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Using inverse kinematics to position articulated figures Kuder, Karen Cynthia 1995

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USING INVERSE KINEMATICS TO POSITION ARTICULATED FIGURES B y Karen Cynth ia Kuder M a t h . (Computer Science and Combinatorics & Optimization) University of Waterloo - 1990 A THESIS S U B M I T T E D IN 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 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 STUDIES D E P A R T M E N T O F C O M P U T E R S C I E N C E 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 BRITISH C O L U M B I A December 1995 © Karen Cynth ia Kuder, 1995 In presenting this thesis in partial fulfillment of the requirements for an advanced degree at the University of Br i t i sh Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his 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 of Computer Science The University of Br i t i sh Columbia 2366 M a i n M a l l Vancouver, Canada V 6 T 1Z4 Date: ^ Abstract Computer-assisted animation is an active research area in computer graphics. W i t h i n this field, many systems are being developed that allow tradit ional animators to utilize computers in the animation process. The ability to position articulated figures is of particular interest. A method called inverse kinematics allows the user to position a figure by specifying a desired goal location for a particular segment of the figure. A n algorithm is employed to compute the required changes to the joint angles of the figure in order to move the segment to the desired location. This thesis describes an experiment that was conducted to compare three different inverse kinematic methods: the Jacobian method, the C C D method and the 1 D O F method. Subjects used the methods to manipulate the pose of a given articulated figure in an attempt to match a specified goal pose. Results from the experiment indicate that overall, the 1 D O F method produced the best matches (in terms of speed and accuracy). However, no single method had superior performance for al l of the positioning tasks that were studied. Consequently, an animation system should offer the user the choice of at least two of the positioning methods. i i Table of Contents Abstract ii List of Tables v i List of Figures xi Acknowledgements xiii 1 Introduction 1 1.1 Character Animat ion 1 1.1.1 Terminology 2 1.1.2 Joints and Joint Limi ts 2 1.1.3 Keyframing 3 1.1.4 Specifying the Position of the Figure 4 1.2 Preview of the Thesis 6 2 Background material 7 2.1 Implemented Methods 8 2.1.1 Implementation Issues 10 2.2 Shape-Matching 12 3 Experiment Design 14 3.1 Design 14 3.1.1 Ordering of Methods 14 i i i 3.1.2 Ordering of Trials 15 3.1.3 Configurations Used in Trials 16 3.2 Subjects 20 3.3 Equipment 20 3.4 Procedure 21 3.4.1 Tutorial 22 3.4.2 Procedure for a Tr ia l 23 4 Data Collection and Analysis 25 4.1 Da ta Collection 25 4.2 Excluded Subjects 26 4.3 Init ial Analysis 27 4.4 Further Analysis 31 4.4.1 Summary of Statistically Significant Results 32 4.4.2 Da ta From A l l Trials 36 4.4.3 Da ta Split B y Group 37 4.4.4 Analysis by Category 39 4.4.5 Analysis by Number of Links 41 4.4.6 Analysis by Tr ia l 43 4.5 Analysis of Intermediate Data 45 4.5.1 Thresholded Group Da ta 47 4.5.2 Thresholded Da ta Split by Group 48 4.5.3 Thresholded Da ta Split by Category 49 4.5.4 Thresholded Data Split by Number of Links 53 4.5.5 Thresholded Data Split by Tr ia l 55 iv 5 Conclusions and Future Research 61 5.1 Conclusions 61 5.2 Future Research 62 Bibliography 65 A Subject Background Information 66 B Sample Forms 71 C Chain Configurations 78 D Tutorial Pages 97 E Experiment Data 108 v List of Tables 4.1 Init ial Error Metr ic Values 28 4.2 Results of A N O V A with A l l Da ta 36 4.3 Results of A N O V A Split by Group 37 4.4 Results A N O V A Split by Category 40 4.5 Results of A N O V A Split by Number of Links 42 4.6 Results of A N O V A Split by Tr ia l 44 4.7 Thresholded Positional Error Values 47 4.8 Results of A N O V A with Thresholded Da ta 47 4.9 Results of A N O V A Split by Group (Thresholded Data) 48 4.10 Results A N O V A Split by Category (Thresholded Data) 50 4.11 Results of A N O V A Split by Number of Links (Thresholded Data) . . . . 54 4.12 Results of A N O V A Split by Tr ia l (Thresholded Data) 56 C . l Sample Tr ia l #1 . 79 C.2 Sample Tr ia l #2 80 C.3 Sample Tr ia l #3 81 C.4 Experiment Tr ia l #1 82 C.5 Experiment Tr ia l #2 . 83 C.6 Experiment Tr ia l #3 84 C.7 Experiment Tr ia l #4 85 C.8 Experiment Tr ia l #5 86 C.9 Experiment Tr ia l #6 : 87 v i C I O Experiment Tr ia l #7 88 C . l l Experiment Tr ia l #8 89 C.12 Experiment Tr ia l #9 90 C.13 Experiment Tr ia l #10 91 C.14 Experiment Tr ia l #11 92 C.15 Experiment Tr ia l #12 93 C.16 Experiment Tr ia l #13 94 C.17 Experiment Tr ia l #14 95 C.18 Experiment Tr ia l #15 96 E . l Subject 1 1st method (Jacobian) 109 E.2 Subject 1 2nd method ( C C D ) 109 E.3 Subject 1 3rd method (1DOF) 110 E.4 Subject 2 1st method (Jacobian) 110 E.5 Subject 2 2nd method ( C C D ) I l l E.6 Subject 2 3rd method (1DOF) I l l E.7 Subject 3 1st method (Jacobian) 112 E.8 Subject 3 2nd method ( C C D ) 112 E.9 Subject 3 3rd method (1DOF) 113 E.10 Subject 4 1st method (Jacobian) 113 E . l l Subject 4 2nd method ( C C D ) 114 E.12 Subject 4 3rd method (1DOF) 114 E.13 Subject 5 1st method (Jacobian) 115 E.14 Subject 5 2nd method ( C C D ) 115 E.15 Subject 5 3rd method (1DOF) 116 E.16 Subject 6 1st method (Jacobian) 116 v i i E.17 Subject 6 2nd method ( C C D ) 117 E.18 Subject 6 3rd method (1DOF) . 117 E.19 Subject 7 1st method (Jacobian) 118 E.20 Subject 7 2nd method ( C C D ) 118 E.21 Subject 7 3rd method (1DOF) 119 E.22 Subject 8 1st method (Jacobian) 119 E.23 Subject 8 2nd method ( C C D ) 120 E.24 Subject 8 3rd method (1DOF) 120 E.25 Subject 9 1st method (Jacobian) 121 E.26 Subject 9 2nd method ( C C D ) 121 E.27 Subject 9 3rd method (1DOF) 122 E.28 Subject 10 1st method ( C C D ) 122 E.29 Subject 10 2nd method (1DOF) 123 E.30 Subject 10 3rd method (Jacobian) 123 E.31 Subject 11 1st method ( C C D ) 124 E.32 Subject 11 2nd method (1DOF) 124 E.33 Subject 11 3rd method (Jacobian) 125 E.34 Subject 12 1st method . (CCD) 125 E.35 Subject 12 2nd method (1DOF) 126 E.36 Subject 12 3rd method (Jacobian) 126 E.37 Subject 13 1st method ( C C D ) . . . . ' 127 E.38 Subject 13 2nd method (1DOF) 127 E.39 Subject 13 3rd method (Jacobian) 128 E.40 Subject 14 1st method ( C C D ) 128 E.41 Subject 14 2nd method (1DOF) 129 E.42 Subject 14 3rd method (Jacobian) 129 v i i i E.43 Subject 15 1st method ( C C D ) 130 E.44 Subject 15 2nd method (1DOF) 130 E.45 Subject 15 3rd method (Jacobian) 131 E.46 Subject 16 1st method ( C C D ) 131 E.47 Subject 16 2nd method (1DOF) 132 E.48 Subject 16 3rd method (Jacobian) 132 E.49 Subject 17 1st method ( C C D ) 133 E.50 Subject 17 2nd method (1DOF) 133 E.51 Subject 17 3rd method (Jacobian) 134 E.52 Subject 18 1st method ( C C D ) 134 E.53 Subject 18 2nd method (1DOF) 135 E.54 Subject 18 3rd method (Jacobian) 135 E.55 Subject 19 1st method (1DOF) 136 E.56 Subject 19 2nd method (Jacobian) 136 E.57 Subject 19 3rd method ( C C D ) 137 E.58 Subject 20 1st method (1DOF) 137 E.59 Subject 20 2nd method (Jacobian) 138 E.60 Subject 20 3rd method ( C C D ) 138 E.61 Subject 21 1st method (1DOF) 139 E.62 Subject 21 2nd method (Jacobian) 139 E.63 Subject 21 3rd method ( C C D ) 140 E.64 Subject 22 1st method (1DOF) 140 E.65 Subject 22 2nd method (Jacobian) 141 E.66 Subject 22 3rd method ( C C D ) 141 E.67 Subject 23 1st method (1DOF) 142 E.68 Subject 23 2nd method (Jacobian) 142 ix E.69 Subject 23 3rd method ( C C D ) 143 E.70 Subject 24 1st method (1DOF) 143 E.71 Subject 24 2nd method (Jacobian) . . 144 E.72 Subject 24 3rd method ( C C D ) 144 E.73 Subject 25 1st method (1DOF) 145 E.74 Subject 25 2nd method (Jacobian) 145 E.75 Subject 25 3rd method ( C C D ) 146 E.76 Subject 26 1st method (1DOF) 146 E.77 Subject 26 2nd method (Jacobian) 147 E.78 Subject 26 3rd method ( C C D ) 147 E.79 Subject '27 1st method (1DOF) 148 E.80 Subject 27 2nd method (Jacobian) 148 E.81 Subject 27 3rd method ( C C D ) 149 x List of Figures 1.1 A Typica l Chain 2 1.2 Mul t ip le Inverse Kinematic Solutions 5 3.1 Example of a Smoothly Curved Object 17 3.2 Example of a Zig-zag 17 3.3 Example of a Branching Structure 18 3.4 Example of a Torso wi th an Attached Pair of Legs 18 C . l Sample Tr ia l #1 79 C.2 Sample Tr ia l #2 80 C.3 Sample Tr ia l #3 81 C.4 Experiment Tr ia l #1 82 C.5 Experiment Tr ia l #2 83 C.6 Experiment Tr ia l #3 84 C.7 Experiment Tr ia l #4 ; 85 C.8 Experiment Tr ia l #5 86 C.9 Experiment Tr ia l #6 87 C I O Experiment Tr ia l #7 88 C . l l Experiment Tr ia l #8 89 C . l 2 Experiment Tr ia l #9 . ' 90 C.13 Experiment Tr ia l #10 91 C.14 Experiment Tr ia l #11 92 C.15 Experiment Tr ia l #12 93 x i C.16 Experiment Tr ia l #13 94 C.17 Experiment Tr ia l #14 95 C.18 Experiment Tr ia l #15 96 x i i Acknowledgement This research was done under the supervision of Dr . David Forsey. Credit for the in i t ia l idea for this project must be given to him. The second reader for this thesis was Dr . David Lowe. The student reader for this thesis was James Bori tz . Michael McAl l i s t e r provided proofreading services. Many suggestions from each reader helped to greatly improve the quality of the final document. I would like to thank Chris Welman for his helpful assistance when I was first starting to investigate inverse kinematics. Helpful comments on the design of the experiment were provided by Dr . Kel logg Booth , Malco lm Greig of U C S and Dr . Peter Graf from the Psychology Department. Comments on the tutorial instructions were provided by Dr . Booth, Nancy Day and various members of the public who used the system during an open house held at U B C . I am indebted to many members of the Department of Computer Science technical staff here at U B C for their assistance during my tenure as a graduate student. These include Car l in Chao, Peter Phi l l ips , George Phi l l ips , Michael Sanderson, Dave Brent, and Br ian Edmonds. Ian Cavers provided very helpful assistance with E T g X during the preparation of this document. In addition to people already mentioned, I would like to acknowledge the following: A n d y Mar t in , Brendan Mumey, Robin Reed, Robyn Edelson, Stephan Mueller, Dave Finkelstein, and Jennifer Shore. I would like to thank al l of the people who participated as subjects. Final ly, I would like to thank my husband Scott. This thesis would never have been completed without his support and encouragement. This document was improved as a result of his proofreading and assistance wi th WF${. x i i i Chapter 1 Introduction Computer systems are increasingly being used to generate animations. Some systems are designed for people who are familiar with traditional animation techniques. In gen-eral, these animation systems attempt to assist an animator in the task of producing an animation. The systems try to facilitate the animation process while allowing the animator to apply skills from traditional animation. This thesis explores the portion of a computer-assisted animation system that allows an animator to produce animations of characters. 1.1 Character Animat ion Many animations involve characters such as humans and animals. To produce satisfactory animated sequences, animators must be able to finely position and move al l parts of the character. In most computer systems, characters are modelled as articulated (jointed) figures. Many of the current computer animation systems use a skeletal approximation of a jointed figure for positioning and motion purposes and assume that overlying muscle and tissue can be added to the figure once the skeletal positioning has been determined. The skeletal approximation is normally modelled as a rooted tree wi th nodes repre-senting pieces of the skeleton and arcs representing joints between the skeletal pieces. A limb, such as an arm or leg, is generally described as a chain of links. Figure 1.1 is an example of a typical chain. 1 Chapter 1. Introduction 2 Figure 1.1: A typical chain with the ith link labelled h and the angle of rotation of the ith joint labelled 8i. The link IQ is at the proximal end of the chain and the link ln is at the distal end of the chain. The set of links U-i, h, ..., ln-i, In is an example of a distal subchain. The filled circle on link l0 represents the inherent root of the chain and the open circle on link /„ represents the location of the end-effector if the entire chain is to be manipulated. 1.1.1 Terminology The fixed end of a chain, where the l imb attaches to the torso, is referred to as the proximal end. The free end that can be moved around in space is referred to as the distal end. A distal subchain is a subset of a larger chain sharing the same distal end. The end-effector is the distal l ink in the chain. The free space refers to the region in space that the end-effector can occupy. For a chain consisting of only 1 link, the free space is the circle in 2D (or sphere in 3D) centered at the proximal end of the link wi th a radius equal to the length of the link. 1.1.2 Joints and Joint Limits The joints involved in articulated figures are generally classified as revolute, having one degree of freedom, or prismatic, having three degrees of freedom (such as a ball-and-socket joint). Joints wi th more than one degree of freedom are often modelled as several one degree of freedom revolute joints. For most articulated figures, joint l imits must be taken into account as these restrict the possible ranges of motion. Chapter 1. Introduction 3 The interaction between joints when manipulating an articulated figure requires an-other assumption to be made. It is assumed that the allowable angle of rotation of a given joint is independent of the other joints. This is an unrealistic assumption when modelling a human figure because the position of one joint can constrain the free space available to the end-effector. For instance, for some orientations of the upper arm given by the rotation of the shoulder joint, normally valid rotations of the elbow wi l l result in the hand being embedded in the torso. Al though the assumption of independent joints is not entirely realistic, a fairly accurate approximation of motion can be obtained wi th the assistance of joint l imits. In a reasonable animation system, the animator can either compensate for these types of situations or ignore them. In general, it is necessary to allow the animator to override controls that prevent unrealistic situations from occurring so that s/he is not prevented from achieving a desired unrealistic configuration as might be required for a cartoon character. 1.1.3 Keyframing Tradit ional animators often use a process called keyframing, in which various key poses of the figure are drawn (the keyframes), and then the remaining inbetween frames containing the interpolated motion are filled in by assistant animators known as inbetweeners. One required component of a computer graphics animation system that uses keyframing is the abili ty to place the parts of a figure at various positions in space. The motion between keyframes is generated later. One method of producing the inbetween frames involves the automatic generation of the motion path from the interpolation of the joint angles between keyframes using splines. This approach can generate very good smooth motion between keyframes, but the animator often has to make many adjustments to the ini t ia l ly generated motion in order to produce the desired motion. B y changing the interpolated motion, the animator may inadvertently change the position of the figure in the keyframe. Chapter 1. Introduction 4 This can cause undesired side effects, such as the foot of a character penetrating the floor. Animators desire better methods for controlling the generated motion and researchers continue to develop these methods. The interpolation process uses forward kinematics to determine the positions of the parts of the figure. Forward kinematics refers to the calculation of the locations of the links in a chain from the position of the root of the chain, the joint angles of al l of the links and the lengths of the links. These positions, which can be calculated using simple trigonometry, are unique. The positioning problem involves solving the inverse kinematics of the figure. The solution determines the angles of revolution of the joints that position the end-effector of the figure in the desired location in space, given the position of the root and the lengths of the links. The inverse kinematic solution is not, in general, unique. For example, in two dimensions, a chain consisting of two links of the same length wi l l have two mirror image solutions for al l attainable end-effector positions except for the case when the chain is stretched out straight. In three dimensions this same chain would have an infinite number of solutions for these cases, wi th the joint between the two links lying anywhere on a circle. Figure 1.2 illustrates an instance of the given example. Art iculated figures used by animators typically consist of chains having many links and many degrees of freedom; for example, a simplified human figure wi l l have least 20 degrees of freedom. For most given positions of the end-effector, there wi l l be multiple possible configurations of the chain. 