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Hierarchical task decomposition and execution for robot manipulation task using a wrist force sensor Kotzev, Shmuel 1990

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H I E R A R C H I C A L T A S K D E C O M P O S I T I O N A N D E X E C U T I O N F O R R O B O T M A N I P U L A T I O N T A S K USING A WRIST F O R C E SENSOR By Shmuel Kotzev B.Sc. T ECHION, Haifa, Israel A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F A P P L I E D S C I E N C E in T H E F A C U L T Y O F G R A D U A T E S T U D I E S M E C H A N I C A L E N G I N E E R I N G We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A September 1990 © Shmuel Kotzev, 1990 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. 1 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 or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver, Canada DE-6 (2/88) Abstract The research developed force-motion strategies and subsequent force and position control algorithms, using a PUMA 560 robot arm and its original controller. A task decompo-sition methodology has been developed that enables a mechanical assembly task to be subdivided into a series of executable subtasks. By applying this methodology to the assembly of a hydraulic gear pump, a library of special purpose, task oriented, subtask programs were created. Most of these programs, though derived for a pump assembly task, are applicable (when used with appropriate parameters) to other assembly tasks. Most of the algorithms require force/torque sensory information that is supplied by a JR3 wrist force sensor. The force control algorithms use that data and system compliance in order to produce new position instructions that are transferred to the controller of the arm. The logic of the control law and system behaviour when contacting the environment, were checked, using the dynamics and compliance of a simplified structure of a robotic arm and its wrist sensor. A demonstration of the pump assembly task, using the arm, force sensor, controller and the derived library algorithms is an integral part of the thesis. ii Acknowledgements I would like to thank my supervisor, Professor Dale B. Cherchas for the support, guidance and encouragement he provided in the development of this work. I would also like to thank Doug Latornell, for fruitful discussions and support that eased both my introduction and experimental work in robotics. Also, I would like to thank Alan Steeves and Gerry Rohling for their good advice, patience and support in the use of the department computer system. Technical assistance was provided by the mechanical and electrical workshops, and especially by Dave Camp and Don Bysouth. I thank them for their assistance in both parts manufacturing and technical support. The robot arm and force sensor were purchased with financial support from the Nat-ural Sciences and Engineering Research Council of Canada (NSERC). The VAXSta-tion 3200 computer system was provided through an equipment grant from the British Columbia Advanced Systems Institute (ASI). iii Nomenclature A - a (n x 6) sensor coupling matrix. At - bolt tensile stress area. c - clearance ratio (^jp)-d - nominal diameter of the thread. F_ - desired force (control algorithm). F e - force error signal in the control loop (F e = F_ — F,). Fj - desired preload. Fn— - vector of nominal measured signals. F , - force sensed by the sensor. Fe - applied forces. Fz - insertion force. G , - compliance matrix. J - the Jacobian of the manipulator. Kjd - vector of proportional gains of the switching controller. K_ - programmable damping matrix. K p - programmable stiffness matrix (desired elastic behaviour). K , - stiffness matrix. K_ - lateral spring constant. K.g - angular spring constant. / - insertion depth. L - lead of the screw. M - moment applied by the support. iv q a - a c t u a l j o i n t d i s p l a c e m e n t . - d e s i r e d j o i n t d i s p l a c e m e n t , q - e r r o r i n j o i n t d i s p l a c e m e n t (q = — q a ) . r - r a d i u s o f t h e p e g . R - r a d i u s o f t h e h o l e . 5 - s i g n a l v e c t o r o f t h e f o r c e s e n s o r . S M O A ! - m a x . m e a s u r i n g s i g n a l s v e c t o r . Sp - b o l t p r o f f s t r e n g t h v a l u e . Tj - t o r q u e r e q u i r e d t o p r o d u c e a g i v e n p r e l o a d . U - l a t e r a l e r r o r o f t h e c o m p l i a n c e c e n t e r . V a a. - a x i a l s p e e d o f t h e s c r e w . w - w i d t h o f t h e c h a m f e r . x 0 - a c t u a l t a s k s p a c e d i s p l a c e m e n t v e c t o r . X j - d e s i r e d t a s k s p a c e d i s p l a c e m e n t v e c t o r . x - d i s p l a c e m e n t e r r o r (x = x<j — x n). 6 - r o t a t i o n a l e r r o r o f t h e c o m p l i a n c e c e n t e r . Lg - d i s t a n c e f r o m c o m p l i a n c e c e n t e r . Sx - a m o u n t o f d e f l e c t i o n a t t h e t o o l ' s t i p . e 0 - i n i t i a l l a t e r a l e r r o r . \ t - t i m e i n t e r v a l o f t h e d i s c r e t e s y s t e m . fi - c o e f f i c i e n t o f f r i c t i o n . A0 - r o t a t i o n a l a n g l e . Ax - a x i a l t r a n s l a t i o n . r - j o i n t t o r q u e s . Table of Contents Abstract ii Acknowledgements iii Nomenclature iv 1 INTRODUCTION 1 2 SYSTEM DESCRIPTION 4 2.1 PUMA 560 ROBOT 4 2.1.1 Arm Structure: 5 2.1.2 Controller and Interfaces: 6 2.1.3 VAL-II Language: 8 2.2 JR3 FORCE / TORQUE SENSOR 10 2.2.1 Introduction: 10 2.2.2 JR3 Force Sensor: 12 2.3 COMPLIANCE DEVICES 13 2.3.1 Remote Center of Compliance (RCC): 13 2.3.2 Linear Compliance Device: 14 3 TASK DECOMPOSITION 19 3.1 INTRODUCTION 19 3.2 LITERATURE REVIEW 20 3.3 ASSEMBLY STRATEGY AND ALGORITHM STRUCTURE . . . . . . 23 vi 3.4 PUMP ASSEMBLY DEMONSTRATION 29 4 FORCE/MOTION SYNTHESIS FOR ASSEMBLY TASK 37 4.1 FORCE CONTROL REVIEW 37 4.1.1 Introduction: . . . 37 4.1.2 Impedance Control: 40 4.1.3 Hybrid Control: 42 4.1.4 Force Control for Assembly Task: 43 4.2 DYNAMIC MODEL ANALYSIS 47 4.3 CONCLUSIONS 51 5 ASSEMBLY SUBTASKS 57 5.1 SUBTASK PICK 58 5.2 SUBTASK PLACE 59 5.3 SUBTASK INSERT 60 5.3.1 Part Mating Analysis 62 5.3.2 Jamming and Wedging Analysis: 65 5.3.3 Strategy and Control: 68 5.4 SUBTASK SCREW 70 5.4.1 Feeding the Bolts: 70 5.4.2 Screwing and Preloading: 71 5.4.3 Tooling: 72 6 ASSEMBLY SUBROUTINES 78 6.1 SUBROUTINE MOVE 81 6.2 SUBROUTINE APPROACH 82 6.3 SUBROUTINE GRASP 84 vii 6.3.1 Grasp Planning: 84 6.3.2 Gripper's Configuration: 85 6.4 SUBROUTINE SEARCH 86 6.4.1 Search strategy: 87 6.4.2 Rotation strategy: 90 6.5 SUBROUTINE COMPLY 91 6.6 SUBROUTINE ROTATE 92 6.7 SUBROUTINE CLEAR 93 7 S E R V I C E P R O G R A M S 103 7.1 PROGRAM PCstop 103 7.2 PROGRAM Nuil.sensor 103 7.3 OVERLOAD CHECKING 104 7.4 FORCE INFORMATION 105 7.4.1 Force/Torque data in tool coordinate frame: 107 7.4.2 Force data using world coordinate frame: 109 7.5 PROCESS CONTROL PROGRAMS I l l 7.6 INITIALIZATION and PARAMETRIC FILES 114 7.7 PROGRAM WEIGHT 115 7.8 PROGRAM REPEAT 116 8 F O R C E C O N T R O L S I M U L A T I O N 119 8.1 SYSTEM DESCRIPTION 120 8.1.1 Applied Force Control: 120 8.1.2 Arm Stiffness: 121 8.1.3 Reduced Parameters: 123 8.1.4 Impact: 125 viii 8.2 MODEL DESCRIPTION 126 8.3 CONCLUSIONS 128 Bibliography 134 A MAIN TASK and SUBTASKS: 140 A . l main program PUMP: 140 A.2 subtask INSERT: 140 A.3 subtask PICK: 141 A.4 subtask PLACE: 141 A. 5 subtask SCREW: 141 B SUBROUTINES and SERVICE PROGRAMS: 142 B. l program APPROACH: 142 B.2 program CLEAR: 145 B.3 program COMPLY: 146 B.4 program COMSCREW: 149 B.5 GEAR1, GEAR2 parameters: 150 B.6 program GRASP: 153 B.7 program JR3.DAT: 155 B.8 program MOVE: 157 B.9 program NULL.SENSOR: 158 B.10 program OVERLOAD: 158 B . l l program PCSTOP: 158 B.12 program REPEAT.BOLT: 159 B.13 program REPEAT.SCREW: 159 B . H program ROTATE: . 161 ix B.15 SCREW parameters: 162 B.16 program SEARCH: 164 B.17 program SHOW.FM: 168 B.18 program TIP: 168 B.19 TOOL parameters: 169 B.20 TOP parameters: 171 B.21 program WEIGHT: 172 x Chapter 1 I N T R O D U C T I O N An assembly task i6 an operation of collecting, mating and aligning (in a specified way) two or more three dimensional objects. Performing a mechanical assembly task is a ge-ometric position problem usually solved by highly sophisticated human operation. In order to accomplish the same assembly tasks by a robotic arm (manipulator), the follow-ing parameters should be part of the system: • both gross and fine motion ability of the arm's tip (end effector). • high speed, high capacity computer hardware utilizing a high level language. The software library must include sophisticated programs that control the manipulator movements, using mostly, a translation of human experience to program instruc-tions (feedback control). • variety of sensors including force/torque or tactile sensors, a vision system etc. These devices enable the system to verify task completeness, to close control loops and, in very advanced systems - to assist in task decomposition. In order to actually execute an assembly task, the theory and algorithms were derived for the robotic system and equipment located in the U.B.C. Department of Mechanical Engineering CAMROL Laboratory. A full description of laboratory facilities and equip-ment is given in chapter 2. As an example, a Pump Assembly Task was performed, using the CAMROL equipment. 1 Chapter 1. INTRODUCTION 2 The system's control is realized hierarchically in several levels. Every control level solves its specific tasks, using special algorithms and hardware. According to Vukobra-tovic [41] the control hierarchy can be realized in three levels: Strategical control, tactical control and executive control. In order to properly control those levels while executing an assembly task, it has to be decomposed according to the laboratory equipment, the mechanical knowledge (movements, forces etc.), the execution strategy and the descrip-tion of the task (Fig. 1.1). Task decomposition can be done automatically by a task planner computer algorithm or manually by a human designer. Chapter 3 deals with the ways to manually decompose a task into smaller programs that can easily be executed and controlled. At the end of chapter 3, there is an example of how a decomposition is implemented on a Pump Assembly Task. Another major objective of the research was to develop a library of necessary force-motion strategies and subsequent force and position control algorithms. Assuming that a library of such programs is stored in the computer memory, the designer can call any desired program in any order to perform a larger overall assembly task. The force control algorithm is part of the execution strategy of the assembly task. Chapter 4 begins with force control review and ends with the description of the algorithms used in this thesis. The main task - the assembly of a pump, is decomposed to use subtasks (chapter 5), subroutines (chapter 6) and service programs (chapter 7). These are VAL-II, high level programs, based on force information data, received from the JR3 force sensor. The programs are task level programming: describing the assembly task as a sequence of positional goals of the object. The control of the assembly tasks is based on fine motion strategies applicable (where possible) to the global assembly tasks. One of the main 6 u b j e c t i v e s of the thesis was to create the programs, based on the description of Pump Assembly Task. Task assembly strategy is the basis of the de-composition and force motion relations and every program is described according to its Chapter 1. INTRODUCTION 3 function. It is important to understand that although the programs (subtasks, subrou-tines and service programs) were derived from the description of pump assembly, they are not oriented to that specific task and can be used in any other assemblies. The structure of every algorithm is based firstly on initialization of parameters that are task oriented. Those parameters are received from a special file (initialization file) written by the operator. Using these initialization parameters, the operator can command the algorithm to execute a subtask according to his specifications. In order to predict the dynamics of simple force-controlled robot system and to un-derstand it's reactions, a force control simulation was created. A description of the simulation and its results is given in chapter 8. Mechanical knowledge Laboratory equipment Assembly strategy Task description (pump example) Task decomposition Library of assembly programs Task main 1 program 1 Desired goals (assembly) Figure 1.1: Task execution structure. Chapter 2 SYSTEM DESCRIPTION The system is built around a PUMA 560 robot arm, its controller, a JR3 force sensor and a workspace. The chapter gives a basic background about the major devices and parameters of the system (Fig. 2.1), used to accomplished both the experimental and analytical parts of the thesis. 2.1 P U M A 560 ROBOT Unimation PUMA 560 arms are an advanced computer controlled, widely used class of industrial manipulators. The PUMA robot system is designed to adapt to a wide range of applications. The robot is capable of applying a max. static force of 58 [N] at the tool point and to move with this load in max. tool velocity of 1.0 [m/s] and max. acceleration of 1.0 [g]. The robot arm operating envelope is approx. a radius of 0.9 [m]. Fig. 2.2 shows the basic unit plus the peripherals in use in CAMROL. The robot system includes the following units: the robot arm, controller, software (memory and floppy disk), teach pendant and I/O module. The robot arm executes the instructions transmitted to it by the controller. The user controls the controller manually, by the teach pendant or by running user programs (developed at VAL-II language). The programs can be executed on the local LSI-11/02 microcomputer (located in the controller) or on an external supervisor computer. In all these cases, the controller transmits the instructions from the computer memory to the motors located in the links of the arm. Position data obtained from incremental encoders and potentiometers (located in the robot joints) are 4 Chapter 2. SYSTEM DESCRIPTION 5 transmitted back to the controller to provide closed-loop control of the arm's motions. The high-level programming language is VAL-II. Generally, VAL-II software and pro-grams are stored in the computer memory which is located in the controller. Programs may also be stored in a floppy disk or an external computer. This interface may be car-ried out by matching the Unimation floppy disk drive protocol, using the existing serial communication line of the floppy drive. Additionally, programs can be executed to implement an interface between the robot and its environment. A peripheral device with a panel switch board, enables the transfer of external input and output signals. Use of these signals in the program enables the programmer to halt a program or branch to another program or subroutine. Communi-cation with sensors or host computers is done through serial ports (RS-232C interface), DMA port or the panel switch board. 2 . 1 . 1 Arm Structure: The arm is a revolute, 6 degrees of freedom (d.o.f) type manipulator (Fig. 2.3) consisting of a trunk (link 0), a shoulder (link 1), an upper arm (Hnk 2), a forearm (link 3), a wrist (hnk 4) and a gripper (links 5 and 6). Each one of the 6 joints is driven by a geared, permanent-magnet D.C. servo motor, activated by a power amplifier board, mounted in the controller box. The motor systems contains the following devices: • Integral brakes: a safety feature which is installed in the major axes (joint 1, 2 and 3). When power is removed from the motors, the electromagnetic brakes are activated and lock the joint at the current position. This prevents the arm from collapsing or movements due to accidental (or deliberate) power removal. • A geared potentiometer is a part of the motor assembly. It supplies low resolution, absolute joint position data. This information, combined with the index signal of Chapter 2. SYSTEM DESCRIPTION 6 an encoder, is used to initialize joint position during calibration process of every power-on of the arm. • An incremental optical encoder is connected to the motor shaft. It supplies high resolution rotation data, as well as the direction and absolute angular position of the motor shaft (index signal every 360 degrees). Approximately every 0.875 [msec], the encoder's outputs are compared with the calculated position, and any necessary corrections are generated allowing overall rated repeatability of ±0.1 [mm]. The PUMA at CAMROL is equipped with an optional pneumatic (710 KPa), com-puter controlled gripper. The two-way solenoid valve enables full pneumatic force in both the open and the closed positions. Special purpose jaws can be mounted onto the gripper according to the desired task. 2.1.2 Controller and Interfaces: The controller is the master component of the electrical system. All signals to and from the robot pass through the controller and are used by it to perform real time calculations to control arm movement and position. Ref. [13] gives an essential summary, while Ref. [38] gives a full description of the subject. The controller box is used for: • Location, protection and connection of the electronics boards and power devices. • Operation and control panel equipped with operating switches and indicators. This enables the user to switch on/off the unit, the arm, the breaks and the execution of the program. • Connector base which connects the robot arm, terminal, floppy disk drive and the I/O modules. Chapter 2. SYSTEM DESCRIPTION 7 Programming is often simplified by constructing the program hierarchically. For manip-ulator programming, the lowest level usually provides the interface with the manipulator sensors and actuators. In the PUMA, the control scheme of the robot arm is a propor-tional plus integral plus derivative (PID) controller. It is realized, in the controller box, by two computers hierarchically arranged: A) . The LSI-11/02 supervisory microcomputer performs two major functions. The user interface enables on line, bidirectional interaction so interpreting, debugging, scheduling and executing of movement commands and coordinates transformations can be easily done. The second function is the joint controller interface that coordinates the con-trollers of the six joints. B) . Six 6503 microprocessors, joint controllers, are at the lower level of the hierarchy. Each joint is controlled and activated separately by its two servo loops and joint mo-tor. The feedback loops control the position and the velocity variables. Both servo loop gains are constant, a property that limits the flexible dynamic response of the system to varying speeds and payloads. The system's control is realized hierarchically in several levels. Every control level solves its specific tasks, using special algorithms and hardware. Fig. 2.4 shows the current structure of the robotic control system at CAMROL. According to Vukobratovic (Ref. [41]) the control hierarchy can be realized in three levels (explained in section 3.2): • Strategical control level. • Tactical control level. • Executive control level. Chapter 2. SYSTEM DESCRIPTION 8 2.1.3 VAL-II Language: A computer-based system provides an easy definition of a task a robot is to perform. Us-ing a computer-based system for programming and controlling industrial robots provides the following: a) , ability to respond to sensory information. b) . improved performance in terms of trajectory generation. c) . allows operation in unpredictable situations or moving frames of reference. Several languages have been developed in order to manipulate robot arms in complex tasks. Some of the major languages are: AL, written in Stanford University, PasRo -Pascal and C for Robots, AML and AUTOPASS by IBM, HELP by General Electric, MCL by McDonnell Douglas, JARS by Jet Propulsion Laboratory and VAL-II - a product of Unimation. VAL-II is a computer-based control system and language designed specifically for use with Unimation Inc. industrial robots (PUMA series). It is a high level, BASIC based, interpreter programming language. VAL-II enables driving the arm by frames manipu-lation or by motion and speed commands directed to the joints. The executed program can activate other programs through call function and run process control (pc) parallel program at the same time. As a real time system, continuous trajectory computation by VAL-II permits complex motions to be executed quickly, with efficient use of system memory and reduction in overall system complexity. The VAL-II system continuously generates robot control commands and can simultaneously interact with a human oper-ator, permitting on-line program generation and modification. VAL-II contains the capability of communicating with external systems, using a rig-orous communication protocol to ensure the integrity of information transferred between the VAL-II system and the external systems. The communication is possible at three Chapter 2. SYSTEM DESCRIPTION 9 levels: • supervisory communication provides a facility for controlling VAL-II system re-motely. Any activity which can be performed at the system terminal can alterna-tively be performed by a remote supervisory system. A standard RS-232C serial line is used for the interface, with a DDCMP protocol. • program level communication sending output and receiving input from the system terminal, floppy disk and other external devices which communicate serial data. • real time trajectory modification can be done using data supplied by an external device such as a sensor. This data can be processed 36 times per second while VAL-II continuously informs the external system where the robot tool is located and the status of communication. In addition to the program level serial communication, VAL-II provides up to sixteen single ended analog input channels and two channels of analog output with hardware option. The following advantages may be gained using those computer interfaces: • an external system can completely supervise the operation of the VAL-II system (even during program execution). • sensory generated data may modify the path of the robot while moving (a real-time path control). • ability to control directly the robot or to create programs in off line and down-line loads (by matching the terminal protocol in the external computer). • more external data storage capacity (by matching the mini-floppy disk drive pro-tocol in the external computer). Chapter 2. SYSTEM DESCRIPTION 10 In CAMROL, we used some of these features of VAL-II. The external computer is the VAX Station 3200 which serves as a terminal and a supervisor controller to the PUMA. 2.2 JR3 FORCE / TORQUE SENSOR 2.2.1 Introduction: Force/torque sensors, used with robots, are devices used to measure the forces and mo-ments developed between the robot gripper and the environment due to contact. Typical applications are assembly (Ref. [39] and contour tracking (Ref. [12]). Industrial applica-tions involving the use of force sensors for feedback force control are quite rare. This is mostly because force sensor data influences the dynamics of the joint servo loops. Most available controllers (including the PUMA 560 controller) do not allow such low level interaction with the robot. Another reason can be found in the force sensor itself that is a fragile instrument and thus very prone to overloading. Mechanical overload protection is a must, but it is very difficult to achieve it properly. The following are the optional locations to place force sensors (Ref. [39]): • in the joint actuators - measures torque/force of the actuator and used mainly by master/slave manipulators. • in the interface between the last joint and the gripper. A multi component force wrist sensor. • on the gripper fingers, mainly by means of strain gauges applied to the fingers. • in the contact area - tactile sensors (artificial skin sensors) placed between the fingers and the grasped object. • in the robot environment - in the table or the mounting fixture. Chapter 2. SYSTEM DESCRIPTION 11 The Puma robot has a wrist force sensor plus electronic system from JR3 company. A wrist force sensor is an elastic (metallic) structure that deforms under applied forces. The structure is usually mapped with strain gauges that have proven to be the smallest, simplest, cheapest and reliable transducers for use in robot force sensors. The produced output voltage is proportional to the strain in the structure (assuming operation within its elastic range). "The raw analog signals of the strain gauge bridges are transferred to the electronics system where they are amplified and processed. Additional processing of the output data is made in the robot controller including calibration, decoupling and coordinate transformations. The correlation between the input force vector (to the sensor) F , (3 force and 3 torque variables) and the inner signal vector of the sensor S, is the output of n different strains measurements output and is given by: S = A F « (2.1) where A is a (n x 6) sensor coupling matrix. For n = 6 the force vector can be resolved by the decoupling matrix A - 1 : F . = A " 1 • S (2.2) If the 6ensor is mechanically decoupled ( A - 1 is diagonal) then every measuring com-ponent is proportional to only one force component. Thus the quality of the force sensor is reflected by the form of its decoupling matrix (a perfect diagonal A matrix can't be obtained in practice). The presence of nonzero diagonal elements cause the cross sensi-tivity of the sensor. Other important features of the sensor are: a) the measuring signals are to reach their max. value Smam when all force components reach their nominal values simultaneously: e (2.3) 3=1 Chapter 2. SYSTEM DESCRIPTION 12 b) to receive the same measuring accuracy on all components, each force component should contribute equally to the measuring signal i.e. 0>i\F\n = ^ Esn = ••• = O-ieFsn = g^in (2-4) 2.2.2 JR3 Force Sensor: The force-moment sensor used with the Puma robot is a standard JR3 Universal Force-Moment Sensor System consisting of: • JR3 monolithic six-degree-of-freedom force sensor. • JR.3 Intelligent Support System That contains: 1. signal conditioning board. 2. data acquisition board. 