i o n ,  and c o n t a i n i n g no i s o l a t e d o b j e c t s . , impression  is  restrictions,  is  i f any, the r e t i n a l impression  examined  for  places on the  IVaTowards the design of a r o b o t - c o n t r o l l e r  FIGURE IV.4  Examples o f . r e g i o n  interpretation.  Max-resegs = 2 ISOLATED OBJECT  Max-resegs = 3 Verge  Max - r e s e g s = 4 Verge  FIGURE IV.5  A doubletake.  In t h i s i n i t i a l p o s i t i o n the robot t h i n k s i t i s c l o s e to the n o r t h edge of i t s environment.  What the robot p r e v i o u s l y thought was verge i s r e - i n t e r p r e t e d as p a r t of an i s o l a t e d object.  186  a c t u a l d i m e n s i o n s of the  world  model.  impression and  c o n s i s t s of  the  retinal  $floor's  a type.  restriction  impression;  conseguently the  rectangle  a  I f the  segment  coincides  consequently  W  type  an  edge  of  of  this  $org-$floor  offset,  containing  rectangle  these r e t i n a l  value  of  initially of  restrictions  given  beyond  and  modified  a  by  the  to  the  side  of  value  of  restriction  of  and  The  sides  $ f l o o r , are as  region  containing  further  the  is  impression;  the  (i*e;,  or  segment  this  restriction.  (0,0,0), default  by  retinal  side  the  INTERIOR  of a f l o o r s p a c e  the  this  rectangle,  be  p o s i t i o n of  of  retinal  which i s i n t e r i o r  boundary  $ f l o o r must l i e a t o r the  may  i s defined  region  $floor  from the  i s EXTERIOR, t h e  the  position  than)  type  $ f l o o r must be  of  with  the  rectangle:of  of  the  containing  The  a floorspace  by  or  and  of  i s computed  boundary of  defined  S,  a value  restriction.  which  rectangle  restriction  I f INTERIOR, t h e  the:containing this  One  containing  f o r each s i d e o f t h e  EXTERIOR. of  the  N,  E,  default of  the  compared  with  necessary to  satisfy  them* Now the  that  $floor  computed. $floor. regions whole o f  the is  The If  fixed, next  none  coincide  of  with  is the  parts to  a retinal within  only  and  containing of  the  derive  the  rectangle  world  model can  actual  shape  s e g m e n t s of b o u n d a r i e s o f  floorspace  Otherwise,  origin  other  item  $ f l o o r appeared  boundaries of the $floor.  coordinate  edge, the  regions  or  retinal are  parts of the  IVnTowards t h e  in  shape  as of  the  be of  floorspace words  impression,  taken  design  other  of  the  then  the  shape  of  $ f l o o r appeared  of a r o b o t - c o n t r o l l e r  187  w i t h i n the r e t i n a l segments lie  of  boundaries  strictly  segment  impression.  within  sequences  segment c i r c u i t  of  rectangle,  have  current to  be  retinal linked  impression..  sequence  are  extended  to  edges  of  the  containing  the c o n t a i n i n g  r e c t a n g l e are i n t r o d u c e d  p a i r o f segment sequences*  The shape of $ f l o o r i s then  o f the r e t i n a l impression,  of  also  marked  complete. isolated-object  and added t o the world  model.  rectangle,  the  i t s c o o r d i n a t e system from $ f l o o r , and i t s shape are  a l l computed. to  existing  to these segments.. Second, h y p o t h e t i c a l segments  an i s o l a t e d - o b j e c t r e g i o n , i t s c o n t a i n i n g  offset  These  up i n t o one continuous  L a s t l y , a node has t o be c r e a t e d f o r each  Given  which  new h y p o t h e t i c a l segments. . F i r s t t h e end  between each c o n s e c u t i v e  region  of  with the e x t e n s i o n s marked as "HYPO" i n the evidence  the  "HYPO",  the: sequences  by c r e a t i n g h y p o t h e t i c a l e x t e n s i o n s t o  each  l i s t s attached along  are  o f r e g i o n s i n t e r p r e t e d as verge,  the  segments and by adding segments  These  the f i r s t  The d e f a u l t world retinal  model has now been accommodated  impression.  IV.4.3 P e r c e p t i o n ; accommodation to - subsequent  retinal  im p r e s s i o n s Once interprets the  a  world  model  has  been c o n s t r u c t e d t h a t c o r r e c t l y  ("explains" i n the analogy  retinal  impressions  received  with so  scientific  f a r , i t i s used  f a c i l i t a t e the accommodation of subsequent r e t i n a l An  overall  view  of  this  accommodation  method)  process  to  impressions. w i l l now be  IV»Towards the design of a r o b o t ^ c o n t r o l l e r  188  described. is  Given the decided-on a c t i o n , a p r e d i c t e d  constructed,  and from t h i s  world model  a p r e d i c t e d r e t i n a l impression  produced by p r o j e c t i n g the p r e d i c t e d  world model onto  structure  with  topologically  T h i s r e t i n a l impression in  identical  a retinal  array  impression.  d i f f e r s from a normal r e t i n a l  impression  t h a t every r e t i n a l c e l l has a p o i n t e r back t o the segment(s)  of the  world  graylevel* impression the  model After  which the  caused  action  i t to  is  have  its  i s compared with the p r e d i c t e d r e t i n a l  differences  between  the  accommodate  the new  retinal  two  used  relation  (r,9)  POSHTO(v) relation (s,$)  If  and  the  is  impression  and  to i n d i c a t e what  line  world model  by  relation  by  (r-v,e).  by (r-v,9)  the  (s+v,<J»). becomes  impression  predicted  is  computed  shape of the f l o o r , model  is  traced  is  If  constructed $org-$floor  the  then the  action  is  $org-$floor  I f the a c t i o n i s TURN(<t) then the (r,6-fr)  and  if  world as  model  follows.  a  the  retinal  Otak  becomes  is  holding  (s,<t> + $) .  predicted  retinal  Each line.segment i n the  verge, or an o b j e c t of the across  to  and the $ f l o o r - $ o b j e c t i r e l a t i o n  $ o b j e c t i then the $ f l o o r - $ o b j e c t i r e l a t i o n From  modified  i s SLIDE (v) then the  the o b j e c t held i s o b j e c t i ,  i s replaced  $org-$floor  action  replaced  i s replaced  retinal  impression.  Given an a c t i o n , the p r e d i c t e d follows..  assigned  executed the a c t u a l  segments and what p a r t s of the world model must be  as  an  is  predicted  world  f i e l d s of the eye and a  p o i n t e r i s s e t from each r e t i n a l f i e l d  i n t e r s e c t e d back  intersecting  c e l l not i n t e r s e c t e d by a  segment.  Any  retinal  IVaTowards the design  to  the  of a r o b o t - c o n t r o l l e r  189 segment o f the border of an o b j e c t the.  object  i s l a b e l l e d by  which e n c l o s e s i t , i f any, and given  the  of  a g r a y l e v e l of  7, e l s e i t i s assumed to be p a r t of $ f l o o r and given of  name  a graylevel  zero. The  next step i s t o compare the g r a y l e v e l s of the p r e d i c t e d  retinal  impression  cell-by-cell,  and  immmediately  focus  and note  the  any  attention  actual  retinal  impression,  The  differences  differences*  on those parts o f the world model  t h a t must be changed.. Some d i f f e r e n c e s can be.accounted f o r changing  the  others require region  parameters  of  by  l i n e segments i n t h e world model;  more d r a s t i c a c t i o n . . For example i f a  non-zero  i n the a c t u a l r e t i n a l impression has no o v e r l a p  with any  non-zero r e g i o n i n the p r e d i c t e d  r e t i n a l impression, then i t has  to be i n t e r p r e t e d and added to the world model as a new i s o l a t e d o b j e c t i n j u s t the.same way as a s i m i l a r retinal model.  impression  i n the  first  i s acommodated by the i n i t i a l d e f a u l t  world  T h i s , i n o u t l i n e , i s the accommodation  In is  a " r e a l i s t i c " simulation  a c t u a l and p r e d i c t e d  process.  where an element of randomness  allowed i n the e f f e c t of an a c t i o n  the;  region  the  differences  between  r e t i n a l impressions may a r i s e from two  sources o f u n c e r t a i n t y : (1)  New p a r t s of the environment coming i n t o view or o l d  parts  seen at higher r e s o l u t i o n ; (2) If  The a c t i o n i s not as p r e d i c t e d . only  (1) i s allowed then any d i f f e r e n c e s must be e x p l a i n e d by  modifying  the  world model;  I f only  (2) i s allowed the problem  IVsTowards the design of a r o b o t - c o n t r o l l e r  190 i s t o r e c o g n i z e what p o s i t i o n i n the world model c o u l d g i v e r i s e to  the  a c t u a l r e t i n a l impression and thus deduce what a c t u a l l y  happened., Since t h e d i f f e r e n c e between the a c t u a l and p r e d i c t e d e f f e c t s o f an a c t i o n w i l l normally be q u i t e small the problem i s one  of  computing  impressions,  the  say  by  disparity trying  If  the  between  the  the  positions  difference  two  retinal  closest  i s too  to the  predicted  position.  disparity  t o be found then i t becomes a pure r e c o g n i t i o n problem  t o be approached, s a y , by matching f e a t u r e s . (2)  occur  together  proposing  a  new  position,  model t o e x p l a i n the remaining impression.  Although  have not attempted  modify  problem  of  the  approach  necessary  impression, t o  to  be  consistent  with  it.  first  process i n t e r p r e t s the r e t i n a l impression, regarded  structured line  array  segments.  locally,  the  The line  continuous l i n e s . lines  with  of  many  retinal  i n c o r p o r a t e d i n my system, I  i s , given the c u r r e n t r e t i n a l  can  impression,  possiblity.  the c u r r e n t world model as This  (1) and  a match i n the  retinal  unmatched p a r t s  t o handle t h i s  for a  and then modifying the world  (2) i s e a s i l y  i.T»H»!i Accommodation, another The  both  then the problem i s t o f i n d  world model f o r as much as p o s s i b l e o f the thus  If  great  be broken down i n t o three processes.  The as  a  g r a y l e v e l s , as a c o n s i s t e n t c o l l e c t i o n o f adjective  segments Moreover changes  'consistent'  implies  that,  make sense or i n o t h e r words form straight of  lines  direction.  are  preferred  The: next  to  process  IV-Towards the design of a r o b o t - c o n t r o l l e r  191 interprets  the  (partial) third a  lines  contours  as  the  of the verge or of an i s o l a t e d o b j e c t .  The  process extends  complete  formed  world  more  follows. 7  model.„  detail,  line  segments  The  one  the  last  two  processes  as  the  are  i s harder..  first  process  can be d e s c r i b e d as  In the fovea the g r a y l e v e l of a r e t i n a l  according  not.  the  these contours by r u l e s of c o n t i n u a t i o n to  s t r a i g h t - f o r w a r d , the f i r s t In  by  field  is 0  or  c o r r e s p o n d i n g TABLE square i s occupied or  T r i v i a l l y , a l i n e segment i s i n s e r t e d between each p a i r of  adjacent c e l l s with d i f f e r i n g  g r a y l e v e l s . , In the middle p a r t of  the  which  retina  the  0,2,4,6,7.  graylevels  Each  graylevel  has  can  a distinct  i n t e r p r e t a t i o n s where an i n t e r p r e t a t i o n occupied  and  vacant  qraylevels 0 , 1 , 7 of  a  graylevel  sguares.  actually  squares.  is  In  the  occur  are  c l a s s of p o t e n t i a l a  2X2  pattern  periphery  all  the  can occur and the p o t e n t i a l i n t e r p r e t a t i o n s are  specified  Each assignment  by  c l a s s e s of 4X4  of a l i n e segment to a  must be c o n s i s t e n t with the assignements  p a t t e r n s of  retinal  of neighbouring  field retinal  f i e l d s , such t h a t the l i n e segments c o n s t i t u t e . a continuous and  preferably  problem tackled  of  of  a  finding  straight line. a  consistent  line  Thus t h i s f i r s t  process i s a  interpretation  and  can  be  by the NC c o n s i s t e n c y a l g o r i t h m of [Mackworth, 1977 ], by  the r e l a x a t i o n a l g o r i t h m s backtracking  algorithms  of of  [ Zucker,  19771],  [ Gaschnig, 1 978 ij.  or  the The  improved latter  two  p r o c e s s e s , l i n e segment i n t e r p r e t a t i o n and c o n t i n u a t i o n , can  be  handled as before. IV«Towards t h e . d e s i g n of a r o b o t - c o n t r o l l e r  192 IV. 4. 