1.1.4 Specifying the Position of the Figure Some animation systems require the animator to describe the position of the figure by typing in the various joint angles. This can be a tedious process as animators do not generally think in terms of the values of joint angles. Rather, they draw something at Chapter 1. Introduction 5 Figure 1.2: Multiple inverse kinematic solutions for a chain composed of two links. The black circle at the top indicates the root and the outlined circle at the bottom indicates the desired location for the end-effector. The two valid solutions in two dimensions are both shown. In three dimensions the valid solutions are represented by the dashed circle which indicates the position of the joint between the two links. whatever angle looks right. Therefore, describing positions by specifying joint angles tends to be an iterative process where an animator uses t r ia l and error to adjust the joint angles unti l the figure appears as desired. Direct manipulation, where the animator selects a part of the figure and indicates desired location for the end-effector using an input device such as a mouse, provides a highly interactive user interface. The correspondence between the motion of the mouse and the motion of the figure on the screen gives the animator the impression of manipulat-ing the figure itself. According to Shneiderman's taxonomy of interaction styles [Shn91], direct manipulation is preferred over all other interaction styles in situations where there is a "natural visual representation." User interfaces that employ direct manipulation are easy to learn and have high subjective satisfaction. Direct manipulation interfaces also encourage exploration because the results are shown immediately and actions are reversible. In order to facilitate the direct manipulation of multiple links at a time, the system Chapter 1. Introduction 6 must determine the inverse kinematics of the figure. Real-time or near real-time solutions to this positioning problem are desired so that animators can interactively use the system to keyframe animated sequences of articulated figures. 1.2 Preview of the Thesis This thesis describes an experiment that was designed and conducted to compare three methods for positioning articulated figures. Chapter 2 describes background work in the area of inverse kinematics. Chapter 3 presents the design of the experiment used to compare the three different positioning methods. Chapter 4 presents and discusses the results of the experiment. Chapter 5 contains the conclusions of the research and provides suggestions for future related research. Chapter 2 Background material The forward kinematic problem can be expressed as the calculation of the position vector X, given and a vector of joint angles q X = f(q) where the function / is nonlinear, continuous, differentiable and depends upon the lengths of the links. This function has a unique solution. The inverse kinematic problem, that of solving for the joint angles given the positions of the root and end-effector and the lengths of the links does not in general have a unique solution. The inverse kinematic equations can be solved using either direct or iterative tech-niques. Iterative techniques generally involve the computation of several steps before converging to a solution. A s a result, direct solutions are usually faster to compute than iterative ones. Some direct techniques calculate al l of the possible solution configurations whereas iterative numerical methods converge to only one solution at a time. If the solution found by an iterative method has to be discarded (for example, i f a joint l imi t is violated), the method generally needs to be start from the beginning again in order to calculate another solution. A n iterative method also requires an in i t ia l estimate of the solution in order to 7 Chapter 2. Background material 8 start the first iteration. The current position of the figure is generally used as the in i t ia l estimate of the solution, but i f the two configurations are far apart, the algorithm may not converge. In this case, a user must specify intermediate goals. Direct solutions are known for many six or fewer degree of freedom industrial robots. However, for most articulated figures used in animation, such as human figures and an-imals, there are more degrees of freedom to be calculated than there are constraining equations. Direct solutions do not exist for these underconstrained systems and thus numerical methods must be used instead. Generally, the calculation involving a numer-ical solution involves a user-defined degree of tolerance and the solution obtained is an approximation of the actual solution, wi thin the specified degree of tolerance. Solving the inverse kinematics of a figure gives positional information but it does not actually specify a motion path for moving the figure from one position to another. The intermediate solutions from the steps of the iteration process could be used to generate motion, but the resulting motion would most likely not be realistic or desired. If al l of the iterations were used for motion generation, jerky motion could result as various steps in the iterative process may actually be converging on different solutions. Even if the iterations were filtered and only those that led to the particular solution were used, unrealistic motion might s t i l l result as the iteration process does not necessarily converge smoothly on the final solution. To avoid these problems and produce smooth motion, splines are typically used to define a motion path that interpolates between the starting and ending joint angles. 2.1 Implemented Methods A system for exploring various positioning algorithms was created. Three different posi-tioning algorithms were implemented in the system. The method that wi l l be referred to Chapter 2. Background material 9 as the cyclic coordinate descent or C C D method [WC91] is an inverse kinematic algorithm from the field of robotics that is based on combined optimization techniques. It is an iterative technique that is a combination of two gradient based non-linear programming techniques and forward recursion formulae. This method first uses the cyclic coordinate descent ( C C D ) method to quickly find a feasible point that is close to the actual solu-tion and then uses the Broyden-Fletcher-Shanno (BFS) variable metric method to find the actual solution to the specified degree of precision. Wang and Chen [WC91] claim that this method is numerically stable and is not sensitive to singular configurations. They also state that the method is computationally efficient and can be applied to serial manipulators (simple chains) having any number of degrees of freedom. The method that wi l l be referred to as the Jacobian method [SS88, GW91] is also an inverse kinematic algorithm from the field of robotics. This iterative technique involves the linearization of a non-linear problem. This method looks at the problem in terms of the relationship between joint velocities q and position velocities X k = J{q)'q where J(q) is the Jacobian matrix df/dq. This relationship can be inverted to obtain 'q = J\q)k where is the Moore-Penrose pseudoinverse defined by J* = JT(JJT)~l. This relation-ship can be further modified to obtain solutions in cases where there are more degrees of freedom than coordinates in the position vector. The method referred to as the 1 D O F method is a degenerate version of the other two methods. In the 1 D O F method, the only joint angle that can change is the one at the currently defined root, independent of the proximity of the root and end-effector. A l l of the links that are between the root and the end-effector are treated as a single solid Chapter 2. Background material 10 object. In the case that the root and the end-effector are chosen to be adjacent links, al l three methods wi l l produce the same results. The term true inverse kinematic methods w i l l be used to refer to the C C D and Ja-cobian methods because they may change the joint angles at any of the joints between the root and the end-effector. This term does not apply to the 1 D O F method because it only adjusts the joint at the root, independent of the placement of the end-effector. 2.1.1 Implementation Issues The same user interface was used for al l three methods so that the user interface would not bias the experiment. To indicate the desired location of the end-effector, the user first presses the left mouse button to select the end-effector and then holds the button down while moving the mouse. The system tracks the mouse cursor. It performs each iteration of the inverse kinematic algorithm using the current mouse position at that time as the desired end-effector location. Because users do not move the mouse very quickly in relation to the speed of calculation of an iteration, there is a relatively small difference in the mouse positions used in consecutive iterations. A s a consequence, the C C D method and the Jacobian method calculate similar configurations and appear almost identical to the user unless the mouse is moved very rapidly. A translation feature, that allowed the user to translate the entire chain in space, was built into the system. This feature was disabled for the experiment as it was decided to only use configurations where translations were not necessary. This decision simplified the subjects' task and also allowed the user interface to be simplified. The C C D method [WC91] and the Jacobian method [SS88] are described in the con-text of robotics. A s a result, these methods assume that the chains being manipulated are simple chains and that these chains are rooted at a fixed end. When implemented, these methods were modified to deal with complex chains that had a branching point. Chapter 2. Background material 11 They were also modified to allow for the placement of the root anywhere on the chain, in-cluding situations where the orientation of the chain was reversed (with the root "below" the end-effector). Bo th the C C D method and the Jacobian method have the abili ty to handle joint l imits. The Jacobian method can also find solutions that avoid obstacles. These aspects of these two methods were not implemented as it was known at the time of implementation that they were not going to be necessary in the experiment. The 1 D O F method was implemented as a version of the Jacobian method rather than as a version of the C C D method. This choice was made because the Jacobian method was easier to implement than the C C D method. This was partly because an iteration step is a one-part process in the Jacobian method and a two-part process in the C C D method. A l l three of these methods include a weighting factor for each joint that controls the resistance to change in position of that joint. This weighting factor is used to modify the step size taken at each iteration. In the paper by Sciavicco and Siciliano [SS88], the term gain is used in place of the term weighting factor. The C C D method [WC91] gives an equation for calculating the weighting factor but this equation includes a sizing factor that is dependent upon the length of the link. No information quantifying this dependency is provided in the paper. Similarly, Sciavicco and Siciliano [SS88] state that an adequate choice for the gain in the C C D method is related to the inverse of the sampling period but no quantification of this relation is given. For the experiment, a weighting factor of 10.0 was used for al l of the joints in al l of the chains for al l of the methods. The value of 10.0 was chosen after experimentation by an experienced user of the system as it provided a balance between controllability and sensitivity. The same weighting factor was chosen in order make al l chains react the Chapter 2. Background material 12 same and to avoid introducing a possible bias into the experiment. 2.2 Shape-Matching The goal of this thesis is to compare the capabilities of the three positioning methods. One approach would involve asking animators to position a figure based on a verbal or written description of the desired final configuration. This approach mimics the normal creative process in which the animator has an in i t ia l mental image of the desired configuration. Animators could be asked to rank the different positioning methods after using each of them to perform a variety of positioning tasks. A weakness of this approach relates to the specification of the final configuration. A verbal or written description can be interpreted differently by different people. If the subjects are not actually t rying to attain the same final configurations, their experiences with the different positioning methods may not be comparable and thus their rankings may not be comparable. In addition, an individual subject may change his/her inter-pretation of the desired final configuration. The interpretation may be biased by the positioning method itself. In this case, it would be difficult for a subject to objectively rank the positioning methods. In addition, this approach relies on the subjective data of rankings by the subjects in order to compare the positioning methods. It is preferable to have a design that allows for the collection of objective data and for the comparison of results for the same task performed using the different positioning methods and by different subjects. In such an experiment, subjects can be asked to manipulate a chain from an in i t ia l given configuration to a specified final configuration. The time taken by the subject to perform the manipulation and the accuracy of the final configuration attained can be measured and analysed. Chapter 2. Background material 13 To allow comparisons of user performance, al l subjects must have the same goal for a particular t r ia l . One way of ensuring this is to change the task from one of creating a configuration from a written or verbal description to one of matching a displayed configuration. The subject has to manipulate the chain from a given ini t ia l configuration to match the given goal configuration as accurately as possible in as lit t le time as possible. This chain-matching approach was used in the experiment. Results from this experiment should carry over to an animator's task of designing and creating a final configuration. A similar application of the shape-matching paradigm has been used to compare formulations for manipulating splines in both 2-dimensions [Rue89] and 3-dimensions [Jan92]. Chapter 3 Experiment Design A n experiment was conducted to compare the performance of subjects on a series of chain matching tasks using the three positioning methods described in Section 2.1. The hypothesis for the experiment was Inverse kinematics provides a faster and more accurate way of positioning articulated figures with many degrees of freedom than manipulating these figures one degree of freedom at a time. The null hypothesis for the experiment was There is no advantage to using inverse kinematics for positioning articulated figures wi th many degrees of freedom. 3.1 Design The experiment consisted of a series of 15 trials that were repeated by each subject for each of the three positioning methods. A La t in square design was used to determine the order in which the 30 subjects encountered the three different methods. This design ensures that al l methods wi l l be evenly affected by learning effects. 