3. processor board. Due to forces/torques acting on the sensor the strain gauges change their response, producing small variations (milivolts) in the measured voltage of the system. The raw analog signals are transferred to the electronics box, where they are amplified, filtered, digitized (12 bit A/D) and processed (digital filtering, load envelope monitoring, etc.). Onboard shunt resistors combined with calibration software offer automatic drift compen-sation. Output can be received as discrete I/O, high-speed parallel interface or through two serial ports. Chapter 2. SYSTEM DESCRIPTION 13 2.3 COMPLIANCE DEVICES 2.3.1 Remote Center of Compliance (RCC): The RCC is a mechanical multi axis passive compliant device. While executing assembly tasks in the CAMROL laboratory, the RCC is mounted between the force sensor (or the linear compliant device) and the gripper as can be seen in Fig. 2.5. The RCC was designed to ease assembly of closefitting objects in spite of lateral or angular misalign-ment by correcting position and angular errors. Typical applications are rivets assembly, screwing bolts, bearing installation etc.. The RCC is widely used in industry due to its price, simplicity of installation and its repeatability and reliable response. The construction of the RCC is a combination of two mechanical parts: translational and rotational. The translational part allows lateral motion while the rotational part allows angular movement of the end-effector. The flexibility of the LORD RCC Series devices is provided by laminated elements made up of elastomer and steel shims. In compression these elements are much stiffer than in shear. This design enables the laminated element to respond correctly to lateral forces or moments. The preferable working point for accurate assembly tasks while using RCC, is at its center of compliance or elastic center. It is a specific projected point along the tool axis (its exact location is a function of the structure of the RCC). For part mating, it is ideal if the stiffness matrix (of the part and the structure supporting it) becomes diagonal at the tip of the part. At that point, force/deflection behaviour of the structure becomes decoupled i.e. pure rotation will occur due to applied moments and pure translation will occur due to lateral contact forces. The major advantage of the RCC is that it absorbs both lateral and angular errors plus twist errors about the insertion axis. Its disadvantages are its limited operating range (suitable only for end-effector/part combination of a single length) and its limited Chapter 2. SYSTEM DESCRIPTION 14 operating speeds. The IRCC is a combination of a force/torque multi degree of freedom sensor, built into the mechanical compliant structure of the RCC. The RCC in CAMROL is from the LORD company. 2.3.2 Linear Compliance Device: For a stiff manipulator and stiff environment, part mating introduces high level forces when a position error occurs (the forces are function of the size of the error and the stiffness of the mating parts). Position errors can be introduced by both the tool and the mating object. Tool position error is introduced due to matrix manipulation resid-uals (locations and inverse kinematics), encoders resolution, tool/gripper misalignment (changing in the relative position due to external forces) etc.. The location of the mating surface is imprecise because of bad positioning in the part location area and unprecise manufacturing. Special perpose precise parts are partial solution but are impractical. Practical ways to overcome the problem are fine arm motion and/or low compliance. a) The ability to use fine motion is part of the robot performance and it is activated using process control program with small gains (a pc program runs parallel to the main program and can altered the arm's trajectory - in this case, according to force data). These gains are used whenever the tool is in the neighborhood of another part. b) The contact forces are function of the dynamic parameters and of the compliance of the arm, sensor and the environment. Decreasing the stiffness of the end effector (or the assembly base) enables the use of higher dynamic parameters (velocity, acceleration) of the arm, without increasing the contact forces. The RCC gives compliance to the system in the (X — Y) plane, while an additional compliant linear device used in the Z direction completes the e-e compliance behaviour. This structure reduces the band width of the system, but in an assembly task, the important parameters are low contact forces and Chapter 2. SYSTEM DESCRIPTION 15 flexible operation, and after it comes high speed operation. The added device (schematically represented in Fig. 2.5) was based on 3 linear bear-ings and a soft spring. The RCC can comply to torques about X, Y and Z axis and to forces in the X — Y plane. The linear device completes the compliance of the system in the Z direction, but was found not to be necessary for the demonstration (Sec 3.4) for slow execution. Figure 2.1: System structure and workspace. Chapter 2. SYSTEM DESCRIPTION 16 Chapter 2. SYSTEM DESCRIPTION 17 TASK SPECFCATIONB CONTROL theory > LEVELS o»*. DESIGNER T A C T I C A L TERMINAL CPU —r DRV-11 A R M I N T E R F A C E RAM TASK DECOMPOSER AUTO TASK PLANNING [3200 SENSOR(S) Accessory Manual box Floppy disk 1 1 VAL EPROM DLV-11J Q - B U S 1 / S503 mp D/A AMP. MOTOR ENCODER 6503 mp CVA AMP. MOTOR ENCODER Figure 2.4: Structure and hierarchy of the CAMROL robot system. Chapter 2. SYSTEM DESCRIPTION 18 COMPLIANCE with LINEAR BEARINGS REMOTE CENTER of COMPLIANCE GRIPPER PEG WORKPIECE XT O O O O O FORCE S E N S O R -T3T O o O O O O Figure 2.5: Structure of the end effector for assembly task. Chapter 3 T A S K D E C O M P O S I T I O N 3.1 I N T R O D U C T I O N One of the objectives of the research was to develop the force-motion strategies and force/position control algorithms for selected assembly subtasks. Those programs are part of a software library that can be used to construct many other assembly tasks, using a manipulator equipped with force sensor. The programs from the library are activated according to the order received by decomposing the main assembly task. This chapter describes the logic behind the decomposition of an assembly task into a set of programs that enables the actual assembly by the arm. The chapter begins with literature review and describes the decomposition hierarchical structure and the way it functions. A specific task, i.e. Pump assembly, was chosen to be in the background for the library of assembly subtasks. The programs derived in the thesis are those that are needed to execute this assembly task. The next sections describe the way the main task is decomposed using subtasks, subroutines and service programs. Here, task planning and the way it can be executed, is based on CAMROL's facilities, on the mechanical structure of the pump and on assembly logic. It is important to emphasize that the library structure developed and described in the following chapters is not exclusively for the Pump Assembly. The subtasks are part of a general library and can be used to generate any special purpose assembly task. The only part that is task oriented is the program P U M P and its related Initialization files. In the future, for other new 19 Chapter 3. TASK DECOMPOSITION 20 assembly tasks, it is likely, that some new programs (subtasks, subroutines and service programs) may be needed. Building those new programs in the same structure logic that is developed in this thesis, will allow the designer to use the other programs of the library together with the new programs. The execution of an assembly program involves contacts between the end effector and the environment. The surface in contact introduces kinematic constraints that modify the motion of the manipulator. The use of force sensory information and force/position con-trol, enables the constrained manipulator to regulate force and torque reactions between the end effector and the environment while simultaneously moving the arm to the desired position and orientation. Force control and force/position relations are the heart of the assembly algorithms therefor, a review and development of the subject is presented in the next chapter. Based on both subjects: task decomposition and force control algorithms, the following chapters describe the way pump assembly task is implemented. 3.2 LITERATURE REVIEW Sophisticated, intelligent tasks can be executed by means of hierarchically intelligent control systems. Manipulators like Telerobots are designed to be controlled both directly by a computer and remotely by a human. This supervisory control, allows the operator to apply his intelligence to the task without having to maintain continuous control. The use of Hierarchically Intelligent Control can be applied (Ref. [35]) based on the following principle: increasing intelligence (additional sensors, suphisticated software) enables the decreasing of the precision (arm, workspace). It can also lower human activity in the manipulator operation. In this chapter, Task Decomposition control level is discussed. It performs real time planning and task monitoring as well as task decomposition of high level goals into low level actions. Chapter 3. TASK DECOMPOSITION 21 According to Vukobratovic (Ref. [41]) the control hierarchy can be realized in several levels, so each control level solves its specific task. The one usually adopted for robotic control system can be realized in the following three levels (Fig. 2.4): • Strategical control level defines mostly trajectories and system actions by using pre-defined (off line) information. In advanced systems, this level uses sensory information to solve problems in real time using high level programing languages. • Tactical control level is mostly implemented by inverse kinematics solutions that use desired position and orientation of the end-effector plus joint and link parameters of the robot in order to calculate the corresponding desired joint angles. • Executive control level has to realize the positions of the robot joints which are imposed by the higher, tactical control level. This level in the PUMA control system has both position and velocity servo loops which critically damp each joint according to the program's specified speeds. In Ref. [35] (Saridis), a three level hierarchical structure is presented: including the models of the upper two. The three levels are: 1. The upper level is the organization level that performs general knowledge processing tasks with little or no precision. This level performs five sequential functions: machine reasoning, machine planning, decision making, feedback and long-term memory. It formulates complete and compatible plans and decides about the best possible plan to execute the user requested job. 2. The coordination level performs specific knowledge processing tasks, by using spe-cific coordinators, each performing its own pre-specified functions. Its purposes are to coordinate the individual tasks, to assign penalty functions and to optimize the performance of the overall plan. Chapter 3. TASK DECOMPOSITION 22 3. The execution level is composed of specific execution devices associated with each coordinator. Ref. [2] (Albus), describes three legged hierarchical architectures that are executed in parallel and have some levels that are function of the desired task. In this case, the decomposition module is not the upper level, instead, each of its levels is executed in parallel to the two other modules: world modeling and sensory processing. In each operational level, the task decomposition module is using world modeling information that is continuously updated by the third module. This is a dynamic way to activate the manipulator in an environment that is changed during operation or in an unpredicted environment. In each level, the task decomposition module consists of the following functions: 1. job assignment manager ie responsible for partitioning the task into distinct jobs to be performed by the planner and the executor mechanisms. At some upper levels it may also assign physical resources against task elements. 2. one or more planners that are responsible for decomposing the jobs into sequence of planned subtasks. The planner hypothesizes some action or series of actions, and the world model predicts the results of the action(s). 3. one or more executors that are responsible for successfully executing the action prepared by the planner. The disadvantage of the architectural models presented in [41] and [35] is that they do not consider the possibility of unpredictable events during plan(s) execution. While in the structure presented in [2], the last three inner parts of the decomposition module are arranged in that hierarchical structure, but they are embedded in another structure Chapter 3. TASK DECOMPOSITION 23 that is updated using real time sensory information. It can concluded that the overall structure in the last case is more developed to act in less predicted workspaces. 3.3 ASSEMBLY STRATEGY AND ALGORITHM STRUCTURE An assembly task is introduced to the system by its specifications. In order to execute it successfully using the robotic system, the specification has to be decomposed to the level of robot instructions. Task decomposition can be done by automatic task planning that is based on artificial intelligence or manually by the designer. Operational programs which are derived on the basis of this decomposition, are built from instructions that can be understood by the arm's controller. This thesis deals with manual decomposition which can be implemented for automatic multi task planning by adding the necessary AI modules. While decomposing an assembly task the designer has to consider the following steps: • Task description: Tasks are generally specified in terms of the desired motions and contact forces of the end-effector. The planner has to create the best strategy for those parameters taking the following into account: assembly goals, environment (workpiece structure and locations of target points and obstacles), end-effector structure and equipment, forces/motions relations and position/velocity states. • Control and Stability: The best ratio between speed and accuracy and the best error handling that can be achieved by applying correct control. The type of sensor, the dynamic (arm, load and environment) and the kinematics of the system must be considered in choosing the control strategy. For example, in dealing with an environmental sensor (touch) a feasible control strategy will be based on constraints. An assembly task is a process of mating two workpieces. One workpiece i6 fixed in the workspace while the other is manipulated by the robot end effector. In fact, the Chapter 3. TASK DECOMPOSITION 24 motions of the arm are constrained due to contact with other surfaces. The natural constraints are the result of the particular mechanical and geometric characteristics of the task configuration (natural position or force constraints). They arise naturally from a particular contacting situation and have nothing to do with the task planning. While the natural constraints avoid movement of the end-effector, the artificial constraints specify the desired motion or force application. The artificial constraints will produce the desired goal trajectory if, and only if, the goal trajectory is the unique solution of the combined artificial plus natural constraints. Returning to assembly strategy, the planner can describe the desired procedure for the task in a sequence of artificial constraints. In general, for many solutions, a set of artificial constraints which are orthogonal to the natural constraints will be chosen. This may be denned thus: 1. a generalized surface is defined by position constraints along its normals and force constraints along its tangents. The position and force constraints are the compo-nents of the natural constraints. They are sometimes declared as "velocity equals zero" and "force/torque" constraints. 2. a constraint frame is a frame in which its origin is located according to the way the planner controls the execution of the task. The frame may be fixed in the environment or may move with the end-effector. The desired motion in a specific subtask can be defined by specifying a list of constraints as the basis of the control algorithm. The structure of an assembly task program has to be simple to understand and easy to operate. This, and the limited memory space in the control box of the robot compel an hierarchical structure. Fig. 3.2 schematically represents this structure, derived here for the example task, shown in Fig. 3.1. The following is an explanation of the hierarchy levels (from lowest to highest) of the programs in the library: Chapter 3. TASK DECOMPOSITION 25 • SERVICE PROGRAMS: at the lowest level of the pyramid there is a group of special purpose programs. They are used for tasks like communication (controller to force sensor electronic box or controller to I/O box), display of information, force and tool transformation, overload checking, signals activating and resetting etc. • SUBROUTINES: there are limited number of basic operations that are the building blocks of a special purpose assembly task. Using a fixed structure subroutine, with appropriate parameters derived from task description, enables actual movement of the arm in the desired trajectories. Assembly subroutines whose controller is based on force information, extensively use Process Control (pc) programs. In this program structure the main subroutine controls arm movements according to position control while, running in parallel, the pc program controls forces by real time alteration of arm movement. • SUBTASKS: under this title there are repeatable operation oriented programs that enable easy understanding and decomposition of the main task. Each subtask is responsible for a series of movements from one target point to another. All the intermediate points are related to those two points. During the execution of a subtask, the end effector configuration can be changed only once. Every subtask contains an initialization file that assigns desired values to a list of execution sub-routines (called by that subtask). The subtask calls the subroutines according to the logic flow of the task, using the structured constructs supplied by VAL-II. • MAIN TASK: every assembly task has one main task that controls its flow from the beginning to its end. This program is broken into initialization programs and subtasks based on task specifications. Into the main task the designer can add check points, decision points and alternative subtasks. Chapter 3. TASK DECOMPOSITION 26 The decomposition of any assembly task should follow the same hierarchy as described above. Task decomposition is the way mechanical knowledge, laboratory equipment and as-sembly strategy are applied to a task description in order to achieve the desired goals. The output of the decompositions are two task oriented programs: the initialization file and the main program that activates the library programs (described in the following chapters). In the library, VAL-II instructions are grouped together to form programs that follow the logic of the assembly strategy. The programs are constrained by VAL-II instructions and limitations, by the special structure of the library and by the memory limitations of the controller. During execution, the memory contains all the declared parameters to be transferred from one program to another. The last values will be used unless they are updated. This can cause unexpected problems (eq. null parameters for locations). A solution (a good programing habit) is to give values to each parameter at the beginning of each program. Fig. (3.3) shows the way it is done in the thesis: each subroutine has a parametric file that contains basic values for all the parameters used in that program. Each initialization file calls other Parametric files (according to the required subtask). This loads a set of parameters with certain values. If for a specific task some values have to be changed, those changes are introducing to the system after calling the parametric file and this last declaration remains during program execution. In this way all the parameters are listed and declared before running the programs and the initialization files are relatively small (contains only the changes) For example, a better understanding of this programing structure can be achieved by carrying out the simple example illustrated in figure 3.1. In this assembly task, the robot manipulator has to screw four bolts into the block located on a table. Task description includes locations of the block's threads, bolt pick up point, bolt dimensions and weight, maximum tightening torque for each bolt and gripper's dimensions and weight. Chapter 3. TASK DECOMPOSITION 27 The basic gross operations that an assembly operator (human or robot) has to do is to Pick up a bolt from the feeder and to Screw it into one of the threads located on the block. Then, to Pick another bolt, change its target point and Screw it into another thread and so on. These two operations (subtasks) are repeated 4 times. The Pick subtask is always the same while in the Screw subtask the target point and the location of the threads change. Fig. 3.2 shows the block diagram for this operation. The main task is decomposed and executed by a series of initialization files and subtasks. In the first initialization file - Pinl.inil all the parameters for the first Pick subtask are included, the same with Pinl.ini2 file that holds the parameters for Screw subtask. If the pick up locations of all the bolts in the feeder are the same, no new initialization is needed before subroutine Pick is executed. But, as on the block, there are four different thread locations, an initialization file has to be included before execution of the Screw subroutines. In this structure, checking or decision points are not included in the main task, they are presented in the lower subroutine level. Entering the subtask level in the algorithm structure (Fig. 3.2), every subtasks is built from subroutines that describe a lower operational level. The following is the operational description of subroutine sequence within Pick and Screw subtasks: 1. Subtask Pick - from any location of the end effector (a) Move the arm to a point above the screw (both bolt location and the height above it were received from initialization file). (b) Approach rapidly in gross movement towards the bolt and near the contact point, change the approaching motion to fine motion, force control approach. (c) Grasp the bolt and weight it to verify that the grasp operation were suc-cessfully completed. If the grasping failed the program will run Pick subtask again. Chapter 3. TASK DECOMPOSITION 28 (d) clear the area to a point above the feeder. 2. Screw - from any location of the end-effector (a) Move the arm (and the screw) to a point above the desired thread location on the block (both thread location, the height above it and bolt size were received from initialization file). (b) A p p r o a c h subroutine is executed to receive low impact contact between the tip of the bolt and the block surface. (c) Search program is executed to verify that the bolt is located within the thread borders (indicated by high normal forces from the thread's edges). If not, Search will move the gripper in a search pattern (while increasing size of the square ribs) until the thread will be located. (d) R o t a t e program will rotate the screw until the desired torque will be reached while complying gripper position and orientation to forces/torques reactions. The subroutine level makes U6e of the service programs. The A p p r o a c h subroutine, for example, approaches the surface using location transformation of the tool and gripper sizes and is terminated when desired normal forces are reached. The information needed is available using service programs like J R 3 . D A T to receive force information or T i p for location transformations. It can be seen that in the same main task - subtasks, subroutines and service programs are executed again and again. It can be done because of the use in the initialization files and the ability to change parameters during program flow. The structure logic, the programs and the way their parameters are derived are a major element in this research and will be discussed in the following chapters. Chapter 3. TASK DECOMPOSITION 29 3.4 PUMP ASSEMBLY DEMONSTRATION Pump assembly was chosen as applicable to represent and demonstrate robot perfor-mance, using force sensory information. This task is a common industrial task with all the basic subtasks that can be found in many other mechanical structures. The external hydraulic gear pump type is a common pump, and the one used as an example in this thesis, is shown schematically in Fig. 3.5. During demonstration, the following parts are manipulated by the arm: Gearl (2), Gear2 (3), Top (4) and 4 Bolts (5). The subtasks in the thesis, are derived in order to assembly those parts. In the figure, like in the workspace, the pump is mounted on a base, with two pins to prevent its movement. The working space that lies inside the operating envelope (ref. [38]) of the arm is divided into an assembly area (workspace) and parts location (feeder). The base of the pump is mounted on an aluminum base in front of the robot. It simulates the part that is moved to its position by a mechanical feeder or a belt conveyer. The parts to be assembled are fed to a nearby location by another feeder. After the assembly of the last part by the arm, the conveyer is moved with the assembled pump and new empty pump base is moved in front the robot to repeat the process. In the laboratory both the base of the pump and the parts are installed on aluminum bases that are located on a wooden (compliant) table. All the parts are located with relatively fixed positions, so no Search pattern is used to locate their position and orientation. The arm i6 equipped as described in chapter 2. The opening range of the gripper was adjusted so it can move all the parts. The devices mounted on the e-e were measured and their relative position from the base of the force sensor is used as an input for position and force transformations (see chapter 6). The following table summarizes arm movements and check points and shows the basic logic behind the main assembly decomposition. Every operation is described and Chapter 3. TASK DECOMPOSITION 30 its relating subtask program and initialization file are enclosed. Each subtask begins or ends with an arm movement (with or without a tool or a part). The pattern of movement includes a horizontal movement that is always made in a safe place (free space) located above the assembly area. Approach and Clear (depart) horizontal movements connect between the free space and the workspace (or the parts location). Pump Ass. Subtasks Description: Subtasks: 1. G E A R 1 : S 1.1 Move to gearl, grasp it and check 1.1.1 GEAR1.INI1 S E the grasping. 1.1.2 PICK U R 1.2 Insert gearl into its place in the 1.2.1 GEAR1.INI2 B V base. 1.2.2 INSERT R I 2. G E A R 2 : O C 2.1 Move to gear2, grasp it and check 2.1.1 GEAR2.INI2 U E the grasping. 2.1.2 PICK T 2.2 Insert gear2 into its place in the 2.2.1 GEAR2.INI2 I P base. 2.2.2 INSERT N R 3. P U M P T O P (COVER): E O 3.1 Move to Cover, grasp it and check 3.1.1 TOP.INI1 S G the grasping. 3.1.2 PICK • 3.2 Place the cover on the gears (two pins 3.2.1 TOP.INI2 insertion) and twist to verify location. 3.2.2 INSERT Chapter 3. TASK DECOMPOSITION 31 PUMP Ass. Subtasks Description: Subtasks: 4. PLACING SCREW1: 4.1 Move to Screwl, grasp it and check 4.1.1 SCREW1.INI1 the grasping. 