5 The  spatial  This  is  planner  the  heart  of  p a t h - f i n d i n g i s done, where a constructed  and  the  plan  system;. for  This  moving  is  an  where  object  where the i n i t i a l task command i s i n t e r p r e t e d .  Given an i n t e r p r e t e d task d e s c r i p t i o n , the s p a t i a l planner the  c u r r e n t world  model as a database and  plan as output.  I f the c u r r e n t world  world"  the  outside  organism  models c l o s e l y enough those for  model r e f l e c t s  p a r t s of the  spatial  planner  array.  the north  world  window  model  execution  of the  v i a the screen*  a simple  east corner" f o r example.  rectangular Utak and  Consider  the  "real least  required  of the  plan  task;  does not produce plans from the  model d i r e c t l y , but i n d i r e c t l y digital  world  accurate  w i l l r e s u l t i n the s u c c e s s f u l completion  uses  produces a s t r u c t u r e d  s u f f i c e n t l y c l o s e l y , or at  t h i s t a s k , then a completely  The  a  world  2-dimensional  p a t h f i n d i n g problem, "Go F i r s t the dimensions  the p o s i t i o n of the d e s t i n a t i o n are computed.. Then the  name  algorithm  of  the  i s used  destination  that  object  ovarlaying  (cf* chapter only  where  two  with  start  to  t r a v e r s e s c e l l s r e p r e s e n t i n g space., I f  adjacent  paths  are  considered.  These  squares of the a r r a y are marked  names of d i f f e r e n t o b j e c t s or is  and  i t . . Then a p a t h f i n d i n g  5) to f i n d a path from  t h i s f a i l s then other p o t e n t i a l  screen  a  which i n c l u d e s both the c u r r e n t p o s i t i o n of  model i s p r o j e c t e d through t h i s window onto the screen  arise  to  of  each square of the screen marked as r e p r e s e n t i n g space: or the  is  where  a  marked with the names of two  single  sguare  or more o b j e c t s .  of  with the These  IV»Towards the design of a r o b o t - c o n t r o l l e r  193  p o s i t i o n s can and,  where  be used t o t r a c e p o s s i b l e such a p o s i t i o n i s adjacent  space, to connect up through  space*  these  possible  I f the path between two  includes  only  the world  model i s p r o j e c t e d onto the  the  the  path  between  t o squares  paths  more d e t a i l then a s m a l l r e c t a n g u l a r  of  paths  at  a  i n c l u d e d as a more d e t a i l e d  subpath  other  paths  objects i s required in  window  higher  representing  with  is  selected  p o t e n t i a l passage between the  traced  objects  that  o b j e c t s . . Then  screen again  and t h i s p a r t  resolution.  The  in  the  result i s  previous  coarser  path*  IV. 5 An - a l t e r n a t i v e approach to The  implementation  implementation sketched above uses a r e p r e s e n t a t i o n  the world model based on the use of then  computes,  via  projection  Cartesian  represent  routes i n the environment.  terms of routes has  been used by Kuipers  representation  large-scale  of  coordinates  The  A representation  to  (city)  edges o f t h i s  model  a  space, and  representation that  then,  is  to  use  the  f o r the world model*  the: complete  skeleton  of  skeleton  T h i s depends a  shape,  The as on  original  shape  in  its  entirety.  IV»Towards the design  The  and  natural  the  basic  the  consisting  s k e l e t a l graph plus the quench f u n c t i o n , can be used to the  in  person's  by Arbib  L i e b l i c h t o model a r a t ' s r e p r e s e n t a t i o n of space. suggestion,  and  onto a screen, the s k e l e t o n , a  g r a p h - l i k e r e p r e s e n t a t i o n of the world model* graph  for  fact of  the  recover  world model then  of a r o b o t - c o n t r o l l e r  194  c o n s i s t s of a graph, environment,  whose edges r e p r e s e n t  together  with  a  routes  through  the  quench f u n c t i o n defined on each  edge.  P a t h f i n d i n g i s done d i r e c t l y on t h i s graph.  One  carry  out p e r c e p t i o n i s t o regenerate the o r i g i n a l shape i n the  p r e d i c t e d r e t i n a l impression and then match i t with retinal  impression.  Any  shape  changes  r e t i n a l impression a r e r e f l e c t e d graph  or  the guench f u n c t i o n .  in  the  to  actual  f o r c e d by the a c t u a l  changes  to  the  skeletal  A l t e r n a t i v e l y , i n s t e a d of doing  matching on shapes, matching can be done on the  way  graphs.  That i s ,  s k e l e t o n of the spaces on the r e t i n a i s matched a g a i n s t the  s t o r e d s k e l e t o n and changes made as a p p r o p r i a t e  to  the  stored  skeleton.  IV.6 Summary The  design  importance first  of  progress  the  f o r my p r o j e c t ;  approach  process  of  that  I  perception  made  whole o r g a n i s m - c o n t r o l l e r i s of major I  described  took, based and  the  i n implementing  i s meant by the phrase  of the world "assigning  a  feature  the  between the  method,  and t h e  i t . There a r e two o u t s t a n d i n g One  i s defining  " c o l l e c t i n g evidence  exactly  f o r a feature  model", and the other i s d e f i n i n g a phrase such  the evidence". each  chapter  on the analogy  scientific  problems inherent i n t h i s approach. what  in this  as  degree of confidence to a f e a t u r e on the b a s i s o f I approached t h e f i r s t both  the  graylevel  problem by r e t a i n i n g  with  values i n the r e t i n a and the  IV«Towards the.design of a r o b o t - c o n t r o l l e r  195  retinal field derived..  s i z e s , from  In  line  with  which the  the  feature  analogy,  f e a t u r e e x p l a i n s the g r a y l e v e l v a l u e s " .  one  parameters  were  can say that "the  The problem  of d e f i n i n g  a measure o f c o n f i d e n c e , showing how i t changes with the r e c e i p t of new evidence, and using the c o n f i d e n c e values to c o n t r o l the  how  f e a t u r e s are allowed t o change when new evidence shows that  a change must be made, i s an important and  interesting  that  of  must  be  solved  p o s s i b l e . . T h i s problem  before  completion  bears comparison  There  depends upon the evidence is  one  major  d e s c r i b e d , namely a l g o r i t h m s  project i s  with the l e g a l  of evidence i n a c o u r t of law, where the degree a statement  this  problem  problem  of c o n f i d e n c e i n  presented.  requirement  that  f o r pathfinding  remains and  to  be  f o r making  plans f o r moving an o b j e c t .  IV-Towards the design of a r o b o t ^ c o n t r o l l e r  196  CHAPTER - V PATH-FINDING AND THE SKELETON OF A PLANAR  The  purposes of t h i s chapter  algorithms,  to  motivate  path-finding, t o introduce skeleton,  are  the a new  of  problem i s t h i s ;  Euclidean  the: skeleton  for  f o r computing  the  algorithms  Given a d e s c r i p t i o n of shapes on the  plane i n terms of the C a r t e s i a n c o o r d i n a t e s  the boundaries of the shapes and the l i n e s  given the c o o r d i n a t e s shapes,  of two p o i n t s S  and  be  reasonably  Further close  of  D  outside  a l l the  a l l the shapes,  requirements a r e t h a t to  being  optimal,  the  movement  in a cluttered  obstacles;  was i n c o r p o r a t e d  T h i s was based on the  space an optimal  of a sequence of l i n e  to be  path.  p a t h - f i n d i n g algorithm  Shakey [ N i l s s o n , 1 9 6 9 J .  due  or to avoid a s m a l l o b s t a c l e , i t should  easy t o r e g a i n the c o r r e c t A  path  and that i f an  organism wanders s l i g h t l y from the c o r r e c t path, e i t h e r inaccurate  points  between them, and  d e s c r i b e a path from S to D that avoids  such a path e x i s t s .  should  path-finding  and t o apply t h e s k e l e t o n t o p a t h - f i n d i n g .  The  if  use  review  algorithm  1-1 I n t r o d u c t i o n to p a t h - f i n d i n g  on  to  SHAPE  segments  observation  that  path between two p o i n t s c o n s i s t s connecting  Thus one s t a r t s with the extreme VaPath-finding  i n the design of  extreme  points  of  (convex) p o i n t s on  and the s k e l e t o n of a planar  shape  197 the o b s t a c l e boundaries and lines  joining  the  c o n s i d e r s the set c o n s i s t i n g of  p a i r s of extreme p o i n t s together  from the s t a r t i n g point S to the extreme points and from  the  extreme  represent  i s then used to f i n d the  p o i n t s connected by l i n e s of v i s i b i l i t y  Cartesian  approach  the  obtained  it of  SD.  The The  Otherwise and  defined  but  There are now  two  situation. series  of  using  a  z e r o ' t h order first  order  the approach  approximation  was  Determine those shapes i n t e r s e c t e d by line  SD  is  the  follows.  candidate  to S,  L1, R1 are the l e f t m o s t *  points  respectively  SD,  required  the  L2,  R2  call  periphery rightmost are  the  of B as seen from  paths a t the f i r s t  I was  approximation  compute four p o i n t s L1,R1,L2,R2 on  leftmost  remaining  still  T h i s was  p o i n t s r e s p e c t i v e l y of B as seen from S, while rightmost,  line  D.  p i c k the o b s t r u c t i n g shape nearest  as  lines  by [ Thomson, 19771] f o r the  robot..  I f none, then the s t r a i g h t  B say, B  line  as f o l l o w s .  i f any.  used  module of the JPL  took to the problem* straight  path.  was  optimal  from S to  path-finding,  representation,  path planning first  to  i n the  lines  Any  so t h a t the  a l l the " l i n e s of v i s i b i l i t y "  A h e u r i s t i c search  Another  with  p o i n t s to the d e s t i n a t i o n p o i n t D.  which i n t e r s e c t s an o b s t a c l e i s d i s c a r d e d , lines  with  the  order  D.  level  of  not  to  r e c u r s i v e l y apply  the  approximation:  where the intersect  P11  = SL1  + L1L2  +  L2D  P12  = SR1  • R1R2  +  R2D  path segments SL1, o b j e c t B..  See  L2D,  SR1,  f i g u r e V.I.  V«Path-finding and  R2D Now  are  known  the s k e l e t o n of a planar  shape  AN/ 0/o(*  APP<*OJ\cH  To  ?«VTH-  199 above procedure t o each of the R1R2,  R2D.  SL1,  E v e n t u a l l y the procedure stops  f i n i t e number of o b j e c t s and the  segments  boundary  of  each  only a f i n i t e  object,  p o s s i b l e paths.  Each path can  length,  number  of  best one  chosen.  The  with  L1L2,  L2D,  , t h e r e being number of  a  SR1,  perhaps  be evaluated  in  only a  points  on  long l i s t  terms  of  of  total  segments, t o t a l angle turned,  e t c . , and  the  disadvantages o f t h i s d i r e c t  approach  to  the path f i n d i n g problem are the f o l l o w i n g * A)  I t i n v o l v e s f i n d i n g the i n t e r s e c t i o n s with  every  object  and  finding  objects intersected, altogether  of  particular  extreme  points  lines  of those  an expensive computation  in  some cases. b)  There i s no n o t i o n of " l e v e l of whatever  size  detail"*  are considered*  boundary o f a shape have  to  and  be  objects  of  a l l l i n e s which form  the  scanned  All  for  intersection  finding. c)  There i s no obvious way  An  advantage  of  this  to g e n e r a l i z e to o b j e c t moving.  