3.1.1 Ordering of Methods The subjects were split into three groups. A l l of the subjects wi th in each group started with the same method first. Subjects wi thin the same group had a common second 14 Chapter 3. Experiment Design 15 and third method as well. Details regarding the placement of individual subjects into a particular group are in Section 3.2. The subjects were numbered by group after the experiment was completed. The numbering of the subjects was not related to the order in which they did the experiment. The first group, consisting of subjects 1 through 9, used the Jacobian method as their first method, the C C D method as their second method and the 1 D O F method as their third method. The second group of subjects, consisting of subjects 10 through 18, used the C C D method as their first method, the 1 D O F method as their second method and the Jacobian method as their third method. Final ly, subjects 19 through 27 made up the third group. They used the 1 D O F method as their first method, the Jacobian method as their second method and the C C D method as their third method. Subjects 28, 29 and 30 were grouped separately due to problems wi th their sessions. These problems are described in Section 4.2. 3.1.2 Ordering of Trials The order of the 15 trials was the same for al l of the subjects and it was the same for al l of the methods. The same trials were presented for each of the methods in order to allow comparison of a subject's results between methods. The order of the trials was kept constant in an attempt to minimize learning effects. The same trials were presented to al l of the subjects to enable the comparison of results from various subjects. In each t r ia l the subject was presented wi th a chain in a given ini t ia l configuration (with the links drawn in alternating light and dark blue and the joints drawn in white) and a given given goal configuration (drawn in yellow). The subject's task was to manipulate the chain representing the ini t ia l configuration to match the goal configuration as closely as possible in as lit t le time as possible. Chapter 3. Experiment Design 16 3.1.3 Configurations Used in Trials W i t h the assistance of our on-staff animator, several classes of positioning configurations were identified. Four of the classes were: smoothly curved objects, zig-zags, branching structures and a torso with an attached pair of legs. Example chains belonging to these four classes were constructed. These chains had between 5 and 10 links. Configurations to be used in the experiment were chosen from the example chains. Figures 3.1 through 3.4 show examples of each of the four classes. In these figures, the goal configuration is displayed in medium gray. The links of the in i t ia l configuration are drawn in alternating light and dark gray and the joints are represented by white circles that are outlined in black. Appendix C contains the specifications of al l of the chains used in the experiment. It includes diagrams showing the in i t ia l and goal configurations for each tr ia l . A n attempt was made to choose a set of in i t ia l /goal pairs where various manipulat ion techniques would be required. For some of the in i t ia l /goal pairs, it was anticipated that single degree of freedom manipulation would be required (i.e. where the capability of an inverse kinematic algorithm to adjust more than one degree of freedom at a time would be of lit t le or no use). It was expected that adjusting many links at a time wi th an inverse kinematic algorithm would allow a subject to perform a more efficient manipulation for other selected in i t ia l /goal pairs. Yet other in i t ia l /goal pairs were chosen where t. here was no advance expectation of the optimal movement technique. To simplify the matching tasks, al l of the in i t ia l /goal pairs of chain configurations were created wi th one coincident joint. In al l of the trials, this is the joint closest to the top of the screen, which is the inherent root of the chain. The experiment system allows subjects to select other joints as the root for purposes of moving the chain and in effect even allows subjects to reverse the orientation of the chain by having the end-effector Chapter 3. Experiment Design 17 Figure 3.2: Example of a Zig-zag Chapter 3. Experiment Design 18 Q Figure 3.3: Example of a Branching Structure Figure 3.4: Example of a Torso with an Attached Pair of Legs Chapter 3. Experiment Design 19 "above" the root. This reversal is not actually necessary to complete any of the trials but the functionality was left in the system to allow for greater flexibility. The trials were ordered in terms of increasing difficulty. The ordering was done subjectively by an experienced user of the system after she used each of the methods to complete each of the trials several times. There are three trials involving a torso and a pair of legs that form a walking sequence. These three trials were treated as one t r ia l for the purposes of ordering the trials and were presented in the experiment in the walking sequence order. The first twelve trials except for t r ia l 10 use simple chains (with no branching points). Tr ia l 10 and the last three trials use complex chains (with a branching point). Some configurations are used in more than one tr ial . Trials 1 through 5, 8 and 11 al l include chains that belong to the class of smoothly shaped objects. The same ini t ia l configuration is used for trials 1, 5 and 8. This con-figuration is identical to the goal configuration for t r ia l 4. The configurations used in trials 4 and 8 are reversals of each other. The in i t ia l configuration of t r ia l 4 is the goal configuration of t r ia l 8 and vice versa. Trials 2 and 11 also use configurations that are reversals of each other. Trials 6, 7, 9 and 12 utilize chains that belong to the zig-zag class. Trials 6 and 7 use chains wi th the same ini t ia l configuration. The chains in trials 9 and 12 have the same goal configuration. Trials 7 and 9 are reversals of each other as are trials 6 and 12. The chain used in trials 13, 14 and 15 represents a pair of legs. The configurations in these three trials form a series that can be used to keyframe a walk cycle. The goal configuration for t r ia l 13 is the in i t ia l configuration for t r ia l 14 and the goal configuration for t r ia l 14 is the in i t ia l configuration for t r ia l 15. Chapter 3. Experiment Design 20 3.2 Subjects Subjects were solicited from three groups: i) students taking a first year undergradu-ate computer science course, ii) senior undergraduate students working in the computer science department and iii) graduate students/post doctoral students either in the com-puter science department or with ties to the computer science department. A l l subjects volunteered to participate and were not compensated for their participation. A total of 30 subjects participated in the experiment. O f these, 19 were male and 11 were female. A l l of the subjects had prior experience using a mouse. Background information was collected from these subjects and is summarized in Appendix A . The subjects were assigned to one of three groups. Each subject's gender and back-ground (first year undergraduate, senior undergraduate or graduate/post doctoral stu-dent) were known before the subjects came for their first experiment session. The subjects were placed into the three groups so that they were evenly divided across the groups along gender lines and along background lines. 3.3 Equipment The experiment was run on an IRIS 4D/240 V G X computer. The subject was the sole user of the computer and all processing took place locally in order to avoid the impact of any network delays. The experiment was conducted in an isolated office. The C P U of the computer was located in another room. The 19" computer monitor was centered on a computer table. A height-adjustable chair on casters was located i n front of the table directly in front of the monitor. Subjects were allowed to adjust the height of the chair and position it as they desired. Typica l viewing distances for subjects while doing the experiment was between 18 and 24 inches. The keyboard was moved off to the left side of the monitor as Chapter 3. Experiment Design 21 it was not used during the experiment. A mechanical mouse and foam mouse pad were on the table in front of the monitor. The overhead lights were off. A desk lamp was located on the back right-hand corner of the computer table and it was ini t ia l ly switched on. 3.4 Procedure The remainder of this chapter details the procedure that each subject followed when performing the experiment. In an attempt to minimize fatigue, the experiment was split into two sessions. Dur ing the first session the subject was asked to fill out a consent form and a subject information form that collected the background information referred to previously (sample forms are in Appendix B ) . After filling out the two forms, the subject was escorted into the experiment room and was told to adjust the chair and the location of the mouse and mouse pad as desired. Subjects were advised that they could leave the desk lamp on or turn it off. Subjects were also told that they could come out of the room to ask questions. When the subject was comfortable, a black curtain was drawn around the subject and computer and the subject was left alone in the room. The curtain isolated the subject from distractions from other objects in the room and also blocked out daylight. The session started with the subject going through an IRIS Showcase ( T M ) slide show that served as a tutorial. More details about the tutorial are in Section 3.4.1. After completing the tutorial, the subject performed the series of 15 trials using one of the three positioning methods. A t the end of each tr ial , the subject rated the match attained. More details about the procedure followed to complete a t r ia l are in Section 3.4.2. After completing the set of trials using a particular positioning method, Chapter 3. Experiment Design 22 the display showed a message that instructed the subject to advise the person supervising the experiment that s/he was finished. The subject then filled out a questionnaire about the particular method just used (copies of the questionnaires are in Appendix B ) . This completed the first session. The date and time of the subject's second session was verified before the subject left. In the second session the subject was immediately escorted into the experiment room. The subject used the tutorial to become familiar with the second positioning method and then completed the series of 15 trials using the second method. The subject then completed a questionnaire. This questionnaire included questions that asked the subject to compare this positioning method to the positioning method used in the first session. The subject then returned to the experiment room, used the tutorial to become familiar wi th the third method and performed the series of 15 trials for the last time. The final questionnaire that the subject filled out asked the subject to compare al l three positioning methods. 3.4.1 Tutorial The tutorial was an introduction to the study and the system used in the experiment. Screen dumps of the tutorial pages are in Appendix D . The tutorial defined and illustrated the concepts of links, joints, pivot points and manipulation points. The terms pivot point and manipulation point were used in the tutorial and questionnaires in place of the terms root and end-effector respectively since the former would be more familiar to people who did not have prior knowledge of inverse kinematics. The tutorial explained how to choose the pivot point and manipulation point and how to move the chain around. The subject was given the opportunity to practice each step as it was presented. Three complete sample trials were presented at the end of the tutorial . Chapter 3. Experiment Design 23 The sample trials were labelled 1, 2 and 3 and increased in difficulty. The sample trials included rating the match. Subjects were asked to do each of the three sample trials at least once but they were told that they could do each sample t r ia l as many times as they desired. Subjects were asked to experiment wi th the sample trials and were advised to not worry about the amount of time being taken to do the sample trials. The tutorial asked the subject to pick different combinations of pivot and manipulation points to see how the particular method reacted under various circumstances. A t the end of the tutorial, subjects were prompted to click on a button when they were ready to start the experiment. A slightly different version of the tutorial was used for the subject's second and third positioning methods. This version told the subject that pivot points and manipulat ion points were selected as before and that the mouse was used to move the chain as before, but that the computer would move the chain differently in response to movements of the mouse. The subject was then given the option of reviewing the instructions or going directly to the sample trials. In either case, the screen with the three sample trials was eventually displayed and the subject was asked to complete each of the three sample trials at least once. The three sample trials that were presented were the same for each of the three methods. The same sample trials were presented each time so that the subjects could explore the differences between the three methods. 3.4.2 Procedure for a Tria l During each tr ial the subject first used the middle mouse button to choose a root. Then the subject used the left mouse button to choose an end-effector. The subject kept the left mouse button down while moving the mouse to indicate the desired location for the end-effector. The subject continued adjusting the chain, picking a different root and/or end-effector as desired unti l s/he wished to terminate the matching process (either the Chapter 3. Experiment Design 24 match was completed to the subject's satisfaction or the subject was unable to improve upon the match). The subject indicated that the match was completed by clicking on a button labelled " D O N E " at the bottom of the screen. After a match was completed, the chains were removed from the screen and the subject was asked to rate the match just completed. The subject was presented with a screen with five large yellow buttons. The row of buttons was displayed in the middle of the screen. . The buttons were labelled "Perfect Match" , "Almost Perfect", "Pretty G o o d " , "Satisfactory" and "Unsatisfactory" from left to right. Rat ing categories wi th a bias towards a good match were used as it was assumed that most subjects would continue manipulating the figure unti l a good match was attained. The "Unsatisfactory" rating category was allowed a subject to indicate that s/he was not happy wi th a match but could not improve upon it. Once a rating button was selected, the buttons were removed from the screen and the experiment paused unti l the subject indicated that s/he was ready to continue by clicking on a green button labelled " N E X T T R I A L " . Chapter 4 Data Collection and Analysis 4.1 Data Collection A t the start of each tr ial , the subject's name, the positioning method being used, the t r ia l number, the goal configuration and the ini t ia l configuration of the chain used during the t r ia l were written to a file. The sequence of joint angles of the chain was used to record each configuration. The data file was written onto the local disk of the computer being used to run the experiment to ensure that the wri t ing of the data and the t iming of the trials would not be affected by network delays. Each joint in the chain was assigned an identification number when the chain was ini t ial ly constructed. During the t r ia l , the joint's identification number was recorded in the data file each time the subject chose it as a root or an end-effector. Each time the subject released the left mouse button and thereby released the end-effector, the current configuration of the chain was also written to the data file. The final configuration of the chain attained by the subject was recorded when the " D O N E " button was pressed. T i m i n g information, in tens of milliseconds, was recorded along wi th each of the events mentioned. The t iming of a t r ia l started when the goal and ini t ia l configurations of the chain were displayed on the screen and ended when the subject pressed the " D O N E " button. As a result, the time taken for a t r ia l included any time that the subject spent looking at the match considering what to do next (including time at the beginning of the tr ial , at the end before hi t t ing the " D O N E " button and during the t r ia l when choosing a 25 Chapter 4. Data Collection and Analysis 26 root, end-effector or moving the chain around). The time involved in moving the mouse cursor from its in i t ia l position centred in the window to the desired spot on the chain and from the final position on the chain to the " D O N E " button centred at the bottom of the screen was also included. 