4.1.2 PICK S 4.2 Move to the desired hole, place it 4.2.1 SCREW1.INI2 E and make 3 turns. ' 4.2.2 PLACE R 5. PLACING SCREW 2: V 5.1 Move to Screw2, grasp it and check 5.1.1 SCREW2.INI1 S I the grasping. 5.1.2 PICK U C 5.2 Move to the desired hole, place it 5.2.1 SCREW2.INI2 B E and make 3 turns. 5.2.2 PLACE R 6. PLACING SCREW 3: O 6.1 Move to Screw3, grasp it and check 6.1.1 SCREW3.INI1 U P the grasping. 6.1.2 PICK T R 6.2 Move to the desired hole, place it 6.2.1 SCREW3.INI2 I O and make 3 turns. 6.2.2 PLACE N G 7. PLACING SCREW 4: E R 7.1 Move to Screw4, grasp it and check 7.1.1 SCREW4.INI1 S A the grasping. 7.1.2 PICK M 7.2 Move to the desired hole, place it 7.2.1 SCREW4.INI2 E and make 3 turns. 7.2.2 PLACE S 8. PICK TOOL: 8.1 Move to Tooll, grasp it and check 8.1.1 TOOL.INI1 the grasping. 8.1.2 PICK Chapter 3. TASK DECOMPOSITION PUMP Ass. Subtasks Description: Subtasks: 9. SCREW 1: 9.1 Move to Screwl, grasp it and turn 9.1.1 SCREW1.INI3 4 turns (controlled torque). 9.1.2 ROTATE 10. SCREW 2: s 12.1 Move to Screw2, grasp it and turn 10.1.1 SCREW2.INI3 E 4 turns (controlled torque). 10.1.2 ROTATE R 11. SCREW 3: S V 11.1 Move to Screw3, grasp it and turn 11.1.1 SRCEW3.INI3 U I 4 turns (controlled torque). 11.1.2 ROTATE B C 12. SCREW 4: R E 12.1 Move to Screw4, grasp it and turn 12.1.1 SCREW4.INI3 O 4 turns (controlled torque). 12.1.2 ROTATE U 13. APPLY TORQUE: T P 13.1 Move to Screwl, Screw2, Screw3 and 13.1.1 REPEAT.INI1 I R Screw4 and tighten them to the 13.1.2 ROTATE N O desired torque as indicated in E G REPEAT.INI1. S R 14. REMOVE ASSEMBLY: A 14.1 Move to the assembly, grasp and 14.1.1 ASSEMB.INI1 M check the grasping. 14.1.2 PICK S 14.2 Move to desired place and place 14.2.1 ASSEMB.INI2 the assembled pump. 14.2.2 PLACE Chapter 3. TASK DECOMPOSITION 33 Fig. 3.4 shows the beginning of the structure that is used in order to execute the Pump Assembly Task. Th e main program calls the initialization files and the subroutines Pick and Place for Base positioning and Pick and Insert for G e a r l insertion. If Insert subtask is taken as example from the table, it is used to insert both G e a r l and Gear2. The insertion of G e a r l is relatively simple: the shaft of the gear is inserted to its bearing in a "peg in a hole" routine, while considering possible interaction between the pump's walls and the tooth of the gear. Inserting the second gear is a little different because while the shaft is inserted and the walls interfere, the teeth have to match during the linear movement. A relative rotation is added to the insertion program to overcome the problem. Those and other details are not included in the table - chapter 5 covers the subtasks in details. Every subtask contains a list of subroutines, part of them are being executed by triggering a software switch in the initialization program. The following table summarizes all the programs contained in the assembly library which allow successful execution of Pump Assembly Task: Main Task Subtasks Subroutines Service Programs Pump- Pick Approach PCstop Assembly Place Grasp Force information Insert Search Process control programs Screw Comply Initialization and Check Clear Parametric files Place Overload checking Move Weight er 3. TASK DECOMPOSITION Figure 3.1: Execution of Block assembly by a robot. MAIN TASK SUB-TASK SUB-ROUTINE MOVE 4 SERVICE PROG. J . GRASP BLOCK A S S E M . CLEAR WEIGHT JR3.DAT APPROACH APPROACH.PC JR3.DAT SEARCH — ~r i r i pfo1.M1 | pm1Jnl2 | p i n i l n H | pin2.ln!2 | P I C K 1 S C R E W 1 P I C K I S C R E W 1 SEARCH.PC JRS .DAT TIP 1 COMPLY OOMPLYJ»C JR3.DAT Figure 3.2: Algorithm structure using Block Assembly example. Chapter 3. TASK DECOMPOSITION 35 subtask PICK APPRMCHfttR INITIALIZATION TOOL conftguntion c*l MOVE.PAR update peramstem OU APPROACH.PAR updatejptrenwtera caB GRASP.PAR update pant meters cad CLEAR PAR update paramcttre subroutine MOVE subroutine APPROACH subroutine GRASP subroutine CLEAR APPROACH.PC Figure 3.3: Decomposition of subtask Pick. BASE. INH PICK P U M P A S S E M B L Y a E A R 2, BASE. INS P L A C E GEAR1.INI1 PICK GEAR1.INI2 INSERT i l-r i H M O V E G R A S P A P P R O A C H I C L E A R S E A R C H C O M P L Y WEIGHT JR3.DAT APPROACH.PC JR3.DAT — 6EARCH.PC _ JR3.DAT TIP COMPLY. PC JR3.DAT Figure 3.4: Beginning of Pump Assembly Task. Chapter 3. TASK DECOMPOSITION 36 Figure 3.5: Pump assembly parts. Chapter 4 FORCE/MOTION SYNTHESIS FOR ASSEMBLY TASK 4.1 FORCE CONTROL REVIEW 4.1.1 Introduction: One of the important problems in executing an assembly task is the kinematic constraint imposed on the motion of the manipulator through contact with the environment. The objective of trajectory control of a constrained manipulator is to regulate force and torque reactions between the end effector (e-e) and the environment while simultaneously regulating desired position and orientation coordinates of the e-e. The basic control of most of the industrial robots is via position/velocity instructions received from its operator. Robot response depends on forces and torques applied by its actuators and by the contacting environment. In cases like part assembly, a slight misalignment (position error) between the tool's tip and the environment usually causes large damaging forces. This is a classical case for using force control algorithms: the contact forces are used as a source of information on the actual position of the end-effector of the robot relative to the environment. Force feedback offers an important means to enlarge the allowed region of uncertainty, thus avoiding more severe requirements on the positioning accuracy of the robot and peripheral equipment. The problem in practical applications of force controlled (on-the-shelf) robots (Ref. [40]) is that the force controller must always be used in conjunction with a position controller. Most commonly, one wants to specify force control only along selected Cartesian degrees of freedom ( D . O . F ) while 37 Chapter 4. FORCE/MOTION SYNTHESIS FOR ASSEMBLY TASK 38 the remainder are controlled according to a position trajectory (Ref. [21]). Force feedback strategy is based on information received from a compliant device that deflects due to contact forces that are the result of previous motions. Thus the strategy is governed (Ref. [45]) by the magnitude of the compliances - arm, device and environment, by the dynamic responsiveness of the arm's actuators and by the control computer. Using a stiffness matrix in the forces control algorithms, the force control is reduced to a position control and the accuracy is reduced to the resolution of the position encoders. Ref. [18] concluded that the capability of the robotic system to perform advanced assembly tasks in unstructured and imprecise environment is strongly dependent on its ability to simultaneously control end-effector movements and active forces. Controlling the movement of the robot arm, while executing an assembly task, has two distinct control phases: 1. gross motion control - an open-loop movement of the arm from its initial location to a (desired) target position/orientation point, along a planned trajectory. In this stage the manipulator performs free (usually high speed) motion without reference environmental contact. 2. fine motion control - a closed-loop motion in which the end-effector interacts with the environment. It is a constrained movement that is carried out using force sensor data. Robot force control research began in the 1950s, mostlly in the areas of remote manip-ulators and artificial arm control. In the last decade, work on force control was done at Stanford by Salisbury, Craig and Khatib. Other works were published by Whitney, Ma-son, Paul, Hogan and many other researchers (like most of the references in this thesis). In Ref. [47], Whitney describes several different block diagrams of force feedback control Chapter 4. FORCE/MOTION SYNTHESIS FOR ASSEMBLY TASK 39 algorithms. Fig. 4.1 shows a basic structure for the major part of the force feedback sys-tems. According to this scheme, the robot is controlled by position or velocity commands (input). The desired trajectory is modified by two feedback loops. A position/velocity loop and a force/torque loop. The common factor to all the force control algorithms (except implicit force feedback) is the use of processed force sensor information in their feedback loops. Algorithms like stiffness control and implicit force feedback use position input, velocity is the input for damping control, while position plus velocity are the inputs for impedance control. Explicit force control use force input while hybrid control uses force plus position/velocity inputs. Using sensory information (position and force), the robot has to be treated a6 a sam-pled data control system. Position trajectory set points are received and acknowledged every 28 (msec), the current position of the internal loops (encoders of the joints) are sampled every 0.875 (msec) and the force sensor information (read by PC program) is received every 28 (msec). The control algorithm must consider the sampling time and the time to process this information to points transformation in order to receive smooth, desired trajectory. Compliant motion control is concerned with the control of a robot in contact with the environment. There are some approaches to Compliant control, among them: Impedance control - deals with the desired dynamic relationships between forces and positions. It is simple and robust to parameters uncertainty but, is restricted to fairly slow motions. And Hybrid control - the dynamics of the manipulator is calculated in terms of the operational coordinates and then controlling position, force, or mechanical impedance along each axis of the compliance frame. Both algorithms are discussed in the following sections. Chapter 4. FORCE/MOTION SYNTHESIS FOR ASSEMBLY TASK 40 4.1.2 Impedance Control: Compliant motion of the manipulator occurs when the manipulator position is con-strained by the task geometry (contact with the environment). According to Ref. [1], compliance may be derived from the following: 1. Passive Compliance: when force is applied at a point along the manipulator arm, the structure between that point and the base will deflect. Usually the force is applied along the tool held by the gripper, so the deflecting structure includes the tool, the gripper, the sensor and the following elements of the arm: arm links, supporting elements (bearings, guide ways), transmission elements (gears, shafts) and servo drive systems (loop gains in the feedback system). . When the environment is not stiff (related to the other parameters), its stiffness must be added. Due to the fact that nonmetallic materials are involved, the compliance of the arm (plus the other objects) is nonhnear. The nonlinear compliance and the presence of disturbance forces causes inaccuracies of the end effector position. Oscillations of the arm are deviations of its motion from the programmed motion. The fundamental natural resonance frequencies of bending compliance (only the arm - links and joints) are relatively low (2 to 30 Hz). It mainly effects the performance of high-speed-high-acceleration manipulators. In this work, we will ignore that phenomenon unless it interferes. Passive mechanical compliance devices like RCC (Remote Center of Compliance) are designed for special-purpose applications (usually in task assembly). Their specifica-tions are known and controlled. They are capable of quick response and are relatively inexpensive (section 2.3.1). 2. Active Compliance: is a programmable device (software algorithm) that enables the operator to modify the end effector's elastic behavior according to different phases of Chapter 4. FORCE/MOTION SYNTHESIS FOR ASSEMBLY TASK 41 an assembly task. In a scheme, suggested in Ref. [34], the position gains in a joint based servo system are modified in such a way that the end-effector appears to have a certain stiffness along the Cartesian frame. Describing the stiffness matrix K p as the desired elastic behavior needed to generate the force F due to small displacements Sx at the end effector: F = KpSx (4.1) The parameters F, K p and 6x are expressed in task space coordinate. K p is generally chosen to be diagonal with low values along directions which stiffness is controlled and high values along the other directions. Transferring task space forces into joint torques, using the manipulator Jacobian Sx = J£q (expressed in task space), we obtain: T = J r F = (J r K p J )£q (4.2) this is an expression for joint torques, necessary to make the hand behave as a six dimensional spring in cartesian (or task) space. The term J r K p J is a non diagonal joint stiffness matrix. This means that position errors in one joint will affect the commanded torque in all the other joints (the joint stiffness are highly coupled with each other). Eq. 4.2 is a relation between the desired six degrees of freedoms, Cartesian spring stiffness and the controlled joint torques that enables to realize it. Here, through use of the Jacobian, a Cartesian stiffness has been transformed to joint-space stiffness. Position control in the joint space can be achieved (in the absence of friction) by: r = K p q + K , q - g(q) (4.3) where q = q^ — q a - the error or the difference between the desired and the actual joint displacement, g(q) is the estimated gravitational torque and the matrices K p and K j (programmable damping) are any symmetric matrices. Chapter 4. FORCE/MOTION SYNTHESIS FOR ASSEMBLY TASK 42 The impedance control is derived using the above development to large task space disc-placements. In this case, joints displacements are replaced with task space displacements vectors (x = xj — x„) to receive the control law: r = J T [ K p x + K,x]-g(q) (4.4) here, by expressing J T , K P and Kj directly in task space coordinates and give desired values to the "stiffness" and "damping" matrices, the task space force [K px + K^x] is transformed into joint torque vector. 4.1.3 Hybrid Control: In most of the assembly programs (Subroutines and Service Programs), the arm is con-strained by the task geometry. Those programs can be described by using a generalized surface that is defined by position constraints along its normals and force constraints along its tangents (section 3.1). The assembly goals or the desired trajectories can be specified by the operator as another set of artificial constraints, described as position or force constraints. The Hybrid Force/Position Control algorithm was designed to deal with the two different criteria (Ref. [30]) related to the two different types of constraints. The hybrid controller allows the use of force control algorithms along certain degrees of freedom (d.o.f.) while allowing the use of position or damping control algorithms along the remaining d.o.f.. The actuators activate the manipulator's links around their joints while task descrip-tion and task constraint are declared in the workspace, usually in Cartesian coordinate frame. As in other robot arm control algorithms, significant work has been done by researchers to translate workspace description to joint space. In Ref. [30] both joint positions, compliance, control separation and force were specified in the cartesian coor-dinate frame. Position errors due to compliance or force received in the cartesian frame Chapter 4. FORCE/MOTION SYNTHESIS FOR ASSEMBLY TASK 43 were then translated back to joint coordinate frame using the inverse Jacobian. A step farther was done (Ref. [28]) by Khatib who resolved the manipulator joint inertia into an effective cartesian inertia. Using the hybrid control scheme, a PID con-troller was implemented to receive forces (from cartesian accelerations and inertia) and transfer them back into desired torques at the joints. In Ref. [48] the authors modified the hybrid control method by showing that a reduction in the computation loads can be achieved simply by transferring the control from the cartesian frame to joint space. The stability problems of the hybrid control is related to its structure, including both stability problems of the force and the position control algorithms in addition to the implementation of the transitions between them. Fig. 4.2 shows a typical hybrid force position diagram. The inputs are the desired forces and positions multiplied by the diagonal matrices S and I — S. The output of this multiplication is the partition of the forces and positions to the desired six d.o.f. expressed in the cartesian space. Parameters that are received in the cartesian space are transferred to joint space using the Jacobian transpose for forces and inverse Jacobian for positions and velocity. 4.1.4 Force Control for Assembly Task: The control algorithms described previously can be applied to a robotic arm, by its manufacturer, as part of the software of its controller. Most of the commercial robots can only be activated by using position instructions. In order to apply advanced control algorithms to the arm, researchers like D.G. Bhim (Ref. [3]) designed a new "Universal Six-Joint Controller", capable of driving a robot manipulator equipped with D.C. joint motors and position optical encoders. Such design can directly control the torque of the joints while using the D.C. power amplifiers of a PUMA controller and bypassing completely Unimation controller. Chapter 4. FORCE/MOTION SYNTHESIS FOR ASSEMBLY TASK 44 Using built-in functions like SLAVE (Unimation feature that enables the user to control the arm controller by a supervisor computer), can increase the computation ability of the PUMA 560, but it doe6 not allow direct torque control of the joints. Another way to apply force control to a commercial arm is by using the compliance of the arm, while moving the tool in controlled position steps. In this solution, used in this thesis, both position and force control algorithms are used. Activating the arm in an assembly tasks, the same logic as in hybrid control is applied, but here force data is converted to position instructions. So both forces and positions are implemented by using the internal PID control algorithm of Unimation controller. Every assembly task is divided into the desired position and force controlled d.o.f.. The position control is implemented by using directly the movement instructions of the robot. While in contact with the environment, forces and torques (in the desired d.o.f.) are received through incremental movements. If force i6 to be increased then a desired, incremental, calculated movement instruction is the output of the force algorithm. The new target point is located in a small segment under the contacting surface (in other words, the robot is instructed to move into the environment). The robot controller responds by calculating (inverse kinematic) some set points. Those are target points used by the inner control loops of the joints to control their movements, using PID control algorithms. A 6 a result, joint actuators will cause the arm (or the environment) to bend until the position error will nullify (joint encoders reaching the desired angles). The result of such pseudo movements will increase forces and torques reactions. Decreasing reactions can be done by entering a target point away from the contacting point. When the use of the robot includes fast movements, structural dynamic characteristics of the manipulator including stiffness, inertia, damping and natural frequencies are to be considered. Using the arm while moving in contact with the environment involves only fine movements, so part of the dynamic characteristics can be ignored. In this case, force Chapter 4. FORCE/MOTION SYNTHESIS FOR ASSEMBLY TASK 45 and torque reactions between the arm and the environment are a function of the step sire and the stiffness of the contacting parts. Stiffness parameters that have to be taken into consideration are arm stiffness, stiffness combination of the sensor, gripper and the tool (held by the gripper) and the stiffness of the environment. Achieving forceB/torques and controlling them through the compliance parameter of the system's components can result in high forces, instability and possible damage to e-e components or to the environment. To avoid that problem and to successively control small forces of a stiff arm and environment, the algorithm must instruct the system to move in small steps, resulting slow arm reactions, an impractical way to execute an assembly task. Lowering assembly or arm stiffness by using the RCC and the Linear Compliance Device is the solution that was selected for this problem. In this way, the basic position control of t h e manipulator (the inner PID algorithm) will still be the high stiffness controlled links required to minimize response to disturbances. Fig. 4.3 shows the block diagram of the controller activated during assembly task using the following parameters: 1. task planning: this is a part of the strategical control level that makes use of task decomposition. Every program, according to its nature, is divided into force and position d.o.f. with t h e i r desired velocity parameters. Positions and their associated velocity parameters are transferred directly to the robot controller while the desired forces are calculated using a special control law. 2. control law: a force error ( F e ) signal is received by subtraction of the sensed force ( F , ) from the desired force ( F j ) . The force error is then processed using the control law shown in Fig. 4.4. The switching control law has a proportional gain ( K / j ) , a dead zone around the desired forces ( F e = 0) and its outputs are bounded to prevent large movements and to receive less nervous control. Usually, the force Chapter 4. FORCE/MOTION SYNTHESIS FOR ASSEMBLY TASK 46 part of the control algorithm, is activated using a pc program. The parameters of the control algorithms are derived from the task profile and its nature, except for the dead zone which is usually fixed and receives values that are ±20% of the desired force. For some tasks, when a movement is not needed, increasing of the dead zone is equal to the cancellation of the movement. 3. robot controller: the input to the manipulator controller is received directly from the task program (usually a Subroutine) with additional real time trajectory alter-ation from a pc program (usually a Service Program). The new desired location is transferred from a' current cartesian or tool frame to joint frame (6 angles) using inner inverse kinematics calculations. Six joints controllers using joint encoders output, close their internal PID control algorithm loops. The resultant movement (AX) of the e-e in one time interval is: A X = X a r m • St for > X a r m - St ( 4-5) X r f for Xd < X o r m • 6t when St - time interval of the system. X a r m - arm velocity (controlled parameter). X j - desired position of the end effector. In this scheme the robot controller includes the dynamic parameters of both the arm, controller and the electro mechanical subsystems like motors, gears and their amplifiers board. 4. process and sensor: the actual forces, locations and velocities of the e-e are function of task specifications, e-e and its equipment and the surroundings environment lo-cation and stiffness. The assembly task deals with known parameters (the unknown Chapter 4. FORCE/MOTION SYNTHESIS FOR ASSEMBLY TASK 47 are the tolerances of those parameters) so they can be precalculated and feed into the task planner. Actual sensor data is transformed to the desired coordinate frame and feed back to the control law. Actual implementation of the block diagram and the parameters discussed above are imbedded in the simulation described in chapter 8 and in the programs that executing the assembly task. 4.2 D Y N A M I C M O D E L ANALYSIS In ref. [11] the authors are looking to model a robot arm and its sensor in order to receive the conditions for unstable behavior while in contact with the environment. A continuous proportional force controller is introduced in the dynamic description to model an overall behaviour of a position servo system. Fig. 4.6 shows the basic model and the block diagram of its controller. Here, the two mass model includes a rigid robot with mass (mP) damped to the ground by a damper (dV). The sensor has stiffness (kt) and a damper (bt). The environment adds to the dynamic description, its mass ( m e n ) , stiffness (ken) and damping (ben). The model dynamic equations are: (K + b.) -b. -K (K + Kn) k, kg - fc, (fc ,-ffc e n ) using the Laplace transformation, the equations can be manipulated to receive the open-loop transfer functions: Xr{») + (bm + b.)s + (km + k.) mr 0 < + 0 TTlen + (4.6) F(a) X e n ( a ) F(*) P(s) b,s + k, (4.7) Chapter 4. FORCE/MOTION SYNTHESIS FOR ASSEMBLY TASK 48 when P{a) = [m r« s + (6r + b,)a + *,] x [m^a* + (6, + bm)a + (k. + *„,)] - [6,a + *,r] 8 " these equations give the relationships between the movements and the forces subjected to the system by the motors of the arm. The force information (system's feedback) sensed by the force sensor is: F . = * . ( * r - X e n ) (4.8) using the proportional control law of the form: F = kjd(Fd - F,) (4.9) The root locus for this simple modeling was calculated and ploted using MATLAB soft-ware. Some of the parameters (of the arm) were measured and calculated (chapter 8) and some were estimated (those of the environment). The proportional software gain of the system (Kj) was changed from low values (0.001) to high values (100,000) and the result is ploted in Fig. 4.6. It can be seen that the system is unconditionally stable for any software gain as well as for any stiffness value of the either the sensor or arm. A more complex structure for the robot arm (that ignors the dynamics of the environ-ment), consist of two masses that represents both rigid body and first vibratory model. The equations for this model are: nt\ 0 0 m 2 fc2 —k3 -fc, (fcj + fc,) x2 (6X + b3) -b2 -h (bi + b.) + Chapter 4. FORCE/MOTION SYNTHESIS FOR ASSEMBLY TASK 49 Once again the Laplace transform is used to obtain the open-loop transfer functions of the equations: X ^ g ) m,*2 + (b. + b7)s + (fc, -I- fe2) X 2 ( s ) b3s + fc2 (4.11) where P(s) = [rms* + (&i + 6,)* + fc2] x [m2aJ + (62 -(- b.)s 4- (fcs + fc.)] - [62* + **] 2 The contact force is given by F , = fc,x2 (4.12) and the proportional control law is F = fc/(J(Fd-F,) (4.13) In this case, compared with the previous one, it can be seen that the dynamics are the same. The cases only differ in the relative position between the force sensor and the activated force. The root locus output of this case is shown in Fig. 4.8. Once again the parameters were either measured or estimated. It can be seen that in this case the system is only conditionally stable. The actual gain values that cause the instability are not plotted because they depend on the parameters of the system. It can be concluded that when structural compliance is presented between the sensor and the actuator - the controller will attempt to regulate contact forces through the dynamic system and using a certain gains can cause system instability. In order to investigate the behaviour of the robotic arm while in contact with the environment, a change has to be made in the approach to the system dynamics. Firstly, Chapter 4. FORCE/MOTION SYNTHESIS FOR ASSEMBLY TASK 50 the analog controller has to be changed so that a discrete control system can be analyzed (discussed in the following paragraph). Secondly, a simulation has to be implemented nsing the basic structure of the arm as previously introduced, adding arm stiffness to the dynamic model. This part is included in chapter 8. In replacing the analog controller by a digital one, a sampler is added between the summing point and the digital controller and a hold (sample and hold) circuit between the digital controller and the plant. This structure produces a time lag (phase lag) that reduces the stability margin of the closed loop system. The transfer function of a zero order hold (see Ref. [17]), may be approximated by: G * « = ! ^ T < 4 1 4 ) Introducing this hold approximation to a continuous time control system, modifies it to the time lag. The modified analog controller can be discretized and the system can be transferred and analyzed in the z Domain. But, in order to continue the previous analysis, the system h a 6 to remain in the s domain. Fig. 4.7 shows the model of the basic, two mass model with first order hold approximation (that model was unconditionally stable using an analog controller). Fig. 4.8 shows the root locus representation of that model. The parameters of the system are the same as in the first, stable case (Fig. 4.5). The root locus shows that the continuous, unconditionally stable system changed to be conditionally stable discrete system. The scheme that was introduced in this chapter is the basis of the strategy and control algorithms imbedded in the programs that are described in the following chapters. In chapter 8 some reduced parameters of the robot will be added to this model. Using ACSL to simulate the system, the desired spring stiffness (sensor stiffness - K f ) (or software stiffness) will be chosen to achive a guarded move. Chapter 4. FORCE/MOTION SYNTHESIS FOR ASSEMBLY TASK 51 4.3 C O N C L U S I O N S 1. closed loop force control algorithms using stiffness matrix and structured according to Fig. 4.7 are subject to possible stability problems due to time "delays or the dynamic response characteristics of the manipulator. 