approach  d e s c r i p t i o n of a path i n  is  "left-of  that  object",  it  can  produce  "right-of  a  object"  terms. Another rectangular example, and  idea network  convert  graph-traversal inserting  is  to of the  problem.  project cells,  the  all  screen  path-finding The  screen  the  shapes  of chapter  problem  i s converted  between every p a i r of adjacent  into  a  IV f o r a  pure  to a graph by  or d i a g o n a l l y  c e l l s an edge of the graph, where each edge i s assigned V«Path-finding and  onto  adjacent a length  the s k e l e t o n of a planar  shape  200  of r o o t 2  or  adjacent cells  one  or  not.  that  do  destination The S  D  application  p a t h s . .. F o r cell and  n> h(p)  finds from  the  edges o f t h i s A*  i s the  sum  optimal  path  generalize objects  a s e c t i o n of the  between  topologically  search  process  choices*  As  independence",  witness  figure  In  V.2.  using  search  goes s t r a i g h t  fills  up  until  t o w a r d s D.  considered.  The  only  the  skeleton initial  the  be  bottom it  the  of  directly,  also  at  a  S to  n  obvious  suffers way  to  to discover  distinction  In a d d i t i o n the "knowledge  actual  independent"  what I mean by  phenomenon  what  "knowledge  illustrated  search  t o go  from  of the  bucket and  S to  and  D,  in the  gradually  r a p i d l y advances  occur*  of the  attraction  topologically  V « P a t h - f i n d i n g and  no  S  algorithm but  between; no  overflows  an  incomplete  e d g e s from  e a s y way  number o f  bucket  from  done by  n t o D,. . T h i s  paths.  heuristic  can  of  i s passing  example  graph.  [ Hart,Nilsson*  include:  distinct  suddenly  the  T h i s can  graph  moving; no  path  t o the  Worse c a s e s  Finally  contains  These  extreme  D of the  to and  currently terminates  from  through the  i n v o l v e s a high an  start  s h o r t e s t path  of  lengths  distance  to handle.object  The  S and  the  graph.  p that  of the  some d i s a d v a n t a g e s .  diagonally  f u n c t i o n f=g+h t o e v a l u a t e  path  Euclidean  find  algorithm  their  incomplete  i s the  the  r e s t a t e d as:  the  are  to t r a v e r s e edges l e a d i n g  mapped o n t o c e l l s  be  using  an  g(p)  are  endpoints  floorspace.  now  of  Raphael, 1 967 i],  its  represent  points  along  as  I t i s forbidden  not  problem can to  according  shape o f t h e  empty  was  skeletal  t h a t the  distinct  the  skeleton  paths of  space  graph  between  a planar  was  two  shape  FIGURE V.2  The bucket phenomenon, which occurs when the A* s e a r c h a l g o r i t h m i s a p p l i e d t o a network r e p r e s e n t a t i o n of space.  M/  //•/fx \ ///'\\\ » • •  m  •  / /• / » ' \. » \# \  / / / ' \ X N-  \ \  \  \  x  202 positions. be then The  Two paths are t o p o l o g i c a l l Y d i s t i n c t i f n e i t h e r  c o n t i n u o u s l y deformed i n t o the other.  The search f o r a path  reduces t o s e a r c h i n g over the t o p o l o g i c a l l y d i s t i n c t choice  correspond  points  in  the  skeleton  seem,  In  addition  there  The  optimum  path,  when r e s t r i c t e d  are  made;  compute any reasonable  through  however,  my  spatial  t o edges o f the  s k e l e t a l graph, i s not i n g e n e r a l the optimum path restrictions  to  i s a great d e a l of i n f o r m a t i o n  a s s o c i a t e d with the s k e l e t o n which can be used i n other problems.,  paths.  intuitively,  to the c h o i c e s we have t o make i n n a v i g a t i n g  obstacles.,  can  initial  when no  concern  such was to  path, not n e c e s s a r i l y an optimal one.  I- 2 The s k e l e t o n [ Blum, 1964 i], who c a l l e d i t the Medial the  first  to  Axis  Function*  was  i n t r o d u c e the s k e l e t o n of a p l a n a r shape.. Since  then i t has been the t o p i c of s e v e r a l i n v e s t i g a t i o n s [ C a l a b i and Hartnett,1968;  Montanari,1968,1969;  Rosenfeld  and P f a l t z , 1 9 6 6 ;  P f a l t z and R o s e n f e l d , 1 9 6 7 ;  and othersi] and has been  distance  the  symmetric  transformation, axis  comprehensively  g r a s s f i r e transformation*  transformation. analysed  called  i t and  [Blum,1973,1974J written  the  or the has  about i t s p o t e n t i a l  a p p l i c a t i o n s t o the d e s c r i p t i o n of shape i n b i o l o g y .  V n P a t h - f i n d i n g and the s k e l e t o n of a planar shape  203 !•2-1  Def i n i t i on and In  the  properties  continuous  Euclidean  plane  several  equivalent  d e f i n i t i o n s of the s k e l e t o n can be given; however when these converted  to a l g o r i t h m s  network i f c e l l s ,  are  to compute the s k e l e t o n on a r e c t a n g u l a r  i t t u r n s out  that t h i s e q u i v a l e n c e  no  longer  holds. First Euclidean  the s e v e r a l e q u i v a l e n t d e f i n i t i o n s i n the plane  w i l l be d e s c r i b e d , second Montanari's a l g o r i t h m  w i l l be d e r i v e d from one why  of these d e f i n i t i o n s , t h i r d  t h i s a l g o r i t h m i s u n s a t i s f a c t o r y , and  to augment algorithm  Montanari's  algorithm  to  J.  Interpret  the  provide  boundary  wavefront which propagates at uniform the  f o u r t h we a  we  will  see  w i l l see  how  satisfactory  f o r the s k e l e t o n on a network of c e l l s .  Definition  of  continuous  shape.  At  of  shape  v e l o c i t y i n t o the  c e r t a i n p o i n t s two  the  is  the  skeletal  initiation  of  the  wavefront  graph  and  the. time  a  interior  boundary  e x t i n g u i s h themselves; the l o c u s of these  extinction  as  or more s e c t i o n s of  wavefront emanating from d i s t i n c t p o i n t s of and mutually  the  the meet  p o i n t s of from  the  to the time of e x t i n c t i o n i s the  quench f u n c t i o n .  D e f i n i t i o n 2.  The  most  purposes  is  contained  i n the shape and  Then  the  probably  concise  skeletal  this.  definition  Consider  partially  order  for  mathematical  the set of a l l c i r c l e s them  by  inclusion.  graph i s the l o c u s of the c e n t r e of maximal  V«Path-finding and  the s k e l e t o n of a planar  shape  204 circles,  and  f o r each point on  maximal c i r c l e g i v e s the  Definition  3.  value  the  graph  the  At every point P of the  where euc  i s the e u c l i d e a n distances.  at  one  plane d e f i n e the shape:  For every p o i n t P there i s  P* t h e r e are at l e a s t two  d i s t i n c t p o i n t s Q1,  d (P*) =euc (P*, Q1) =euc (P*,Q2) .  p o i n t s f o r P*. points  function  point Q 6 shape such t h a t d (P)=euc(P,Q), while  certain points that  its  | Q 6 shape)  d(P)=min{ euc(P,Q)  such  of  of the quench f u n c t i o n * .  d t o be the minimum d i s t a n c e from P to the  least  radius  i s the  The  l o c u s of p o i n t s  with  Q1, two  Q2 or  for Q2  are  contact  more  contact  s k e l e t a l graph and the value of the f u n c t i o n d at  each p o i n t of the graph i s the quench f u n c t i o n . ,  Definition  4.  Given a p o i n t P, a minimal path  boundary of the shape i s a s t r a i g h t on the boundary. graph  if  point;  it  In the  P i s defined  does  not  l i n e segment PR  to be a  belong  from  point  of  to  the  where R l i e s the  skeletal  t o a minimal path of any  mountain metaphor, t h i s says t h a t any  r i d g e - c r e s t or peak does not l i e on the f a l l - l i n e point.  P  other  point on  of some higher  T h i s i s the d e f i n i t i o n used by [ Montanari, 1968 i ] ;  D e f i n i t i o n 3 lends i t s e l f t o the f o l l o w i n g v i s u a l i z a t i o n the  skeleton.  s h o r e l i n e : of  Imagine an i s l a n d ,  angle of 45° out with  a  peaks and  the  boundary  of  the  shape  as  which everywhere r i s e s uniformly  of a calm ocean, thus forming a mountain ridges.  I t i s p o s s i b l e f o r three  VaPath-finding  and  the s k e l e t o n  of the  at an range  or more r i d g e s  of a planar  shape  205 to meet a t a j u n c t i o n which i s not a peak. are  to be v i s u a l i z e d  of the r i d g e s and  Holes i n  as lagoons at ocean l e v e l *  j u n c t i o n s to the plane of  the  function  d,  yourself  standing  on the c r e s t of the r i d g e ; i n your immediate  the  there are e x a c t l y two  to t r a v e l along a junction more  Picture  the r i d g e , "forwards" or "backwards"., Now  stand  or more r i d g e s meet there*  providing  three  w e l l - d e f i n e d d i r e c t i o n s of t r a v e l .  That  i s the content  of [ C a l a b i and  return  point  e x a c t l y two  function.  which  ; three  a  quench  r i d g e at each p o i n t ,  well-defined directions in  corresponding  to  the  is  the  gives  of  ocean  i*e*  or  height  projection  graph  at  the  shape  skeletal  vicinity  and  the  The  the  Hartnett,1968,  on the r i d g e c r e s t and  Now  note that there  skiers  The  points  where the f a l l - l i n e s from a r i d g e p o i n t or peak enter the  ocean  are  from  called  the  contact  descent, or f a l l - l i n e s  are  in  parlance,  l i n e s of steepest  Theorem 6 ] . .  r i d g e - p o i n t down t o the ocean*  points.  Back at a j u n c t i o n again,  r i d g e s meet, note t h a t there are a l t e r n a t i n g with the r i d g e s . Hartnett, 1968, At  any  n  That i s the content  can  be  r i d g e s meet. circumference  junction  there  can  seen as f o l l o w s .  be  points  the  ocean,  of [ C a l a b i  and  of  at  most one  ridge which  must be descending from i t .  Suppose P i s a j u n c t i o n where 3  Let the three contact  g,  r  the maximal c i r c l e centre P. . One  may  l o s s of g e n e r a l i t y c o n s i d e r three  to  Theorem 7iJ,  ascends away from i t ; a l l the others This  fall-lines  where n  alone*  the  Consider  V«Path-finding and  p o i n t s be p*  skeleton  generated  on  the  without  by  these  the r i d g e which s t a r t s at P the s k e l e t o n of a planar  and  shape  206 passes midway decrease  between  from  p  and  g.  P t o the midpoint  The  guench  function  must  of p and g, s i n c e the d i s t a n c e  pg i s l e s s than the diameter o f the maximal c i r c l e , unless p and g  l i e on the ends of a diameter through P i  the guench f u n c t i o n i n c r e a s e s at P as one  In t h i s l a t t e r begins  to  case  move  out  along the r i d g e . . A l s o , s i n c e pg i s a diameter, n e i t h e r gr or rp can  be a diameter, and hence the value of the guench f u n c t i o n as  one s t a r t s out along these other two r i d g e s i s decreasing.  X * 2.2 approximating  the E u c l i d e a n  plane  To o b t a i n the s k e l e t o n of a shape between two a r b i t r a r y  the  points i s reguired.  given as a d i g i t a l image,  that  is  to  euclidean  distance  But when the shape i s say  network o f c e l l s where each c e l l i s marked  as  a  rectangular  with a 1 (outside the  shape) or a 0 ( i n s i d e the shape), t h i s network can be t r e a t e d as an  approximation  c e l l to a between  number cells  by  approximation  is  16-connected  cells  to  the  of  i t s neighbours  summing  and The  n  and  By connecting measuring  each  distance  a l l the l i n k s between them an  Figure  figure  V.4  V.3  shows  4-,  8-,  shows networks of 4-, 8-,  directions  of  the  links  in  an  network w i l l be r e f e r r e d t o as the major d i r e c t i o n s  of the network.  The higher  approximation.  Using  two c e l l s  over  obtained.  16-connected c e l l s . n-connected  e u c l i d e a n plane.  