4.2 Excluded Subjects Results from three of the 30 ini t ia l subjects were not used in the analysis. The data analysis was done wi th subjects 1 through 27. Data from these subjects appears in Appendix E . Subject 28 was unable to get the sample trials to appear on the screen. Rather than seeking help wi th this problem, she continued on to the experiment trials. The tutorial did not force subjects to complete al l three sample trials before starting the experiment trials, but the instructions did ask subjects to try each one at least once before continuing. Since subject 28 did not have any practice before starting the experiment trials using her first method, her results from the first session included learning effects that were not present in her second session or in the first sessions of the other subjects. As a consequence, subject 28's data was unsuitable for inclusion in the data analysis. Dur ing subject 29's first session, the computer crashed in the middle of the sixth experiment t r ia l . After a delay of several minutes while the machine rebooted, the subject resumed the session starting at the beginning of the sixth t r ia l . Since al l of the other subjects completed all 15 trials using a particular method without such a delay, this disruption was considered significant enough exclude subject 29's data. Subject 30 started her second session but was unable to stay to complete the entire second session. She completed the first part of the second session and filled out the cor-responding questionnaire but then, due to time constraints, could not stay to participate Chapter 4. Data Collection and Analysis 27 in the second part of the second session. She completed the portion of the experiment involving her third method in a thi rd session which was held four days later. Since al l of the other subjects completed the entire experiment in only two sessions, which were at most three days apart, this subject's participation was considered unusual enough to exclude her data. The problems wi th these three subjects arose early enough in the experiment cycle that it was possible to maintain the balance of the three groups according to gender and background category. For each of these three subjects, another subject of the same gender from the same background category who had not yet started the experiment was chosen as a replacement and was put in the appropriate group. 4 . 3 Initial Analysis Init ial analysis of the data included the calculation of two error metrics for determining the "closeness" of the configuration attained by the subject to the goal configuration. One error metric is the sum of the squares of the differences in joint angles between the goal position of the chain and the position attained by the subject. This error metric, henceforth referred to as the angle error, has units of degrees squared. The second error metric is the sum of the squares of the Euclidean distances between endpoints of the corresponding links of the goal configuration and the configuration attained by the subject. This error metric is called the positional error. The Euclidean distances are calculated in world coordinates and therefore the positional error metric has units of world coordinates squared. For reference purposes, the links in each chain were rectangles that were 10 units wide and 20 units high in world coordinates. The same scale for measuring errors was used for each tr ia l . This allowed data from various trials to be grouped even though the trials were not al l of the same difficulty. Chapter 4. Data Collection and Analysis 28 Tr ia l Angle Error Positional Error 1 100.00 153.83 2 150.00 97.15 3 3375.00 225.63 4 750.00 128.12 5 1200.00 88.19 6 8325.00 229.85 7 133200.00 571,32 8 750.00 128.12 9 133200.00 571.32 10 5850.00 439.19 11 150.00 97.15 12 8325.00 229.85 13 11506.25 63.71 14 550.00 71.87 15 1375.00 38.46 Table 4.1: Initial Error Metric Values Table 4.1 summarizes the values of the angle error metric and the positional error metric at the beginning of each tr ial (rounded to two decimal places). Trials 13,14 and 15 use the chain that represents a torso wi th an attached pair of legs. The links that make up the two legs of this chain are interchangeable. When calculating the values of the error metrics for these three trials, the data was tested to check i f the subject had interchanged the two legs. This check was made to ensure that error metrics would not be inflated by a subject swapping the legs. None of the subjects interchanged the legs so no corrections for this needed to be made. Also determined during the ini t ia l analysis were counts of the number of joints chosen to be roots and end-effectors during each tr ial . This is an upper bound on the number of roots and end-effectors actually used for positioning as the data was not filtered. If, for example, a subject picked one joint as the root and then decided to pick another joint as the root without choosing an end-effector or moving the chain in between, both Chapter 4. Data Collection and Analysis 29 occurrences would increase the count of the number of roots selected. In addition, the distance between the root and end-effector was calculated for each root/end-effector pair. The distance between the root and the end-effector is the number of links separating the two joints. The values for the distance can range from 0, when the root and the end-effector are chosen to be the same joint, to the number of links in a simple chain having no branches, when the root and end-effector are at opposite ends of the chain. The distance is negative if the end-effector is "above" the root. The system did not actually prevent the subject from choosing the same joint for the end-effector that s/he had already chosen for the root. If, however, the root and the end-effector were chosen to be coincident, the configuration of the chain was not affected by any mouse movements. The data was sorted by the time taken for a match and by each of the final values of the two error metrics. The data was sorted in order to check for outliers, where an outlier was considered to be any value that was anomalous when compared to the main group of data. Subject 10 Sorting the data revealed outlying error values corresponding to trials 2 through 15 for subject 10 when using the 1 D O F method. She ranked 13 of these 14 matches as Unsatisfactory. She had ranked al l of the sample matches in the tutorial for the 1 D O F method as Unsatisfactory as well. This subject did not appear to understand the general strategy required to attain a match using the 1 D O F method. She always set the root to be the top joint of the chain and then proceeded to position the chain by picking various joints as the end-effector and moving the mouse cursor. Selecting different end-effectors does not change the fact that the 1 D O F method only modifies the joint angle at the root. Thus, it is impossible Chapter 4. Data Collection and Analysis 30 to adjust any angles other than the top one using subject 10's strategy wi th the 1 D O F method. It is possible to use this strategy with the 1 D O F method to attain a match for t r ia l 1 as the only difference between the ini t ia l configuration and the final configuration for t r ia l 1 is the joint angle at the top of the chain. It is also possible to attain a reasonable match using this strategy with either of the true inverse kinematic methods. For t r ia l 1, subject 10's strategy did not preclude exact matches for any of the three positioning methods and other subjects used a similar strategy for this t r ia l . However, for the remaining trials, subject 10's strategy could not be used to attain a reasonable match for the 1 D O F positioning method. As a consequence, subject 10's data for trials 2 through 15 using the 1 D O F method was not analysed along with the data from al l of the other subjects. Subject 12 Sorting the data for the two error metrics revealed that subject 12 did not improve upon the ini t ia l match given for t r ia l 11 using his second method, which was the 1 D O F method. The trace data for this match showed that subject 12 did not attempt to adjust the in i t ia l match given. He did not pick a root or an end-effector but just looked at the match and then clicked on the " D O N E " button. He rated this match as Pretty Good so it does not appear as i f he accidentally hit the " D O N E " button before completing the match. The completed questionnaire filled out by subject 12 after finishing the set of trials using the 1 D O F method mentioned that one tr ial during this session "was already done" for h im. According to the trace data, t r ia l 11 was displayed properly and thus was not 'already completed. If this t r ia l was the t r ia l that the subject claimed was already completed, it is puzzling why he only gave the match a rating of Pretty Good as this is the middle rating category. Chapter 4. Data Collection and Analysis 31 Since this t r ia l was not actually attempted by subject 12 when using the 1 D O F method, it was removed from further analysis. Subject 12's 44 other trials (all 15 Jacobian trials, al l 15 C C D trials and trials 1 to 10 and 12 to 15 using the 1 D O F method) were used in the remaining analyses. •i 4.4 Further Analysis Addi t iona l analysis involved the data as a complete set, split by subject group, by t r ia l category, by the number of links in the chain and by tr ia l . In addition, the data was thresholded based on the positional error and the analyses were repeated wi th the thresh-olded data. This additional analysis involved a statistical analysis of variance ( A N O V A ) calcula-tion using the data for the time, angle error metric and positional error metric at the end of each tr ia l . A 95% confidence interval was used in the calculation of the A N O V A . For each A N O V A , an F value and a p value are reported. The F value is a ratio of the differences between groups to the differences wi thin a group. A value higher than 1.0 indicates more of a difference between groups than within groups. The p value is a measure of the probability that this difference is due to random chance. A Fisher's protected least significant difference ( P L S D ) post hoc analysis of significant results was used to determine the cause(s) of the significance. The significance level was set at 5%. This test uses a t statistic to evaluate al l pairwise differences in the data. More complete explanations of these various statistical tools can be found in intro-ductory statistics books [Kep91, Moo85]. Chapter 4. Data Collection and Analysis 32 4.4.1 Summary of Statistically Significant Results When all of the trials were grouped together, the data showed that subjects took signifi-cantly more time to complete trials using the Jacobian method as compared to the 1 D O F method. The positional errors attained when using the 1 D O F method were significantly less than those attained when using either of the other two methods. Complete results of the statistical analyses are in Table 4.2 and the discussion of the significant results is in Section 4.4.2. The data was split according to the subject group (which determined the ordering of the methods used). The group that started wi th the Jacobian method first took significantly longer to complete the trials using the Jacobian method as compared to the C C D method and the 1 D O F method. The group that started with the C C D method took significantly longer to complete the trials using the C C D method as compared to the other two methods. Results from the group that started with the 1 D O F method first showed that these subjects made significantly more accurate matches (according to the positional error metric) with the 1 D O F method than with the Jacobian method. Table 4.3 contains the results of the analyses and Section 4.4.3 contains the discussion of the significant results. When the trials were grouped according to the method that was expected to generate accurate matches in the shortest period of time, there was a significant difference in the times and positional errors for the trials in the 1 D O F category. These trials, for which the 1 D O F method was expected to produce the best results, were done significantly faster when the 1 D O F method was used than when the Jacobian method was used. The positional errors attained for the trials in this category were significantly less when the 1 D O F method was used as compared to the Jacobian method as well. The results of the analyses are in Table 4.4 and a discussion of the significant results is in Section 4.4.4. Chapter 4. Data Collection and Analysis 33 The trials were also grouped according to the number of links in the chain used in each tr ial . For trials using a chain with 6 links, the matches made wi th the C C D method were significantly faster than those made with the 1 D O F method. For trials involving a chain wi th 9 links, the positional error values attained using the 1 D O F method were significantly less than those attained using either of the other two methods. The matches made with the 1 D O F method were significantly faster than those made wi th the Jacobian method for the trials involving chains wi th 10 links. The positional errors for these trials done using the 1 D O F method were significantly less than those done wi th the C C D method. The complete set of results from the analyses are in Table 4.5 and a discussion of the significant differences appears in Section 4.4.5. The data was also analysed separately for each tr ial . The t r ia l 1 matches that were made wi th the 1 D O F method were significantly more accurate (according to the angle error metric) than those made wi th the C C D method. The t r ia l 9 matches that were performed using the 1 D O F method were completed in significantly less time than those performed with either the Jacobian method or the C C D method. A complete listing of the results is in Table 4.6 and a discussion of the significant results is in Section 4.4.6. The data was thresholded based on the positional error metric (more information on the thresholding process is in Section 4.5). The same analyses were repeated on the thresholded data. Since the data was thresholded using the positional error value, it is not surprising that several analyses that showed statistically significant differences in positional errors when using the original data no longer showed statistically significant differences when using the thresholded data. In the analysis of the entire set of thresholded data treated as one group, the trials done wi th the Jacobian method once again took significantly longer than those done wi th the 1 D O F method. Table 4.8 displays the results for the thresholded data and Section 4.5.1 contains the discussion of the statistically significant result. Chapter 4. Data Collection and Analysis 34 The thresholded data split according to subject group showed statistically significant differences in the time taken for the trials completed by the group of subjects who used the Jacobian method first. These subjects once again took significantly longer to perform trials using the Jacobian method than they took when using either of the other two methods. The results of the analyses are in Table 4.9 and the discussion of the significant result is in Section 4.5.2. When the thresholded data was grouped according to the method that was expected to generate accurate matches in the shortest period of time, there was at least one statistically significant difference in each of the four categories. Table 4.10 contains the results of the analyses for all of the categories and Section 4.5.3 contains the discussion of all of the significant results. In the category consisting of trials for which the 1 D O F method was expected to have the best performance, the matches were made in significantly less time when the 1 D O F method was used than when either of the other two methods were used. The category containing trials for which the two true inverse kinematic methods were expected to have the best performance had two significant results. The matches attained when using the 1 D O F method were less accurate than those attained wi th the C C D method when measured by both the angle error metric and the positional error metric. The matches made with the 1 D O F method were also less accurate than those made with the Jacobian method, according to the positional error metric. It was expected that using either of the two true inverse kinematic methods to manip-ulate pieces of the chains at once would produce the best results for the trials in the thi rd category. For these trials, the matches made with the 1 D O F method were significantly faster than those made with the Jacobian method. The last category consisted of trials that did not fit into any