2. applying a discrete controller even to the simple case of the two mass model shows conditional stability. That means that the robot, sensor and environment parame-ters have to be modeled and simulated. Using the output of that model some parts (stiffness, dampers) have to be designed taking into account model parameters and desired performance. 3. using the measured stiffness of the arm, sampling time of the controller (0.028 [sec]), estimated damping values and low software gains (K/^ < 1) in the control law -the robot model is stable (further work on this part is included in chapter 8). 4. both Roberts (Ref. [32]) and Maples (Ref. [21]) come to the conclusion that a mechanically compliant wrist sensor (or compliant environment) permits larger control gains. It has some advantages, due to smaller impact forces (while meeting) and lower contact forces at equilibrium for given approach velocities. Chapter 4. FORCE/MOTION SYNTHESIS FOR ASSEMBLY TASK 5 2 0RK3MAL MOTION BMRCHMENT posmoN COMMAND rCH NEW MOTION COORD CONV JOINT SERVOS TOOL POSITION H O DEFORM. STIFFNESS REACTION COMMANDS STRATEGY COORDINATE CONVERTON SENSOR FORCE Figure 4.1: Basic force control architecture. Figure 4.2: Hybrid control block diagram. Chapter 4. FORCE/MOTION SYNTHESIS FOR ASSEMBLY TASK 53 Figure 4.4: Proportional control law. Chapter 4. FORCE/MOTION SYNTHESIS FOR ASSEMBLY TASK F m , AA r L b , b . x, rVWVj b . ^0 KJ Fc(s) Figure 4.5: Two mass model structure and block diagram. 2000 1500 1000 500 o -500 -1000 -1500 -2000 Kf-1000 • j ! ! ! 1 i ) i i i i i ! i t : i i t i 1 i ' I : i i -0.001 t y ! ! ' i : : : : t : : t " 1 K f 1 H 1 • ; : j ! t i—*0 i £ j j i j—«*o t i i 1 ! ' i | i t i ! ! ! t i i i i i • i t i ! i i i i . ( | : t • 16 -14 -12 -10 -8 Real -2 Figure 4.6: Root locus to the model in figure 4.5. Chapter 4. FORCE/MOTION SYNTHESIS FOR ASSEMBLY TASK 55 Fd(s) FWVVI bs x2 *i(u ) Kf X2(a) Ks ) F(8) FC(6) Figure 4.7: Rigid and fir6t vibratory model structure and block diagram. 400 300 200 100 I 0 -100 -200 -300 -400 -3 i ! ^ J i ! I i i j Kf-0.001^ •—" i i ! ! 1 > i 7 • " I t j t j | | i j j t i » 1 • ,w..... i i i i r j i ! I ^ 1 j — j i ! i -2 0 Real Figure 4.8: Root I O C U B to the model in figure 4.7. er 4. FORCE/MOTION SYNTHESIS FOR ASSEMBLY TASK 56 Figure 4.9: Adding zero order hold to two mass model. 200 150 100 50 o -50 -100 -150 Kf-0.01 j Kf-0.01 Kf-1000 Kf-1000 -200 -80 -70 -60 -50 -40 •30 Real -20 -10 10 20 Figure 4.10: Root locus to the discrete model (figure 4.9). Chapter 5 A S S E M B L Y S U B T A S K S An assembly subtask can be a relative operation between the e-e and a tool or a part, such subtasks are Pick and Place. Another group of subtasks are those that the operation is between the tool or the part and between the environment (workpiece), such subtasks are Insert and Screw. All subtasks are repeatable operations - they are not oriented to any specific case. In fact, each subtask program contains call instructions that activate subroutines and service programs. According to the logic structure of the assembly library, the main program calls an initialization file before running the desired 6ubta6k. Those values of the parameters stay in the robot memory until replaced by new values. So those parameters whose values need no change (during the execution of the main task), can be declared just once in order to save memory space. On the other hand, every subtask has its constant structure including that of the initialization file. It is both easy to program and reduce possible system failure keeping this structure - this is the way chosen for the library programs. Taking Fig. 5.1 as an example, Pick initialization file initializes four subroutines. The parameters of each subroutine are discussed widely in the next chapter, but the fact that all subtasks are using the same subroutines enforced the presence of a list of needed parameters at the end of each subtask section. Those parameters are to be included in the initialization file of each subtask. As mentioned before, obstacle avoidance and trajectory optimization is not part of this thesis. Thi6 problem is avoided simply by declaring a "Free Space" above the workspace 57 Chapter 5. ASSEMBLY SUBTASKS 58 where the e-e .with its tool can move freely in the horizontal directions. The straight movement to and from that free space is done by Approach and Clear subroutines. Every subtask begins and ends in that Free Space. The subtasks described in the following sections are derived for the special main task - Pump Assembly. Naturally, the library can be used in any other assembly task as well. Thus, it is very likely, that in other assembly tasks, new subtask,subroutines and service programs will be needed. Building those programs, in the logic described here, will increase the library power and flexibility. 5.1 SUBTASK PICK Subtask Pick is designed to pick up a tool or a part from a known target point. Pick structure is based on activating four subroutines (Fig. 5.1): Move, Approach, Grasp and Clear. Move brings the e-e to a point above the target point. This movement is done in the free space above the workspace to avoid obstacle collision. Subroutine Approach brings the e-e to contact with the part while Grasp subroutine is responsible to grasp it and to confirm the presence of the grasped object - the confirmation is done if a software switch in the initialization file is set to on. Without a vision system, the only way to confirm the grasp is by using the force sensor and weight the object. Clear subroutine moves the e-e holding the part back to the free space, ready to make another horizontal movement. The output of Pick subtask is the e-e equipped with a part or a tool. The rela-tive position between the parts is important because forces and moments are activating between them. If it is possible, the designer should avoid to relate on friction as the transformation media for forces and moments. More is given about the subject - in the Grasp section. Chapter 5. ASSEMBLY SUBTASKS 59 As shown in the algorithm's structure, the Pick initialization file has to initialize four subroutines. The following are the desired parameters that are to be added to the system through every Pick initialization file: 1. free space basic height. 2. target point location. 3. movement speeds. 4. end effector configuration (for tool transformation). 5. part 6 izes from grasping point to tip (tool/force transformation after the grasp). 6. forces to terminate Approach subroutine. 7. the followings are special case inputs: • max forces to stop Grasp subroutine • weight and weight trigger=on in cases that grasp verification (by weight) is needed. 5.2 S U B T A S K P L A C E Place subtask was created in order to satisfy a very basic movement of a part or a tool from the free space to the target point, using simple position instructions. In some cases, when the target point is not an accurate point, a position plus basic force control algorithms is used in order to verify contact. This option is activated by a software switch. As all other subtasks, Place is built from a list of subroutines, activated by an initialization file. Place algorithm structure includes the following subroutines: Move, Chapter 5. ASSEMBLY SUBTASKS 60 Approach and Clear (Fig. 5.2). The e-e moves horizontally in the free space to a point above the target point, Approachs with (or without) force control to the target point, opens the gripper and Clears back to the free space. The following are the desired parameters that are to be added to the system through every Place initialization file: 1. free space basic height. 2. target point location. 3. movement speeds. 4. end effector configuration (for tool transformation). 5. part sizes from grasping point to tip (for tool and force transformation after the grasp). 6. forces to terminate Approach. 5.3 S U B T A S K INSERT Most assembly tasks commonly use a precise insertion process. Basic examples are tasks such as inserting a pin into a hole or a shaft into a bearing. The insertion task begins while the peg is normal to the hole plane, localized between the hole's boundaries. Execution of insertion tasks is taking place a6 far as the peg is sliding in the direction of assembly while maintaining the contacts. After the first contact between the mating parts, the insertion task is relatively slow, with small movements. For these reasons, the dynamic parameters of the robot and its loads are ignored. The usual term for insertion task in the literature is 'peg in hole'. Its repeated use is the reason for receiving fairly large attention in research (mathematical models) Chapter 5. ASSEMBLY SUBTASKS 61 and implementation. Two primary methods were developed for executing these tasks: passive mechanical compliance device and active compliance, implemented in software control loops. The RCC and the HI-T-HAND are special purpose, passive accommodation devices, designed and built for the peg in hole problem. The basic concepts and the U6e of the Remote Center of Compliance (RCC) is described in chapter 2. The HI-T-HAND Expert-1 was developed at Hitachi Ltd., Japan (see [14]). It is a tactile controlled robot with flexible wrist and delicate touch which can insert a peg in to a hole with clearance of approximately 20/im. The construction is based on a flexible wrist, equipped with a plate spring. The plate is capable of detecting relative displacements in the cartesian coordinate frame due to the attached strain gauges. The insert operation is performed by correcting and controlling each position and direction, using the sensors data and the flexible wrist. Active compliance can be implemented using software to change hardware perfor-mance. For example, the compliant controlled wrist in reference [7] enables the fine motion of the end-effector. Generally, however, the implementation of active compliance is used as feedback algorithm to control forces and motions of the arm. In controlling a task like peg in hole, both passive control (RCC) and force feedback algorithms are used. In the following sections, the cylindrical peg in hole insertion will be developed through both a geometrical and force equilibrium viewpoint. The discussion is divided into: part mating analysis and jamming and wedging analysis. Both sections yield the following results: • understanding the process in order to derive successful algorithm. • mathematical representation of the forces and moments involved so constraints and control can be applied to the task. Chapter 5. ASSEMBLY SUBTASKS 62 The last part of the analysis is a summary of the information which leads to insertion strategy and control for successful insertion task. 5.3.1 Part Mating Analysis The first stage in the insertion process is the mating of the peg and the hole. There are different ways to carry out this process: a) Reference [39] recommends that during the Approach process, the peg has to be subjected to a certain angular rotation while bringing its lowest point between the hole boundaries. After contact with one flank, the peg is moved to its original orientation and new aligned position. The difficulty of the method is the synchronization between the axes. vanBrussel's experimental system included a wrist, capable of rotation and a jig mounted on an X — Y table (planar demonstration). b) Reference [46] recommends the use of chamfered holes and summarizes the allowed lateral and angular errors. This basic method is well developed to robot wrist equipped with RCC, while the mating part is mounted on stable jig. For an assembly process, with manipulator equipped with compliance device, the second method is more efficient (time consuming) and simple. The following subsections gives the forces and moments equations that are to be calculated in order to have force limits and decision points. The peg is a rigid body, supported by a compliant structure (wrist with or without RCC, robot arm and sometimes the jig of the mating object). The compliance matrix is diagonal at a certain coordinate frame. Placing the compliance center (cc.) at that specific origin point, simplifies the analyzing and eases the control of the insertion process. In t h i 6 way the compliant support may be represented as lateral spring constant K e and angular spring constant Kg. The tip's peg is located a distance LB from the cc. (Fig. 5.3). To analyze the forces and moments applied by the support, they are re-expressed Chapter 5. ASSEMBLY SUBTASKS 63 in peg tip coordinates in terms of Fm, F x and M (reference [33]). During insertion the following phenomena usually occur: • chamfer crossing. • one point contact. • two point contact. For each phenomenon, the basic information required i 6 the geometric description of the peg and the hole. In order to achieve the successful task, the allowable position errors and extreme forces must be calculated. The following variables are described as a function of the object's geometry and the compliant of the support: • U - lateral error of the compliance center. • 6 - rotational error of the compliance center. • Ft - insertion force. By controlling the arm via force information from the wrist force sensor and the end-effector movements, all variables are projected to that point. The section describes the geometric analysis of those phenomena. This information will be combined with the force analysis to achieve a complete description of the insertion task. Chamfer crossing: The first part of insertion is the contact between the peg's tip and the face of the chamfer. This part ends when the peg's tip leaves the chamfer and one point contact begins. Fig. 5.4 shows the geometry and forces acting during chamfer crossing. Chapter 5. ASSEMBLY SUBTASKS 64 let: p = coefficient of friction A — coact + painct B =ainct — pcoact The expressions of the lateral and angular errors which lead to the desired insertion force are: Tj-rj | Ke{z/tana)B U ~ U o + (KmL\ + K9)B - KxL,rA ( 5 1 ) Km{z/tana){LaB-rA  6 - 9 o + {KmL\ + * *)S - ( 5 2 ) F KmKeA(z/tana)  1 {KmL\ + K6)B - KmLgrA K } It must be emphasized that in order to begin the insertion: occur: M < w (5.4) Where e0 is the initial lateral error and w is the width of the chamber. One point contact: Fig. 5.5a shows the geometry and forces acting during one point contact, let A = K.(Lg -l-ur) (5.5) where / is the insertion depth and is zero when the peg's tip reaches the bottom of the chamfer. The expressions of the lateral and angular errors which lead to the desired insertion force are: TT - JT K ' ( E ° ~ R + R + W ° ) {. U - U o ~ C(L,-l) + K0) ( 5 6 ) a C(e0 -R-rr + Lg90) + K86Q 9 = C(La -l) + Ke ( 5 7 ) _ pKmK,{eo-R + r + W0)  F ' ~ C{L, -l) + K9 ( 5 8 ) Chapter 5. ASSEMBLY SUBTASKS 65 Two point contact: Fig. 5.5b shows the geometry and forces acting during two point contact. Ft = -f [D(90 - cD/l) + E] + 4- ftd/l)[F(e0 - cD/l) - E/Lg] (5.9) where D = KmL\ + Ke (5.10) E = KtLB{e0 + cR) (5.11) F= -KtLg (5.12) Differentiating F r with respect to /, in addition to some reasonable geometrical assump-tions yield to a certain point /* during insertion, where the insertion force F r and the contact forces are maximum. 5.3.2 Jamming and Wedging Analysis: During insertion, two phenomena are acting to prevent the successful completion of the task: jamming and wedging (see [33] and [45]). Jamming is a condition in which the insertion does not proceed in the direction of assembly when a particular force is applied to the peg. It is due to wrong proportions of the forces and moments acting on it. In wedging, no motion is possible in the direction of assembly. This problem occurs due to geometric conditions. The chapter analyses these two phenomena in order to receive the force restrictions for successful insertion task. (4D + 2Fnd)cD (5.13) 2D90 + E(l - ftd/Lg) + F(eotid - cD) Chapter 5. ASSEMBLY SUBTASKS 66 Jamming Analysis: There are six possible contact patterns between a peg and the edges of a hole (Fig. 5.6). The equilibrium equations which describe the shding of the peg developed, assuming that the insertion angles are small enough to be ignored. Combining the equilibrium equations for a peg in two point contact (Fig. 5.5b) and defining A = l/2ru, force description becomes: ^ = ± A - ^ ( A + 1) (5.14) Fig. 5.5a describes equilibrium position for the peg's flank in contact with the hole (one point contact). Force description in this case is: ^ = - A - ^ f ( l + A) (5.15) Deriving the other possible contact patterns between a peg and a hole are described in the jamming diagram (Fig. 5.6). All the points He on the two lines: ^ = - A - ^ f ( A + 1) (5.16) The jamming parallelogram is defined for certain material combination and lubrication (fi) and for certain geometrical conditions (r,l). The relations between F e , F t and M defined a point on the diagram. The parallelogram area and boundaries represents sliding-in situation. The diagram emphasizes the following: • fi ie a parameter that can drastically expand the parallelogram's edge6 and thou ease the insertion task. Chapter 5. ASSEMBLY SUBTASKS 67 • in order to avoid jamming, the relation between the forces and the moment must be a point within the parallelogram borders. So, the following equations must exist: if; i< \ - <5-"> and l ^ + ^ f (A+l) |<A (5.18) Wedging Analysis: Wedging is a phenomenon dependent on the geometrical relation of the mating parts and on the material combination and lubrication condition (u). To understand the two point contact phenomenon let us declare: • at least one of the mating parts is elastic, though still stiff compared with Kx and Ke. • the item I is as large as possible, but still allows wedging. • a cone angle is generated by rotating a line, with angle 9 = tan-1p, to the normal force. A 6 long as the line of action of the applied force F z lies within thi6 cone, there will be no relative motion. This is so, regardless of the magnitude of Ft. Fig. 5.6b shows a possible position for wedging. The force f3 at the right side is within the friction cone so there is no relative movement. The reaction force f\ at the left side points along the lower extreme of the friction cone, indicating that this side is attempting to move out of the hole. Let lw be the largest depth at which wedging could still occur, assuming 9 and c (c = 1 — r/R) are small variables (Fig. 5.3) 19 = CD Chapter 5. ASSEMBLY SUBTASKS 68 lw = fid (5.19) assuming d « D to receive the smallest angle at which wedging could occur c 6* = - (5.20) In order to avoid wedging, the peg's angle must obey c \8w\ < - (5.21) or, using the angle description for two point contact 0O + J e 0 < ± - (5.22) fi where *=irn^ (5-23) The plot of the geometry constraints on lateral and angular error (while crossing the chamfer) is a parallelogram, received by combining the two restrictions. The allowed errors are those whose solutions are between the boundaries of the parallelogram. 5.3.3 Strategy and Control: The analysis presented in the last two subsections was carried out in order to achieve tools to ensure successful insertion assembly. The first tool is a correct algorithm based on the understanding of the insertion process. The second tool is the constraints which can be built and controlled between calculated extremes. The following gives the relations between the applied forces, moments and the geometry of the mating parts: Chapter 5. ASSEMBLY SUBTASKS 69 Chamfer crossing: the lateral error of the pin's edge (e0) must be smaller than the width of the chamfer: H < w (5.24) Jamming avoidance: l ^ + ^ f ( A + l ) l<A (5.25) and The following are the major parameters that are to be added to the system through every Insert initialization file: 1. target point location. 2. movement speeds. 3. end effector configuration (for tool transformation). 4. part sizes from grasping point to tip (for tool and force transformation after the grasp). 5. forces to terminate Approach. 6. forces, torques, gains, boundary parameters (forces, torques and positions) to con-trol Comply. 7. rotation switch on, during the insertion of Gear2 and Top. Chapter 5. ASSEMBLY SUBTASKS 70 5.4 S U B T A S K S C R E W An important, typical assembly task is the use of fastening (joining) parts, using bolts, nut, cap screws etc.. In the Pump, four U.N.F., 3/8 hexagonal head, machine screws, fasten the Cover of the pump to its Base. Some design parameters and logic are to be considered while moving those screws from their initial location to their final location on the pump: • feeding the bolts to their target locations. • screwing and preloading parameters and the ways to control it. • tooling. Subtask Screw deals with these parameters for the spacial case of the pump. As usual, it can be expended to any other case by modifying both task parameters and part of the subroutines. 5.4.1 Feeding the Bolts: For a commercial use, it is efficient to design and operate an automatic screw feeder, that feeds successive bolts to exactly the same loading position. Such a design cancels any position computation, frees memory space and enables the use of the same program to load all the bolts, however in this thesis, to simplify mechanical structures the bolts were placed in an array with equal distances between them. Pick subtask is used to pick all the b o l t 6 , using relative transformations (from first bolt location) to define the successive shifted location of all the other screws. One of the solutions for automatic interface between a bolt and its target thread can either be a guidance structure in the screw (shoulders) or a bore before the thread, in the threaded part. It allows guidance of the screw to the beginning of the thread and Chapter 5. ASSEMBLY SUBTASKS 71 an alignment of the center line of the screw with the center line of the thread. In the pump, the threads are located in the base, and the cover has through holes that serves as guidance to the beginning of the thread. Using the holes in the cover, it is easy to solve location problems using Approach and Search subroutine. At the end of Pick subtask, the end effector lives the bolt in the hole, the center lines are quit aligned and it is relatively easy to begin rotating (screwing) the part. The logic applied here to put the bolts in their target location (before the actual screw operation), can be used to the opposite task - to unscrew the bolt and move them back to the parts location. 5.4.2 Screwing and Preloading: When a body moves in a rotation movement, combined with translation along the same axis, it has an helical motion. When screwing a bolt, the screw, the tool and its driver (in our case - the end effector) has to make an helical motion of rotation and, at the same time, translation along the axis of rotation. The relation between the rotational angle A0 and the axial translation Ax of a screw with a lead L is A0 A - - a £ (5.27) the relation between the axial speed of the screw = 4f that is rotated in angular speed iv = 4j is At _ . ie At V M = ^ ~ (5.28) A possible way to control screw movement is to follow these equations, using both position and velocity instructions. In this case one can calculate the number of turns, required to turn the bolt, to the snug tight condition. From this position, all additional turning develops the useful tension (preloading) in the bolt. For hexagonal structural bolts, like those used in the pump, the turn of the nut (or the screw) should be 180 minimum from the snug tight point, under optimum conditions. Ch&pter5. ASSEMBLY SUBTASKS 72 A better approach can be applied to the rotating procedure, using the information received from the force sensor. By studying the behaviour of the torques and forces between the tool and the rotating screw, end effector locations and orientations can be monitored to received just the desired rotating torque. This torque is derived and simplified in reference [36] to be Ti = 0.20F<<f (5.29) where Tt- - the torque required to produce a given preload (F,). 0.20 - an average value to the torque coefficient (for fi = 0.15). d - nominal size or basic major diameter of thread. Fi - desired preload: F< = 0.90SpAt. Sp - proof strength. A t - tensile stress area. Using those equations and the parameters of the 3/8" bolts of the pump, the calcu-lated desired torque is 65[iVm]. This is the basic, minimum torque to receive preload while ignoring environment influences (fatigue). Such torques cannot be handled directly by the arm or by a tool installed in the gripper (and transfers the torques to the arm). For high torques a special arrangement must be added to the arm, in the thesis, lower torques were used in order to show the ability of the robot to handle complicated tasks. In the next chapter, the description of Rotate Subroutine shows the actual way the arm moves using force information to control the screw action. 