the  connectivity  the  better  only 4 - c o n n e c t i v i t y , t h e : d i s t a n c e  i n a network can be  as  much  as  41%  out  the  between  from  the  e u c l i d e a n d i s t a n c e , whereas with 8 - c o n n e c t i v i t y i t can be 8% out V»Path-finding and the s k e l e t o n of a planar  shape  J? CoMNCCTED It  FIGURE  ¥ 3  CONNECTED  2 0 9  333 Mil CoN NJGCTED  FIGURE  $  V  *4.  '  COW tV£CTED MET WORK  209 1 6 - c o n n e c t i v i t y only 2.7%  and with  Given  two  out. ,  c e l l s i n a network, i f the l i n e connecting  happens t o l i e p a r a l l e l to one  of  the  major  them  directions  then  there i s a unique s h o r t e s t path between the two  cells,  otherwise  there w i l l  be  them*  This  illustrated  i n f i q u r e V*5*  path  many  shortest  paths  Hontanari's Osing  s t r a i g h t l i n e segments.  algorithm  d e f i n i t i o n 4 above Montanari showed t h a t the  f i n d i n g problem was  equivalent  to  a  problem,  derived  two  part a l g o r i t h m  and  is  Note t h a t there i s always a s h o r t e s t  c o n s i s t i n g of e x a c t l y two  V.2.3  between  thus  a  certain  skeleton  optimal  policy  which can  be  s t a t e d as f o l l o w s . a)  For  each  cell  of the network f i n d the minimum d i s t a n c e to  the boundary of the shape  (the " h e i g h t " ) , and  fall-lines  at l e a s t one)  (necessarily  find  all  from the c e l l  to  the the  boundary. b)  Classify  as s k e l e t o n p o i n t s those c e l l s which do not  a f a l l - l i n e descending from any The  distance  algorithm will  to  shape  which r e q u i r e s only two  now  be  described.  between c e l l s i n t o two fiqure  the  V.6.  The  other can  the  c l a s s e s , OPPEH and  first  pass  cell.. be  computed  passes over the  Divide  is  l i e on  using  network, which  d i r e c t i o n s of the LOWER,  i n forward  an  as  links  shown  in  r a s t e r order  and  computes the minimum d i s t a n c e to the boundary  when  with  second pass i s i n  UPPER  directions  are  considered..  The  only  V«Path-finding and the s k e l e t o n of a planar  links  shape  210 FIGURE V . 5  (a) The u n i q u e s h o r t e s t p a t h f r o m P t o Q.  S h o r t e s t p a t h s i n an 8 - c o n n e c t e d  network.  £<!Xj (b) Multiple shortest, p a t h s f r o m P t o Q.  FIGURE V.6  upper*  ,jp  ow e  tow  L  P<  P e  E"  -^  r\  UPPER and LOWER d i r e c t i o n s o f l i n k s "are c o n s i d e r e d i n t h e f i r s t and second passes r e s p e c t i v e l y o f t h e i t e r a t i v e algorithm.  212 backward  raster  computation,  order  and  continues  these  correctly  distance  adding i n those l i n k s with LOWER d i r e c t i o n s .  i s s p e l t out i n steps 1 and 2 of after  the minimum  two  passes  SKEL-3  below.  This  Surprisingly,  the minimum d i s t a n c e a t every c e l l i s  computed, even f o r c e l l s  whose  fall-line(s)  l i n k s with both UPPER and LOWER d i r e c t i o n s .  include  A proof o f t h i s can  be found i n [ Montanari, 1968 ]. Some: n o t a t i o n  i s i n order.  forward r a s t e r order be P1,P2,  L e t t h e . network c e l l s i n  ...  ,Pn.  Cells  neighbours  i f there  HV-adjacent  i f they are neighbours and t h e i r l i n k  or  vertical..  P i , P j are  i s e x a c t l y one l i n k between them, and a r e i s horizontal  L e t T i j = T ( P i , P j ) be t h e d i s t a n c e between P i and  Pj.  In t h e case of an 8-connected  for  T i j are 1 and the sguare r o o t of 2, and i n a 16-connected  network, 1, the square r o o t of 2 OPPERJPil_ traversing  (LOWER (Pi).} one  link  denotes i n an  NBBS(Pi)=UPPER(Pi) u LOWER(Pi) the shape.  network, the p o s s i b l e  and  the square  the c e l l s UPPER and  reached  {LOWER}  root  values  o f 5.  from P i by  direction.  Let  l e t I be the c e l l s o u t s i d e  D i , the minimum d i s t a n c e from P i t o the boundary  the shape, i s t o be computed f o r i=1,2, ....  of  ,n*  V a P a t h - f i n d i n g and the s k e l e t o n of a p l a n a r shape  213 Algorithm 1.  SKEL-1.  [Forward r a s t e r scan3. For i=1,2,  .  ,n  do  I f P i 6 I, Di=0 I f Pi £ I, Di=  0 0 i f UPPER(Pi) i s empty | Pj e UPPER(Pi) }  Di=min{ Tij+Dj  otherwise.  2. . [Backward r a s t e r scan.]. For i=n,n-1, ...  ,1  do  Di=min{ D i , { Tij+Dj 3.  [Define skeleton  | Pj e LOWER (Pi) }  };  points]..  SKEL={ P i | Di ? Dk-Tik f o r a l l Pk 6 NBRS(Pi)  Two figure  s k e l e t o n s computed with t h i s V*7.  skeletons. suffers  Note  how  they  As can be seen from  two  deficiencies*  compare this  First,  graph  structure.  general disconnected,  Second,  the  with  example,  are  shown  in  their  euclidean  this  algorithm  the output i s an  set o f p o i n t s - no method i s provided a  algorithm  }.  unstructured  to l i n k up the p o i n t s  into  set of s k e l e t o n points i s i n  so t h a t i t would be  impossible  to  form  a  T h i s l a s t d e f i c i e n c y can be remedied by using d e f i n i t i o n  3,  graph s t r u c t u r e anyway.  V.2.4  The  new  algorithm  which d e f i n e s the s k e l e t o n to be the l o c u s VaPath-finding  of  points  with  and the s k e l e t o n of a planar  at  shape  Figure  V.7  .1 I I I I I  I  I I  I  I  I * I * I * * * * * * * * * * * * * * I * I I * * * * * I I I I I I I * I I I I I I I * * I I I I I I I * * I * I * * * * I * * * * * * * * I * * I * I I * I I I I I I I I I I I I I I I I I I I I I .1 I .1 I I I I I I I  .1 I I I  *  I  I  I  I  I  I  I I  I I i  * * * * * * *e* * * * *  *  I  *  I I I I XT I I I I I I I I I I I I I I I I I I I  *  * * * * * * * * * * * * *  * *  * *  I I I I I I  I  .1 I I I I I I  *  I  I I * * * * * * * * * * * * * * * * * * * * I I * I I * I I I I I I I I I I I I I I  I  I  I I  I  * I  * I  I I I I I I I I X I I I I I I I I I  215 l e a s t two  contact points.  follows;  F i r s t , while computing the  figure,  T h i s suggestion  can  minimum  be:implemented distance  to  compute a l s o the c o n t a c t p o i n t s f o r each c e l l .  c l a s s i f y a l l c e l l s with at l e a s t two  c o n t a c t p o i n t s as  as the  Second, belonging  to the s k e l e t o n ; Since the f a l l - l i n e s and defined  until  c o n t a c t p o i n t s of a c e l l cannot  the f i n a l value of the minimum d i s t a n c e from  c e l l to the shape has  been computed, they  computed  backward  until  the  r e g u i r e s an e x t r a o p e r a t i o n * step  3  must  be  replaced.  raster  cannot  scan  begin  of SKEL-1.  another r a s t e r scan i s This  results  in  to  the be  Step 2  needed  the  be  and  following  algorithm.  Algorithm 1.  SKEL-2.  [Forward r a s t e r scan],; For i = 1,2, If  •,•,;.. ,n  do  P i 6 I , Di=0  I f Pi £ I, Di=  oo i f OPPER(Pi) i s empty  Di=min{ Tij+Dj 2.  | Pj e UPPER (Pi)  } otherwise. .  [Backward r a s t e r scang. . For i=n,n-1, ...  ,1  do  Di=min{ D i , { Tij+Dj Contacts (Pi) =U  | Pj S LOWER (Pi)  { c o n t a c t s (Q)  }  }.  | Q 6 LOWER(Pi) & d(Pi)=T(Pi,Q)+d(Q) }  3.  [Second forward  r a s t e r scam],  V«Path-finding and the s k e l e t o n of a planar  shape  216 For i=1,2, ...  ,n do  contacts(Pi)=contacts(Pi) u U  | Q 6 UPPER (Pi) &  { contacts (Q)  d(Pi)=T(Pi,Q)+d(Q) j 4. . [ D e f i n e s k e l e t o n p o i n t s J. SKEL={ P i | number-of-contacts-of(Pi)  This improves matters a l i t t l e , as  skeleton  f o ri t correctly  p o i n t s many p o i n t s omitted  time, u n f o r t u n a t e l y , straight  > 1j  corridor  at of  places  in  classifies  by SKEL-1. . Rt the same  the  skeleton  such  as  a  even width, where SKEL-1 would compute a  double row of s k e l e t o n p o i n t s , SKEL-2 computes none. What  i s needed  i s t h e : i n t r o d u c t i o n of p o i n t s i n between  c e l l s of the array as of  introduce  a s k e l e t o n p o i n t between  disjoint  sets  V. 7,.  points,  examples  with  figure  skeleton  of  The  contact  as  obvious any  suggested  way two  points*  t o do t h i s i s to HV-adjacent  This  however, because many p a i r s of HV-adjacent c e l l s , ridge-line,  have  HV-adjacent  contact  conservative  neighbourly one  member  algorithm  and  two  i f they  non-empty  sets  are  any  consequently  Consequently a  identical  S I , S2  i f there i s at l e a s t one neighbourly of  f a r from  c o n d i t i o n must be used. , Define two c e l l s o f  the network to be neighbourly HV-adjacent,  cells  doesn't work,  p o i n t s , and  many s p u r i o u s ridge p o i n t s would get introduced. more  by the  or a r e  of c e l l s t o be p a i r of  the pair from S1 and one from S2.  cells,  The modified  i s as f o l l o w s ; V»Path-finding and the s k e l e t o n of a planar  shape  217 Alqorithm  SKEL-3.  Steps 1,2,3 4,  as f o r SKEL-2.  [Create ridge p o i n t s ] . For a l l i,j=1,2, ... n, ( i < j)  do  i f not neighbourly (contacts (Pi) , c o n t a c t s (Pj) ) then c r e a t e - r i d g e - p t R i j between P i and P j . 5,.  [ Define . s k e l e t o n p o i n t s ] , SKEL=  { a l l created ridge-points ] u ( P i | number-of-contacts-of (Pi) > 1 j  F i g u r e V.8 shows the r e s u l t of using SKEL-3 on two examples..  1*2.5  Ridge-foliowing The  cells.  points  the  A r i d g e c e l l may  network  or  network. ridge  of  a  point  skeleton be  either  created  a  cell  of  the  an  unordered  collection  which, t o be u s e f u l , must be organized  of l i n k e d r i d g e c e l l s ; to the o p e r a t i o n ,  neighbouring  chains  I use the term r i d g e - f o l l o w i n g to  refer  on a network to which SKEL-3 has been a p p l i e d ,  ridge  resulting  collection  connected  graph  of  structure  graph o f the corresponding Return  again  of  into  o f i n s e r t i n g l i n k s between r i d g e c e l l s and assembling more  original  between two c e l l s of the o r i g i n a l  The output of SKEL-3 i s  cells  w i l l be r e f e r r e d t o as r i d g e  to  the  cells cells,  into  "junctions"  links,  closely Euclidean  and  three  or  so that the  junctions  is  a  approximating the s k e l e t a l shape.  mountain metaphor;. Imagine  s t r a d d l i n g a r i d g e with one's l e f t and r i g h t f e e t  just  oneself to  V«Path-finding and the s k e l e t o n of a planar  the shape  c  m  9  J5  ^  'S  "a  3  3  3  ©  d  #  i ®  %  #  3j?  '3  4>  %  <»  f»  *  §  *  220 left  and  right  respectively  of  contact p o i n t s of the f a l l - l i n e s left The  the  which  crest,  originate  and r i g h t f e e t and descend on opposite p o s i t i o n s o f these two contact  one's  position  on  the  ridge  and observe the under  one's  s i d e s of the r i d g e .  p o i n t s vary c o n t i n u o u s l y  crest,  with  except when a c r o s s o v e r  p o i n t , where t h r e e or more r i d g e s meet,  i s passed.  exceptions  when t h e : s e t of c o n t a c t  t o t h i s statement could occur  The  only  p o i n t s i n c l u d e s an a r c of a c i r c l e - but t h i s cannot happen polygonal  f i g u r e s or a d i g i t a l  image.  r i d g e - c r e s t from which a f a l l - l i n e on  the  shoreline  Conversely  the p o i n t on a  descends t o a  varies continuously  with  contact  point  with the p o s i t i o n of the  contact  point.  In a network, t h i s says t h a t two r i d g e c e l l s are  to  linked  only i f t h e i r contact  be  neighbourly To  i n pairs.  make  introduced. cell  at  this  precise  some  more  each  by  corner. .  Any  of t h e . f o u r  a  constructed  centre  ridge  configurations  illustrated they  are  must  cell.  Two r i d g e c e l l s  l i e on a common csquare.  crested  and  with  a  c e l l s may be a  each  side  Thus  a csquare may  are  2 =256 8  are  may  be  possible  contiguous i f  Only contiguous r i d g e c e l l s  and when t h a t happens l e t us say the  be  of r i d g e c e l l s on a csquare.. T h i s i s  i n f i g u r e V.9.  