of the first three cate-gories. There was no advance expectation of which positioning method would work best Chapter 4. Data Collection and Analysis 35 for these trials. For trials in this category, the matches made wi th the 1 D O F method were significantly less accurate (in terms of the positional error metric) than those made wi th either of the other two methods. Statistically significant results were also found when the trials were grouped according to the number of links in the chains. For the group of trials with 6 links, the matches made with the 1 D O F method were less accurate (according to both error metrics) than those made wi th either of the two other methods. For the group of trials wi th 10 links, the matches made using the 1 D O F method were significantly faster than those made with either of the other two methods. The results of the analyses are in Table 4.11 and the discussion of the significant results is in Section 4.5.4. The analysis of the thresholded data split by tr ial showed at least one statistically significant result for trials 1, 2, 3, 7, 8, 9 and 11. Table 4.12 contains complete results of the analyses for al l of the trials and Section 4.5.5 contains the discussion of the statistically significant results. The t r ia l 1 matches that were made with the 1 D O F method were more accurate (according to the angle error metric) than those made with the C C D method. The tr ial 2 matches made with the 1 D O F method were less accurate (according to both error metrics) than those made wi th the C C D method. When the matches made for t r ia l 3 were examined, those trials performed using the 1 D O F method were less accurate (according to the angle error metric) than those performed using either of the other two methods. According to the positional error metric, the t r ia l 3 matches made wi th the C C D method were more accurate than those made wi th either of the other two methods. The tr ial 7 matches made wi th the 1 D O F method were significantly more accurate (according to both error metrics) than the matches made wi th either the C C D method or the Jacobian method. Chapter 4. Data Collection and Analysis 36 Experiment Variables F Value p Value Time and method Angle error and method Positional error and method 4.200 2.771 6.064 0.0152 0.0630 0.0024 Table 4.2: Results of ANOVA with All Data When the data from the tr ia l 8 matches was analysed, the matches made wi th the 1 D O F method were found to be less accurate (according to the positional error metric) than those made wi th the Jacobian method. The t r ia l 9 matches were found to have been done faster wi th the 1 D O F method than with either of the other two methods. The t r ia l 11 matches that were made wi th the 1 D O F method were found to be less accurate (according to the angle error metric) than the matches made wi th either the Jacobian method or the C C D method. 4.4.2 Data From A l l Trials A n ini t ia l A N O V A was done using al l of the data from subjects 1 through 27 except for subject 12's tr ial 11 using the 1 D O F method and all but tr ial 1 of subject 10's trials. A summary of the results of the A N O V A are in Table 4.2 wi th the significant results shown in bold face. The post hoc analysis showed that subjects generally took longer when using the Jacobian method than when using the 1 D O F method. The matches attained wi th the 1 D O F method were significantly more accurate (in terms of the positional error metric) than those made with either of the other two methods. Addi t iona l analyses were done to explore and account for the various differences. A s the data is split in various ways, there are fewer values in each individual group and thus Chapter 4. Data Collection and Analysis 37 Group Experiment Variables F Value p Value Jacobian Time and method 14.000 < 0.0001 Method Angle error and method 1.648 0.1937 First Positional error and method 1.339 0.2633 C C D Time and method 6.052 0.0026 Method Angle error and method 1.889 0.1527 First Positional error and method 1:192 0.3047 1 D O F Time and method 1.879 0.1541 Method Angle error and method 0.953 0.3864 First Positional error and method 4.247 0.0150 Table 4.3: Results of A N O V A Split by Group differences wi thin the groups are magnified. 4.4.3 Data Split B y Group A s part of the additional analysis, the data for the three groups of subjects was analysed separately. A summary of the results of the A N O V A using the data split by subject group is in Table 4.3. The data was split by group to see i f the order in which the subjects encountered the various methods had any effect on their results. The data for the group who used the Jacobian method first included the data from subjects 1 through 9. The data for the group who used the C C D method first included the data from subjects 10 through 18. The data for the group who used the 1 D O F method first consisted of the data from subjects 20 through 27. Group Using Jacobian Method First For the group of subjects who used the Jacobian method first, the subjects took sig-nificantly longer to complete the trials when using the Jacobian method as compared Chapter 4. Data Collection and Analysis 38 to the other two methods. This group of subjects started wi th the Jacobian method, used the C C D method second and the 1 D O F method third. The mean time for their trials using the Jacobian method was 48.72 seconds. It was 35.79 seconds for their trials done wi th the C C D method and 31.05 seconds for the trials that they completed wi th the 1 D O F method. The decrease in times across the three sets of trials was probably caused by learning effects due to the subjects becoming more familiar wi th the system as they performed the set of trials for the second and third times. In addition, when using the system for the first time, subjects may have found that taking extra time did not necessarily result in much improvement in the quality of the match. A s a consequence, subjects may have not tried to make matches that were as perfect the second and third times. This supposition is explored in Section 4.5. Group Using C C D Method First For the group of subjects who used the C C D method first, the trials done using the C C D method took significantly longer than those done using either of the other two methods. This group of subjects started wi th the C C D method. They used the 1 D O F method second and the Jacobian method last. The mean time for their trials using the C C D method was 40.63 seconds. It was 33.76 seconds for their trials using the 1 D O F method and 32.60 seconds for their trials using the Jacobian method. Once again the decrease in the times could be attributed to learning effects. Group Using 1 D O F Method First For the group of subjects who used the 1 D O F method first, the trials done using the 1 D O F method were significantly more accurate (in terms of positional error) than those done using the Jacobian method, with no significant differences in the time taken. The mean positional error using the 1 D O F method was 3.833. It was 4.907 for the trials Chapter 4. Data Collection and Analysis 39 using the C C D method and 5.421 for the trials using the Jacobian method. This group of subjects used the 1 D O F method first, the Jacobian method second and the C C D method third. In this case, the first method used by these subjects produced the most accurate matches. The mean positional error was highest for the matches made wi th the second method used by these subjects. It was surprising that this group of subjects did not exhibit learning effects that were similar to the other two groups. Reviewing the link distance data for these subjects showed that these subjects did not just use the strategy of adjusting one l ink at a time with their second and third methods. They actually d id take advantage of the abili ty of the Jacobian method and the C C D method to move more than one l ink at a time. It is possible that there was actually a learning effect but that the increased familiarity with the system was offset by the increased difficulty in using the true inverse kinematic methods as compared to the 1 D O F method and thus no significant difference was evident. 4.4.4 Analysis by Category The ini t ia l /goal configuration pairs had been chosen so that some were expected to be easier to match using the true inverse kinematic methods and others were expected to require manipulation of one link at a time. The data was split into categories according to these expectations for further analysis. The trials were placed in one of four categories according to the expectation of which method would be easiest to use to complete the match. This expectation was based in part on the perception of an experienced user using al l of the methods to try to attain an accurate match in a short period of time. Trials 1, 9, 10, 13, 14 and 15 were placed in the 1DOF category as it was expected that the manipulation of one link at a time would be required in order to achieve an accurate match. The IK category contained trials 2, 3 and 11. It was possible to attain Chapter 4. Data Collection and Analysis 40 Category Experiment Variables F Value p Value 1 D O F Time and method 4.039 0.0182 Angle error and method 0.642 0.5267 Positional error and method 3.049 0.0483 I K Time and method 1.721 0.1812 Angle error and method 1.686 0.1875 Positional error and method 1.025 0.3605 I K Time and method 2.545 0.0807 Pieces Angle error and method 2.421 0.0911 Positional error and method 2.230 0.1098 Unknown Time and method 0.258 0.7729 Angle error and method 0.853 0.4274 Positional error and method 2.050 0.1310 Table 4.4: Results ANOVA Split by Category an accurate match in a very short period of time for each of these three trials using either of the true inverse kinematic methods to manipulate the entire chain at once. Trials 6, 7 and 12 were placed in the IK Pieces category. For these three trials it was possible to attain an accurate match in a short period of time using one of the inverse kinematic methods if the chain was treated as several groups of links and one group was matched at a time. The remaining trials (4, 5 and 8) were placed in the Unknown category as there was not an apparent optimal way of making a match in these trials. The results of the analyses of the data grouped by category are in Table 4.4. The only significant results were in the 1 D O F category. Subjects took longer to complete trials when using the Jacobian method than when using the 1 D O F method. The trials performed using the Jacobian method were less accurate (in terms of the positional error metric) than those performed using the 1 D O F method. It is not surprising that faster and more accurate results were obtained when using the 1 D O F method as this group contained trials for which the 1 D O F method was expected to give the best Chapter 4. Data Collection and Analysis 41 performance. It is surprising that there was not a significant difference between the C C D method and the 1 D O F method for these trials. These differences (and lack thereof) are further explored in Section 4.5.3. 4.4.5 Analysis by Number of Links Chains wi th similar ranges of motion had similar possible values for both the angle error metric and the positional error metric. The trials were grouped according to the number of links in the chain used in each t r ia l in order to compare chains wi th similar ranges of motion. This grouping also compensated for possible differences in task complexity due to the number of links in the chain. Trials 2 and 11 used chains wi th 6 links. The chains in trials 13, 14 and 15 each had 8 links. Trials 1, 4, 5, 8 and 10 util ized chains wi th 9 links. Chains with 10 links were used in trials 6, 7, 9 and 12. Tr ia l 3 was the only t r ia l that used a 5-link chain. The results of the analyses wi th the trials grouped by number of links are in Table 4.5. Analysis for t r ia l 3 was not included in this section as a l l trials are analysed separately in Section 4.4.6. For the group of trials using chains wi th 6 links, the matches made with the C C D method were significantly faster than those made wi th the 1 D O F method. The true inverse kinematic methods were expected to have superior performance for both of the trials in this group so it is not surprising that the matches made wi th the 1 D O F method took longer. It is surprising that the matches made wi th the Jacobian method were not significantly faster than those made wi th the 1 D O F method. The matches made with the 1 D O F method were significantly more accurate (in terms of the positional error metric) than those made wi th either of the other two methods for the group of trials using chains with 9 links. The trials using chains wi th 9 links were either in the category of trials for which the 1 D O F method was expected to have superior performance or in the category of trials where it was unknown which method would have Chapter 4. Data Collection and Analysis 42 Links Experiment Variables F Value p Value 6 Time and method 3.655 0.0282 Angle error and method 2.459 0.0890 Positional error and method 0.259 0.7721 8 Time and method 0.711 0.4920 Angle error and method 0.261 0.7705 Positional error and method 0.956 0.3858 9 Time and method 1.353 0.2597 Angle error and method 1.494 0.2257 Positional error and method 4.704 0.0096 10 Time and method 4.671 0.0100 Angle error and method 2.134 0.1201 Positional error and method 3.508 0.0312 Table 4.5: Results of ANOVA Split by Number of Links superior performance. Given that the times taken when using the three methods were not significantly different and that the 1 D O F method was expected to have superior performance for some of the trials in this group, it is not surprising that in similar amounts of time, the 1 D O F method produced results that were more accurate in terms of the positional error metric. For the trials using chains wi th 10 links, the matches made wi th the 1 D O F method took significantly less time than those made with the Jacobian method. These trials were all ones for which either the 1 D O F method was expected to give faster performance or for which the true inverse kinematic methods needed to be used to manipulate pieces of the chain rather than the entire chain at once. The difference in time can be partly attributed to the fact that many subjects reported trying to manipulate the entire chain at once in trials 6 and 7 and then giving up on that strategy after it did not produce quick results. The trials using chains with 10 links also had significant differences in the positional Chapter 4. Data Collection and Analysis 43 errors attained when using the various methods. The trials completed using the 1 D O F method were more accurate than those completed using the C C D method. This difference can also be attributed to the nature of the trials involved. If similar amounts of time are taken when using both methods and the approach of manipulating the entire chain at once is taken wi th the C C D method, the final error attained wi l l be greater for the C C D method as this method tends to not make adjustments evenly along the chain. 4.4.6 Analysis by Tria l The data for each tr ial was also analysed individually in case significant differences for particular trials were being masked by the various groupings of the data. The results of the analyses are in Table 4.6. The data from tr ia l 1 showed a significant difference in the angle errors attained. The matches made wi th the 1 D O F were more accurate than those made with the C C D method. Given the construction of the ini t ia l and goal configurations for t r ia l 1, this result is not surprising. The only difference between the in i t ia l and goal configuration for t r ia l 1 is at the top joint. The ini t ia l configuration has a joint angle of 10 degrees and the goal configuration has a joint angle of 20 degrees. The rest of the joint angles are identical, so only the top angle needs to be adjusted in order to make a match. Using the 1 D O F method, as long as the top link is chosen as the root, only the joint angle at the top of the chain wi l l be adjusted, independent of which joint is chosen to be the end-effector. Thus, other joint angles that do not need to be changed wi l l not be affected. Most subjects reported a matching strategy that involved starting at the top of chain and this strategy would work favourably for this tr ial wi th the 1 D O F method. O n the other hand, since the C C D method is a true inverse kinematic method, al l joints between the root and the end-effector may be adjusted. If a subject picked the root Chapter 4. Data Collection and Analysis 44 Trial Experiment Variables F Value p Value 1 Time and method Angle error and method Positional error and method 0.646 3.607 2.565 0.5272 0 . 