5.4.3 Tooling: For the tasks described before, one has to consider how to move the bolts in the workpiece and how to tighten them, using the desired, calculated torques. The fact that the bolts Chapter 5. ASSEMBLY SUBTASKS 73 in the Pump Assembly have hexagonal heads made the first task easy. The pneumatic gripper, with 90 groves in its jaws, can grasp the hexagonal head and move the bolts in the workpiece. As for applying low torques, a square bar, welded to a 3/8" socket, is used to rotate the screws. The bar fits the grooved jaws, and the clearance between the socket and the head of the bolts, lower coupling forces while rotating. A possible problem lays in the fact that while rotating, the contact forces between the square bar and the groves of the gripper tend to open the jaws. For relatively high torques, a small locking, passive device can be added to the square rod that while mounted, enables only small opening of the jaws. For full preloading, torques must be transferred to the environment. This can be done by using a tool that has a rotary part that rotates the screw and a stationary part, aligned with the environment. In this case, the robot part in the task is to move the tool to its desired locations and activate it through its I/O Module. The positioning of the tool must be done in a spacial way because it has to locate both the screw and the desired location in the environment (double insertion etc.). The following are the major parameters that are to be added to the system through every Screw initialization file: 1. target point location and free space location. 2. movement speeds. 3. end effector configuration (for tool transformation). 4. part sizes from grasping point to tip. 5. forces to terminate Approach. 6. force and torque, gains and boundary parameters around Z axis. Chapter 5. ASSEMBLY SUBTASKS 74 INITIALIZATION MOVE paramatara subtask PICK MOVE APPROACH GRASP CLEAR Figure 5.1: Algorithm •trncture of subtask Pick. INITIALIZATION MOVE parameters APPROACH parameters CLEAR paramates subtask PLACE MOVE APPROACH OPEN CLEAR Figure 5.2: Algorithm structure of subtask P lace. Chapter 5. ASSEMBLY SUBTASKS Figure 5.4: Chamfer crossing. Chapter 5. ASSEMBLY SUBTASKS 76 Figure 5.5: One (a) and two (b) point contact. ONE-POINT CONTACTS ONE-POINT CONTACTS Figure 5.6: The jamming diagram (a) and geometry of wedging condition. Chapter 5. ASSEMBLY SUBTASKS INITIALIZATION Move par. Approach par. Search par. Comply par. Clear par. subtask INSERT 1. Move 2. Approach 3. Search 4. Comply 5. Clear Figure 5.7: Algorithm structure of subtask Insert. INITIALIZATION Move par. Approach par. Search par. Comply in par. Software switch Comply screw par. Clear par. subtask S C R E W o 1. Move F 2. Approach e 3. Search ° 4. Comply (In) <» 5. Comply (sw) •o 6. C l e a r Figure 5.8: Algorithm structure of subtask Screw. Chapter 6 A S S E M B L Y S U B R O U T I N E S During the execution of an assembly task, the subtasks are calling (using call instruction) subroutines that are the repeatable active part in the execution of an assembly task. This chapter describes the principal ways in which those subroutines are carried out, their basic logic structure and the way control algorithms and errors handling are being used. The following subroutines are described in this chapter: • Subroutine MOVE: is used to move the end effector from its current position, to another point, located above the target point, while rotating the tool to a desired orientation. • Subroutine APPROACH: the vertical movement to contact can be done towards a tool or a part in order to grasp them, or, the movement can be done with a tool or a part, in order to contact the environment. Both can be achieved using Approach subroutine with its two stages of movements: 1) rapidly, from a clear point above the workspace to certain height above the contact point. 2) slow, fine motion approach controlled by force feedback loop information. • Subroutine GRASP: to execute an assembly task, parts and took m u 6 t be moved from one place to another after being grasped by the gripper of the end effector. Reducing assembly time depends on the flexibility of the gripper and its suitability to task applications. The gripper structure is designed according to the nature of 78 Chapter 6. ASSEMBLY SUBROUTINES 79 the task and the configuration of the grasped objects using three principal consid-erations: safety, reachability and stability. • subroutine SEARCH: after the first contact, the end-effector must obtain a certain angle with the object's plane. Applying a desired search pattern while moving maintains certain contact force (guarded movement). • subroutine COMPLY: causes the tool to react to force information by setting them to the desired values. Forces cause lateral movement and torques cause rota-tional movements. A force sensor with Comply subroutine, acts like an improved (changeable parameters) RCC. • subroutine ROTATE: during screw or unscrew of a bolt, this s subroutine causes the rotation of the tool, while maintaining a constant normal force between the tool and the head of the screw. • subroutines CLEAR: moves the arm back to a point above the workspace or the part location. Using VAL-II to control the PUMA 560 robot through it's original controller, the only controllable parameters are position and speed of the end effector (or any other point that is declared through "Tool" parameters). Robot locations are used to specify the destinations of robot motions. Two types of locations (both position and orientation) representations are available within VAL-II: • precision point: robot location is represented by the exact position of the individual robot joints. For the PUMA 560, it is defined by the value of angles of the six joints. • transformations: robot location is defined in terms of a cartesian (X,Y,Z) reference frame that is fixed to the base of the robot. The position of the tip of the tool is Chapter 6. ASSEMBLY SUBROUTINES 80 defined by X, Y, and Z coordinate and its orientation is denned by three angles measured from those coordinate axis. Arm movement to a desired location can be executed either by joint interpolated motion or by a movement along a straight hne. Real time path control can be imple-mented only for straight line movements. In this thesis, desired and planned movements are usually activated by subroutines while path modifications are carried out by service programs using real time control algorithms. Those process control programs are acti-vated, and deleted by receiving internal software signals from an appropriate subroutine. Other information is transferred between the pc program and the subroutine using both signals and variable names. This chapter deals with subroutines that were created for the Pump assembly task and the next chapter describes their associated pc programs. However, for most of the subroutines, pc programs are unseparated modules that are executing parallel to the subroutine. For this reason, any specific functions related to a specific related to a specific subroutine, is described in the following sections. Every subroutine is executed from a list of subroutines that is the main part of each Subtask. Each subtask is one point oriented and it manipulate all its subroutines around its specific target point. It is very important that tool transformation (the location of the gripper or the tip of the equipment mounted to the end effector) will be properly introduce to the system before the subroutines are executed. If the tool has one setting while using the "teaching mode" to define the target point transformation, and arm movements are done with another tool setting, correction transformation has to be entered to the system or catastrophic results may occur. Chapter 6. ASSEMBLY SUBROUTINES 81 6.1 S U B R O U T I N E M O V E The way in which the end effector (with or without a tool or a part) moves, approaches and depart from the assembly area (workspace) or from the part location, can be achieved in many ways. Most of the advanced strategies are based on a model which describes the geometric and physical properties of the robot, the objects and their locations in the workspace. The manipulator trajectory can then be planned according to that model. For this thesis, a free space was located above both the assembly area and the parts location. This volume is used to move the arm freely in horizontal directions using Move subroutine. Vertical movements between the free space and the workspace (or the parts area) is done using vertical movements controlled by Approach and Clear subroutines. Fig. 6.1 shows the flow chart of subroutine Move. The subroutine controls the horizontal movements of the end effector within the free space. It calculates the transfor-mation from the current location to a point above the target point and move the tip of the tool to that new position using certain speed. In order to receive correct movement pattern, the difference between the current Z position (height) and the target Z positions is calculated. If the target location is higher, a vertical movement to that height is exe-cuted before the horizontal movement. If the target location is lower, the first movement is in the horizontal plane, followed by the vertical movement towards the target point. Using this pattern, horizontal movements are always done in the safe part, defined by the higher point. If a certain software switch (rotate=l) is active, the movement to the target point is followed by a rotation to a certain angle. The movement to screw a bolt is an example to the need of a such starting position. Chapter 6. ASSEMBLY SUBROUTINES 82 Subroutine Move (like subroutine Clear) is executed when there is no contact be-tween the end effector and the environment. So, no force information is needed and no pc program is activated, the program is carried out, using only the built in position control. 6.2 SUBROUTINE APPROACH Subroutine Approach starting point is when the tool is aligned (perpendicular to the workspace) and its tip is located in the free space a specified distance above the target point. There are two modes in which Approach is activated. The first is when the arm approaches (open gripper) a tool or a part in order to grasp it. The second is the approaching with the tool or the part towards contact with another part located in the work area. Every execution of Approach subroutine is done towards a pre defined target point. That point can be the grasp point of a tool (part) located in the parts area or it can be on the desired contact point on the mating part located in the workspace. Approaching to grasp: this movement will be usually executed towards a point located in the parts location in order to grasp a part or a tool. When open.grip = 1 and weight.ex = 1 are declared in the initialization program, Weight service program will weight the end effector configuration before it start to move. The gripper is then opened and a rapid motion begins towards the shift point (previously calculated using the target point as reference). The rapid motion is not force controlled because system reactions to overloads are faster then those of the arm due to force control so if something does happen, arm power will shout down. The movement from the shift point to the target point is done slowly and the program is terminated when it reaches the target point. Approaching to contact: this approach mode is activated when the gripper is equipped with a part or a tool and the movement is towards the contact with an assembly part or towards the parts location, to return a tool. As before, the first movement towards Chapter 6. ASSEMBLY SUBROUTINES 83 the shifting point is done rapidly (close gripper, no weighting). At the shift point, Approach.pc is activated and real force information is transferred to the main program. Here, no path modifications are needed and a pc program was activated in order to quick program response. The movement towards the target point is done while checking force data to confirm contact. The movement can be terminated (control return to the subtask) either by reaching a certain maximum force or certain lower position. If those contact forces are detected before the tip of the tool reaches target point location, the program will be terminated. If movement continues (maximum force are not detected) until the tool reaches certain lower point beyond the target point (min.z), the program is terminated and a software switch will indicate that Search subroutine should not be executed (search.ex=0). For some applications, its is reasonable (according to task description) that the end effector will face forces before the desired point is reached. The contact between the tool and the bolt's head is an example when a special small rotation is activated during the approaching pattern (activated by a software switch). This enables contact forces to end the approach movement, according to force information received from a contact that occurs while the screw's head is inside the tool (desired location) and not outside it (possible first contact). Approach subroutine and its pc program Approach.pc flow charts are shown in Fig. 6.2. A l l the parameters needed to properly execute those programs (tool transformation, locations, speeds and force limitations) are basically defined in Approach.par and are to be properly changed in the appropriate initialization file. Chapter 6. ASSEMBLY SUBROUTINES 84 6.3 S U B R O U T I N E G R A S P 6.3.1 Grasp Planning: In order to execute an assembly task, the target object (parts or tools to be grasped) must be grasped and moved to a certain point, in a certain path. The movement and the proceeding operations are deeply influenced by the shapes of the gripper and the target object and by the choices made during grasping. In Ref. [22] the authors designed a multi-functional gripper that can handle all the actions desired during task execution. Based on coasts calculation and productivity, they concluded that for minimum assembly time (and costs), in complex applications, the gripper requires the greatest attention. Grasp configuration is usually based on the following: • Reachability: the robot must be able to reach the object without interference. Then, to move to its target point in a collision free path, while holding the target object. • Safety: during approaching (with or without the object) and moving procedures, the robot must be safe. • Stability: the grasp should be stable due to forces acting on the target object during transfer motions and parts mating operations. A n important issue in controlling the grasp operation is the verification that the target object was grasped correctly. This means that the target object was successfully grasped between the gripper's jaws and its position and orientation are as planned. Checking this information can be done easily by using a vision system or a tactile gripper. A force sensor (like the one in C A M R O L ) can be used to weight the object after grasping (Weight subroutine). Using this subroutine can verify that the object is held by the gripper's jaws, but it tells nothing about how it is being held, that is an important input for the following steps. Chapter 6. ASSEMBLY SUBROUTINES 85 In order to by pass this problem, a servo-controlled gripper can be used along with the force sensor. Alternatively, by working with the force sensor alone, the movement has to consider the part, the gripper and the workspace. A n example can be taken from the way the gears are being grasp in Pump assembly task. Approach movement is ended in a point along the gear's shaft, Grasp continues this movement in a guarded move and apply sliding motion on the shaft until the gripper hits the structure of the tooth. This ensures fixed relative position between the tip of the gear and the tool's coordinate frame. For other parts, other logic is applied - all in order to align the grasped part with the pre-defined location of its tip. If there is no possibility to verify the relative location of the grasped object during the grasp action, the object can be moved to contact (force controlled) with the edges of a cube. Using force information, compliance data of the arm and the grasped object and the relative location of the cube's edges, the location of the tip of the object can be calculated. 6.3.2 Gripper's Configuration: One of the dominant principles in grasp planning is the interaction of the gripper's shape and that of the target object. In planning the assembly task, the designer must choose a gripper's shape that will match the target objects and its function in the whole task. Another constraint on the configuration of the gripper is its interaction with the environment. According to [4], the candidate grasp configurations are those having the gripping surfaces in contact with the target object while avoiding collisions between the manipulator and other objects. Current proposals for grasp planning assume a limited class of object models: polyhedra and cylinders. The popular, simple type of gripper is a parallel-jaw gripper. A parallel-jaw gripper, pneumatic actuated, is used in C A M R O L . Many of the target objects are screws, pins, screw driver heads (alien keys) etc. Chapter 6. ASSEMBLY SUBROUTINES 86 While grasping those objects the gripper must align their Z axis with its own Z axis. The designer of the gripper should take the following problems into consideration: parallelism of the jaws: usually,,parallel tracks at the base of the gripper cause the parallel movement of the jaws. Extensively used jaws which were subjected to high forces and moments may no longer be parallel and cannot align with the target tool while grasping it. Using short jaws with 3 designed contact points (2 in one jaw and 1 in the other) can improve the problem considerably. relative position along the Z axis: moving in guarded motion or while parts mating occurs, the tangential forces acting up on the target object from the environment are restricted by UNIMATION to 58 [N]. Assuming static friction coefficient of 0.5, the normal forces supplied by the jaws must be 116 [N]. However, with the current system this cannot be achieved, unless a mechanical stopper is placed in an aligned position or, the tip of the gripper is pressed to a groove in the part. torque transmission: applying torques on bolts heads or any other shape that is not rounded, applies normal opening forces on the gripper's jaws. For application that the forces are higher than the jaws's closing force, either the tool (screwdriver), or the gripper, must have mechanical stopers that prevent the opening of the jaws while rotating. Grasp subroutine and its pc program Grasp.pc flow charts are shown in Fig. 6.3. All the parameters needed to execute properly those programs (software switches, tool trans-formation, locations, speeds and force limitations) are basically denned in Grasp.par. 6.4 S U B R O U T I N E S E A R C H One of the modes of subroutine Approach is the approaching to contact. The gripper is equipped with a part or tool that is moved towards the environment for first part mating. The last movement is done slowly to a pre denned contact point. At this last Chapter 6. ASSEMBLY SUBROUTINES 87 stage, either the normal forces will increased, indicating that part mating had occurred or, force information will not changed. If the forces are not changing while the tool's tip passes certain location, either the desired point was not found (the assembly part is not in its place) or, an insertion process has began. If subroutine Approach is ended because normal forces were detected (in a point near the location of the target point), then the active Insert subtask will call subroutine Search to locate the desired insertion point. 6.4.1 Search strategy: Search subroutine was created in order to detect points that cause change in the force information when contacting the tip of the tool. Such points are hole edges, part borders, walls etc.. T he actual pattern can be divided into two basic movements: • full square search pattern, when the movements are in the X - Y plane, along the X and Y coordinate frame. This pattern is usually used when the desired location was not found and it is assumed that the location of the hole is near the tip of the tool. • a search pattern along one axis in the X - Y plane. Usually this search is the com-plementary task to the full square search, when one edge was located the search continue in one direction in order to find the second edge. Fig. 6.4 shows the square pattern of the search movements in the X - Y plane. Every second change in the direction of the movement, increases the size of square's ribs. The movement along each rib is done by using an internal do loop that breaks the movement into a series of small steps. After each step, force signals from the pc program are checked, so the main program can easily react and stop the movement at that certain point, where the possible edge was found. The square search pattern is then changes into Chapter 6. ASSEMBLY SUBROUTINES 88 a movement, perpendicular to the detected force. This axis search pattern uses the point where the force was detected as a new Ref. point, and the steps are around that point. The program ends when a desired force in the second axis is detected. During program execution, it is important to have certain points that are related to the workspace. The beginning point of the program is the denned, target point of subroutine Approach. That point i6 used to calculate temporary target points, located at the end of each rib during arm movement in the square pattern. Arm movements around that point can be done easily, using SHIFT instruction while the number of steps is increased and the sign (movement direction) is changed. However, it was found, that when a lot of successive transformations are executed (one related to the other), the arm will not reach the location target. It may be a result of a cumulative error, created by the controller while calculating a large amount of transformations of small numbers. The error causes relatively high arbitrary shift in arm location from the desired, designed trajectory and target points. From the structure of the square search pattern, it can be seen that in order to continue four full movements, x and y are moved twice to a position located —Sx and —Sy from the starting point (ini.pnt). After another full movement the final position is located in a distance that is —2 * deltax and —2 * Sy from ini.pnt and so on. Around those locations, the algorithm moves the end effector, using small, force controlled steps. In this way, even if there is a shift while the arm is moved (using relative transformation) in any rib of the square, it will recover due the use of a known location in the followed step. During the movement, directions are changed (sign of the movement), the number of cycles are increased and so are the number of steps used to reached the end of each rib. Fig. 6.5 shows the parameters and the way they are used to achieved a complete search pattern (using VAL-II instructions). When the square pattern is changed to a one axis Chapter 6. ASSEMBLY SUBROUTINES 89 movement, those parameters are null, and the movement in the direction of the detected force is canceled. The movement if the direction, perpendicular to the detected force, is executed using same scheme as was used for the square pattern. While the main program uses position control to moves the arm in the X-Y plane, the pc program (Search.pc) is used to maintain contact with the surface, using force control algorithm that alters the movement in the Z direction. Search.pc is also used to send forces signals to the main program, indicating edges and contact forces. This kind of movement that follows the shape of the part in contact is called - guarded move. There are two ways to control the contact forces with the environment: • to use high gains between the force information and the movement in the Z direction so the arm will response quickly to any change in the environment location (can not be implemented without addition compliance device). • to use sensory information about the contact forces. If they do not remain between desired boundaries, the movements in the X-Y direction is stopped, a movement from or toward the environment is performed until the contact forces receive their desired values. Only then the X-Y movement continue. the first mode is quicker, sensitive and nervous. Small jumps will happen if the guarded move follows a sloped contour. The second way is smooth but slow, it will be used for very small motions, while working with closed fitted parts, both modes can be used with the basic algorithm, for the pump - the first mode is used. In some special cases, a successive insertion has to be performed after the first inser-tion. In this case, a certain region of the part has to perform search pattern, while another region is constrained and can not be moved in the X-Y plane. Using the constrained re-gion as rotating plane, the search pattern is performed using rotational movement instead of the lateral movements described before. This procedure make use of rotation around X Chapter 6. ASSEMBLY SUBROUTINES 90 and around Y while the pc program enables guarded move, using tool coordinate frame. Fig. 6.6 shows a possible situation that occurs while inserting the gears to their locations in the pump. Subroutine Search (Fig. 6.7) is a good example where a compliant device, installed in the Z direction, can make the program and the process simple, reliable and much quicker. With the high stiffness of the arm, only small steps can be used to move the arm into the environment and slow movement must be used in the X-Y directions. Otherwise, when small tolerances are presented, movements in the Z direction will not be able to constantly trace the surface, and the part will miss the edges of the hole (this part is discussed and checked in chapter 8 by simulating a guarded move). 