get l i n k e d together  corner  of  c o n t a i n up to eight r i d g e c e l l s , and there different  terminology  A csquare i s a u n i t square i n the: network  r i d g e c e l l , and i n a d d i t i o n the occupied  p o i n t s a r e the same or are  link  between  that  ever they  them i s a c r e s t . . Now the  c o n d i t i o n f o r c r e s t i n g two r i d g e c e l l s can be p r e c i s e l y s t a t e d : V«Path-finding and the s k e l e t o n of a planar  shape  FIGURE V.9  O  A.  O  A.  A CSQUARE i n a network. Each c o r n e r r e t i n a l c e l l may be c l a s s i f i e d as a r i d g e - c e l l and the t r i a n g l e s mark the p o s i t i o n s of p o t e n t i a l c o n s t r u c t e d r i d g e cells.  222 Two contiguous r i d g e c e l l s R1, R2 can be c r e s t e d i f f t] p o i n t s C11, C12 6 c o n t a c t s (R1) and r| p o i n t s C21, C22 6 c o n t a c t s (R2) such that  neighbourly(C11,C12) and neighbourly (C21,C22) .  The  b a s i c scheme f o r i n s e r t i n g c r e s t s and forming  junctions  i s as f o l l o w s * . A l l csquares i n the network are examined and the number of r i d g e c e l l s two  are ignored.  i n each determined.  Those with l e s s  than  I f a csguare has two r i d g e c e l l s then u s u a l l y  they w i l l be c r e s t e d although there  are e x c e p t i o n s .  it  may have c r e s t s to more than  i s p o s s i b l e t h a t one r i d g e c e l l  In t h i s way  two other  contiguous r i d g e c e l l s ; such a r i d g e c e l l i s c a l l e d  junction  cell.  I f a csguare has three  or more r i d g e c e l l s some  p a i r s o f r i d g e c e l l s w i l l be c r e s t e d and/or a s e t more  ridge  of  three  a  or  c e l l s may be grouped i n t o a j u n c t i o n s e t . Examples  of j u n c t i o n c e l l s and j u n c t i o n sets appear i n f i g u r e V.10.. define  a  graph  as f o l l o w s .  Now  Every r i d g e - p t , j u n c t i o n - c e l l , or  j u n c t i o n - s e t , i s a vertex,  and every c r e s t i s an  graph.  a connected graph and i s the s k e l e t a l  This  is  always  edge  of  this  graph o f a connected region of a d i g i t a l image. Although  there  are  256  d i f f e r e n t csguare  t h i s reduces t o e x a c t l y 51 d i s t i n c t rotations  are  accounted  appendix A.2, together A should  note  on  cases a f t e r r e f l e c t i o n s and  f o r . A proof  of t h i s f a c t appears i n  with a l i s t i n g of the 51 cases.  implementation  be made here.  configurations  of  the  arithmetic  A l l q u a n t i t i e s involved  V«Path-finding and the s k e l e t o n  operations  i n the computation of a planar  shape  FIGURE V.10  224 of  the  skeleton  on  a • b*root2 where a, constitute  an  an b  8-connected are  integral  using  integer  integers,  domain,  a r i t h m e t i c a l l a r i t h m e t i c and  network  so  that  are i n the form i s to  say  they  than  use  real  operations  are  done  rather  comparison  a r i t h m e t i c on p a i r s of i n t e g e r s (a,b).  In other  words Gaussian a r i t h m e t i c i s used*  V. 2.6 Using p a r a l l e l i s m - t o compute-the s k e l e t o n The scans,  above  algorithm  computes the s k e l e t o n i n f o u r r a s t e r  i n c l u d i n g one f o r forming  crests.  [Montanari,1968]  junction  sets  g i v e s an a l g o r i t h m  and  which proceeds by  wave-front expansion i n p a r a l l e l and i s e q u i v a l e n t The  to  SKEL-1.  a l g o r i t h m SKEL-3 can be m o d i f i e d t o compute the s k e l e t o n i n  a similar parallel  V.2.7  fashion.  Paths between o b j e c t s and s u p e r f l u o u s With  this  new  correct,  in  branches  a l g o r i t h m there i s an edge o f the s k e l e t a l  graph emanating from every accordance  corner o f a d i g i t a l image. with  the  the.axes as borders, are r o t a t e d s l i g h t l y , many  superfluous  This  t h i s i s of no concern.  aligned  with  But when the shapes  many corners appear i n a d i g i t i z a t i o n  edges appear i n t h e s k e l e t a l graph.  and  There are  ways t o handle t h i s problem, depending on the s i t u a t i o n .  there  are several isolated objects  is  d e f i n i t i o n o f the s k e l e t o n .  When the shapes i n v o l v e d have long s t r a i g h t l i n e s  two  inserting  If  (an archipelago) , and one i s  only concerned t o f i n d a route through the a r c h i p e l a g o , then the VaPath-finding  and the s k e l e t o n of a planar  shape  225 only  edges  that  need t o be r e t a i n e d are those  s k e l e t o n p o i n t s have c o n t a c t r e f e r t o these  points  on  distinct  The i n t e r n a l edges can  be  one has to f i n d paths from place t o connected  shape,  object.  I f the c o n t a c t close zero  Various  point  pruning  and  the  then  this  within  that  zero,  point  to  the  same  and  are  very  as  would  occur  T h i s handles the  i n t h e s k e l e t a l graph.  other  in a  by the d i g i t i z a t i o n of a l i n e  p o i n t of an edge remains constant contact  the  45°., The t h r e s h o l d number used t o decide  i s represented  single  s t r a t e g i e s are a v a i l a b l e .  c o n t a c t p o i n t s a r e "very c l o s e t o g e t h e r " c o n t r o l s bay  a  a l l l i e : on  edge may be removed.  case of s m a l l steps introduced approximately  place  value of the guench f u n c t i o n goes t o  (not a minimum g r e a t e r than  passageway),  On the other hand,  p o i n t s of an edge remain the same  together,  and the  a l l the edges are i n t e r n a l s i n c e the  c o n t a c t p o i n t s of every s k e l e t o n surrounding  I  edges as  discarded  s e a r c h r e s t r i c t e d t o the i n t e r - o b j e c t edges.  complex  objects.  as i n t e r - o b j e c t edges, and the remaining  i n t e r n a l edges.  if  along which the  while  the  at  when two size  of  I f one c o n t a c t  the d i s t a n c e  from  c o n t a c t p o i n t decreases,  this  and the  value of the quench f u n c t i o n on the edge goes t o zero, then  this  edge  edge  may  introduced  be  removed.  This  handles  the  case  of  an  i n t o the s k e l e t o n by a small step i n the d i g i t i z a t i o n  of a s l i g h t l y  inclined straight  line.  V» P a t h - f i n d i n g and the s k e l e t o n of a planar  shape  226 V,3  Using Use  the  skeleton  of the  skeleton  promised  to  heuristic  search  First D l i e on  overcome for  the  as  the  cells  junctions.  spatial  If  the  from  start  then the  S*  D',  the  encountered. several to  D,  the  from  of  the  the  use  of  the  pathgraph graph  be  searching  This  To  simplify graph,  is  correspond  to  an  corresponds to the  the  using  D on  can  be  chain  pathgraph  as  skeletal  pathfinding  distinct graph  considerably  less  directly.  on the  the  skeletal  skeletal  done  before.  If  graph are  equally  algorithm  V « P a t h - f i n d i n g and  the  by  it  requires  skeleton  is  a standard  i s searched not  edge  corresponding  topologically  with  t o S and  junction  g r a p h , and  the  a  and  skeletal  between  pathgraph,  for  graph,  following  p o i n t upwards u n t i l t h e . s k e l e t a l g r a p h  proceed the  the  pathgraph  f o u n d by  found.  S to D along  i t s corresponding  all  points  cell  i s needed.  skeletal  network o f c e l l s  at that  on  network  t o the  junction c e l l s  S or d e s t i n a t i o n D are  Then  a  destination  path.. In  v e r t i c e s of the  Now  nearest  points then  S and  where a c h o i c e  g r a p h and  on  must f i r s t  fall-line  the  S to D are  when t h e  the  cell  graph*  skeletal  algorithm  than  on  objections  a spatial  or sets)  V.11.  figure paths  the  start  v e r t i c e s o f the  graph and  The  A skeletal  traversing search  of  p a t h g r a p h , homomorphic t o t h e  (cells  in  shown i n  places  follows.,  two  shape d e l i n e a t e d  graph* , Then a p a t h  skeletal  only  junctions  between of  the  search  defined  most  graph i s c e r t a i n l y  are  this  of the  pathfinding.  skeletal  path through the sets  path-finding  assume t h a t t h e  the  skeletal  for  of  is  happens  that  c l o s e to  S  a  or  trivial  a planar  shape  FIGURE V . l l  A s k e l e t a l graph and i t s pathgraph.  228 modif i c a t i o n .  V, 3.. 1. D e s c r i b i n g a s k e l e t a l path A path s p e c i f i e d by a path through the s k e l e t a l be  naturally  model.  described  in  terms  For i n s t a n c e i n f i g u r e V.12  described  graph  of the o b j e c t s of the  the path from S to D can  ob1)  5  ( k e e p - l e f t - o f ob2) )  d1)  (move ( ( k e e p - r i g h t - o f  ob3)  &  ( k e e p - l e f t - o f ob2) )  d2)  (move ( ( k e e p - r i g h t - o f  ob3)  &  ( k e e p - l e f t - o f ob5) )  d3)  (move ( ( k e e p - r i g h t - o f ob4)  &  ( k e e p - l e f t - o f ob5) )  d4)  &  ( k e e p - l e f t - o f ob5) ) d5).  (turn r i g h t  60)  (move ( ( k e e p - r i g h t - o f ob6) Such a path d e s c r i p t i o n can by examining the two One  be generated from t h e . s k e l e t a l graph  c o n t a c t p o i n t s of each  belongs t o the nearest  and the other belongs to the nearest So  long as no two  between  distinct  the  o b j e c t on the o b j e c t on  then  the  only change  the  the  right  hand  run i n t o spatial  membership of at  junctions  d e s c r i p t i o n of r i d g e c e l l s along any  the pathgraph remains  on  l e f t hand s i d e  i s always a channel of  objects,  contact c e l l s of r i d g e c e l l s can therefore  ridge-cell  d i s t i n c t o b j e c t s on the screen  each other, t h a t i s t o say there cells  be  45°)  (turn r i g h t  side.  world  as  (move ( ( k e e p - r i g h t - o f  path.  can  one  the and  edge of  constant.  VaPath-finding  and  the s k e l e t o n of a planar  shape  229  FIGURE V.12  S k e l e t a l p a t h between o b j e c t s . The skeleton allows a " n a t u r a l " d e s c r i p t i o n t o be e a s i l y d e r i v e d .  230 V.3.2  Opt i m i z i n q a s k e l e t a l path The example i n f i g u r e V.13 shows that i t i s necessary  consider  o p t i m i z i n g a s k e l e t a l path.  c o n s e c u t i v e c o r r i d o r s i n the f i g u r e , optimized  path  I f 9 i s the angle between then  in  that  length  o f the  if 9  i s , say, 45°  case the optimized path i s approximately 0.1 as  l o n g as t h e s k e l e t a l In  the  i s sin(9/2) times the length of the unoptimized  s k e l e t a l path, a c o n s i d e r a b l e improvement since  to  certain  path.  s p e c i a l cases, the o p t i m i z a t i o n can be c a r r i e d  out roughly as f o l l o w s . . Let S,D be the s t a r t and d e s t i n a t i o n of the  skeletal  path  t o be o p t i m i z e d , and d e f i n e a f u n c t i o n e on  the s k e l e t a l path by e(p)=perpendicular d i s t a n c e from p skeletal  path to the s t r a i g h t l i n e  f i n d t h e maximum of the positive  nothing  function  needs  SD.  be  at  P*  As p v a r i e s from S to D  e(p)-g(p);  i f this  i s not  be done, f o r i n t h i s case the s t r a i g h t  l i n e SD i s the s h o r t e s t path from S t o maximum  on the  Di  Otherwise  l e t the  and apply t h i s a l g o r i t h m r e c u r s i v e l y to the  paths SP* and P*D.  U n f o r t u n a t e l y t h i s method cannot be  carried  out i n general* The  problem  problem,  here  described  might be as  christened  follows.  