0 3 1 7 0.0834 2 Time and method Angle error and method Positional error and method 1.783 1.035 0.824 0.1751 0.3603 0.4428 3 Time and method Angle error and method Positional error and method 0.082 0.003 1.951 0.9218 0.9972 0.1493 4 Time and method Angle error and method Positional error and method 0.120 0.478 0.557 0.8869 0.6222 0.5754 5 Time and method Angle error and method Positional error and method 0.048 0.367 0.909 0.9535 0.6941 0.4075 6 Time and method Angle error and method Positional error and method 0.791 0.765 0.685 0.4573 0.4690 0.5071 7 Time and method Angle error and method Positional error and method 2.162 1.667 1.578 0.1223 0.1958 0.2131 8 Time and method Angle error and method Positional error and method 1.595 0.084 1.338 0.2097 0.9195 0.2685 9 Time and method Angle error and method Positional error and method 5.616 0.033 1.259 0 . 0 0 5 3 0.9674 0.2899 10 Time and method Angle error and method Positional error and method 1.640 0.218 0.926 0.2008 0.8048 0.4006 11 Time and method Angle error and method Positional error and method 1.823 1.452 0.105 0.1687 0.2408 0.9007 12 Time and method Angle error and method Positional error and method 0.506 0.254 0.591 0.6052 0.7762 0.5562 13 Time and method Angle error and method Positional error and method 1.576 0.012 0.670 0.2135 0.9879 0.5149 14 Time and method Angle error and method Positional error and method 0.057 0.238 1.070 0.9448 0.7887 0.3482 15 Time and method Angle error and method Positional error and method 0.252 0.229 0.178 0.7779 0.7960 0.8376 Table 4.6: Results of ANOVA Split by Trial Chapter 4. Data Collection and Analysis 45 to be the top joint and the end-effector to be the second joint, the performance would be similar to the 1 D O F method. If any other root/end-effector pair was chosen, angles that did not need to be adjusted to make the match would be adjusted and thus a less accurate match would be attained in the same amount of time. It is surprising that a similar difference between the 1 D O F method and the Jacobian method was not evident, as the Jacobian method is also a true inverse kinematic method. The t r ia l 9 matches made with the 1 D O F method were significantly faster than those made with either of the other two methods. This tr ial involved straightening a chain that was ini t ia l ly in a zig-zag configuration. Many subjects tried to put the root at one end of the chain and the end-effector at the other end and "pul l" on the chain to get it to straighten. Since the true inverse kinematic methods tended to not make adjustments evenly along the chain, but rather tended to adjust angles closer to the end-effector (in part due to the user interface for indicating the desired position for the end-effector) this strategy was very time consuming. The direct approach of moving one or two links at a time was faster. Subjects often abandoned the "pulling" strategy in favour of moving a small number of links at a time, starting at the top of the chain. Trials 2 through 8 and 10 through 14 did not show any significant differences. 4.5 Analysis of Intermediate Data In addition to the data obtained at the end of each t r ia l (when the subject clicked on the " D O N E " button), data was also collected during each t r ia l whenever the subject released the left mouse button (and thereby reset the end-effector). The data for each tr ial was sorted to determine the value of the greatest final positional error that was not an outlier. The greatest final positional error for the t r ia l was divided by the number of links in the chain used in the tr ial to obtain a per l ink positional error. Chapter 4. Data Collection and Analysis 46 The greatest of the fifteen per link positional errors was used to calculate a threshold value for each tr ial . The threshold value for a t r ia l was set equal to the greatest per link positional error multiplied by the number of links in the t r ia l . Table 4.7 indicates the greatest final value obtained for the positional error metric, the per link positional error and the thresholded value used for each tr ia l . The thresholded value is also shown (rounded to two decimal places) as a percentage of the trial 's in i t ia l positional error for reference purposes. The experiment data was cut off for three reasons. First , thresholding the values meant that the data from subjects who spent time near the end of the t r ia l t rying to perfect a match could be compared more equally with subjects who did not try to make matches that were as precise. Second, there were trials in which some subjects ended up with a final match that was not as accurate as one of their intermediate matches for that t r ia l . In t rying to improve the match, the subject actually made the match worse (according to the error metrics) and did not attain the same level of accuracy by the end of the t r ia l . Th i rd , in other cases the subject did end the t r ia l wi th the most accurate match of the t r ia l , but s/he spent a considerable amount of time to produce a final match that was only marginally better than an intermediate match. The data was filtered and the first time at which the positional error was less than or equal to the cutoff value was recorded. The value of the angle error metric was also recorded. Out of the 1215 total trials, there were 11 trials for which this filtering caused a change and 16 trials that were outliers. The 11 filtered trials and the 16 outlier trials are identified as such in the data in Appendix E . The 16 outlier trials al l belonged to one of three subjects (subject 10, subject 12 or subject 19). A l l remaining analyses did not include the 16 trials that were identified as outliers. The results of the analyses of the thresholded data for the remaining 1199 trials are Chapter 4. Data Collection and Analysis 47 Tr ia l M a x . Error Per L ink Error Threshold Error % of Init ial Error 1 15.00 1.6 26.46 17.20 2 7.29 1.215 17.64 18.16 3 6.20 1.24 14.70 6.52 4 9.93 1.10 26.46 20.65 5 26.46 2.94 26.46 30.00 6 23.55 2.355 29.40 •12.79 7 20.00 2.0 29.40 5.15 8 11.22 1.246 26.46 20.65 9 22.85 2.285 29.40 5.15 10 13.18 1.464 26.46 6.02 11 8.50 1.416 17.64 18.16 12 17.24 1.724 29.40 12.79 13 11.15 1.39375 23.52 36.92 14 13.65 1.70625 23.52 32.73 15 19.81 2.47625 23.52 61.15 Table 4.7: Thresholded Positional Error Values Experiment Variables F Value p Value Time and method Angle error and method Positional error and method 4.891 0.268 0.409 0.0077 0.7647 0.6644 Table 4.8: Results of ANOVA with Thresholded Data shown in Table 4.8. 4.5.1 Thresholded Group Data As with the original data, there was a significant difference in the time taken to make matches using the different positioning methods. The mean time for the matches wi th al l of the methods combined was 26.21 seconds. For the individual methods, the mean times were 28.28 seconds for matches made wi th the Jacobian method, 26.58 seconds for matches made with the C C D method and 23.71 seconds for matches made wi th the Chapter 4. Data Collection and Analysis 48 Group Experiment Variables F Value p Value Jacobian Time and method 7.369 0.0007 Method Angle error and method 0.032 0.9689 First Positional error and method 0.070 0.9326 C C D Time and method 2.499 0.0844 Method Angle error and method 0.908 0.4042 First Positional error and method 0.007 0.9935 1 D O F Time and method 0.603 0.5475 Method Angle error and method 0.182 0.8339 First Positional error and method 0.673 0.5105 Table 4.9: Results of ANOVA Split by Group (Thresholded Data) 1 D O F method. The difference in times for the matches made with the Jacobian method and those made with the 1 D O F method was significant. Since the data was thresholded based on an error value, it is not surprising that there was not a significant difference for either of the two error values, even though the original data showed a significant difference in the positional error. 4.5.2 Thresholded Data Split by Group Once again the data was split into the three groups according to the method that the subjects first used. The results from the analyses are in Table 4.9. Group Using Jacobian Method First A s before, the group of subjects who used the Jacobian method first took significantly longer to complete matches when using the Jacobian method as compared to either of the other two methods. This difference could, once again, be attributed to learning effects as these subjects were least familiar with the system when using the Jacobian method. Chapter 4. Data Collection and Analysis 49 Group Using C C D Method First There were no statistically significant results in the thresholded data from the group of subjects who used the C C D method first. The time was no longer significant, as it had been in the analysis using the original data. The mean tr ia l times wi th the original data were 40.63 seconds for trials using the C C D method, 33.76 seconds for trials using the 1 D O F method and 32.60 seconds for trials using the Jacobian method. W i t h the thresholded data, the mean tr ial times were 28.26 seconds for trials using the C C D method, 23.63 seconds for trials using the l D O F method and 23.94 seconds for trials using the Jacobian method. It appears as i f the significant difference in the original data was due to subjects spending more time trying to perfect a match when using their first method (the C C D method). When the data was thresholded and this extra effort was removed, the trials did not show statistically significant differences between the three methods. Group Using 1 D O F Method First There were no statistically significant results in the data from the group of subjects who used the 1 D O F method first. The only significant result in the original data for this group was in the positional error analysis. Because the data was thresholded based on the positional error, many of the small values for the positional error of a t r ia l were replaced by earlier, larger values and thus the positional error data was more homogeneous. A s a result, the positional error no longer had significant differences in it. 4.5.3 Thresholded Data Split by Category As before, the data was split according to the four categories (1DOF, I K , I K Pieces and Unknown). The results of the analyses of the thresholded data grouped by t r ia l category Chapter 4. Data Collection and Analysis 50 Category Experiment Variables F Value p Value 1 D O F Time and method 3.757 0.0241 Angle error and method 0.410 0.6642 Positional error and method 0.578 0.5617 I K Time and method 1.224 0.2960 Angle error and method 3.705 0.0260 Positional error and method 10.05 < 0.0001 I K Time and method 4.801 0.0090 Pieces Angle error and method 1.309 0.2720 Positional error and method 0.429 0.6519 Unknown Time and method 0.463 0.6302 Angle error and method 0.835 0.4353 Positional error and method 3.744 0.0251 Table 4.10: Results ANOVA Split by Category (Thresholded Data) are in Table 4.10. Results for Trials in the 1 D O F Category In the original data, there were statistically significant differences in the time taken using the three methods for the trials in the 1 D O F category (trials 1, 9, 10, 13, 14 and 15). In the thresholded data, there were st i l l statistically significant differences in the time taken using the three methods. W i t h the thresholded data, the mean times for the trials in the 1 D O F category were 21.58 seconds for trials using the 1 D O F method, 26.04 seconds for trials using the C C D method and 26.69 seconds for trials using the Jacobian method. The differences between the 1 D O F method and the other two methods were significant. This analysis supports the categorization of these trials as ones for which the 1 D O F method produces accurate matches in the shortest period of time. There was also a statistically significant difference in the positional error in the original data for the trials in the 1 D O F category. Once again, the lack of such a difference in the Chapter 4. Data Collection and Analysis 51 analysis using the thresholded data is explained by the fact that the data was thresholded based on the positional error. Results for Trials in the I K Category Analyses of the error metric data from trials in the I K category (trials 2, 3 and 11) indicated statistically significant differences. In terms of the angle error, the matches made with the C C D method were more accurate than those made wi th the 1 D O F method. In terms of the positional error, the matches made with the 1 D O F method were less accurate than those made with either of the other two methods. These differences were not statistically significant in the original data. The significant results in the thresholded data can be attributed to the thresholding process itself. W i t h the two true inverse kinematic methods, multiple links can be adjusted at once. Large changes in both error metrics can result from one choice of root and end-effector. In particular, these trials can be done in one step wi th the true inverse kinematic methods if the root is placed at the top, the end-effector is placed at the bottom and the chain is swung smoothly. W i t h the 1 D O F method, it is necessary to move the links one at a time. If subjects start at the top of these chains and work down to the bottom, the threshold value can be passed before the bottom links have been adjusted at a l l . For example, in trials 2 and 11, the threshold can be passed after matching the top three links, without manipulating the bottom three links. Thus, the thresholding process wi l l cut off the latter sections of trials performed using the 1 D O F method in which continued improvement is s t i l l being made. This can result in statistically significant differences in the error metrics between the 1 D O F method and the two true inverse kinematic methods wi th the 1 D O F method having the least accurate matches. Chapter 4. Data Collection and Analysis 52 Results for Trials in the I K Pieces Category There was a statistically significant difference in the times taken to perform the matches using the various positioning methods for the trials in the I K Pieces category (trials 6, 7 and 12). The mean time for the trials done using the 1 D O F method was 35.66 seconds. It was 41.54 seconds for the trials done using the C C D method and 49.79 seconds for the trials done using the Jacobian method. The difference between the 1 D O F method and the Jacobian method was statistically significant. These three trials al l involved chains that had an in i t ia l zig-zag configuration. Tr ia l 6 involved uncompressing a tight zig-zag into a looser one. Tr ia l 7 involved straightening out the same zig-zag and t r ia l 12 involved compressing a looser zig-zag into a tighter one. The angle adjustments that were necessary to match the goal configuration were spread evenly along the chain. These trials were put in the I K pieces category because the optimal movement strategy involved manipulating a small number of links at a time. Many subjects reported trying to "pull" down on the end of the chain for these configurations. If subjects used the capability of the true inverse kinematic methods to attempt to manipulate the entire chain at once, the t r ia l would take longer as the true inverse kinematic methods d id not adjust the links evenly along the chain. Subjects would need to further adjust the links to attain an accurate match. A s a consequence, the direct strategy of moving one link at a time would be faster than the strategy of trying to move a large number of links at a time. Results for Trials in the Unknown Category For the trials in the Unknown category (trials 4, 5 and 8), the trials done wi th the 1 D O F method were significantly less accurate (in terms of the positional error) than those done Chapter 4. Data Collection and Analysis 53 with either of the other two methods. The trials done using the 1 D O F method had a mean positional error of 16.957. Those done using the C C D method had a mean positional error of 15.217 and those done using the Jacobian method had a mean positional error of 15.126. As wi th the trials in the I K category, it was possible to cross the threshold for the positional error metric without adjusting al l of the links in the chain. The thresholding process w i l l cut off latter sections of trials performed using the 1 D O F method in which continued improvement is st i l l being made. This can result in statistically significant differences in the error metrics between the 1 D O F method and the two true inverse kinematic methods with the 1 D O F method having the least accurate matches. 