6.4.2 Rotation strategy: There are many cases (Ref. [40]) where an easy detection of the hole can be done after subjecting the tool (part) to an angular rotation. • rotate the tool to a certain angle (usually 70) with the X-Y plane. • bring the front edge of the tool between the hole's boundaries. This is done by pointing with the tip of the edge to the direction of the target point. • apply full search pattern until edges forces are received (that means that there is contact between the edge of the tool and the edge of the hole. • while maintaining contact, rotate the tool back to be perpendicular to the surface of the environment. To use this mode, tool parameters has to be carefully define and the rotation must be done using tool coordinate frame. In the thesis, the rotation part was used in the assembly of the Top of the pump. Chapters. ASSEMBLY SUBROUTINES 91 6.5 SUBROUTINE COMPLY All the program that are using the force sensor data are built to react to feedback information by analysing it and moving the arm according to the program logic and the control law. In many cases where the arm has to follow a contour (even an insert task is done by sensing, reacting and in a way, following the hole's contour), good results may be achieved by complying tool movements to the forces and torques acting on the contact point. In this case, the robot will react to forces and torques that exceed certain envelope, by moving to certain directions that will drive the forces and torques values to be inside the desired envelope. The next chapter deals with the ways to transfer force data to any desired location in any angle. This allow the program to resolve force information to its components and to rotate it to the same coordinate frame that is used to control the movement of the arm. Force information is translated to the contact point location (approximately known), using tool transformation and arm movements are controlled according to that point. By manipulating forces and torques to the same location and coordinate frame that i6 used to control the movement of the tool, each degree of freedom can be handled alone. It is important particularly when arm control is applied by putting special constraints on one (or more) d.o.f. and it is also ease task programing and assembly debugging. In a way, all the control programs in the thesis are acting on the same base. For example: Approach subroutine moves the arm to contact and reacts to small forces by continue the movement in the Z direction towards contact. Once a contact was reached, the program is terminated. Usually, Comply is activated using all the six degrees of freedom. Each d.o.f. has the same force/position control structure and the same proportional force control law. But each d.o.f. has other initial conditions that defines the borders of its force envelope, direction of movements and gains. Chapter 6. ASSEMBLY SUBROUTINES 92 Comply subroutine and its pc program Comply.pc flow charts are shown in Fig. 6.8. All the parameters needed to execute properly those programs (control low borders and gains, tool transformation, locations and force limitations) are basically defined in Comply.par. 6.6 SUBROUTINE ROTATE Subroutine Rotate is the actual part in subtask Screw that rotates the screw in either clockwise or counter clockwise directions. The very original designed structure of rotating the screw was to use Comply subroutine with the certain set point that will cause arm rotation around the sixth d.o.f. (rotation about Z axis). This can be done by using a DELAY instruction in the main program. Delay instructs the robot to move to nowhere and enables the pc program to alter and rotate the arm according to force information. Here, instead of complying all the six d.o.f., the tool is rotated until certain, desired torque is reached. Here again, as in Search subroutine, using the pc program to rotate the end effector causes the calculation of large number of transformations. This is done with one trans-formation follows the previous one and the result is a shift in the tool's location and instead of pure rotation, an arbitrary movement is executed that causes undesired forces and torques between the tool and the screw. Using the structure showed in Fig. 6.9, the rotation is done in the main program, using the starting point as reference location. The pc program (Rotate.pc) detect the torque and if it reach certain level, an inner signal causes the end of the program. The pc program alters arm's movement only in the Z direction when a constant normal force is needed. As in the other cases, Rotate parameters are listed in the file Rotate.par. Rotate subroutine shows the way and the ability of the end effector, but actually, Chapter 6. ASSEMBLY SUBROUTINES 93 the screw is not rotated to the d e B i r e d torques, calculated according to the equations derived in chapter 5. For a 3/8" bolt, the minimum desired torque to receive preload is 65[JVm] (ignoring fatigue loading calculations). Such torques cannot be handled directly by the arm and so, are not applied using this subroutine. 6.7 S U B R O U T I N E C L E A R Arm movements is done using locations and speeds combined with Move instructions. Subroutine C lear makes the opposite movements of subroutine A p p r o a c h , it moves the arm from contact point to a point located in the free space. The subroutine is used to depart with or without a tool or a part. This information is received from the initialization file using a software switch. Fig. 6.10 shows the flow chart of subroutine Clear . The subroutine controls arm movement using locations and speed, combined with MOVE instructions. Chapter 6. ASSEMBLY SUBROUTINES 94 START MOVE CALLPCSTOP reset system Z below target point? no MOVE to a point above the target MOVE down to the desired height MOVE i desirec jp to the 1 height 1 MOVEt abovetf o a point ie target BREAK ZERO.POSITION==1 ? no I ROTATE JOINT #6 RETURN Figure 6.1: Subroutine Move flow chart. Ch*pta6. ASSEMBLY SUBROUTINES START APPROACH reset system I CALLPCSTOP I DECOMPOSE target point location CALCULATE shift point location EXE. APPROACH.PC MOVE rapidly to shift point MOVE a discrete step in Z direction CALLPCSTOP and RETURN YES REACHED Z.MIN? > - i START APPROACH.PC CALL TIP in tool frame CONTINUE RETURN START WEIGHT RETURN Figure 6.2: Subroutine Approach flow chart. Chapter 6. ASSEMBLY SUBROUTINES 96 START GRASP 1 CALL PCSTOP reset system CLOSE gripper CALLJR3.DAT I APPROACH env. DEPART, WAIT I WRITE: error - failour.. WRITE: grasped the tool 1 RETURN Figure 6.3: Subroutine Grasp flow chart. Chapter 6. ASSEMBLY SUBROUTINES 97 Figure 6.4: Search pattern. Counter Sign Cycle* No. of steps Mov. In X direction P Mov. in Y direction |~ Figure 6.5: Search parameters. Chapter 6. ASSEMBLY SUBROUTINES 98 Figure 6.6: Successive insertion. Chapter 6. ASSEMBLY SUBRO UTINES STARTSEARCH CALLPCSTOP iratsystvn MOVEinYdrctan CHANGE SIGN and STEP SEE CALLPCSTOP and RETURN SRARTSEARCHK CALL TF tow. in vorid frw SWTTCHNGLAW: monitor iorcM in Z drecbon RETURN Figure 6.7: Subroutine Search flow chart. Chapter 6. ASSEMBLY SUBROUTINES 100 START COMPLY CALLP resets CSTOP system ___ STARTCOMPLY.PC CALL PCSTOP and RETURN check and cal. forces and torques using co cal. desired ntrol law movement MOVES the arm to new position/orientation RETURN Figure 6.8: Subroutine C o m p l y flow chart. Chapter 6. ASSEMBLY SUBROUTINES START ROTATE CALLPCSTOP reset system EXE ROTATE.PC ROTATE TOOL DELTA.ANGLE CALLJR3.DAT CALLPCSTOP and RETURN SWITCHING LAW: monlor forces in Z direction RETURN Figure 6.9: Subroutine Rotate flow chart. Chapter 6. ASSEMBLY SUBROUTINES START SEARCH CALL F reset 'CSTOP system CHANGE SIGN and STEP SIZE CALLPCSTOP and RETURN CALL TIP forces in world fram SWITCHING LAW: monitor forces in Z direction RETURN Figure 6.10: Subroutine Clear flow chart. Chapter 7 S E R V I C E P R O G R A M S 7.1 P R O G R A M PCstop PCstop program was created in order to reset parameters that are repeatedly used by the programs of the library. Executing the program helps to avoid problems like moving the arm while an undesired pc program is still active or receiving interrupts from unexpected signals sources. While examining the robot, it is good practice to call PCstop at the beginning and at the end of every subroutine. While running a debugged task, the call instruction can be used only at the beginning. PCstop includes the following functions: 1. NOALTER - terminate real-time control of robot motion (the pc program may still running but without an effect on arm movement). 2. PCEND - signals the process control program to stop at the end of its current execution cycle. 3. SIGNALS - turns some specific internal software signals on and off. All those signals are used for communications between subroutines and their related pc programs. 7.2 P R O G R A M Null.sensor There are some tasks where force information is required as a relative to the previous data and in other task a absolute force information is required. Using Grasp subroutine for example, in order to know whether the part was grasped by the arm, the end effector 103 Chapter 7. SERVICE PROGRAMS 104 weight can be measured before and after the grasp action. In this case, it is quicker to null the output of the sensor before the grasp, and to compare the absolute measured weight with the actual weight, stored in the initialization file. Another important use of the null function lies in the fact that there iB a drift in the force information during use. Although there is an automatic gain drift compensation, software controlled through the serial port, this option can not be realized in real time, using VAL-II instructions. To reset all force signals, the program sends an external signal, that activates the first relay of the I/O Module. The relay (using the digital ground - pin 24) transfers high bit to the Reset offsets pin (pin no. 5) of the discrete I/O connector located on the JR3 electronic support system. This action executes a soft reset routine that clears error and trips point flags and loads envelope latched status byte and by this, reset force vector. 7.3 O V E R L O A D C H E C K I N G Both the robot controller and the force sensor data translator (JR3 .DAT) have built in functions that react whenever overload occurs. The robot controller reacts by removing the electric power of the arm. The force sensor reacts by sending bad data envelope or, for less severe cases, by printing an error massage on the monitor screen. For some delicate tasks, maximum forces have to be carefully controlled. Those forces are much lower than those of the system and for practical reasons, built in overload protections are not to be changed. Upon request, the program Over load simply check the received force information and compare it with the another list of maximum forces. If a bigger force is detected, a signal is transferred to the calling program and an immediate termination can be executed. Chapter 7. SERVICE PROGRAMS 105 7.4 FORCE INFORMATION Applying a synchronous, real time, on hne trajectory changes (path control) to the PUMA 560 using VAL-II, can only be done by using Process Control program. This feature of VAL-II is extensively used while task specifications are a function of the data generated by a sensor. In our case, pc programs are used to modify the robot desired locations (while it is moving), using force data information. In this mode, the main program is responsible to move the arm according to the desired task positions and to activate or terminate the pc program. The pc program is responsible for receiving force information, comparing it with the desired forces and subjecting the force errors to the desired control law (as above). The set of new desired locations, that represent force errors in the force controlled axes, is used to alter arm movement (in all axes) that is currently controlled by the main program (using position control). A pc program is very powerful primarily because it uses real time path control, ex-ecutes in parallel and synchronized with the main program. ALTOUT is the VAL-II instruction that generates path modification (while the robot is moving) by sending 6 parameters corresponding to the X, Y and Z displacement data and Xr, Yr and ZT rota-tional data. The input data words (2 bits) specify the amount by which VAL-II modifies the nominal tool-tip trajectory using scale factors. The scale factors yield a 16 bit words and their values are 32 for distances (using [mm]) and 182 for rotations (using [deg.]). For the translation components the trajectory is modified by adding the ALTOUT values to the nominal robot location. For large rotations in noncumulative mode, the change in tool tip orientation is computed by first rotating about the X axis, then the Y axis and finally the Z axis by the specified amounts. Force information is translated to position instructions using the control law as de-scribed previously. This section describes the way force data, received in the wrist sensor, Chapter 7. SERVICE PROGRAMS 106 is manipulated and transformed to the desired coordinate frame and location. Two co-ordinate frames are being used in the library to control arm movement: 1. TOOL coordinate frame - is used for applications where the trajectory is altered by the process control program and no location data is needed for other programs. Complying the arm to the orientation of the hole during inserting task is a good example because this information used by the pc program and no other users needs it. 2. WORLD coordinate frame - is used when force information has effect on the fol-lowing programs and is easy to understand, calculate and manipulate the arm according to this information. Searching program or Edge Follower are programs that are easy to control using world coordinate frame. Force/torque information, received by the sensor, is the sensor's reactions to forces and torques mostly acting on the tip of the tool of the part being held in the gripper. This information i6 amplified, filtered, digitized, processed and sent via both serial and parallel communication lines. The robot, on his communication side, has to receive, check and process that data. JR3 company supplied with the force sensor an interface program called GETDATA. The program provides the necessary VAL-II code to retrieve forces and torques data from JR3 force sensor system's DMA communication link. The program was changed to a new program (JR3.DAT) that has the following features: • checking received data vector for control words (start word and trailer word) and checking words (checksum and maskword). This is a check that the data received by the robot is the same as the data that was sent by the sensor. The checking part includes repeat operations and messages to the operator. Chapter 7. SERVICE PROGRAMS 107 • checking overload for the force sensor (or other parts - using the desired transfor-mations). • using the dimensions of the part held by the gripper (tool, peg, screw etc.) the program uses the Jacobian to transform force information from the sensor's coor-dinate frame to the tool's coordinate frame. The data i 6 stored in a force/torque array (f.m[l]...f.m[6j). This part is described in the following subsections). 7.4.1 Force/Torque data in tool coordinate frame: The relative position between the force sensor location and an arbitrary point of interest i 6 shown in Fig. 7.1. Typically, the point will be the contact point between the tool and the environment. The relative position can either be measured (assuming rigid body construction between the gripper and the object) or it can be calculated using forces and stiffness data. Assuming two sets of generalized, independent coordinate frames q = [qlfqn]T and p = [pi, ...,pm]T and their corresponding forces and torques Q = [Qi,...,# n] r and P = [Pi,P m ] T . In order to transfer forces and torques from one coordinate system to the other, a virtual displacement Ap is considered to take place at the contact point. Considering a complete set of generalized coordinates Aq at the sensor, the mapping is function is a m x n Jacobian matrix related with the coordinate transformation: Ap = JAq (7.1) Infinitesimal translations and rotations of the rigid body are represented by a six dimen-sional vector: dq = [dx, dy, dz, d<f>m, d<f>y, d<f>z]T with respect to the tip's coordinate frame O — uvw and by the vector: Chapter 7. SERVICE PROGRAMS 108 dp = [du, dv, dw, d<f>u, d<j>v, d<j>w]T with respect to the sensor coordinate frame O' — xyz. In matrix form, the transformation from dq to dp is given by du 1 0 0 0 rz ~rv dx dv 0 1 0 -rt 0 r* dy dw 0 0 1 rv -rm 0 dz d<f>u 0 0 0 1 1 1 d<p* d<j>v 0 0 0 0 1 0 d<py d(f>w 0 0 0 0 0 1 d<t>* (7.2) Force/torque processed data vector is received from the sensor by a program called GET.DATA, supplied by JR3 company. In order to receive a force/torque vector at the contact point (usually at the tool's tip), the program was modified. The generalized forces P, measured by the sensor, are transformed to the generalized forces Q at the tool's tip by Q = J r P (7.3) or, in matrix notation /.m[l] 1 0 0 0 0 0 Fu /.m[2] 0 1 0 0 0 0 Fv /.m[3] 0 0 1 0 0 0 Fw /.m[4] 0 -rz rv 1 0 0 Mu /.m[5] rz 0 -rx 0 1 0 Mv /.m[6] ~rv r« 0 0 0 1 Mw (7.4) JR3.DAT is a modified program. The geometric specifications of the tool: r = (rm,ry,rz)T must be added in order to receive the transformed force/torque vector. The program S H O W . F M enables to see on the monitor force information received Chapter 7. SERVICE PROGRAMS 109 from JR3.DAT (or any other force transformation program). This program was cre-ated mostly for checking and calibrating the force sensor and for checking force data transformations. 7.4.2 Force data using world coordinate frame: For some applications, it is convenient to control arm movement using world coordinate frame (Fig. 7.2). Mostly, the relevant force information is located at the tip of the tool. So, force data must be transformed from the wrist sensor to the contact point, and there to be transformed to world coordinate frame. The end effector location (or the tool's location - if its parameters are specified) is expressed in VAL-II using the following parameters: X ,Y ,Z positions in right hand world coordinate frame and 3 Euler angles Orientation, Altitude and Tool (O.A.T.). This set of angles (used by UNIMATION) corresponds to the following sequence of rotation (refer to Fig. 7.3): 1. a rotation of 0 angle about the OZ axis (Rz,o) • 2. a rotation of A angle about the rotated OV axis (RV,A) • 3. a rotation of T angle about the rotated 0W axis (RW,T) • The initial alignment of tool coordinate frame n,s,a relative to XYZ is: the hand points (a axis) to the negative yo axis and s axis points to the positive x0 axis. The transformation that describes the orientation of n,s,a with respect to base coordinate frame Xo, yo> *o is received by rotating around Zo axis and then around yo axis: 0 1 0 0 1 0 0 1 0 Rzo ,9=-BO-Rvo,4>=»0 — -1 0 0 -1 0 0 = 0 0 -1 (7.5) 0 0 1 0 0 1 -1 0 0 Chapter 7. SERVICE PROGRAMS 110 Matrix T is a 4 x 4 homogeneous transformation matrix that maps a vector expressed in OUVW coordinates system to OXYZ coordinate system XYZ = T P uvw (7.6) using tool notation T = nm ax am pa ny sy ay py nr sz ax pz 0 0 0 1 R P* Pv Pz 0 0 0 1 (7.7) the rotational part R can be defined using the Euler angles that are resolved from the PUMA controller: R = fly CLy = Rz,0 0 1 0 0 0 - 1 - 1 0 0 cA 0 sA 0 1 0 -sA 0 cA R;ARa,T = cO -sO 0 0 1 0 sO cO 0 0 0 -1 0 0 1 - 1 0 0 -sOsAcT + cOsT sOsAsT + cOcT aOcA cOsAcT + sOsT -cOaAsT + sOcT -cOcA -cAcT cAaT -aA cT -aT 0 aT cT 0 0 0 1 (7.8) Using J R 3 . D A T transfers both forces and torques from force sensor location to the desired contact point. In order to change this data into world coordinate frame, the program W O R L D . D A T has to use just the rotating part (R) of the homogeneous matrix T. The following matrix describe the rotation transformation of the e-e (or tool's Chapter 7. SERVICE PROGRAMS 111 tip) of the Puma into world coordinate frame: du a* 0 0 0 dx dv n y Sy 0 0 0 dy dw n z *z 0>z 0 0 0 dz d<f>u 0 0 0 a* d<f>* d<j>v 0 0 0 fly Sy d<f>y d<f>w 0 0 0 nx Sz az d<j>z (7.9) In the first part of WORLD.DAT, the vector /.m[1...6] (received from JR3.DAT) is labeled as a new vector (£emp[1...6]). After rotational transformation, the name of the output vector has the same name as the output vector of JR3.DAT. In this way, the following programs can be operated with either programs without any changes. Once again, the transposed Jacobian is applied to the translated forces and torques at the contact point, in order to resolve it into world coordinate frame: /.m[l] nx Tly nz 0 0 0 temp[l] /.m[2] 8V 8 Z 0 0 0 temp[2] /.m[3] Cty az 0 0 0 i temp[3] /.m[4] 0 0 0 n* Tly nz temp[4] /.m[5] 0 0 0 *V »z temp[5] /.m[6] 0 0 0 a* ay O-z temp[6] (7.10) the notation parameters (n„...a,) are defined by equation 7.8. 7.5 P R O C E S S C O N T R O L P R O G R A M S In the previous chapter, subroutines were described. The relations between subroutines and pc program in controlling arm movement lays in the fact that pc programs modify Chapter 7. SERVICE PROGRAMS 112 arm path that was assigned by subroutines. This real time path modification is achieved by applying force data to an appropriate control algorithm. Every pc program contains call instructions that call for force data in tool or world coordinate frame. The position control movements of the arm are altered by real time path modifications that are cal-culated using proportional control law and appropriate parameters (received from the initialization file). In chapter 4 the basics of the control law were discussed. In this section, a discrete time analysis is performed, in order to get the best relations between the stiffness of the parts taking part in the assembly process (arm structure, sensor, tool and environment - K , ) and the software gains. Referring to Fig. 4.3, the contact forces across the sensor (F,) are the output variable of the closed loop system (F a) F a = K . X , (7.11) Implementing a proportional control law in the system, the feedback gain Kjd multi-plies the difference between the desired force Fd and the actual force F 0 . The parameter Kfd serves as gain that changes force errors into position errors. X e = KfJ(Fd - F„) (7.12) Using a discrete time relation between the current and the previous positions X,(fc +i) = X,(fc) + Kfd(Fd - F 0 ) (7.13) and changing arm stiffness parameter into a serial of springs (indicate serial connec-tions of some stiffness like arm, sensor, compliance device etc.) X , ( f c ) = F o ( f c ) ( ^ - + i - ) (7.14) Chapter 7. SERVICE PROGRAMS 113 X,(fc +i) = F 0 ( f c + i ) ( — + — ) using equation 7.14 yields + J ~ ) = Fk(~ + ^~) + K,dFd - KjdFa (7.15) or F o ( f c + 1 ) = F « . , ( l - ) + F ( , ( r T ^ T 1 ) (7.16) The following can be concluded: 1. between the wrist force sensor and the environment in contact, there is the mass of the sensor, end effector and a part (or a toll). Transient motions of those masses are received by the force sensor as reaction forces. The above discussion ignores this input and is implemented just to relatively slow, in contact tasks. 2. the net added force is a function of the gain and the serial stiffness. Smooth movements can be achieved by either low gain or by a compliance device. When a compliance device is not added to the system and there is no contact with the environment, the software gain (Kfd) has to receive high values so that the system can response quickly (Approach Subroutine). 3. decreasing time interval between cycles (every cycle includes sampling, calculations and actual movement) can improve drastically the reactions of the system, using low software gains without a compliance device. When the proportional control algorithm is used in a pc program like Comply.pc, it is applied to the six degrees of freedom at the same time. It means that there is coupling between the movements and the designer has to consider parameters like friction when calculating the input parameters of each control low. The parameters are: desired force Chapter 7. SERVICE PROGRAMS 114 (Fj), proportional gain (K/j), dead zone around the desired force (DZ) and the bounded forces (F m o a t ,F m , n ) . 7.6 INITIALIZATION a n d PARAMETRIC FILES Every subroutine and part of the service programs, use a list of parameters during their execution. In the library those parameters are stored using two categories: Parametric and Initialization files. Parametric files are program oriented and include all the parame-ters the program is using during its execution (actually it is part of the program that was changed into a file). Initialization files are task oriented and contain only those parame-ters that are to be change before a specific task is executed. As described earlier, the first part of task execution is to call to the Initialization files. Each file is divided according to the subroutines of that specific task. For each subroutine, the appropriate Parametric file is called, followed by a list of task oriented changes. Fig. 3.4 shows a block diagram of programs relations while Fig. 7.4 includes the beginning of an initialization file. This structure is not the simplest but it is modular and relatively low memory con-suming. It allows the designer to define all the basic and the desired parameters before the actual execution of every subtask. Building the library in this structure means that there are not stand alone programs. Using a subroutine without activating properly its parametric files can cause problems because the manipulator controller will use the last declarations that remains in its memory. It means risky movements to unexpected locations with unexpected speeds. Every Initialization program begins with part configuration that serves as input for force manipulation (previously discussed) and Tool transformation. Every subtask has its own tool or part being held and activating by the arm. Mostly, While executing a program, the interested part of the arm is the tool's tip and it has to be declared in Chapter 7. SERVICE PROGRAMS 115 a TOOL transformation. This relative tool transformation is automatically taken into consideration each time the location of the robot is requested, when a command is issued to move the robot to a location defined by a transformation. If no transformation value is specified, the tool transformation is set equal to "null tool". This transformation has its center at the surface of the mounting flange of the sixth joint. Tool transformation must take into consideration the sizes of the force sensor, RCC, gripper and any other devices attached to the last joint. If "teach" mode is used to record points locations to the robot memory, it must be done using the same Tool transformation as in actual execution. Once again, risky location may be reached using improper Tool transformation. 