Given  the r o p e - t i g h t e n i n g an  environment  a r b i t r a r y two dimensional shapes on a t a b l e t o p * two p o i n t s S, at  vacant  spots,  and  a  rope  laid  s k e l e t a l --or a r b i t r a r y - - path: compute  out a  from  of D  S to D along a  description  of the  curve assumed by the rope when t e n s i o n i s a p p l i e d a t S or D, any s l a c k being taken  up  as  required.  Preferably  the  solution  V«Path-finding and the s k e l e t o n of a planar shape  I  P A T H  >*  S kCLGTAL  v . p<\ q T  \  FIGURE V.13  Example i l l u s t r a t i n g a s k e l e t a l path.  t h e need t o o p t i m i z e  232 should be s t a t e d i n terms of an array of c e l l u l a r One  obvious  automata..  s t r a t e g y i s to move the path i n  the  direction  of the centre of c u r v a t u r e at p o s i t i o n s where t h e : a b s o l u t e  value  of the r a d i u s of c u r v a t u r e  local  has  a  local  minimum.  minima of the r a d i u s of c u r v a t u r e correspond rope and the e f f e c t local  centre  of  of moving such curvature  r a d i u s of curvature local  operator  along  to the bends i n the  inwards  towards  the  i s to smooth out these bends.,  at a point p of the path can be found  The  by  a  that looks at a small set of adjacent p o i n t s of  the path centred on p pass  points  The  the  (say f i v e neighbouring  whole  r a d i u s of curvature*  path determines  I f such  p o i n t s ) . . Then  one  the l o c a l minima of the  a p o i n t i s a l r e a d y adjacent  to  a  p o i n t of an o b s t a c l e on the same s i d e as the r a d i u s of curvature it  cannot be moved any  minimum  is  further.  moved to the c l o s e s t g r i d  of the centre of c u r v a t u r e . path  Otherwise each p o i n t B of  were  point B * i n the  direction  I f the adjacent p o i n t s to B i n  A, C, then the adjacent p o i n t s to B' i n the new  remain A, C.  The  process i s now  repeated  local  u n t i l e i t h e r the.  the path path  i s s t r a i g h t , with i n f i n i t e r a d i u s of curvature at a l l p o i n t s , or e l s e the only p o i n t s of i n f l e c t i o n round  an  occur  where  the  path  extreme p o i n t of an o b s t a c l e , the path being  goes  straight  otherwise. What  I  have  just  sketched  o b t a i n i n g a curve whose second except  for  points  where  the  i s a r e l a x a t i o n algorithm f o r  derivative  is  zero  everywhere  curve c o n t a c t s an o b s t a c l e . . In  e f f e c t i t simulates the r o p e - t i g h t e n i n g . V«Path-finding and the s k e l e t o n of a planar shape  233 7.3.3  Comparison of s k e l e t a l and The  the  complexity  network,  A*- path f i n d i n g  of both i s l i n e a r i n the number of c e l l s  except  that  the  g r e a t e r i n the s k e l e t a l case..  constant  of l i n e a r i t y i s much  This i s c l e a r f o r  A*  since  number of nodes expanded by A* i s bounded by the number of i n the network. two  and  in  The  the  first  hand  a  it  out w e l l . replaced  is  the  path  cells  has  a  natural  On  the  description is  in  considered,  l i k e l y t h a t the s k e l e t a l p a t h - f i n d i n g method comes  a  algorithm  for  the  skeleton  is  p a r a l l e l wavefront-expanding method, i t takes w the  maximum  value  of  the  quench  A l l the r i d g e - c r e s t l i n k s can be computed i n  p a r a l l e l operation,  except f o r  operations  required.  would be  I-i* Other a p p l i c a t i o n s of the The  are  of nodes expanded by a graph  I f the use of p a r a l l e l i s m  wave-front expansions when f u n c t i o n i s w.  i s l i n e a r i n the number of  number  I f the r a s t e r scan by  cells  searching  i s bounded by the number of c e l l s .  skeletal  environmental terms. then  operation  second,  traversal, a l g o r i t h m other  the  In the case of s k e l e t a l p a t h - f i n d i n g there  p a r t s to c o n s i d e r , f i n d i n g the s k e l e t a l graph and  the graph.  in  skeleton  can  also  some  junction  sets  where  one two  skeleton be  a p p l i e d to f i n d i n q a path f o r  moving an o b j e c t , f i n d i n q empty space, and  other  problems..  I  d e s c r i b e each a p p l i c a t i o n i n t u r n .  V«Path-finding and  the s k e l e t o n of a planar  shape  234 V,4.1 pbjeet  moving -  Suppose there i s an environment of o b s t a c l e s to  be  moved  and an  object  from one p o s i t i o n to another,, The simplest  shape  f o r which a path can be found by the s k e l e t o n i s a c i r c l e .  V. 4. 1.1. C i r c u l a r shaped object o f -radius r F i r s t f i n d the pathgraph of the empty space and remove from it  any edge whose c h a i n of c e l l s i n the s k e l e t a l graph  a cell  at which the value  Then, i f the i n i t i a l and shape  are  of the guench terminal  S and D, apply  f u n c t i o n i s l e s s than r .  positions  the  arms  of  the  skeletal  f u n c t i o n along  t h i s path i s everywhere  the . c i r c u l a r  shape  provided  can  certainly  from  graph.„  The  the  circular  S  to  D  be  that  Since the guench  at l e a s t as great moved  the centre of the shape i s kept on  V.4. JL 2 Other o b j e c t  of  a h e u r i s t i c graph t r a v e r s a l algorithm  to the pathgraph to f i n d the s h o r t e s t path follows  contains  along  as  r,  t h i s path  the:path..  shapes  b a s i c i d e a o f t h i s approach i s t o f i n d the s k e l e t o n o f  the empty space, the skeleton of the shape t o be moved, and work with  the  skeletons  instead  of  the  c o n d i t i o n f o r a shape to be contained s t a t e d in terms of the s k e l e t o n s (*) Let t h e quench  within  a  shapes. space  The  can  be  as f o l l o w s :  f u n c t i o n of the s k e l e t o n of the shape be  g and the quench space be r .  original  f u n c t i o n of the s k e l e t o n of the empty  Then f o r a l l p o i n t s x of the s k e l e t o n  VaPath-findinq  of  and the s k e l e t o n of a planar  shape  235  the shape, there must exist at least one point y on the skeleton of the space such that the circle centre x radius q (x) is contained in the circle centre y radius r (y). Consider a lonq thin shape like a stick., By addinq semi-circular ends if necessary, its skeletal graph is a straight line segment. C l e a r l y if this line segment can be kept aligned with the skeletal graph of the space while the shape is being moved then condition (*) is easily checked, since then points of the shape's skeletal graph lie on the space's skeletal graph. V. 4 . 1_-3  An  L-shaped  object  is an awkward problem for humans at the:best of times and in retrospect it was perhaps overly optimistic to think that a clean approach to its solution could be obtained through the use of skeletons. Although the skeleton does provide a clean approach to the problem of a circular shaped object, I have not yet found a useful application of it to the.problem of moving more complex shaped objects.. The L problem can be viewed as Requiring the simultaneous solution of two interacting sabprobleras. , Namely, since each arm is a rectangular stick, first solve the problem of moving a stick though the doorway. Then, tackle the L problem by simultaneously solving two problems of moving a stick through the doorway, one from each arm of the L, with the complication This  r  VoPath-finding  and the skeleton of a planar shape  236 t h a t any  V.4.2  movement of one  s t i c k causes a movement i n the  other.,  F i n d i n g empty space An i n t e r e s t i n g  findspace  problem:  application  of  find  on a c l u t t e r e d t a b l e t o p to  down another o b j e c t . i 1973*3.  The  skeleton  is  T h i s i s the FINDSPACE problem  position  the t a b l e t o p can  space  the  of the  to  of  the put  Sussman  maximum s i z e d c i r c u l a r spaces on  be found d i r e c t l y  from the guench  function  of  the s k e l e t o n of the empty space.  T h i s i s done by t r a v e r s i n g the  s k e l e t a l paths and  local  function.  finding  the  I f the c i r c l e with  maxima  of  r a d i u s equal t o the  quench f u n c t i o n i s s u f f i c i e n t to c o n t a i n the e x t r a the  problem  is  solved;  c i r c l e s w i t h i n the the extra  V.4.3  not,  the  maximum of object  p o s i t i o n s of the  space are good candidates  guench the then  maximal  f o r the p o s i t i o n of  object.  F i n ding the s h o r t e s t d i s t a n c e - between two-shapes Given two  between  them  following  i s o l a t e d planar  shapes, a s h o r t e s t s t r a i g h t  can  by  way.  surrounding  be  the  found  First find  the  shapes,  s k e l e t a l graph having are  if  the  inter-shape  one  the an-d  means  of the s k e l e t o n i n the  skeleton retain  of  Then,  the  only  c o n t a c t p o i n t on  edges..  line  empty  space  those edges of each  find  a  shape. point  P  the  These on  the  inter-shape  edges at which the guench f u n c t i o n takes i t s minimum  value.  s t r a i g h t l i n e j o i n i n g the two  The  contact  then a s h o r t e s t s t r a i g h t l i n e between the two VaPath-finding  and  points of P i s  shapes.  the s k e l e t o n of a planar  shape  2 37 i; Rather than developing  the extensive  mathematical machinery  necessary to make the above d e s c r i p t i o n r i g o u r o u s ,  I  following.  intuitive  point  inter-shape  edge one  point,  radius  the  justification.  centred  guench f u n c t i o n t h e r e , and As the i n t e r - s h a p e  expands and c o n t r a c t s i n r a d i u s .  r a d i u s of t h i s d i s c i s assumed at one inter-shape  every  can draw a c i r c u l a r d i s c  p o i n t on each shape. disc  At  edges.  At  such  a  F i n d i n g nearest  The or  more  points  of  P.  points i s  also  tessellation  p o i n t s of Lemma. the  The  the  disc,  and  edges.  The  nearest  known  point  as &  the  neighbourhoods of a c o l l e c t i o n  the  Voronoi  Sibson,1978§.  objects  other point i n  p,q,r,...  diagram Consider  or  the  of  Dirichlet  the s k e l e t o n  corresponding  to  of the  P.  The  points  edges of the s k e l e t a l graph of the  space  P form the boundaries of the nearest  of the p o i n t s of  P.  Proof  Every  sketch.  from two  nearest  the the  a point p S P c o n s i s t s of a l l p o i n t s x on  [Green  the plane with  of  the  regions  plane such t h a t x i s c l o s e r to p than to any collection  of  connecting  a diameter of the  neighbourhood  that  contact  minimum value  Let P be a c o l l e c t i o n of p o i n t s i n the plane.. neighbourhood  at  an  edges are t r a v e r s e d  moreover i s a l i n e of s h o r t e s t d i s t a n c e between the  V.4.4  the  on  with one  point the l i n e  contact p o i n t s of the d i s c must be  offer  surrounding  neighbourhoods  point of the plane i s e i t h e r e q u i d i s t a n t  or more p o i n t s of P, or e l s e i s VaPath-finding  and  closer  to  one  the s k e l e t o n of a planar  point shape  238 than  t o any other  point of P.  I n the f i r s t case:the point  on the s k e l e t a l graph of the space surrounding in  the points of  the second case the point i s i n the nearest  some p o i n t of P. space x  is  arbitrarily  neighbourhood of  not  the p o i n t s of P, with contact a  vertex  of  the  skeletal  p o i n t s p,q 6 P. graph.  In  any  s m a l l neighbourhood of x, there are p o i n t s c l o s e r to  p than to any other other  P,  Let x be a p o i n t i n the s k e l e t a l graph of the  surrounding  Thus  lies  point o f P, p o i n t s c l o s e r t o g than  to  any  p o i n t of P, and p o i n t s of the s k e l e t a l graph. . Hence x i s  a boundary p o i n t of the nearest nearest  neighbourhood of p  and  o f the  neighbourhood of q.. S i m i l a r l y , i f x i s a v e r t e x t of t h e  s k e l e t a l graph with contact p o i n t of the n e a r e s t Thus  the  of  is a  boundary  neighbourhoods of p,g,r,..,...  