4.5.4 Thresholded Data Split by Number of Links As in the original analysis, the trials using chains wi th the same number of links were grouped together and the thresholded data was analysed. The results of the analyses are in Table 4.11. Once again, t r ial 3 was not included in any group in this section as it is the only t r ia l wi th a chain composed of 5 links. Trials Using Chains W i t h 6 Links Trials 2 and 11 both involved chains with 6 links. The matches made wi th the 1 D O F method were significantly less accurate in terms of both error metrics than those made wi th either of the other two methods. These two trials were both in the I K category. Bo th of the error metrics were also significant in the I K category analysis and the thresholding explanation presented in that section also applies here. Chapter 4. Data Collection and Analysis 54 Links Experiment Variables F Value p Value 6 Time and method Angle error and method Positional error and method 2.08 6.451 5.685 0.1283 0.0020 0.0041 8 Time and method Angle error and method Positional error and method 0.169 0.666 0.136 0.8442 0.5146 0.8728 9 Time and method Angle error and method Positional error and method 1.400 0.873 0.432 0.2470 0.4186 0.6493 10 Time and method Angle error and method Positional error and method 7.867 1.537 0.931 0.0005 0.2167 0.3951 Table 4.11: Results of ANOVA Split by Number of Links (Thresholded Data) Trials Us ing Chains w i t h 8 L inks Trials 13, 14 and 15 all involved a chain with 8 links. There were no statistically significant differences shown in the analyses done using the thresholded data from these three trials. The analyses done using the original data did not have any significant differences either. Trials U s i n g Chains w i t h 9 L inks Chains with 9 links were used in trials 1, 4, 5, 8 and 10. There were no statistically significant differences for the analyses done using the thresholded data from these trials. In the original data, there were significant differences in the positional errors attained using the various methods for these trials. Since the data was thresholded based on the positional error, it is not surprising that the analysis wi th the thresholded data d id not show a statistically significant difference in the positional error metric. Chapter 4. Data Collection and Analysis 55 Trials Using Chains with 10 Links Trials 6, 7, 9 and 12 all used chains with 10 links. There was a statistically significant difference in the time taken to complete these trials. The mean time for the trials using the 1 D O F method was 36.38 seconds. It was 44.88 seconds for the trials using the C C D method and 50.95 seconds for the trials using the Jacobian method. The differences in times between the 1 D O F method and each of the other two methods were significant. In the original data, the difference between the Jacobian method and the 1 D O F method was significant and it was more significant in the thresholded data. The difference between the C C D method and the 1 D O F method was not significant in the original data but it was significant in the thresholded data. The explanation for the difference between the 1 D O F and the Jacobian methods in the original data also explains the differences in the thresholded data. The analysis of the original data for the group of trials using chains wi th 10 links showed a statistically significant difference in the positional error. This error was not significant in the thresholded data and once again the lack of significant difference is attributed to the fact that the data was thresholded based on the positional error. 4.5.5 Thresholded Data Split by Tria l Once again, the data was split by t r ia l in order to see if there were statistical differences for particular trials. A s before, trials 4, 5, 6, 10, 12, 13, 14 and 15 did not have any statistically significant differences. Table 4.12 contains the results of the analyses. Trials with Significant T ime and Method Results Only Results from the analysis showed statistically significant differences in time for t r ia l 9. The trials done using the 1 D O F method took a mean time of 38.53 seconds. The mean Chapter 4. Data Collection and Analysis 56 Trial Experiment Variables F Value p Value 1 Time and method Angle error and method Position error and method 2.850 4.007 2.341 0.0639 0.0221 0.1030 2 Time and method Angle error and method Position error and method 0.602 3.534 4.783 0.5502 0.0340 0.0110 3 Time and method Angle error and method Position error and method 0.038 7.321 6.934 0.9629 0.0012 0.0017 4 Time and method Angle error and method Position error and method 0.915 0.564 0.645 0.4050 0.5712 0.5276 5 Time and method Angle error and method Position error and method 0.103 1.071 1.121 0.9020 0.3476 0.3313 6 Time and method Angle error and method Position error and method 2.692 0.516 2.837 0.0741 0.5989 0.0647 7 Time and method Angle error and method Position error and method 2.549 9.048 10.00 0.0847 0.0003 0.0001 8 Time and method Angle error and method Position error and method 0.040 1.492 3.253 0.9609 0.2314 0.0440 9 Time and method Angle error and method Position error and method 6.742 2.343 2.616 0.0020 0.1028 0.0796 10 Time and method Angle error and method Position error and method 0.560 0.475 0.697 0.5737 0.6234 0.5014 11 Time and method Angle error and method Position error and method 1.85 3.224 1.646 0.1637 0.0453 0.1996 12 Time and method Angle error and method Position error and method 1.300 1.566 0.462 0.2791 0.2154 0.6318 13 Time and method Angle error and method Position error and method 2.790 1.797 1.078 0.0675 0.1728 0.3453 14 Time and method Angle error and method Position error and method 0.074 0.501 0.098 0.9289 0.6080 0.9064 15 Time and method Angle error and method Position error and method 1.000 1.288 0.250 0.3727 0.2818 0.7797 Table 4.12: Results of ANOVA Split by Trial (Thresholded Data) Chapter 4. Data Collection and Analysis 57 time for the trials done using the Jacobian method was 54.45 seconds and it was 54.95 sec-onds for the trials done using the C C D method. Similar results also appeared in the original data but both results are more significant in the thresholded data. The same explanation of this result applies to both the thresholded data and the original data. Trials with Significant Angle Error and Method Results Only Trials 1 and 11 showed statistically significant differences in the angle error for the matches made using the various methods. For tr ial 1, the mean angle error for the trials done using the 1 D O F method was 2.294 degrees squared. It was 74.646 degrees squared for the trials done using the Jacobian method and 142.410 degrees squared for the trials done using the C C D method. The difference between the 1 D O F method and the C C D method was statistically significant. This difference was also significant in the original data, but it is more significant in the thresholded data. The same explanation presented in the section discussing the difference in the original data also applies to the thresholded data. The analyses using the original data for t r ia l 11 did not reveal any statistically sig-nificant results. The analysis of the thresholded data showed that there was a significant difference in the angle errors using the three positioning methods. The mean angle error for the trials using the 1 D O F method was 83.719 degrees squared. It was 59.617 degrees squared for the trials using the C C D method and 57.772 degrees squared for the trials using the Jacobian method. The differences between the 1 D O F method and the other two methods were statistically significant. The ini t ia l configuration of the chain used in t r ia l 11 is a gentle curve to the right wi th each link being rotated 5 degrees more than the previous one. The goal configuration has the chain hanging straight down with joint angles of zero. W i t h the C C D and Jacobian methods, it is possible to complete this t r ia l by putt ing the root at the top and the Chapter 4. Data Collection and Analysis 58 end-effector at the bottom and manipulating the al l of the joint angles at the same time. This is not an option wi th the 1 D O F method as only one joint angle can be adjusted at a time. Once again the thresholding process can explain the significance as the threshold can be reached for this t r ia l after positioning only the top three links in the chain. Trials with Significant Positional Error and Method Results Only In the data from tr ia l 8, the mean positional error for the trials that were completed using the 1 D O F method was 17.490 units squared. It was 15.263 units squared for the trials that were completed using the C C D method and 14.414 units squared for the trials that were completed using the Jacobian method. The difference in the errors between the 1 D O F method and the Jacobian method was statistically significant. This t r ia l involved straightening an s-shaped curve, where more adjustment was re-quired at the bottom than at the top. The strategy of putt ing the root at the top of the chain and the end-effector at the bottom of the chain would be moderately successful. Once again it is possible to cross the threshold before adjusting al l of the links in the chain when the 1 D O F method is used to adjust the chain from top to bottom. The threshold-ing process would cut off later sections of a tr ial in which continued improvements were made to the match by adjusting the bottom links in the chain. Trials with Significant Results for Both Error Metrics Results from the analysis of the two error metrics and the method were statistically significant for trials 2, 3 and 7. The mean angle error for the tr ial 2 matches made using the 1 D O F method was 96.786 degrees squared. The mean angle error for these matches made using the Jacobian method was 70.739 degrees squared. For the matches made with the C C D method, the mean angle error was 56.964 degrees squared. The mean positional error was 12.441 units Chapter 4. Data Collection and Analysis 59 squared for the trials performed using the 1 D O F method, 10.009 units squared for the trials performed using the Jacobian method and 8.284 units squared for the trials per-formed using the C C D method. The difference between the both of the errors for matches made wi th the 1 D O F method and those made with the C C D method were significant. The chain used in t r ia l 2 was straight in its ini t ia l configuration and smoothly curved to the right in its goal configuration. Using either of the true inverse kinematic methods, it was possible to make the match choosing only one root and one end-effector. This could be accomplished by putt ing the root at the top of the chain and the end-effector at the bottom of the chain and moving the mouse to the right. The match could also be performed by manipulating smaller chunks of the chain at a time. W i t h the 1 D O F method, each link needed to be moved separately. The thresholding process could once again account for the poor performance of the 1 D O F method as the threshold can be crossed when only the top three links in the chain have been positioned. A s a consequence, the thresholding process removes later portions of the tr ial where continued improvements occur. The mean angle error for the t r ia l 3 matches performed using the 1 D O F method was 1109.19 degrees squared. It was 568.394 degrees squared for the matches made using the C C D method and 821.726 degrees squared for those made using the Jacobian method. The mean positional error for the trials completed using the 1 D O F method was 11.849 units squared. It was 10.733 units squared for the trials that were done wi th the Jacobian method and 8.170 units squared for the trials that were done using the C C D method. The differences in both of the error metrics between the 1 D O F method and the other two methods were significant. A l l of these differences can once again be attributed to the thresholding process. This t r ia l involved a chain wi th an ini t ia l configuration that was curved to the left and a goal configuration that was curved to the right. The differences in the angles between Chapter 4. Data Collection and Analysis 60 the in i t ia l configuration and the goal configuration increase from the top of the chain to the bottom of the chain. It is possible to cross the threshold for this t r ia l before al l of the links have been adjusted. In particular, the last l ink, with the greatest difference in angles between the ini t ia l configuration and the goal configuration, does not need to be adjusted. A s a consequence, the thresholding process wi l l cut off the last sections of trials using the 1 D O F method where adjustments are made to the last l ink thereby improving the final match. In the data from tr ial 7, the differences between the values attained for both error metrics using the 1 D O F method and the other two methods were statistically significant. The mean angle error for the matches made using the 1 D O F method was 86.085 degrees squared. It was 555.824 degrees squared for the matches made using the Jacobian method and 947.248 degrees squared for the matches completed using the C C D method. A s wi th the angle error, the mean positional error was smallest for the matches made using the 1 D O F method (5.629 units squared). It was 13.081 units squared for matches made using the C C D method and 13.567 units squared for matches made using the Jacobian method. Tr ia l 7 used the same ini t ia l configuration as t r ia l 6 (a compressed zig-zag chain wi th 120 degree angles). The final configuration for tr ial 7 was a straight chain. Once again, when using the two true inverse kinematic methods, the strategy of setting the root to be the top joint in the chain and the end-effector to be the other end of the chain and "pulling" on the chain would not be very effective as the bottom part of the chain would straighten more quickly than the top part. For this t r ia l , a faster and more accurate match would result if the chain was adjusted one or two links at a time. Since the 1 D O F method has this constraint built in, it is not surprising that in similar amounts of time, the matches made using the 1 D O F method were more accurate than those made wi th either the C C D method or the Jacobian method which do not have this restriction. Chapter 5 Conclusions and Future Research 5.1 Conclusions This thesis presented an experiment that compared three different methods for position-ing articulated figures. The analysis of the data from the experiment yielded several statistically significant differences between various pairings of the positioning methods under various conditions. Thresholding the data based on the positional error metric enhanced some of the results found in the in i t ia l data. Overall , it appears to be possible to use the one degree of freedom (1DOF) method to produce better matches (faster and/or more accurate) than can be produced wi th either the C C D method or the Jacobian method. However, this is not the case for several particular categories of matches. In general, the C C D and Jacobian methods had superior performance when used for matches involving only smoothly shaped curves. The 1 D O F method was superior in cases where a configuration involved a large change in the orientation of adjacent links. Thus it seems necessary to include both a 1 D O F positioning method and a true inverse kinematic method in an animation system as the most effective positioning method wi l l depend upon the desired configuration. The task of adjusting a given chain to match a target chain was shown to have biases related to the configurations of the two chains. For example, if the roles of the given chain and the target chain are reversed (as in trials 4 and 8) different results were obtained. The tr ial 8 matches made with the 1 D O F method were significantly less accurate than 61 Chapter 5. Conclusions and Future Research 62 those made wi th the Jacobian method. For tr ial 4, there were no differences between the matches made wi th the three positioning methods. Learning effects appeared to be present as the order in which the subjects used the three methods had an impact on the quality of the matches that they made. Given that many subjects could not distinguish between the C C D method and the Jacobian method, it is surprising that there are several cases where there are statistically significant differences between the C C D method and the 1 D O F method but not between the Jacobian method and the 1 D O F method. Similarly, there are other cases where the differences between the Jacobian method and the 1 D O F method are statistically significant but the differences between the C C D method and the 1 D O F method are not. It is possible that some of the differences are not actually significant but that random chance made one significant. Similarly, other differences might actually be significant but random chance made them not significant. 