7.7 PROGRAM WEIGHT A simple and quick way to check whether a Grasp task succeeded is by checking the weight of the part hanged on the force sensor and to compare it with the data received before the Grasp action. If the program Null.sensor was used before the Grasp action, the net weight of the grasped part is received from the program. The weighted data is then compared with the actual weight of the part (must be located in the active initialization file). If the result is lays between the boundaries, specified by the program - Grasp operation is confirmed and control may advanced to the next step. If the force information is lower then the expect value - another Grasp attempt is activated. Two unsuccessful grasps attempts transfer control either to Search pattern or terminate task execution. One of the problems with weighting the part was arm acceleration or deceleration and its influence on the accuracy of the results, it is very important to avoid a next try to grasp the part because the it is already held by the end effector and a new approach will cause hand opening and possible damage to the part and environment when it fall down. Chapter 7. SERVICE PROGRAMS 116 To avoid arm movements during the actual force measurements (Jr3.dat), a BREAK and WAIT (1 [sec]) instructions are executed. In order to receive accurate data, the force sensor is sampled 25 times (can be changed in the initialization file). The information is averaged and only those inputs that their values are in the region of ±20% are used for a new set of averaging. The waiting and averaging make the program time consuming, and it is a good examples how the use of a vision system, instead of force sensor, can drastically save time and increase reliability. 7 . 8 P R O G R A M R E P E A T For repeating operations like inserting the four screws in their holes in the top of the pump, a repeat procedure can save memory space and ease programing and debugging. Repeat, like an initialization file, is a special purpose program that is created for special task and has certain, fixed structure. The program has an extension according to the task that is repeated and in this way several programs can be located in the same subtask. The program will be located after the initialization tasks and the subroutines that are used to perform the repeated task, so this program will execute the second and the following repetitions. The program uses a do-loop to call the initialization programs, after updating the desired information the desired subroutine is called until the task is completed. Figure 7.2: Force/torque rotation into world coordinate frame. apter7. SERVICE PROGRAMS 1 1 8 Figure 7.3: Orientation, Altitude and Tool (O.A.T.) angles. I ; GEAR1 .INI2 (May. 24 /Kotzev) 2 ; 3 ; TOOL configuration: 4 z.sensor - 31 5 z.rcc - 43 6 z.gripper -112 7 TOOL TRANS(0.0,z.sensor+z.rcc+z.gripper,90,-90,45) 8 mass-0.18 9 ds[1]-8 10 ds[2]-8 II z.tool - 57 12 d[3] - z.rcc+z.gripper+z.tool 13 ; MOVE parameters: 14 CALL move.par 15 SET tool.pnt - gearl .pnt2 16 safe.z-300 17; APPROACH parameters: 18 CALL approach.par 19 weight.ex « 1 Figure 7.4: An Initialization file structure example. Chapter 8 F O R C E C O N T R O L S I M U L A T I O N Most of the algorithms that solved the dynamics of robotic arms are derived for an open kinematic chain configuration. In a case that refers to any manipulation task in which the gripper is not allowed to move freely but its motion is subject to some constraints resulting from the interaction with the environment - a closed kinematics (and dynamics) chain is to be solved. Ref. [41] and [42] consider that problem including analysis of manipulator with constraints on gripper motion. In order to predict the dynamics of simple force-controlled robot system and to un-derstand it's stability, the authors of Ref. [11] developed a series of lumped-parameter models that included effects of robot structural dynamics, sensor compliance and work-piece dynamics. Checking some models that included combinations of the robot dynamics and the dynamics of its workpiece, an instability has been shown to exist for robot mod-els which include representation of a first resonant mode of the arm. The mode modeled could be attributed to either drive train or structural compliance (or both). The insta-bility is present because the sensor is located at the point remote from the actuator. The controller then attempts to regulate contact force through a dynamic system. In order to have a better understanding in the force and position control of the arm, a numerical simulation was coded. The model simulates the end effector, the discrete controller of the robot, the control law, the sensor and the environment. A guarded move task was chosen, because it is used frequently in assembly tasks and is a classic case to apply both position and force control algorithms to a robot manipulator. In the 119 Chapter 8. FORCE CONTROL SIMULATION 120 simulation, parameters like arm compliance, B e n s o r stiffness, environment position etc. can be changed and it's influence on task performance can be calculated. Running a subtask like plane searching (for hole, edge etc.) causes the tool to move in a square pattern, perpendicular to the plane, while increasing the rib's dimensions. The force sensor is used to sense normal and tangential force acting on the tool's tip. Under position control, the tool is moved in its X — Y plane to a desired location and under force control the tool remains in contact (desired force) with the environment. Increasing in the plane (tangential) forces indicates an edge, an obstacle or a simple increasing of the friction forces that cause strategy changes according to the program's logic. 8.1 S Y S T E M D E S C R I P T I O N 8.1.1 Applied Force Control: Using the P U M A 560 with its original controller and V A L - I I language, a force control algorithm can be implemented through position commands. There are primarily two ways to receive and apply force information to the arm movement: R o b o t c o n t r o l program: according to task specifications, the designer can build two control algorithms in the main program. Some axes (designate in world or tool coordinate frame) are controlled via force data, while the others are position controlled. While running the program, force information is received by calling J R 3 . D A T and then (if needed) the program calls T I P to transform force/torque information to the desired location. In the axes that are controlled via force information, the force data is compared to the desired forces. Subjecting the force errors to the task's control law, force errors are represented by new desired positions that can be understood and executed by the robot control box. After this stage all the axes (both position and force control), has motion representation. The robot controller can derive an inverse kinematic solution and move Chapter 8. FORCE CONTROL SIMULATION 121 the arm to the new desired location. Process Control program: as described in the previous chapter, a pc program is very powerful primarily because it is a real time path control, parallel and synchronized with the main program. A L T O U T is the V A L - I I instruction that generates path modification by sending 6 parameters corresponding to the X, Y and Z displacement data and XTt Yr and Zr rotational data. The input data words (2 bits) specify the amount by which V A L - I I modifies the nominal tool-tip trajectory using scale factors. The scale factors yield 16 bit words and their values are 32 for distances (using [mm]) and 182 for rotations (using [deg.]). For the translation components the trajectory is modified by adding the A L T O U T values to the nominal robot location. For large rotations in noncumulative mode, the change in tool tip orientation is computed by first rotating about the X axis, then the Y axis and finally the Z axis by the specified amounts. Timing Considerations: according to Ref. [38], using internal alter (the altering mode of pc program), V A L - I I expects an A L T O U T program instruction to be executed every 28 [msec] to pass control data to the robot motion controller. Because of computation time required by V A L - I I to perform the transitions between motion segments, there is a limit on how closely spaced commanded locations can be. When locations are too close together, there is not enough time for V A L - I I to compute and perform the transition from one motion to the next, causing a break in the continues path motion. This means that the robot stops instantaneously at intermediate locations. To prevent this, straight line motions can be used if the motion segment take more than about 140 [msec] or about 60 [msec] for joint interpolated motions. 8.1.2 Arm Stiffness: As described previously, applying force control algorithm to the robot is done by in-troducing small movements to the end-effector while in contact with the environment. Chapter 8. FORCE CONTROL SIMULATION 122 W h e n the desired set point is located a small segment into the surface, the controller will try to move the arm to that point. The joint motors will cause the arm to bend until the position error will null (joint encoders reaching the desired angles). The result of such pseudo movement will increase force/torque reactions. Decreasing force/torque reactions is done by moving the end-effector to the opposite direction. W h e n the use of the robot includes fast movements, structural dynamic characteristics of the manipulator including stiffness, inertia, damping and natural frequencies are to be considered. Using the arm while moving in contact with the environment involves fine movements so part of the dynamic characteristics can be ignored. In this case, force/torque reactions between the arm and the environment are a function of the step size and the stiffness of the contacting parts. Stiffness parameters that have to be taken into consideration are arm stiffness ( K o r m ) , stiffness combination of the sensor, gripper and the tool (held by the gripper) ( K # e n ) and the stiffness of the environment (Ke„ v ) . In order to be able to simulate an assembly task, parts stiffness parameters have to be calculated or measured. When working against a stable environment (the usual case while performing an assembly task), the stiffness values of both the sensor and gripper/tool combination can be measured or calculated, because they are linear and contact orientation is known. The robot arm, on the other hand, has many optional contact positions and orientations, so the nonlinear stiffness values are not constant. This problem can be solved in the following ways: • stiffness envelope: for a particular robot a measurement stiffness envelope can be derived and applied according to the end effector locations and force/torque direction (assuming it is working at a known point). Using interpolation between known point can give good estimation to arm stiffness. A measurement of some principal points was done on the P u m a in the C A M R O L Lab. and is shown in Fig. Chapter 8. FORCE CONTROL SIMULATION 123 8.1. • stiffness calculations: using reduced parameters equations (described in the fol-lowing subsection) and approximated linear terms, arm Stiffness can be derived according to its position and orientation. The assembled parts of the pump are very stiff, it cause the force control algorithm to move the arm using small steps. Dealing with tracking high sloped environment contours, small steps movement is relatively slow. One of the possible ways to improve system performance, is by introducing a compliance device (like linear spring) to the system. It has to be compliant relatively to the other components of the system, so their stiffness can be ignored. The compliant device can be located in places like the basis of the assembled structure or to the base of the robot. The simplest and easiest to install location is the manipulator wrist (shown schematically in Fig. 2.5). 8.1.3 Reduced Parameters: A complex mechanical system like robot arm has many compliant components, inertia and energy dissipating unit6 (dampers). Reflecting the values of all those components to a selected point (or part), enables to reduce the complexity of the system without affecting neither natural frequencies nor modes of vibration. The overall stiffness (or compliance) of a reduced model would be the same value received by the ratio of the applied force (or torque) to the resulting deflection (ref. [31]). Fig. 8.2 shows the arm (maximum outstretched) in rotation around a horizontal axis. The arm components compliance can be reduced to torsional compliance around the shoulder axis Chapter 8. FORCE CONTROL SIMULATION 124 where - angular compliance (^)-$ - angular deflection of the beam. I - distance between load operation point to pivot. using linear parameters, the linear compliance ey is a function of the linear displacement yj caused by the force F at the force application point (mostly the end effector): y ~ F ~F ~F~~ * ( 8 } The linear compliance can be transformed (and 60 it can be reduced) to any intermediate point at a distance o from the center The overall reduced torsional compliance ep of the robot in a considered mode, at a specific point p (like the end-effector) can be written * = * ? = (j|+ £ + • • • ( 8 . 4 ) where e 0 , e l r . . are compliant parameters of the system and / 0 , / i , . . . are their distance from the pivot axis. Calculation of a stretched PUMA 560 arm shows that its approximate compliance is about 10_B [rad/Nm] or, using arm length of about 830 [mm], the approximate stiffness is 120 [N/mm]. Fig. 8.1 shows the data received from measurements of the arm in the lab. The measured data shows uniform force/displacement line. This stiffness is half the calculated stiffness, a reasonable result regarding the approximation in the calculation and the age of the robot (wear, backlash etc.). In the simulation the measured data is being used. Chapter 8. FORCE CONTROL SIMULATION 125 Using the same logic, mass reduction can be perform (Fig. 8-2) based on the expres-sions of the kinetic energy for the masses before and after reduction. mp = (m0ll + m1l21-r ... + mfl})^ (8.5) p where T n 0 , m j , . . . are the initial masses, / i , / 2 > " a r e their distance from the pivot point and mp is the reduced mass. Calculation of the reduced structural mass at the end effector must be based on estimations of joint masses and their locations (there is no information on that subject in Ref. [38]). Using those estimations and verifying the result by Ref. [31], 3.5 [Kg] was used in the simulation as the effective structural mass at the end effector. Fig. 8.3 represents a linear model of the robot arm moving towards the environment. In this model both the arm structure, the sensor (plus a tool) and the environment are compliant and has some damping capabilities. 8.1.4 Impact: An impact problem is denned to be the collision of two bodies with known energy loss and a contact force with defined direction. An impact between the tip of the tool and the environment is an essential part in Approach subroutine (part matting) and in the guarded move task. In this case we assume a central impact - the line of action of the contact forces passes through the mass center of each body so there is no rotation of either body. In the simulation, the movements of the contacting parts (sensor/tool and environment), were based considering the following: a) Conservation of linear momentum (collinear case): mx(Vi - V l ) = -m 2 (V 2 - v2) (8.6) where m^mj are the masses of the bodies and vi)V2,v'ltv'i are their velocities before and after the collision. Chapter 8. FORCE CONTROL SIMULATION 126 b) Conservation of energy: \ m i v l + \ m 2 v l = \ m i V i + \ m 2 v l + E (8-7) where E is the energy loss during impact (known). Using the coefficient of restitution [e = (V2 — Vi)/(vi — V2)], the following equations give the velocity of each body following the collision: mjui + m2v2 — em2(vi — v2) rrix + m2 m^vx + m2v2 + emx(vx - v2) V2 = (8.8) TTIJ -+- m2 For a spacial case of collision between small mass and relatively big mass, (like the case of fixed environment), the change in the velocity of the big mass is negligible and the relative velocity becomes: V1 = -evx (8.9) For steel (balls) the coefficient of restitution was found to be e = 0.55 and this value is used in the simulation. 8.2 M O D E L D E S C R I P T I O N The force control algorithm applied' in the simulation is according to the force control block diagram explained in chapter 4. The environment was derived so that hard tracking topography can be checked. In the simulation, movement in the X direction begins from the moment the arm begins with the approaching towards the environment. This gives a better orientation and timing while studying the results. Like in the Search subroutine, there is no coupling between the movement in the X and Z direction, i.e. using the arm in actual tracking a contour, if forces exceeded high values or normal forces becomes zero (no contact) - the actual movement is the sum of the force controlled movement in Z direction and the continuous, position controlled movement in X direction. Chapter 8. FORCE CONTROL SIMULATION 127 At time T = t0, the arm begins a rapid movement towards a target point located 10 [mm] above the environment. The movement is achieved by using a discrete (AT = 0.028[aec]) simulation and control low that add to the dynamic equations, the desired location and velocity. The time interval and the restricted desired steps of the arm prevent high forces due to high velocities and damping (without actual contact). After the first approach to the desired location, the vertical velocity is lowered to approx. 16 [mm/sec]. For fixed environment, the dynamic equations of the arm and the sensor (without the input from the control low) are: (8.10) when subscript r - arm parameters, subscript a - sensor (or tip of the tool), the equation for arm motion is: mrzr = -irbr + (z„ - zr)bt - zTK + (z, - zr)k. (8.11) the control algorithm is added by adding the desired position (%*) and desired velocity (id) as input to the contact point (Fig. 7.3) of the spring and damper of the arm. The equation that simulate arm movements (in the simulation) is m r z r = (id - zT)br + (z. - zr)b. + (zd - *r)K + (z, - zT)k, (8.12) The second mass (sensor + tool) is moving according to the Eq. 8.10. In the simulation, contact position is indicated by comparing the sensor's location to that of the environment. If at the end of a certain step, the sensor is located Sz, under the Chapter 8. FORCE CONTROL SIMULATION 128 environment, then the time it moves after impact (till next step) is St = y*. Using the velocity after impact (£o = — e z « ) , part of the kinetic energy (after collision) is transferred to potential energy stored in the springs of the system. Using the conservation of energy and movement time, the velocity at the end of the integration step is calculated and the new location of the arm (above the environment) is found. The new position and velocity is then fed to the control low and to the integration routine. Other parameters that are being checked and updated are the maximum and minimum distances between the sensor and the arm that indicate true spring limitations. Figures 8.4 to 8.8 are selected outputs of the simulation, discussed in the next section. 8.3 C O N C L U S I O N S A ) While moving the arm in search pattern, for practical reasons, the velocity should be the maximum that still can locate desired locations. Figures 8.4 and 8.5 shows the same arm configuration with other plan velocities. For the surface shown, the higher speed (5 [mm/sec], causes the loss of much information. B) Using a high stiffness configuration causes jittery movements of the arm and unstable contact with the environment (Fig. 8.5 and 8.7). The contact forces in the stiff arm are relatively high (Figures 8.6 - 8.8). This increases the friction forces in the X — Y plan and sometimes can cause distractive contact with the environment. Complicated software has to be used in order to relate forces in the Z direction and the plane forces and to filter the friction forces (interference with the direction of edge information). C ) Another important advantage that is added by the compliance of the sensor, is its fast reactions to the opposite direction of the preload (faster then the reaction of the force control). When searching for a hole, the location of the hole is found by force information due to contact with the edges of the hole. For movements in the X — Y plan in velocity of Chapter 8. FORCE CONTROL SIMULATION 129 2 [mm/sec], in extreme cases, when the tolerances between the peg and the hole are less then 0.056 [mm], there is good possibility that the force controller will not react at all. For other cases, with wider tolerances, the reaction (inserting the peg) can be too small for "good" contact that will alter and stop the search program due to force information. So, although compliance device reduces the bandwidth of the system, it is useful for most force controlled, assembly tasks. Chapter 8. FORCE CONTROL SIMULATION 130 Force [Nt] 0.4 0.6 0.8 def lec. [mm] 1.2 Figure 8.1: PUMA 560 measured arm stiffness. F I mp /77T7777 //////// Figure 8.2: Reduction of translational compliance and mass to different location. Chapter 8. FORCE CONTROL SIMULATION Figure 8.3: Linear model of the robot arm. F O R C E G A U R D E D M O U E O F ARM ( K - 5 5 N /MM) ^ A N D S E N S O R ( K - 5 N / M M ) . c ° U E L O C I T Y IN X D I R . - 5 ( M M / S E C ) D i s t a n c e i n X d i r . (*100 o n ) . Figure 8.4: low stiffness sensor spring, high velocity. Chapter 8. FORCE CONTROL SIMULATION 132 FORCE GAURDED MOUE OF ARM ( K - 5 5 N/MM: AND SENSOR ( K - 5 N/MM). o 5 o-o o UELOCITY IN X D I R . - 2 (MM/SEC) 0.00 0.32 0.64 0.96 Distance l n X d i r . (*100 am) LP 1.28 1.60 Chapter 8. FORCE CONTROL SIMULATION 133 o o FORCE GAURDED MQUE OF ARM (K-55 N/MM: AND SENSOR (K-55 N/MM). UELOCITY IN X DIR.-2 (MM/SEC) i . o o • *» 8 o o o ( 1 Iiiii l i l i llllllll.. M (POT TI Tjl' ^0.00 D.32 0.64 0.96 D i a t a n c a In X d i r . (*100 D I ) 1.28 1.60 0.00 1.28 0.32 0.64 0.96 Siatanea i n X d i r . <»100 mm). Figure 8.6: High stiffness sensor spring, low velocity. 1.60 Bibliography [1] Asada H., Slotine J.J.E. 1986 by John Wiley & Sons, Inc. Robot Analysis and Control. 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Appendix A MAIN TASK and SUBTASKS: A . l main program PUMP: 1 ; main t a B k PUMP (May. 24 /Kotzev) 2 ; 3 ATTACH 4 CALL g e a r l . i n i l 5 CALL pick 6 CALL gearl.ini2 7 CALL insert 8 CALL gear2.inil 9 CALL pick 10 CALL gear2.ini2 11 CALL insert 12 CALL t o p . i n i l 13 CALL pick 14 CALL top.ini2 15 CALL insert 16 CALL screwl.inil 17 CALL pick 18 CALL screwl.ini2 19 CALL place 20 CALL repeat.bolt 21 CALL t o o l . i n i l 22 CALL pick 23 CALL tool.ini2 24 CALL Bcrev 25 CALL repeat.screw 26 CALL tool.i n i 3 27 CALL place 28 CALL pcstop A.2 subtask INSERT: 1 ; subtask INSERT (May 25 / Kotzev) 2 ; 3 TYPE »***••*** INSERT started " 140 Appendix A. MAIN TASK and SUBTASKS: 4 CALL move 5 CALL approach 6 IF search.pc 1 GOTO 10 7 CALL search 8 10 CALL comply 9 CALL clear 10 TYPE "******** INSERT ended " 11 RETURN A .3 subtask PICK: 1 ; subtask PICK (Jan.12 /Kotzev) 2 ; 3 TYPE "******** PICK started " 4 CALL move 5 CALL approach 6 CALL grasp 7 CALL clear 8 TYPE ********* PICK ended " 9 RETURN A.4 subtask PLACE: 1 ; subtask PLACE (June 6 - Kotzev) 2 ; 3 TYPE "******** PLACE started 4 CALL move 5 CALL approach 6 OPEN 7 CALL clear 8 TYPE "******** PLACE ended " 9 RETURN A .5 subtask SCREW: 1 ; subtask SCREW (June 18 - Kotzev) 2 ; 3 TYPE "******** SCREW started 4 CALL move 5 CALL approach 6 CALL rotate 7 CALL clear 8 TYPE "******** SCREW ended " 9 RETURN Appendix B SUBROUTINES and SERVICE PROGRAMS: B.l program APPROACH: 1 ; subroutine APPROACH (June 21 - Kotzev) 2 CALL pcstop 3 TYPE " ++++++++ APPROACH started" 4 ; Weight the end effector equipment: 5 IF weight.ex -• 1 THEN 6 CLOSEI 7 TIMER (1) = 0 8 WAIT TIMER(l) > 1 9 IF null.ex -= 1 THEN 10 CALL null.sensor 11 IF n u l l . f a i l =» 1 GOTO 5 12 GOTO 25 13 END 14 mass.before = weight 15 25 TYPE "- f .m[3j = ", /F6.2, mass .before, "[Kg]" 16 END 17 IF open.grip =«= 1 THEN 18 OPENI 19 END 20 ; Move in X Y plane and on Z axis to temp.pnt (shifting point): 21 SPEED speed.high ALWAYS 22 SET temp.pnt « SHIFT(HERE BY shift.x, B h i f t . y , 0) 23 MOVES temp.pnt 24 DECOMPOSE a[] - tool.pnt 25 sx » a[0]+shift.x 26 sy «= a[l]+®hift.y 27 sz «* a[2]+shift.z 28 SET temp.pnt » TRANS(sx, sy, BZ, a[3], a[4], a[5]) 29 MOVES temp.pnt 30 BREAK 31 IF open.grip == 1 THEN 32 SPEED speed.appro ALWAYS 33 MOVES tool.pnt 34 GOTO 100 35 END 142 Appendix B. SUBROUTINES and SERVICE PROGRAMS: 143 36 ; Move from the shift point to contact: 37 TYPE " APPROACH.PC started " 38 PCEXECUTE approach.pc, -1, 0 39 ALTER (-1, 18, , 1) 40 SPEED speed.appro ALWAYS 41 IF shift.x > 0 THEN 42 delta.x = delta.shift 43 END 44 IF shift.y > 0 THEN 45 delta.y • delta.shift 46 END 47 IF shift.z > 0 THEN 48 delta.z = delta.shift 49 END 50 10 SET point.appro = SHIFT(HERE BY -delta.x, -delta.y, -delta.z) 51 count = count+1 52 shift.max a shift.x+shift.y+shift.z+shift.over 53 IF (count*delta.shift) > (shift.max) THEN 54 IF position.appro 1 THEN 55 search.pc • 1 56 GOTO 15 57 END 58 END 59 MOVES point.appro 60 BREAK 61 IF SIG(2025) THEN 62 IF force.appro •= 1 THEN 63 IF rot.appro «• 1 THEN 64 count.rot = count.rot+1 65 TYPE count.rot 66 IF count.rot > 5 GOTO 15 67 SIGNAL -2025 68 HERE temp.pnt 69 DECOMPOSE a[] = temp.pnt 70 r[5] = 6*count.rot 71 SET temp.pnt - TRANS(a[0], a[l], a[2], a[3], a[4], 5) 72 MOVES temp.pnt 73 GOTO 600 74 END 75 GOTO 15 76 END 77 END 78 500 GOTO 10 79 ; 80 15 CALL pestop Appendix B. SUBROUTINES and SERVICE PROGRAMS: 81 TYPE " «=-«»™ f [3] = ", /F6.2, f [3] , " 82 100 TYPE " ++++++++ APPROACH finished " 83 RETURN 1 ; APPROACH.PAR (June 5 - Kotzev) 2 ; 3 second = 0 4 count = 0 5 count.rot = 0 6 rot.appro = 0 7 search.pc • 0 8 weight. ex = 1 9 null.ex » 1 10 search.pc = 0 11 open.grip • 1 12 force.appro • 1 13 position.appro • 1 14 shift.x = 0 15 shift.y = 0 16 shift.z = 5 17 delta.shift =0.3 18 shift.over * 5 19 delta.x = 0 20 delta.y • 0 21 delta.z = 0 22 speed.high = 50 23 speed.appro = 10 24 appro.max[1] • 2; Forces during approach 25 appro.max[2] s 2 26 appro, max[3] =2.75 1 ; program APPROACH.PC (June 5 - Kotzev) 2 ; 3 IF SIG(2020) — 0 THEN 4 TYPE " APPROACH. PC ended 5 HALT 6 END 7 ; 8 ; Check forces in X, Y and Z directions: 9 CALL jr3.dat 10 FOR pc = 1 TO 3 11 IF ABS(f.m[pc]) > appro.max[pc] THEN 12 SIGNAL 2025 Appendix B. SUBROUTINES and SERVICE PROGRAMS: 145 13 END 14 END 15 ALTOUT 0, 0, 0, 0, 0, 0, 0 B.2 program C L E A R : 1 ; subroutine CLEAR (June 21 - Kotzev) 2 ; 3 CALL pcstop 4 TYPE " ++++++++ CLEAR started " 5 SPEED speed.clear ALWAYS 6 IF clear.grip == 1 THEN 7 OPEN 8 TIMER (1) - 0 9 WAIT TIMER(l) > 0 10 END 11 IF second — 1 THEN 12 SET temp.pnt « SHIFT(HERE BY clear.x, clear.y, clear.z) 13 MOVES temp.pnt 14 BREAK 15 END 16 DECOMPOSE b[] - tool.pnt 17 HERE temp.pnt 18 DECOMPOSE a[] - temp.pnt 19 MOVES TRANS(a[0], a[l], b[2]+safe.z, a[3], a[4], a[5]) 20 BREAK 21 IF clear.rotate « 1 THEN 22 SPEED speed.rotate ALWAYS 23 HERE #temp.pnt 24 DECOMPOSE a[] = #temp.pnt 25 MOVE #PP0INT(a[0] , a[l] , a[2] , a[3] , a[4] , dear [5]) 26 BREAK 27 END 28 TYPE " ++++++++ CLEAR ended " 29 RETURN 1 ; CLEAR.PAR (July 21 - Kotzev) 2 ; 3 Bpeed.clear • 100 4 clear.rotate • 0 5 clear[5] • -260 6 clear.grip = 0 7 clear.x =0 8 clear.y E 0 Appendix B. SUBROUTINES and SERVICE PROGRAMS: 9 clear.z • 0 10 RETURN B . 3 program C O M P L Y : 1 ; subroutine COMPLY (August 29 - Kotzev) 2 ; 3 CALL pcstop 4 TYPE " ++++++++ COMPLY started " 5 ; t[] was decomposed to be the target point (done by the 6 ; initialization program) . 