skeleton  generalization  p o i n t s p,q,r,.,., x  the  of  a  collection  of  shapes  boundaries of the nearest  is  a  neighbourhood  regions of a c o l l e c t i o n of points..  V.5 Summary In  this  path-finding  chapter and  I  sketched  approach  approaches  I  In  order  to  implement  developed a new i t e r a t i v e algorithm  this  f o r the  s k e l e t o n t h a t i s guaranteed to compute a connected s k e l e t o n a connected shape.  to  proposed one based on the use of the s k e l e t o n  of the shape o f the empty space. latter  various  from  I sketched how the s k e l e t o n c o u l d be used as  a h e u r i s t i c a i d i n the s o l v i n g of  object-amoving  problems,  V»Path-finding and the s k e l e t o n of a planar  and shape  239  showed how the s k e l e t o n could distance  be a p p l i e d t o f i n d i n g the s h o r t e s t  between o b j e c t s and t o  finding  nearest  neighbourhood  regions, With t h i s chapter on p a t h f i n d i n g I have s p e c i f i e d of  algorithms  a  class  which can be used as a b a s i s f o r the s o l u t i o n of  p a t h f i n d i n g and o b j e c t moving problems i n the Thus the o u t l i n e design  spatial  planner.  o f the r o b o t - c o n t r o l l e r i s complete..  V«Path-finding and the s k e l e t o n  of a planar  shape  240  CHAPTER VI SUMMARY, CONCLUSION, AND FUTURE WORK  V I . ! Summary After  an  introductory  the nature of A r t i f i c i a l of  simulating  chapter,  I n t e l l i g e n c e , introduced  system f o r s i m u l a t i n g  Then  I  features  of  the  i t on the notion o f  implemented  approach  design  described  in  some  detail  a  an environment and the sensori-motor p a r t s  of an organism t o i n h a b i t i t .  basing  the  a made up organism, and reviewed s e v e r a l c l o s e l y  r e l a t e d p i e c e s of work.  overall  I reviewed a t some l e n g t h  was  important  In  chapter  IV  I  sketched  the  c o n t r o l program of such an organism, the  action  described  cycle, ,  One  partially  and an a l t e r n a t i v e approach  proposed.,  An  particular  f o r i t s c o n t r o l l e r , i s a p a t h - f i n d i n g a b i l i t y . . To  t h i s end I d e s c r i b e d based  on  the  reguirement  i n chapter  skeleton  of  V an  a  f o r any  approach  shape.  organism,  to  path-finding  The s k e l e t o n , which was  o r i g i n a l l y motivated by p h y s i o l o g i c a l c o n s i d e r a t i o n s applied  to  shape  description,  i s also  a  and  useful  p a t h - f i n d i n g and as a h e u r i s t i c f o r other s p a t i a l developed a new i t e r a t i v e algorithm  in  t o compute i t .  a c t u a l amount o f computation t o f i n d the s k e l e t o n  first  tool  problems.  for I  Although t h e on  a  serial  VI»Summary, c o n c l u s i o n , and f u t u r e work  241  machine  may  be  path-finding, i t  greater  than  reduces  the  that  for  other techniques  heuristic  search  required  for for  f i n d i n q a route between o b s t a c l e s . . So l e t me and  stand  back and  what problems uncovered?  work?  What  Intelligence  take How  contribution  does  enterprise?  The  stock.. What has  been  solved  does t h i s work r e l a t e to it  make  to  the.  advances contained  other  Artificial i n t h i s work  are t h r e e f o l d .  (a) In the f i r s t action  cycle  before.  The  analogy  between  place I e x p l i c i t l y  for  a  robot-controller;  implementation done the  method whereby one of hypotheses and form of sensory  process  thus  the  t h i s has not been done  far  was  of p e r c e p t i o n and  based the  on  the  scientific  i s always a c t i n g on the b a s i s of a c o l l e c t i o n g a t h e r i n g evidence  input  f o r these  hypotheses i n the  data.  (b) A s p a t i a l reasoning part  l a i d out the f e a t u r e s of  module i s  an  important  and  essential  of any r o b o t - c o n t r o l l e r . . I t makes plans f o r a c t i o n on  the  b a s i s of the c u r r e n t c o l l e c t i o n of hypotheses about the form  of  the environment.  The  second advance i s the development of a  approach to problems of s p a t i a l reasoning the has  skeleton  of a two-dimensional shape.  based on  the  r e g u i r i n g a constant  of  When the environment  been drawn on an array of p o i n t s l i k e a s c r e e n , an  algorithm  use  new  iterative  amount of computation reduces  p a t h f i n d i n g problem to a simpler g r a p h - t r a v e r s a l problem.. VlaSummary, c o n c l u s i o n , and  any Each  f u t u r e work  242 edge  of  the  graph  c o r r e s p o n d s t o a p a t h between two  e a c h node c o r r e s p o n d s t o while  the  number  of  amount of  heuristic  do  that  this  s h a p e s of shapes  in  the  network.  based  on  which w i l l  reguire  here c o u l d  have  a c t u a l l y used  the  more  There are  other  paths, Thus  the  ways  to  representation  much more  search  have  One  i s called  found  one  t i g h t e n the  path  technical moving an  be  computed  by  ponder i f t h i s  functioning  a  As  robot my  simulation  a Cartesian  possible  t h r o u g h a doorway.  I I and  were d e s c r i b e d collision  major robot  representation of  points  given  of  and  there. two  Nilsson  The by  I  I I I there  Cartesian  When  you  do  The  you  other  details  for one  problem. ,  have been  the  full  Mine i s the  Becker  coordinates and  of  first  to  s h a p e s . . Of  & Merriam  represents  VlsSummary, c o n c l u s i o n ,  several  details  S Raphael used a  Cartesian  this  presented  dimensional  simulations,  and  shapes,.  full  s o l u t i o n to t h i s  programs w r i t t e n b e f o r e  two  way?  the  in  p o i n t s , how  t o e l u c i d a t i n g the  i n chapters  movement and  representation of  relates  simulation  previous  series  shortest  f o r a p p r o a c h i n g the  discussed  robot  the  L-shaped o b j e c t  handle the the  to  of  brain.  problem.  p a t h between two  The  neuronal  i s one  mammalian  rope-tightening  reasonable  problem  suggestion  (c)  the  the  i f • the  Some: i n t e r e s t i n g t e c h n i c a l p r o b l e m s were u n c o v e r e d approach..  of  much e x t r a n e o u s d e t a i l . ,  clearly  by  or  t o a minimum.  a Cartesian  Thus i t i s i n t e r e s t i n g t o  algorithms  three  i s reduced.  environment  method p r e s e n t e d  of  nodes i s r e d u c e d  search  are  objects,  a junction  objects,  used  digital  s h a p e s as  a  while  the  future  work  243 d i g i t a l represents  a shape d i r e c t l y  as an array of points l i k e  screen.,  previous  object  Of  the  and  Funt and  Baker used d i g i t a l r e p r e s e n t a t i o n s .  a  combination  representations  used  motion  Eastman  use  Pfefferkorn  rigid  of  the:  to simulate  simulations,  Cartesian representations My  Cartesian  the motion and  a  while  advance was  and  to  the  digital  c o l l i s i o n of  objects  on a t a b l e t o p .  VI.2  Conclusion I  began  the t h e s i s by asking  are r e g u i r e d f o r s p a t i a l the  what computational  reasoning.,  My  c o n c l u s i o n of the t h e s i s , i s t h i s .  i n c o r p o r a t i n g algorithms planar  shape  reasoning  VI.3  may  answer,  processes  and,  briefly,  Computational  processes  f o r computing the d i g i t a l s k e l e t o n of a  prove  to  be  sufficient  for  the  spatial  of a r o b o t - c o n t r o l l e r .  Research problems T h i s c o n s i s t s of a l i s t  of  problems  encountered  in  the  course of our p r o j e c t , t h a t need f u r t h e r i n v e s t i g a t i o n . 1. (a)  Problems r e l a t e d t o the simulated Extend  TABLETOP to compute exact  robot or o b j e c t and this and  environment.  an o b s t a c l e .  were d e s c r i b e d  collision Two  p o i n t s between  methods  i n I I I . 3 , which should  for  doing  be implemented  tested. VlaSummary, c o n c l u s i o n , and  f u t u r e work  244 (b)  Simulate  parallel  operating  hardware  to  c a r r y out  the  TABLETOP s i m u l a t i o n . (c)  G e n e r a l i z e the TABLETOP s i m u l a t i o n t o three  (d)  Design a more i n t e r e s t i n g can  be  done,  effects;  a  Trivially,  Since any  corresponding  by a l l o w i n g independently  extension  increase  organism-controller,  in  no  handled by the c u r r e n t  2. Problems r e l a t e d t o the Alio;* a r e s t r i c t e d  moving  of the environment r e q u i r e s the  such  capabilities extension  contemplated u n t i l the c u r r e n t environment i s  (a)  this  f o r example, by a l l o w i n g randomized a c t i o n  less t r i v i a l l y ,  objects.  environment..  dimensions.,  of  the  should  be  competently  organism-controller.  organism-controller.  form of n a t u r a l language input f o r  the  task•statement. (b)  Design a more ' r e a l i s t i c *  (c)  Implement  the  experimentation  form of  s p a t i a l planner. with  the  vision. In p a r t i c u l a r ,  L-shaped  object  extensive  problem  is  required.  3. Problems r e l a t e d t o the (a)  skeleton.  Implement s k e l e t o n algorithms  t h a t use  16-connected  cells  rather  cells,  and  their  than  8-connected  performance with the a l g o r i t h m and (b)  with true E u c l i d e a n  Extend  the  skeleton  for  compare  8-connected  networks  skeletons. algorithms  to  apply  VI«Summary, c o n c l u s i o n , and  to  three  f u t u r e work  245 dimensions. "the  locus  The  short  of the  centre  general  t h e 3D s k e l e t o n  however,  be o f  objects  i n three  definition  some  of  maximal  i s a surface  use  in  o f t h e 3D s k e l e t o n i s spheres", not a l i n e .  planning  the  and  in  I t may,  movement  of  dimensions.  VI«Summary, c o n c l u s i o n ,  and f u t u r e  work  246 APPENDICES  h-1 TABLETOP user's manual  Run  LISP, then type the f o l l o w i n g t o b r i n g up the TABLETOP  system: (DISKIN RSR1:BASIC RSR1:SRW#LISP RSR1:ENVIRONMENT#5 C0H4:SRW#0H) (OHSENSE) A  snapshot  o f the environment i s then d i s p l a y e d on the s c r e e n ,  and the bug can now be c o n t r o l l e d by a s m a l l number of commands. After  each  command i s given the r e t i n a l impression and t a c t i l e  impression o f Otak are d i s p l a y e d . In  the  following  negative number compass  with  direction  a  commands, decimal  "distance" point.  i s a p o s i t i v e or  "orientation"  is a  (one of N,NE,E,SE,S,SW,W,NW) o r a p o s i t i v e or  negative number with a  decimal  point.  A  zero  number  means  north,  a p o s i t i v e number means an angle measured clockwise from  north,  and  a  anti-clockwise  negative  means  an  angle  measured  from n o r t h . . " r a d i a n s " i s a p o s i t i v e or negative  number, o r one of positive  number  the  angles  PI  or  or negative number.. For both  PI/2.  "degrees"  " r a d i a n s " and  a p o s i t i v e number means a clockwise t u r n and a  is a  "degrees",  n e g a t i v e . number  247 means an a n t i - c l o c k w i s e (SLIDE  distance  turn..  orientation)  The  bug  moves  approximately  " d i s t a n c e " u n i t s i n the d i r e c t i o n " o r i e n t a t i o n " . (HOLD) i f the bug i s immediately adjacent then  a  movable  object  a f t e r t h i s command i s executed t h e bug and the  adjacent one  to  o b j e c t a r e cemented together  rigid  and  move  as  o b j e c t . . The PUSHTO and TURN commands must  now be used. (LETGO)  Undoes can  the e f f e c t of HOLD. move  freely  A f t e r t h i s command the bug  again,  by  means  of  the  SLIDE  held  move  command. (PUSHTO d i s t a n c e o r i e n t a t i o n ) The bug and the o b j e c t  (TURN  as  one r i g i d  the  approximate d i r e c t i o n " o r i e n t a t i o n " . .  radians)  The  bug  u n i t approximately " d i s t a n c e " u n i t s i n  and the o b j e c t held t u r n as o n e . r i g i d  u n i t through an  angle  of  approximately  "radians"  radians. (TURND degrees) The bug and t h e o b j e c t held t u r n unit  through  an  angle  as  of approximately  one  rigid  "degrees"  degrees. (WORLD  integer)  This  sets  up  " i n t e g e r " must l i e predefined  between  environments;  f o r s e t t i n g up an functions  a new environment f o r the bug. . 0  8.  there are a l s o  environment  START-SRW,  and  directly  These  are  facilities using  the  CREATE-OBJECT, and PUTPUSHER.  Examples of t h e i r c a l l i n g seguences can be found  in  HSE1:ENVIE0N#5. ,  249 1.2  1 c o m b i n a t o r i a l lemma  A it,  csguare  is  d e f i n e d as a sguare with e i g h t l o c a t i o n s on  one at each c o r n e r and one a t the  Each  l o c a t i o n may  be occupied or vacant.  csguares c o n t a i n s 2 =256 members.  Now  e  rotations  midpoint  of  each  side.  Thus the set S of a l l  c o n s i d e r the group  and r e f l e c t i o n s of a sguare i n t o i t s e l f .  G  of  G has e i g h t  elements, c o n s i s t i n g of the i d e n t i t y , t h r e e r o t a t i o n s , and  four  r e f l e c t i o n s . . Each element of G a c t s as a permutation of the s e t S.  Two  group  elements of s1, s2 of S are e g u i v a l e n t - i f element  g  such  that  gs1=s2..  This  there  is  a  i s an e q u i v a l e n c e  r e l a t i o n t h a t d i v i d e s S i n t o a number of eguivalence c l a s s e s . Lemma.  The number of e g u i v a l e n c e c l a s s e s of csguares under the  group G of r o t a t i o n s and r e f l e c t i o n s of a csquare i s 51. Proof.  By  Burnside's  lemma  (see  for  example,  B r u i j n , 1964,p. 150 fj) the number of equivalence c l a s s e s  is  [de given  by p s i (g)  where |G| denotes the number o f elements of G, and, f o r each p s i (g)  denotes  the  g,  number of elements of S t h a t are i n v a r i a n t  under g, that i s , the number of s6S f o r which gs=s., For j G | =8.  the  group G of r e f l e c t i o n s and r o t a t i o n s of a square,  3 = {I,R1„E2,R3,RR1 ,RR2, RR3, RR4}  Ri,i=1,2,3 reflections.  are Then  the one  rotations, has  and  where I i s the RR j , j= 1,2,3,4  p s i (I) =256;  identity, are  the  p s i (R1) =psi (R3) =4 ;  250  psi(R2)=16;  p s i (RR1) =psi (RR2) =psi (RR3) =psi (RR4) =32.  Thus  the  number of e q u i v a l e n c e c l a s s e s i s 1/8{256 + 4 + 16 + 4+4*32}=408/8=51. One r e p r e s e n t a t i v e from f i g u r e A2.1.  each  equivalence  QED.  class  is  shown  in  2  Figure 0  m  •  &2. 1  •  •  •  m  *  *>  0  m  m  *  •  0  a t  0  0  m  a t  •  *  \  *  -4>  •  a t  *  0  -  •  • 0  *  m  0  a t  * * •  0  *  m  * a *  m  •  0  -  *  a t  *  •  •  m  •  a t  0  0  0  0 •  *  •  •  *  0  *  0  0  *  m  •0  0  *  •  m  *  *  *  G  •  . *0  0  0  *  •>  *  m  *  m  *  a t  m  *  •  m  m  0  *  0  0  *  0  0  *  m  0  *  0  0  *  0  0  *  <m  m  *  0  *  0  * *  *  * •  0  *  *  •  0  m  *  *  *  0 * 0  •  *  m  0 * 0 * *  0  *  0 • , 0  0  *  *  •  *  0  *  o  *  m  •  a t  *  *  0  •  *  •  •t 0  *  *» .  0  m  0  <•  *»  0  0  0  •m .  0  0  #  * •  * a t  *  *  *  0  *  • •  *  m  0  *  *  *  * 0  * 0  •  0  *  * *  0  *  m  *  0  0  a»  •  *  0  .0 0  *  0  •  0  0  *  m  <•  *  0  G  0  *  #  o  *  *  a*  0  -m  0  0  m  *  0 0  a*  •  0  m  *  0  -m  *  0  0  *  0  0  *  *  a t  m  *  0  0  *  0  *  * 0  * 0  m  •  •  *  0  *  *  m  *  *  0 •  *  *  0  *  0  0  0  -  0  0  *  0  • a  *  m  *0 m  *  5T0fa)  251 A-3-On Funt's r i g i d  s h ape r o t a t i o n - a l g o r i t h m  Let a s i t u a t i o n be an arrangement of sguares on the WHISPER array and  l e t a r o t a t i o n be an ordered  angle of r o t a t i o n ) . new  situation.  pair  A r o t a t i o n transforms  {centre a  of  rotation,  situation  T h i s i s d e f i n e d p r e c i s e l y as f o l l o w s .  into  Suppose a  r o t a t i o n rho={C,alphaj i s used to r o t a t e s i t u a t i o n SIT1 new  situation  rotating R  of  SIT2. .  The  transformation  each sguare Q i n SIT1  is  independently.  into  a  out  by  carried The  a  image  square  Q a f t e r r o t a t i o n rho i s computed by the f o l l o w i n g method.  Let P be the c e n t r e p o i n t of square Q., radius  CP,  rotate  centre  C  and  p o s i t i o n P'  and  determine which square of the array c o n t a i n s P'.  This i s R,  the  square  and  may  P'  situation  by amount alpha  with  to a new  image  P  Now  of Q under rho.,  have  any  value  SIT2  consists  Note t h a t the d i s t a n c e between R  up  to  root2/2.  The  transformed  of the s e t of a l l image sguares under  rho. The  s i m p l e s t examples i l l u s t r a t i n g  why  o b j e c t on the array d i s i n t e g r a t e s are shown Note  in  figure  t h a t the d i s t a n c e between the c e n t r e s of two  sguares i s one diagonally of two the  the d e p i c t i o n of A3.1  edge-adjacent  whereas the d i s t a n c e between t h e . c e n t r e s  corner-adjacent  sguares i s root2.  edge-adjacent sguares,  same - square.  This  is  S i m i l a r l y , the c e n t r e s of two  Merge of two  corner-adjacent  of  Thus the  when r o t a t e d by 45°, can a  an  centres  map  squares i n t o squares  two  can  into one. map  0  \  R  Re  SPLIT STAGGERED  ROT AXIOM  SHRINKING  L E ^ *  a»\Tt <. 5* < ^ S* fumttfcs  Q -• o ' . t j  R  to  FIGURE  4  fVi.i  2 53  FIGURE A3.1  (continued)  254 into  two  non-edge-adjacent  between two situation the  and  situation  have the  previously  been  a  squares i n a row., T h i s i s a s p l i t  adjacent  squares.  sequence of r o t a t i o n s ,  applied of  of  two  squares  Then the f o l l o w i n q  of  the  be  the  line  such  sequence  joininq  that  their  be a s i t u a t i o n with e x a c t l y  n  lemmas hold.  For any two-square s i t u a t i o n there i s  rotations  initial  i n s u c c e s s i o n to the i n i t i a l s i t u a t i o n . . L e t  c e n t r e s . , L e t a n-square s i t u a t i o n  Merge lemma.  an  the f i n a l - s i t u a t i o n i s  a r i s i n q a f t e r a l l the r o t a t i o n s  centre-line  squares.  Given  the  final  a  sequence  s i t u a t i o n i s a one-square  situation..  S p l i t lemma. number  X,  situation  For any two-square s i t u a t i o n  and a r b i t r a r i l y  there i s a sequence of r o t a t i o n s i s a two-square s i t u a t i o n  large  such that the f i n a l  and the d i s t a n c e between the  c e n t r e s o f the squares i s a t l e a s t X.  Three f u r t h e r  Staggered  lemmas are needed to prove the s p l i t / m e r g e lemmas.,  rotation  lemma..  In  a two-square s i t u a t i o n l e t the  centre-line  of the two squares l i e at  horizontal  and  c e n t r e s be n. each  some  45°. L e t the h o r i z o n t a l Then two sequences o f  o f which keeps the h o r i z o n t a l  of the squares equal t o n,»  angle  between  the  d i s t a n c e between t h e i r  rotations  can  be  found,  d i s t a n c e between the c e n t r e s  One has p r o p e r t y  (a)  and  one  has  255 property  (b) i n the corresponding f i n a l  situations.  (a)  The c e n t r e - l i n e o f the two sguares i s h o r i z o n t a l .  (b)  The  c e n t r e - l i n e of the two squares  makes an angle of 45°  with the h o r i z o n t a l .  The sguares  staggered have  r o t a t i o n lemma e s s e n t i a l l y says t h a t  a  45°  i n t e r m e d i a t e sguares  centre  (n>0),  line  then  and  they  are  can  i f two  separated  be  rotated  by  n  in a  staggered  f a s h i o n so t h a t they have a h o r i z o n t a l centre l i n e but  are s t i l l  separated  conversely.  To  by  be  exactly  n  i n t e r m e d i a t e , sguares;  more p r e c i s e , suppose t h a t i n a two-square  s i t u a t i o n the c o o r d i n a t e s o f one square are  (ix,iy).  Then  m = Max {| i x j , | i y | j . any  two-sguare  and  the  axis  relative  to  the  other  d i s t a n c e between the squares i s  The staggered r o t a t i o n lemma then says t h a t  situation  can be transformed  i n t o any other i n  which the a x i s d i s t a n c e between the sguares i s the same..  Shrinking  lemma.  Given  a  two-square  situation  with  axis  d i s t a n c e n between the squares, and suppose (m - 1)*root2 < n < m*root2 holds  f o r some i n t e g e r m > n.  r o t a t i o n s such that i n the f i n a l  Then there e x i s t s a sequence of situation  the  axis  distance  between the squares i s m. (Proof: one 45° r o t a t i o n The  proof  of  the  plus one staggered r o t a t i o n . ) merge  lemma  now f o l l o w s by a l t e r n a t e  a p p l i c a t i o n s of the s h r i n k i n g lemma and the  staggered  rotation  256 lemma.  Expanding  lemma.  Given  a  two-square  situation  with  axis  d i s t a n c e m between the squares, and suppose n - 1/2 < m*root2 < n + 1/2 holds f o r some i n t e g e r n > m. rotations  such  that  between t h e squares  in  Then there e x i s t s a  sequence . of  the f i n a l s i t u a t i o n the a x i s d i s t a n c e  i s n.  (Proof: one staggered r o t a t i o n plus one 45° r o t a t i o n . ) The  proof of the  applications lemma.  of  split  lemma  the expanding  now  follows  by  alternate  lemma and the staggered  S u c c e s s i v e a p p l i c a t i o n s of the  merge  lemma  rotation  prove  the  following  Collapsing,  theorem.  Given  any  sequence of r o t a t i o n s such t h a t  initial  the  final  s i t u a t i o n there i s a situation  contains  only one square.  Conversely,  the question i s whether t h e . s p l i t lemma can be  g e n e r a l i z e d to multisquare s i t u a t i o n s .  Spreading an  theorem.  arbitrarily  The answer i s yes.  Given any s i t u a t i o n with S squares and given  l a r g e number X, there i s a sequence of r o t a t i o n s  such that i n the f i n a l s i t u a t i o n t h e r e are s t i l l  S  squares  and  the d i s t a n c e between any two squares i s a t l e a s t X. Proof  (outline).  Pick a  pair  of  squares  with  minimum  axis  257 distance  and  take  the c e n t r e of one  of these as the c e n t r e of  rotation for a l l following rotations. in  t u r n u n t i l a l l the sguares  l i n e s through to  occur  rotation  moving any  closer  rotate  other squares,  squares,  as  would  so  that  the  other.  occur  diagonal  allowed  centre  the  any  lines  diagonal  of  In p a r t i c u l a r ,  in  up without  sguare  can always be  by p i c k i n g a  than any  of an o b j e c t , can be s p l i t  4 5°  No merges must be  An i n d i v i d u a l sguare  t o t h a t square  •compact' s e t s of depiction  l i e on e i t h e r of the two  the centre of r o t a t i o n .  in this jiggling.  moved without  F i r s t j i g g l e each  original  merges..  are  in  Now the  h o r i z o n t a l / v e r t i c a l p o s i t i o n , then c a r e f u l l y stagger back to the diagonal position.  45° r o t a t i o n  does  the  standard  position.  s u f f i c i e n t spreading has  occurred.  staggering  regains  The  The c o l l a p s i n g and  the  splitting, Repeat t h i s  spreading theorems are  t h a t Funt's o b j e c t r o t a t i o n scheme cannot work.„  enough  to  the until  show  258 REFERENCES  [ Amarel, 1 968 ] Amarel,S. 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