7 TYPE " COMPLY.PC started " 8 PCEXECUTE comply.pc, -1, 1 9 ALTER (-1, 17, ,1) 10 ; Rotate i f rotate==l: 11 10 DELAY delaytime 12 IF SIG(2025) THEN 13 IF comply.force « 1 THEN 14 HERE temp.pnt 15 DECOMPOSE aa[] • temp.pnt 16 IF ABS(aa[2]-t[2]) > delcomply.z GOTO 20 17 END 18 END 19 HERE temp.pnt 20 DECOMPOSE aa[] = temp.pnt 21 IF ABS(aa[2]-t[2]) > (lower.pnt-3) GOTO 20 22 GOTO 10 23 ; 24 20 CALL pcstop 25 TYPE " ++++++++ COMPLY ended " 26 RETURN 1 ;COMPLY.PAR (August 28 - Kotzev) 2 ; 3 delaytime = 1 4 rotate • 0 5 comply.force = 0 6 mid.pnt •= 60 7 delcomply.z » 50 8 lower.pnt • 100 9 f.max[l] • 10; information to stop comply. 10 f .max[2] - 10 11 f.max[3] - 3 12 f.max[4] * 1000^ Appendix B. SUBROUTINES and SERVICE PROGRAMS: 13 f.max[5] - 1000 14 f.max[6] = 250 15 comax[l] = 0.5 16 comin[l] = -0.5 17 comax[2] =0.5 18 comin[2] • -0.5 19 comax[3] = 0.5 20 comin[3] = -0.5 21 comax[4] = 30 22 comin[4] = -30 23 comax[5] • 30 24 comin[5] « -30 25 comax[6] = 30 26 comin[6] = -30 27 gain[l] = 10 28 gain[2] • 10 29 gain[3] • 10 30 gain[4] • 0.5 31 gain[5] • 0.5 32 gain[6] = 1 33 del.max[1] • 30 34 del.max[2] - 30 35 del.max[3] » 30 36 del.max[4] = 20 37 del.max[5] • 20 38 del.max[6] • 50 1 ; COMPLY.PC (Aug. 3 - Kotzev) 2 ; 3 IF SIG(2020) — 0 THEN 4 TYPE " COMPLY.PC ended 5 HALT 6 END 7 HERE temp.pnt 8 DECOMPOSE a[] • temp.pnt 9 IF ABS(b[2]-a[2]) > lower.pnt THEN 10 SIGNAL 2026 11 END 12 CALL jr3.dat 13 ; Monitor forces to stop the program: 14 IF ABS(f.m[3]) > ABS(f.max[3]) THEN 15 SIGNAL 2025 16 END 17 ; Initilate f sign[] : Appendix B. SUBROUTINES and SERVICE PROGRAMS: 18 FOR pc - 1 TO 6 19 fsign[pc] » 0 20 END 21 ; Monitor forces in X dir.: 22 IF f .m[l] > comaxCl] THEN 23 fsign[l] - -ABS(f .m[l] -comax[l] ) 24 END 25 IF f.m[l] < comin [1] THEN 26 fsign[l] = ABS(f .m[l] -comin[l] ) 27 END 28 ; Monitor forces in Y dir.: 29 IF f .m[2] > comax[2] THEN 30 fsign[2] - -ABS(f.m[2]-comax[2]) 31 END 32 IF f.m[2] < comin[2] THEN 33 f sign [2] - ABS(f .m[2]-comin[2] ) 34 END 35 ; Monitor forces in Z dir.: 36 IF f .m[3] > comax[3] THEN 37 f sign[3] « ABS(f .m[3] -comax[3] ) 38 END 39 IF f.m[3] < comin[3] THEN 40 fsign[3] - -ABS(f .m[3]-comin[3]) 41 END 42 ;Monitor torques around X: 43 IF f .m[4] > comax[4] THEN 44 fsign[4] - -ABS(f.m[4]-comax[4]) 45 END 46 IF f.m[4] < comin[4] THEN 47 fsign[4] - ABS(f.m[4]-comin[4]) 48 END 49 ; Monitor torques around Y: 50 IF f.m[5] > comax[5] THEN 51 fsign[5] = -ABS(f.m[5]-comax[5]) 52 END 53 IF f.m[5] < comin[5] THEN 54 fsign[5] - ABS(f.m[5]-comin[5]) 55 END 56 ; Monitor torque around Z: 57 IF f.m[6] > comax[6] THEN 58 fsign[6] • ABS(f.m[6]-comax[6]) 69 END 60 IF f.m[6] < comin[6] THEN 61 fsign[6] • -ABS(f.m[6]-comin[6]) 62 END Appendix B. SUBROUTINES and SERVICE PROGRAMS: 63 ; 64 FOR pc - 1 TO 6 65 del[pc] = f 8ign[pc]*gain[pc] 66 IF ABS(del[pc]) > del.max[pc] THEN 67 del[pc] = del. max [pc]*f sign [pc]/ABS(f sign [pc] ) 68 END 69 END 70 ALTOUT 0, del[l], del [2], del [3], del [4], del [5], del [6] B.4 program C O M S C R E W : 1 ; subroutine COMPLY.SCREW (June 21 - Kotzev) 2 ; 3 CALL pestop 4 TYPE " ++++++++ COMSCREW started " 5 TYPE " COMPLY.PC started " 6 50 PCEXECUTE comply.pc, -1, 1 7 ALTER (-1, 17, , 1) 8 HERE #temp.pnt 9 DECOMPOSE b[] = #temp.pnt 10 10 HERE #temp.pnt 11 DECOMPOSE a[] - #temp.pnt 12 IF a[5] > 0 GOTO 20 13 IF ABS(b[5])-ABS(a[5]) > 60 THEN 14 CALL pestop 15 GOTO 50 16 END 17 DELAY delaytime 18 IF SIG(2025) GOTO 20 19 TYPE del[l], del [2], del [3], del [4], del [5], del [6] 20 GOTO 10 21 ; 22 20 CALL pestop 23 TYPE " ++++++++ COMPLY ended " 24 RETURN 1 ; COMSCREW.PAR (July 21 - Kotzev) 2 ; 3 comply.force = 1 4 comax[3] • -0.6 5 comin[3] • -0.5 6 comax[6] «= -250 7 comin[6] = -240 8 del.max[l] • 0 Appendix B. SUBROUTINES and SERVICE PROGRAMS: 9 del.max[2] - 0 10 del.max[3] » 3 11 del.max[4] • 0 12 del.max[5] = 0 13 del.max[6] - 250 B.5 GEAR1, GEAR2 parameters: 1 ; program GEAR1.INI1 (May. 24 /Kotzev) 2 ; 3 CALL p c B t o p 4 TYPE " " 5 TYPE " GEAR1 ASSEMBLY " 6 TYPE " " 7 ; CONFIGURATION: 8 z.sensor = 31 9 z.rcc = 43 10 z.gripper • 112 11 TOOL TRANS(0, 0, z.sensor+z.rcc+z.gripper, 90, -90, 45) 12 mass • 0.17 13 dB[l] - 8 14 ds[2] - 8 15 z.tool • 57 16 ds[3] = z.rcc+z.gripper+z.tool 17 ; MOVE parameters: 18 SET tool.pnt = gearl.pntl 19 safe.z = 300 20 speed.move = 100 21 zero.position = 0 22 ; APPROACH parameters: 23 CALL approach.par 24 ; GRASP parameters: 25 temp.force » 10 26 speed.grasp • 10 27 weight.z • 30 28 ; CLEAR parameters: 29 CALL clear.par 1 ; program GEAR1.INI2 (Aug. 3 - Kotzev) 2 ; 3 CALL pestop 4 ; CONFIGURATION: 5 z.tool = 57 6 TOOL TRANS(0, 0, z.sensor+z.rcc+z.gripper+z.tool, 90, -90 Appendix B. SUBROUTINES and SERVICE PROGRAMS: 151 7 mass =0.17 8 ds[l] = 8 9 ds[2] - 8 10 ds[3] • z.rcc+z.gripper+z.tool 11 ; MOVE parameters: 12 SET tool.pnt = gearl.pnt2 13 safe.z • 300 14 speed.move = 100 15 ; APPROACH parameters: 16 CALL approach.par 17 weight.ex = 0 18 open.grip • 0 19 shift.over • 10 20 ; SEARCH parameters: 21 CALL search.par 22 Bpeed.xy • 2 23 delx =0.3 24 dely =0.3 25 delsearch.z = 3 26 ; COMPLY parameters: 27 CALL comply.par 28 comply.force = 1 29 f.max [2] =2.5 30 delcomply.z = 10 31 lower.pnt = 31 32 speed.comply = 5 33 comax[3] = -0.6 34 comin[3] = -0.5 35 ; CLEAR parameters: 36 CALL clear.par 37 clear.grip = 1 1 ; GEAR2.INI1 (August 28 - Kotzev) 2 ; 3 CALL pcstop 4 TYPE " " 5 TYPE 11 GEAR2 ASSEMBLY " 6 TYPE " " 7 ; CONFIGURATION: 8 DECOMPOSE t[] • gearl.pntl 9 SET gear2.pntl - TRANS(t [0] , t[l]+43, t [2] , t [3] , t[4], t[5]) 10 z.sensor = 31 11 z.rcc = 43 12 z.gripper = 112 Appendix B. SUBROUTINES and SERVICE PROGRAMS: 152 13 TOOL TRANS(0, 0, z.sensor+z.rcc+z.gripper, 90, -90, 45) 14 mass = 0.17 15 ds[lj » 8 16 ds[2] - 8 17 z.tool » 97 18 ds[3] • z.rcc+z.gripper+z.tool 19 ; MOVE parameters: 20 SET tool.pnt = gear2.pntl 21 safe.z • 300 22 speed.move • 100 23 zero.position = 0 24 ; APPROACH parameters: 25 CALL approach.par 26 ; GRASP parameters: 27 temp.force • 10 28 speed.grasp • 10 29 weight.z = 70 30 ; CLEAR parameters: 31 CALL clear.par 1 ; GEAR2.INI2 (August 28 - Kotzev) 2 ; 3 CALL pcstop 4 ; CONFIGURATION: 5 DECOMPOSE t[] - gearl.pnt2 6 SET gear2.pnt2 = TRANS(t[0], t[l]+30, t[2], t[3], t[4], t [5]) 7 z.tool » 97 8 TOOL TRANS(0, 0, z.sensor+z.rcc+z.gripper+z.tool, 90, -90, 45) 9 mass = 0.17 10 ds[l] - 8 11 ds[2] - 8 12 ds[3] = z.rcc+z.gripper+z.tool 13 ; MOVE parameters: 14 SET tool.pnt = gear2.pnt2 15 safe.z = 300 16 speed.move • 100 17 ; APPROACH parameters: 18 CALL approach.par 19 weight.ex =0 20 open.grip » 0 21 shift.over « 10 22 position.appro • 1 23 ; SEARCH parameters: 24 CALL search.par Appendix B. SUBROUTINES and SERVICE PROGRAMS: 25 ; COMPLY parameters: 26 CALL comply.par 27 comply.force = 1 28 lower.pnt = 63 29 delcomply.z = 63 30 comax[3] = -1.2 31 comin[3] =-1.1 32 comax[6] • 25 33 comin[6] • 20 34 gain[3] - 10 35 del.max [3] = 62 36 ; CLEAR parameters: 37 CALL clear.par 38 • clear.grip = 1 B.6 program GRASP: 1 ; program GRASP (Feb.5 /Kotzev) 2 CALL pestop 3 TYPE " ++++++++ GRASP started " 4 IF open.grip == 1 THEN 5 CLOSE 6 END 7 IF temp.force > 0 THEN 8 DO 9 CALL jr3.dat 10 APPRO HERE, -0.5 11 UNTIL ABS(f.m[3]) > temp.force 12 END 13 IF weight.ex -- 1 THEN 14 SPEED speed.grasp ALWAYS 15 DEPARTS weight.z 16 BREAK 17 TIMER (1) = 0 18 WAIT TIMER(l) > 2 19 CALL weight 20 mass.after = weight 21 TYPE " f.m[3] = ", /F6.2, mass.after 22 temp.mass = ABS(mass.after-mass.before) 23 IF ABS(temp.mass) < 0.7*mass THEN 24 TYPE " ERROR - failure to grasp the tool ' 25 ELSE 26 TYPE " grasped the tool " 27 END 28 END Appendix B. SUBROUTINES and SERVICE PROGRAMS: 29 TYPE " ++++++++ GRASP ended " 30 RETURN 1 ; program GRASP.SUB 2 . Last modification 28 - 9 - 5 3 ; PARameters: CLOSE.GAP = to face the peg's sholders. 4 ; 5 PCEND 6 close.gap »= -2 7 TYPE " GRASP.SUB started " 8 SPEED speed.grasp.sub ALWAYS 9 DECOMPOSE t[] = work.point 10 SET temp « TRANS (t [0] , t [ l ] , t[2]+30, t [3] , t [4] , t [5] ) 11 MOVE temp 12 BREAK 13 SIGNAL 1 14 TIMER (1) = 0 15 WAIT TIMER(l) > 1 16 CALL weight 17 m a 8 8 t o o l l . O = weight 18 TYPE " f.m[3] - ", /F6.2, masstooll.O, "[Kg]'1 19 OPEN 20 MOVE work.point 21 BREAK 22 CLOSE 23 TIMER (1) = 0 24 WAIT TIMER(l) > 1 25 APPRO work.point, close.gap 26 BREAK 27 TIMER (1) = 0 28 WAIT TIMER(l) > 1 29 MOVE temp 30 BREAK 31 CALL weight 32 masstooll.l «= weight 33 TYPE " f.m[3] = ", /F6.2, masstooll.l, "[Kg]" 34 tooll.mass = masstooll.1-masstooll.0 35 IF ABS(tooll.mass) < 0.1 THEN 36 TYPE " Error - failure to grasp the tool " 37 OPEN 38 MOVE SHIFT(HERE BY 0, 0, 0.1) 39 flag.tooll • 0 40 ELSE 41 TYPE " grasped the tool" Appendix B. SUBROUTINES and SERVICE PROGRAMS: 42 flag.tooll • 1 43 END 44 TYPE " GRASP.SUB ended " 45 RETURN B.7 program JR3 .DAT: 1 ; program JR3.DAT (Jan.10 /Kotzev) 2 ; 3 ; The program is based on GET.DATA to recieve force/moment 4 ; information at the tool's tip in [Kg] and [Kg*mm] units. 5 ; in order to receive the correct data, TOOL trans, must be 6 ; included in the prog, i.e: TOOL TRANS(rx, ry, rz, 0, -90, 0) 7 ; This includes the 90 degees shift in the JR3 force sensor. 8 ; 9 8tart.err = 0 10 mask.err «= 0 11 sat.err = 0 12 check.err • 0 13 trailer.err = 0 14 ; 15 fmax[l] = 25 16 fmax[2] • 25 17 fmax[3] - 50 18 fmax[4] • 75 19 fmax [5] «= 75 20 fmax[6] « 75 21 ; 22 ;CHECKING THE "START" WORD: 23 1 start = I0GET(-1028) 24 IF start <> 0 THEN 25 start.err = start.err+1 26 IF start.err > 10 THEN 27 TYPE " JR3 error - problems with the START word" 28 GOTO 500 29 END 30 WAIT 31 GOTO 1 32 END 33 ; 34 ;CHECKING THE "MASK" WORD: 35 2 mask - I0GET(-1028) 36 IF mask BAND "40377 <> "356 THEN 37 IF mask BAND "377 <> "356 THEN 38 mask.err • mask.err+1 Appendix B. SUBROUTINES and SERVICE PROGRAMS: 156 39 IF mask.err > 10 THEN 40 TYPE " JR3 error - problems with the MASK word" 41 GOTO 500 42 END 43 GOTO 1 44 END 45 IF mask BAND '40000 THEN 46 sat.err * sat.err+1 47 IF sat.err > 10 THEN 48 TYPE " JR3 error - SATURATION error" 49 GOTO 500 50 END 51 GOTO 1 52 END 53 END 54 ; 55 z.dl = I0GET(-1028) 66 z.d2 - I0GET(-1028) 57 z.d3 - I0GET(-1028) 58 z.d4 « I0GET(-1028) 59 z.d5 - I0GET(-1028) 60 z.d6 - I0GET(-1028) 61 ; 62 ; Cheking the CHECK word (check-sum) : 63 3 check - I0GET(-1028) 64 IF (z.dl+z.d2+z.d3+z.d4+z.d5+z.d6+check) <> 0 THEN 65 check.err • check.err+1 66 IF check.err > 10 THEN 67 TYPE " JR3 error - CHECK word incorrect" 68 GOTO 500 69 END 70 GOTO 1 71 END 72 ; 73 ; Checking the TRAILER word: 74 4 trailer • IOGET(-1028) 75 IF trailer <> "100000 THEN 76 trailer.err • trailer.err+1 77 IF trailer.err > 10 THEN 78 TYPE " JR3 error - TRAILER word incorrect" 79 GOTO 500 80 END 81 GOTO 1 82 END 83 ; Forces in [lb] and torques in [lb-in]: Appendix B. SUBROUTINES and SERVICE PROGRAMS: 157 84 f[ l ] - z.dl*.122E-01 85 f[2] = -z.d2*.122E-01 86 f[3] = z.d3*.244E-01 87 f[4j = z.d4*.336E-01 88 f[5] - -z.d5*.336E-01 89 f[6] = z.d6*.336E-01 90 ; 91 FOR j r - 1 TO 6 92 IF ABS(f [jr]) > fmax[jr] THEN 93 TYPE "JR3 error - OVERLOAD" 94 END 95 END 96 ; Forces in [Kg] and Torques in [Kg-mm] : 97 f.m[l] - 0.445*f[l] 98 f .m[2] - 0.445*f[2] 99 f.m[3] - 0.445*f[3] 100 f.m[4] » 11.3*f [4]+ds[3]*f .m[2]-ds [2] *f .m[3] 101 f.m[5] - 11.3*f[5]-ds[3]*f.m[l]+ds [1] *f .m[3] 102 f.m[6] « 11.3*f[6]+ds[2]*f.m[l]-ds [1] *f .m[2] 103 500 RETURN B.8 program MOVE: 1 ; subroutine MOVE (June 22 - Kotzev) 2 ; 3 CALL pestop 4 TYPE " ++++++++ MOVE started " 5 SPEED speed.move ALWAYS 6 DECOMPOSE b[] = tool.pnt 7 HERE temp.pnt 8 DECOMPOSE a[] » temp.pnt 9 IF a[2]-safe.z > b[2] THEN 10 MOVES TRANS(b[0] , b[l], a[2] , b[3] , b[4] , b[5]) 11 BREAK 12 MOVES TRANS(b[0] , b[l] , b[2]+safe.z, b[3] , b[4] , b[5]) 13 BREAK 14 ELSE 15 MOVES TRANS (a [0] , a[l] , b[2]+safe.z, a[3] , a[4] , a[5]) 16 BREAK 17 MOVES TRANS(b[0], b[l] , b[2]+safe.z, b[3] , b[4] , b[5]) 18 BREAK 19 END 20 IF zero.position 1 THEN 21 HERE #temp.pnt 22 DECOMPOSE a[] - #temp.pnt Appendix B. SUBROUTINES and SERVICE PROGRAMS: 158 23 MOVE #PP0INT(a[0] , a[l] , a[2] , a[3] , a[4] , start [5] ) 24 BREAK 25 END 26 TYPE " ++++++++ MOVE ended " 27 RETURN B.9 program N U L L . S E N S O R : 1 ; Null.sensor (June 17 - Kotzev) 2 ; 3 count = 0 4 n u l l . f a i l • 0 5 10 SIGNAL 1 6 count • count+1 7 IF count > 10 THEN 8 n u l l . f a i l - 1 9 TYPE " can't reset force data! " 10 GOTO 20 11 END 12 CALL jr3.dat 13 IF ABS(f.m[3]) > 0.1 GOTO 10 14 mass.before • f.m[3] 15 20 SIGNAL -1 16 RETURN B.10 program O V E R L O A D : 1 ; program OVERLOAD (31.10.89 Kotzev) 2 ' 3 ; checking for overloads 4 CALL jr3.dat 5 FOR over = 1 TO 6 6 fabs[over] • ABS(f.m[over]) 7 IF fabs[over] > 3*pcmax[over] THEN 8 SIGNAL 2030 9 END 10 END 11 RETURN B . l l program P C S T O P : 1 ; program PCSTOP (Jan.12 /Kotzev) 2 ; 3 NOALTER Appendix B. SUBROUTINES and SERVICE PROGRAMS: 4 SIGNAL -2020 5 TIMER (1) * 0 6 WAIT TIMER(l) > 1 7 PCEND 8 SIGNAL -2010, -2011, -2012, -2013, -2014, -2015, -2016 9 SIGNAL -2017, -2018, -2019, 2020, -2025 10 RETURN B.12 program R E P E A T . B O L T : 1 ; REPEAT.BOLT (June 18 - Kotzev) 2 ; 3 FOR repeat • 2 TO 4 4 CALL screwl.inil 6 IF repeat « 2 THEN 6 SET tool.pnt - SHIFT(screwl.pntl BY -25, 0, 0) 7 END 8 IF repeat »«= 3 THEN 9 CALL screwl.inil 10 SET tool.pnt - SHIFT(screwl.pntl BY -50, 0, 0) 11 END 12 IF repeat -- 4 THEN 13 SET tool.pnt • SHIFT(screwl.pntl BY -75, 0, 0) 14 END 15 CALL pick 16 CALL screwl.ini2 17 IF repeat 2 THEN 18 SET tool.pnt - SHIFT(screwl.pnt2 BY 60, -60, 0) 19 END 20 IF repeat — 3 THEN 21 SET tool.pnt » SHIFT(screwl.pnt2 BY 0, -60, 0) 22 END 23 IF repeat «== 4 THEN 24 SET tool.pnt - SHIFT(screwl.pnt2 BY 60, 0, 0) 25 END 26 CALL place 27 END 28 RETURN B.13 program R E P E A T . S C R E W : 1 ; REPEAT.SCREW (Sep. 10 - Kotzev) 2 ; 3 screwl = 10 4 screw2 • 10 Appendix B. SUBROUTINES and SERVICE PROGRAMS: 5 screw3 «= 1 6 screw4 = 1 7 SIGNAL -2001 8 FOR i - 1 TO 20 9 com.z = 15*i; Movement due to screw pitch 10 FOR repeat = 1 TO 4 11 FOR same.screw = 1 TO 3 12 CALL tool.ini2 13 IF repeat 1 THEN 14 IF screwl - • 10 GOTO 50 15 SET tool.pnt - SHIFT(tool.pnt2 BY 0, 0, 0) 16 END 17 IF repeat ~ 2 THEN 18 IF screw2 10 GOTO 50 19 SET tool.pnt • SHIFT(tool.pnt2 BY 60, -60, 20 END 21 IF repeat 3 THEN 22 IF screw3 • - 10 GOTO 50 23 SET tool.pnt - SHIFT(tool.pnt2 BY 0, -60, 0 24 END 25 IF repeat «== 4 THEN 26 IF screw4 10 GOTO 50 27 SET tool.pnt - SHIFT(tool.pnt2 BY 60, 0, 0) 28 END 29 CALL screw 30 50 IF SIG(2001) THEN 31 IF repeat - - 1 THEN 32 screwl • 10 33 END 34 IF repeat 2 THEN 35 screw2 = 10 36 END 37 IF repeat 3 THEN 38 screw3 «= 10 39 END 40 IF repeat » 4 THEN 41 screw4 • 10 42 END 43 SIGNAL -2001 44 END 45 END 46 END 47 END 48 RETURN Appendix B. SUBROUTINES and SERVICE PROGRAMS: 161 B.14 program ROTATE: 1 ; subroutine ROTATE (June 21 - Kotzev) 2 ; 3 CALL pestop 4 TYPE " ++++++++ ROTATE started " 5 SPEED speed.rotate ALWAYS 6 ; IF zero.position == 1 THEN 7 ; HERE #temp.pnt 8 ; DECOMPOSE a[] = #temp.pnt 9 ; MOVE #PP0INT(a[0], a[l], a[2], a[3], a[4], start[5]) 10 ; BREAK 11 ; GOTO 100 12 ; END 13 TYPE " ROTATE.PC started " 14 ; PCEXECUTE rotate.pc, -1, 1 15 ; ALTER (-1, 17, , 1) 16 FOR rotate «= 1 TO rot.steps 17 HERE temp.pnt 18 DECOMPOSE a[] « temp.pnt 19 r[5] • a[5]+rot.dir*delta.o 20 SET temp.pnt « TRANS(a[0], a[l], a[2], a[3], a[4], r[5]) 21 MOVES temp.pnt 22 BREAK 23 IF SIG(2015) GOTO 100 24 END 25 100 CALL pestop 26 TYPE " ++++++++ ROTATE ended " 27 RETURN 1 ; ROTATE.PAR (June 21 - Kotzev) 2 ; 3 speed.rotate 81 100 4 rot.dir • -1 5 delta.o = 10 6 rot.steps • 30 7 torque[5] • 300 8 rotmax[3] = -0.7 9 rotmin[3] = -1 10 del.rotmax[3] • 5 11 RETURN 1 ; ROTATE.PC (June 19 - Kotzev) Appendix B. SUBROUTINES and SERVICE PROGRAMS: 2 ; 3 ; halting PC program when SIGNAL changes: 4 IF SIG(2020) == 0 THEN 5 TYPE " ROTATE.PC ended " 6 HALT 7 END 8 ; 9 CALL jr3.dat 10 ;force calculation and overload checking: 11 FOR pc = 1 TO 3 12 fabs[pc] - ABS(f .m[pc] ) 13 IF fabs[pc] > flimit[pc] THEN 14 SIGNAL 2013 15 END 16 END 17 ; Check torques around Z axis: 18 IF ABS(f.m[6]) > torque[5] THEN 19 SIGNAL 2015 20 END 21 ; Monitor forces in the Z direction: 22 fsign[3] = 0 23 IF f.m[3] > rotmax[3] THEN; above the env. 24 f sign[3] «* -ABS (f .m[3]-rotmax[3] )*gain.in[3] 25 END 26 IF f.m[3] < rotmin[3] THEN 27 fsign[3] - ABS(f.m[3]-rotmin[3])*gain.out[3] 28 END 29 del[3] = fsign[3] 30 IF ABS(fsign[3]) > del.rotmax[3] THEN 31 IF fsign[3] == 0 GOTO 15 32 del[3] = del.rotmax[3]*fsign[3]/ABS(fsign[3]) 33 15 END 34 ALTOUT 0, 0, 0, del[3], 0, 0, 0 B . 1 5 S C R E W p a r a m e t e r s : 1 ; program SCREW1.INI1 (June 6 - Kotzev) 2 ; 3 CALL pcstop 4 ; CONFIGURATION: 5 z.Bensor = 31 6 z.rcc • 43 7 z.gripper • 112 8 TOOL TRANS(0, 0, z.Bensor+z.rcc+z.gripper, 90, -90, 9 mass = 0.17 Appendix B. SUBROUTINES and SERVICE PROGRAMS: 163 10 ds[l] - 8 11 ds[2] = 8 12 z.tool • 40 13 d[3] = z.rcc+z.gripper+z.tool 14 ; MOVE parameters: 15 SET tool.pnt • B c r e w l . p n t l 16 safe.z • 300 17 speed.move • 100 18 ; APPROACH parameters: 19 CALL approach.par 20 ; GRASP parameters: 21 temp.force • 10 22 speed.grasp = 10 23 weight.z = 50 24 ; CLEAR parameters: 25 CALL clear.par 26 RETURN 1 ; SCREW1.INI2 (June 6 - Kotzev) 2 ; 3 CALL pestop 4 ; CONFIGURATION: 5 z.tool «= 40 6 TOOL TRANS(0, 0, z.sensor+z.rcc+z.gripper+z.tool, 90, -90, 45) 7 ma 8s = 0.17 8 ds[l] - 8 9 ds[2] - 8 10 d[3] • z.rcc+z.gripper+z.tool 11 ; MOVE parameters: 12 SET tool.pnt = screwl.pnt2 13 safe.z • 300 14 speed.move = 100 15 ; APPROACH parameters: 16 CALL approach.par 17 weight.ex • 0 18 open.grip • 0 19 shift.z - 15 20 speed.appro = 20 21 delta.shift = 1 22 ; CLEAR parameters: 23 CALL clear.par 24 clear.rotate • 1 25 RETURN Appendix B. SUBROUTINES and SERVICE PROGRAMS: 164 B.16 program S E A R C H : 1 ; subroutine SEARCH (June 17 - Kotzev) 2 ; 3 CALL pestop 4 TYPE " ++++++++ SEARCH started " 5 TYPE " SEARCH.PC started " 6 PCEXECUTE search.pc, -1, 1 7 ALTER (-1, 19, , 1) 8 ; If rotate==l, rotate the part: 9 IF rotate == 1 THEN 10 FOR search - 1 TO 10 11 r3 « r[3]+rot[3] 12 r4 = r[4]+rot[4] 13 r5 - r[5J+rot[5] 14 SET temp.pnt « TRANS(r[0], r [ l ] , r[2], r3, r4, r5) 15 MOVES HERE:temp.pnt 16 BREAK 17 END 18 END 19 SPEED speed.xy ALWAYS 20 ; Reset parameters for f i r s t force signal: 21 60 cycle « 0 22 count.search • 0 23 nstep = 0 24 ; Check i f movement exceeded delsearch.z: 25 HERE ini.pnt 26 DECOMPOSE b[] = ini.pnt 27 50 HERE temp.pnt 28 DECOMPOSE a[] » temp.pnt 29 IF ABS(b[2]-a[2]) > delsearch.z THEN 30 TYPE " reached min. location " 31 GOTO 100 32 END 33 ; Movement parameters: 34 stepx • 0 35 stepy • 0 36 5 IF count.search •» 0 THEN 37 cycle • cycle+1 38 nstep = nstep+1 39 count.search * 1 40 IF SIG(2010) GOTO 15 41 stepx • (ABS(b[0]-a[0])+delx*cycle)/nstep 42 IF SIG(2011) GOTO 20 43 GOTO 10 Appendix B. SUBROUTINES and SERVICE PROGRAMS: 165 44 END 45 15 IF count.search •« 1 THEN 46 count.search • 2 47 IF SIG(2011) GOTO 25 48 stepy « (ABS(b[l]-a[l])+dely*cycle)/nstep 49 IF SIG(2010) GOTO 30 50 GOTO 10 51 END 52 25 IF count.search «« 2 THEN 53 nstep = nstep+l 54 count. search «= 3 55 IF SIG(2010) GOTO 35 56 stepx = -(ABS(b[0]-a[0])+delx*cycle)/nstep 57 IF SIG(2011) GOTO 20 58 GOTO 10 59 END 60 35 IF count.search «= 3 THEN 61 count.search • 0 62 IF SIG(2011) THEN 63 IF SIG(2010) GOTO 100 64 GOTO 5 65 END 66 stepy = -(ABS(b[l]-a[l])+dely*cycle)/nstep 67 IF SIG(2010) GOTO 30 68 GOTO 10 69 END 70 10 FOR search • 1 TO nstep 71 SET temp.pnt - SHIFT(HERE BY stepx, stepy, 0) 72 MOVES temp.pnt 73 BREAK 74 IF SIG(2010) GOTO 60 75 IF SIG(2011) GOTO 60 76 END 77 GOTO 50 78 20 FOR search = 1 TO nstep 79 SET temp.pnt - SHIFT(HERE BY stepx, 0, 0) 80 MOVES temp.pnt 81 BREAK 82 IF SIG(2010) GOTO 100 83 END 84 GOTO 50 85 30 FOR search « 1 TO nstep 86 SET temp.pnt » SHIFT(HERE BY 0, stepy, 0) 87 MOVES temp.pnt 88 BREAK Appendix B. SUBROUTINES and SERVICE PROGRAMS: 166 89 IF SIG(2011) GOTO 100 90 END 91 GOTO 50 92 ; Search movements ended, rotate the part: 93 100 IF rotate 1 THEN 94 FOR search « 1 TO 10 95 r3 - r[3]-rot[3] 96 r4 - r[4]-rot[4] 97 r5 - r[5]-rot[5] 98 SET temp.pnt - TRANS(r[0], r [ l ] , r[2], r3, r4, r5) 99 MOVES HERE:temp.pnt 100 BREAK 101 END 102 END 103 CALL pcstop 104 TYPE " ++++++++ SEARCH finished " 105 RETURN 1 ; SEARCH.PAR (May 26 /Kotzev) 2 ; 3 rotate = 0; ROTATE par. 4 r[0] - 0 5 r[l] - 0 6 r[2] = 0 7 r[3] = 0 8 r[4] = -90 9 r[5] - 90 10 rot[3] - 0 11 rot[4] - 0 12 rot[5] - 0 13 ; 14 count .max *= 50 15 delx =0.5 16 dely =0.5 17 search.gain[3] = 10 18 speed.xy = 5 19 speed.rotate • .1E-01 20 semax[l] = 1 21 semin[l] = -1 22 semax[2] = 1 23 8emin[2] = -1 24 semax[3] = -0.7 25 8emin[3] = -1 Appendix B. SUBROUTINES and SERVICE PROGRAMS: 26 del. Bemax [3] = 5 27 gain.in[3] =1.5 28 gain.out[3] =0.2 29 flimit [1] = 3 30 flimit[2] = 3 31 flimit[3] • 5 32 delsearch.z = 5 33 RETURN 1 ; SEARCH.PC (June 6 - Kotzev) 2 ; 3 ; halting PC program when SIGNAL changes: 4 IF SIG(2020) — 0 THEN 5 TYPE " SEARCH.PC ended " 6 HALT 7 END 8 ; 9 CALL jr3.dat 10 ;force calculation and overload checking: 11 FOR pc = 1 TO 3 12 fabsLpc] = ABS(f .m[pc]) 13 IF fabsLpc] > flimit[pc] THEN 14 SIGNAL 2013 15 END 16 END 17 ; Check force in the X direction: 18 IF fabs[l] > semax[l] THEN 19 SIGNAL 2010 20 END 21 ; Check force in the Y direction: 22 IF fabs[2] > semax[2] THEN 23 SIGNAL 2011 24 END 25 ; Monitor forces in the Z direction: 26 fsign[3] = 0 27 IF f.m[3] > semax[3] THEN; above the env. 28 fsign[3] • -ABS(f.m[3]-semax[3])*gain.in[3] 29 END 30 IF f.m[3] < semin[3] THEN 31 fsign[3] = ABS(f.m[3]-semin[3])*gain.out[3] 32 END 33 del[3] = fsign[3] 34 IF ABS(fsign[3]) > del.Bemax[3] THEN 35 IF fsign[3] == 0 GOTO 15 36 del[3] = del.Bemax[3]*fsign[3]/ABS(fsign[3]) Appendix B. SUBROUTINES and SERVICE PROGRAMS: 168 37 15 END 38 ALTOUT 0, 0, 0, del[3], 0, 0, 0 B . 1 7 program SHOW.FM: 1 2 3 4 5 6 8 9 10 11 12 13 14 program SHOW.FM (Feb. 26. 90 Kotzev) DO CALL jr3.dat TYPE "Fx [Kg] =' /F6.2, f.m[2], TYPE "Mx [Kg-t-mm]"1 /F7.2, f.m[5], Fy [Kg] -" /F6.2, f.m[3] My [Kg*mm]=", /F7.2, f.m[6] /F6.2, f.m[l], Fz [Kg] =' /F7.2, f.m[4], Mz [Kg*mm]=". weight - SQRT(f .m[l]*f .m[l] +f .m[2]*f .m[2] +f .m[3]*f .m[3]) TYPE "Weight- ", weight TYPE "press REC botton on teach pendant to stop" TYPE " " TIMER (1) - 0 WAIT TIMER(l) > 5 UNTIL (PENDANT(1) BAND 1) <> 0 B.18 program TIP: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ; program TIP (Jan.10 /Kotzev) CALL jr3.dat fmax[4] = 75 f [1] - z.dl*.122E-01 f[2] = z.d2*.122E-01 f [3] - z.d3*.244E-01 f[4] = z.d4*.336E-01 f[5] - z.d5*.336E-01 f[6] - z.d6*0 FOR j r = 1 TO 6 IF ABS(f[jr]) > fmax[jr] THEN TYPE "JR3 error - OVERLOAD" END END f.m[l] - 0.445*f[l] f.m[2] - 0.445*1 [2] Appendix B. SUBROUTINES and SERVICE PROGRAMS: 22 f.m[3] = -0.445*f[3] 23 f .m[4] - l l * f [4]-ds[3]*f .m[2]+di» [2] *f .m[3] 24 f.m[5] - 11.3*f[5]+d8[3]*f.m[l]-ds[1]*f.m[3] 25 f.m[6] « -11.3*f [6]-ds[2]*f .m[l]+ds[l]*f .m[2] 26 HERE point 27 DECOMPOSE a[] - point 28 nx - -SIN(a[3])*SIN(a[4])*C0S(a[5])+C0S(a[3])*SIN(a[5]) 29 ny - C0S(a[3])*SIN(a[4])*C0S(a[5])+SIN(a[3])*SIN(a[5]) 30 nz - -C0S(a[4])*C0S(a[5]) 31 B X • SIN(a[3])*SIN(a[4])*SIN(a[5])+C0S(a[3])*C0S(a[5j) 32 ay = -C0S(a[3])*SIN(a[4])*SIN(a[5])+SIN(a[3])*C0S(a[5]) 33 sz - C0S(a[4])*SIN(a[5]) 34 ax - SIN(a[3])*C0S(a[4]) 35 ay - -COS(a[3])*C0S(a[4]) 36 az = -SIN(a[4]) 37 f [1] * nx*f .m[l ]+Bx*f .m[2]+ax*f .m[3] 38 f [2] = ny*f .m[l]+sy*f .m[2j+ay*f .m[3] 39 f [3] = nz*f .m[l]+8z*f .m[2]+az*f .m[3] 40 f [4] = f .m[4] 41 f [5] = f.m[5] 42 f [6] - f .m[6] 43 500 RETURN B.19 TOOL parameters: 1 ; program T00L.INI1 (June 17 - Kotzev) 2 ; 3 CALL pcstop 4 ; CONFIGURATION: 5 z.sensor = 31 6 z.rcc = 43 7 z.gripper = 112 8 TOOL TRANS(0, 0, z.sensor+z.rcc+z.gripper, 90, -90, 45) 9 ma8s • 0.17 10 ds[l] - 8 11 ds[2] = 8 12 z.tool • 40 13 ds[3] • z.rcc+z.gripper+z.tool 14 ; MOVE parameters: 15 SET tool.pnt = tool.pntl 16 safe.z • 300 17 speed.move = 100 18 ; APPROACH parameters: 19 CALL approach.par 20 ; GRASP parameters: Appendix B. SUBROUTINES and SERVICE PROGRAMS: 170 21 temp.force • 10 22 speed.grasp » 10 23 weight.z » 50 24 ; CLEAR parameters: 25 CALL clear.par 26 clear.rotate • 1 27 clear[5] - -260 28 RETURN 1 ; T00L.INI2 (June 21 - Kotzev) 2 ; 3 CALL pestop 4 ; CONFIGURATION: 5 z.tool = 31 6 TOOL TRANS(0, 0, z.sensor+z.rcc+z.gripper+z.tool, 90, -90, 45) 7 mass = 0.17 8 ds[l] = 10 9 ds[2] - 10 10 d[3] • z.rcc+z.gripper+z.tool 11 ; MOVE parameters: 12 SET tool.pnt « tool.pnt2 13 safe.z = 25 14 speed.move = 100 15 ; APPROACH parameters: 16 CALL approach.par 17 speed.high = 5 18 speed.appro • 5 19 weight.ex = 0 20 open.grip = 0 21 rot.appro a 1 22 shift.z • 4 23 shift.over =15 24 speed.appro • 10 25 delta.shift » 1 26 ; COMSCREW parameters: 27 CALL cornscrew.par 28 lower.pnt • 20 29 ; CLEAR parameters: 30 CALL clear.par 31 speed.clear = 20 32 clear.rotate = 1 33 Bpeed.rotat • 100 34 RETURN Appendix B. SUBROUTINES and SERVICE PROGRAMS: B.20 TOP parameters: 1 ; T0P.INI1 (June 5 - Kotzev) 2 ; 3 CALL pestop 4 TYPE " " 5 TYPE " TOP ASSEMBLY " 6 TYPE " " 7 ; CONFIGURATION: 8 z.sensor * 31 9 z.rcc • 43 10 z.gripper =112 11 TOOL TRANS(0, 0, z.sensor+z.rcc+z.gripper, 90, -90, 45) 12 mass =0.17 13 ds[l] = 8 14 ds[2] = 8 15 z.tool = 20 16 d[3] •• z.rcc+z.gripper+z.tool 17 ; MOVE parameters: 18 SET tool.pnt • top.pntl 19 safe.z = 300 20 speed.move * 100 21 ; APPROACH parameters: 22 CALL approach.par 23 shift.x = 25 24 delta.y = 0 25 delta.z = 0 26 ; GRASP parameters: 27 temp.force = 1 28 speed.grasp = 10 29 veight.z = 30 30 ; CLEAR parameters: 31 CALL clear.par 1 ; T0P.INI2 (June 5 - Kotzev) 2 ; 3 CALL pestop 4 ; CONFIGURATION: 5 z.tool • 0; rotation axis 6 TOOL TRANS(0, 0, z.sensor+z.rcc+z.gripper+z.tool, 90, -90 7 mass =0.5 8 ds[l] » 80 9 ds[2] = 20 10 d[3] • z.rcc+z.gripper+z.tool Appendix B. SUBROUTINES and SERVICE PROGRAMS: 11 ; MOVE parameters: 12 SET tool.pnt = top.pnt2 13 safe.z = 300 14 speed.move = 100 16 ; APPROACH parameters: 16 CALL approach.par 17 weight. ex = 0 18 open.grip = 0 19 shift.z = 0 20 shift.over • 0 21 position.appro = 0 22 appro.max[3] >= 0.2 ; no contact during approach 23 ; SEARCH parameters: 24 CALL search.par 25 rotate = 1 26 rot[4] =2.5; multiply 10 times 27 pc[l] - 0.5 28 pc[2] • 0.5 29 pc[3] - 0.5 30 delsearch.z = 10 31 gain.in[3] =0.3 32 gain.out[3] =0.1 33 delx - 1 34 dely = 1 35 ; COMPLY parameters: 36 CALL comply.par 37 lower.pnt • 25 38 speed.comply = 4 39 comax[3] = -1.5 40 comin[3] = -1.4 41 comin[5] = -250 42 comaz[5] = -200 43 gain[4] » 0 44 gain[6] = 0 45 ; CLEAR parameters: 46 CALL clear.par 47 clear.grip = 1 48 clear.y • 15 B .21 program WEIGHT: 1 ; WEIGHT (June 16 - Kotzev) 2 ; 3 PCEND 4 sigmal • 0 Appendix B. SUBROUTINES and SERVICE PROGRAMS: 173 5 s a m p l e s «= 25 6 FOR i » 1 TO B a m p l e s 7 [ i ] = f .m[3] 9 sigmal • sigmal+force[i] 10 END 11 s i g a v e r a g e «= s i g m a l / s a m p l e s 12 sigdel = ABS (s igaverage*0.1) 13 sigma2 • 0 14 t e m p c o u n t = 0 15 FOR i • 1 TO samples 16 IF ABS(ABS(force [ i ])-ABS (s igaverage)) > B i g d e l THEN 17 sigma2 • sigma2+force[i] 18 t e m p c o u n t • t e m p c o u n t+1 19 END 20 END 21 IF t e m p c o u n t > 0 THEN 22 w e i g h t = sigma2 / tempcount 23 ELSE 24 w e i g h t = s i g a v e r a g e 25 END 26 w e i g h t = ABS (we igh t ) 27 RETURN 

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