5.2 Future Research Further experimentation could be done to investigate the significant differences revealed by this experiment and to further delineate performance differences between the methods under various circumstances. Currently there is no common time at which data is collected for a l l subjects, other than at the start of the t r ia l . The system could be modified so that information about a t r ia l was recorded on a regular basis in addition to it being recorded in response to a specific action by the subject. If the current configuration of the chain was recorded every second, for example, it would be easier to compare trials. This additional data logging must not adversely affect the response time of the system. Interpolation of the collected data could be used to generate this information, but due Chapter 5. Conclusions and Future Research 63 to the nature of the nature of the subject's task, it could be very misleading. Currently the data is collected when the subject releases the end-effector and therefore temporarily stops moving the chain. However, there is no guarantee that the subject reached the cur-rent configuration in a manner that could be approximated by any type of interpolation. For example, a subject could swing the entire chain back and forth and end in a position that was unchanged from the starting position. In this case, interpolation would miss the entire action of the subject. The user interface for picking the final position could be modified. Currently the user presses the left mouse button to select the end-effector and then holds the button down while moving the mouse. The system tracks the mouse cursor and does each iteration of the inverse kinematic algorithm using the mouse position at that time. Alternatively, the user could click with the left mouse button to select the end-effector, move the mouse cursor to the desired location for end-effector and then click there. In this case, the path of the mouse cursor to the new end-effector location would not be used. This user interface could be compared to the current user interface wi th particular attention paid to in i t ia l /goal configurations where the chain needs to be straightened. The experiment could be modified to use different trials, including more complex chains and configurations. Some of these trials could involve chains where the in i t ia l and goal configurations do not have an ini t ia l coincident link. If trials involving chains without an in i t ia l coincident link are used, the translation feature of the system should be enabled to facilitate the matching process. If configurations are used that have branching structures wi th overlapping parts (as in t r ial 13), the trials should be constructed so that it is possible to position the left branch without moving the right branch out of the way. Most people reported using a top-to-bottom and left-to-right strategy for matching and did not react favourably when this strategy had to be changed. Chapter 5. Conclusions and Future Research 64 The experiment could be extended to use 3-Dimensional chains. In this case, either three orthogonal views of the chain would be needed (with the abili ty to manipulate the chain in any of the three views) or else a simple method of rotating the chain/view would be required, such as the one used in the 3-Dimensional shape-matching experiment by Jang [Jan92]. Addi t iona l inverse kinematic methods, such as the one used by Zhao and Badler [ZB89] could be implemented and compared to the three methods used in the in i t ia l experiment. In addition, various methods of ut i l izing joint l imits and constraints could be compared. In order to make it possible to do a statistical analysis of the ratings done by each subject at the end of each tr ial , an ini t ia l calibration step could be done. A series of matches would be presented to each subject at the beginning of the two sessions and the subjects would be asked to rank the accuracy of the matches. The same matches would be presented at the start of both sessions so that the results could be compared to see i f the subject had changed his/her rating criteria after doing the first part of the experiment. The subject would have to base the rating of these matches solely on the accuracy of the match itself, and this should increase the likelihood that each subject would use only that criteria for rating the matches attained during the experiment trials. A s the complexity of the trials increases, the possibility of subject fatigue also in-creases. Care must be taken to ensure that the overall number and difficulty of the trials does not increase the length of a subject's session to beyond 30 to 45 minutes. Bibliography [GW91] Michael Gleicher and Andrew W i t k i n . Differential Manipulat ion. In Graphics Interface, pages 61-67, 1991. [Jan92] Stanley Jang. 3D Interaction Studies Using the Shape-Matching Paradigm. Master's thesis, University of Br i t i sh Columbia, 1992. [Kep91] Geoffrey Keppel . Design and Analysis: A Researcher's Handbook. Prentice Ha l l , 3rd edition, 1991. [Moo85] David S. Moore. Statistics: Concepts and Controversies. W . H . Freeman and Company, 2nd edition, 1985. [Rue89] Pau l Ruest. A n Evaluation of Tension within an Extensible Spline Testing Facil i ty. Master's thesis, University of Waterloo, 1989. [Shn91] Ben Shneiderman. A Taxonomy and Rule Base for the Selection of Interac-tion Styles. In B . Shackel and S. J . Richardson, editors, Human Factors for Informatics Usability, chapter 14, pages 325-342. Cambridge University Press, Cambridge, 1991. [SS88] Lorenzo Sciavicco and Bruno Siciliano. A Solution Algor i thm to the Inverse Kinemat ic Problem for Redundant Manipulators. IEEE Journal of Robotics and Automation, 4(4):403-410, August 1988. [WC91] L i - C h u n Tommy Wang and C h i h Cheng Chen. A Combined Opt imizat ion Method for Solving the Inverse Kinematics Problem of Mechanical Manipu-lators. IEEE Transactions on Robotics and Automation, 7(4):489-499, August 1991. [ZB89] J ianmin Zhao and Norman I. Badler. Real T ime Inverse Kinematics W i t h Joint L imi t s and Spatial Constraints. Department of Computer and Information Science MS-CIS-89-09, University of Pennsylvania, January 1989. 65 Appendix A Subject Background Information In this table, the names of the subjects have been replaced by subject numbers. The numbers do not reflect the sequence in which subjects d id the experiment; rather, subjects were grouped by the first of the three methods used. 66 Appendix A. Subject Background Information No. Program Gender Age Hand Mouse A n i m . I K 1 B A S c N M F 18 R E Mi) N 2 — M 28 R E M 2 ) N 3 B A S c E E M 20 R M N N 4 BSc CS M 21 L M M 3 ) N 5 BSc N M M 18 R E E ( 4 ) N 6 BSc CS F 25 R M N H 7 M S c CS M 25 R E L ( 5 ) N 8 BSc C S F 18 R L N N 9 BSc N M M 28 R M N N 10 BSc N M F 21 R M M 6 ) N 11 P h D CS M 31 R E N H 12 BSc CS M 18 R M M7) N 13 BSc CS/Phys ics M 22 R E M8) H 14 BSc N M M 19 R E M (9) H 15 BSc N M F 19 R M N N 16 P h D Physiology M 25 R M M (10) H 17 BSc N M F 18 R E N N 18 BSc CS M 19 R E M (11) N 19 BSc N M F 18 R L N N 20 P h D CS M 31 R E N H 21 BSc Bio M 22 R E E ( 1 2 ) N 22 M S c CS M 22 R E N N 23 BSc Physics M 19 R E L ( 1 3 ) H 24 M S c MIS F 33 R E N N 25 BSc CS M 20 R E L ( 1 4 ) N 26 BSc CS F 20 R M N N 27 BSc CS M 18 R E E ( 1 5 ) N 28 BSc C S F 26 R E N N 29 B A S c E E M 18 R M L ( 1 6 ) N 30 M S c CS F 26 R E N N Appendix A. Subject Background Information 68 • Program — a combination of a program and a department (for students only) — Program B A S c Bachelor of Appl ied Science (Engineering) BSc Bachelor of Science M S c Master of Science P h D Doctor of Philosophy — Department Bio Biology C S Computer Science E E Electrical Engineering M I S Management Information Systems N M no major (students who do not yet have a declared major) • Gender M Male F Female • Hand — predominant hand used L Left-handed R Right-handed • Mouse — experience using a mouse N None L L imi ted M Moderate E Extensive Appendix A. Subject Background Information 69 • A n i m . — experience using animation software N None L L imi ted M Moderate E Extensive • Animat ion software used (names are as provided by subjects) 1. Mar io Paint 2. P C based package (subject forgot name) 3. Sprite Wor ld 4. Animator , Animator Pro, DPaint , 3D Studio and others 5. Al ias , Wavefront 6. L ion K i n g Screen Saver 7. has written animation software 8. Al ias Sketch, Stratavision 3D 9. Lightwave 3D, 3D Studio 10. Al ias , Wavefront, Vertigo 11. has programmed animations 12. Disney Animat ion Studio, Deluxe Paint, Light Wave, Imagine 13. Autodesk Animator 14. Apple l i e program (subject forgot name) 15. Autodesk Animator , A A P r o , Autodesk 3D-studio, shareware programs 16. a Windows drawing package (subject forgot name) • I K — familiarity with inverse kinematics N Never heard of it H Have some idea about it K Know all about it Appendix A. Subject Background Information 70 Notes: For I K familiarity, subject 6 put in know what it is". This was recorded Subject 28 writes wi th her left hand the extra field "Heard of it, but don't really as "have some idea about i t" . and uses the mouse wi th her right hand. Appendix B Sample Forms The following forms were filled out by each subject who participated in the experiment. The "Consent Form" and "Subject Information Form" were filled out by the subject at the beginning of his/her first session. The first "Comments Form" was filled out by the subject after completing the trials using his/her first method (the only method used in his/her first session). The second "Comments Form" was filled out by the subject midway through the second session, after completing his/her second method (the first method used in his/her second session). The third and final "Comments Form" was filled out by the subject at the end of his/her second session after completing his/her th i rd method. The version of the last "Comments Form" given to the subjects was printed double-sided on one page. 71 Appendix B. Sample Forms 72 Inverse Kinematic Chain Matching Experiment Consent Form I agree to participate in the study entitled Inverse Kinematic Chain Matching Experiment being conducted by the Imager Laboratory of the Department of Computer Science at the University of Br i t i sh Columbia. I understand that the data gathered by the computer program wi l l only be seen by the researchers. The results which wi l l be summarized in the experiment supervisor's Master's thesis w i l l be stripped of al l identifying codes. I understand that my participation is voluntary and that I may withdraw from the study at any time. Signature: Date: Appendix B. Sample Forms 73 Inverse Kinematic Chain Matching Experiment Subject Information Form Please provide the information requested below. This information wi l l be held in strict confidence by the researchers. Name: .— • Program and department (if student): . Sex: Current Age: Are you primari ly left-handed or right-handed? Indicate your experience using a mouse: none l imited moderate extensive Indicate your experience using animation software: none l imited moderate extensive List any animation software that you have used: Indicate your familiarity wi th inverse kinematics: never heard of it have some idea about it know all about it Appendix B. Sample Forms 74 Inverse Kinematic Chain Matching Experiment Comments Form Please complete this form after using the first method. Name: How many of the different sample trials did you try? What specific strategy did you use in moving links to achieve a match? What criteria did you use in rating your satisfaction with each match? (i. e. accuracy of match, time taken, difficulty, etc. ) Please list any problems with or comments on the tutorial. Please list any other problems with or comments about this session. Thank you. Please verify the time and date for your next session. Appendix B. Sample Forms 75 Inverse Kinematic Chain Matching Experiment Comments Form Please complete this form after using the second method. Name: D i d you review the tutorial instructions? How many of the different sample trials did you try? What specific strategy did you use in moving links to achieve a match? (indicate any differences in strategy from last time) What criteria did you use in rating your satisfaction wi th each match? (i. e. accuracy of match, time taken, difficulty, same as last t ime etc. ) D i d you find it easier to manipulate the chains with this method or the last one? Why? Do you think that you were more successful with your matches this t ime or last time? W h i c h time did you prefer? Please list any other comments about or problems with this session. Appendix B. Sample Forms 76 Inverse Kinematic Chain Matching Experiment Comments Form Please complete this form after using the final method. Name: D i d you review the tutorial instructions? How many of the different sample trials did you try? What specific strategy did you use in moving links to achieve a match? (indicate any differences in strategy from the previous times) What criteria did you use in rating your satisfaction wi th each match? (i. e. accuracy of match, time taken, difficulty, same as previous etc. ) D i d you find it easier to manipulate the chains with this method, the first method or the second one? Why? Do you think that you were more successful with your matches using this method, the first method or the second method? (please rank the 3 methods) (please turn over) Appendix B. Sample Forms W h i c h time did you prefer? (please rank the 3 methods) 77 Please list any other comments about or problems with this session. Thank you very much for participating in the study. Appendix C Chain Configurations During the experiment, al l of the chains were displayed wi th the inherent root at the same point on the screen. This in i t ia l inherent root position was centred horizontally on the monitor and was near the top of the screen. O n the screen, goal chains were displayed in yellow and user manipulated chains were displayed in alternating light and dark blue links wi th the joints drawn on top in white. These chains were displayed against a black background. In this appendix, goal chains are drawn in a 50 percent gray level. The links of the user manipulated chains are drawn in alternating light and dark gray and the joints have been outlined in black. The tables in this appendix contain the angles for the in i t ia l and goal configurations for the chains used in the three sample trials (in the tutorial) and the 15 experiment trials. A l l of the values for the angles are in degrees and represent the z rotation of the corresponding joint. The angles are expressed relative to the rotation of the previous joint and thus are cumulative. The joints have been numbered with the inherent root of each chain being joint number 1. For chains wi th branches, joint numbers are reused in this numbering to indicate the branching points. The repeated joint number is the joint at which a branch occurs. The first value for that number and al l values for increasing joint numbers unti l the repeated joint number occurs again are the values for the "left" branch. The second value for the repeated joint number and al l values following it are values for the "right" branch. 78 Appendix C. Chain Configurations 79 O Figure C . l : Sample Trial #1 Joint 1 2 3 Init ial 0.0 0.0 0.0 Goa l 30.0 30.0 30.0 Table C . l : Sample Trial #1 Appendix C. Chain Configurations Figure C.2: Sample Trial #2 Joint 1 2 3 3 Init ial -15.0 15.0 -90.0 45.0 Goa l 0.0 0.0 -90.0 90.0 Table C.2: Sample Trial #2 Appendix C. Chain Configurations Figure C.3: Sample Trial #3 Joint 1 2 3 4 5 6 7 5 6 Init ial 0.0 0.0 0.0 0.0 -60.0 0.0 0.0 60.0 0.0 Goal 15.0 45.0 -15.0 30.0 -30.0 15.0 15.0 45.0 -30.0 Table C.3: Sample Trial #3 Appendix C. Chain Configurations Figure C.4: Experiment Trial #1 Joint 1 2 3 4 5 6 7 8 9 Init ial 10.0 -10.0 -10.0 -10.0 -5.0 5.0 10.0 10.0 10.0 Goa l 20.0 -10.0 -10.0 -10.0 -5.0 5.0 10.0 10.0 10.0 Table C.4: Experiment Trial #1 Appendix C. Chain Configurations O Figure C.5: Experiment Trial #2 Joint 1 2 3 4 5 6 Init ial 0.0 0.0 0.0 0.0 0.0 0.0 Goa l 5.0 5.0 5.0 5.0 5.0 5.0 Table C.5: Experiment Trial #2 Appendix C. Chain Configurations Figure C.6: Experiment Trial #3 Joint 1 2 3 4 5 Init ial -10.0 -10.0 -10.0 -10.0 -10.0 Goal 5.0 10.0 15.0 20.0 25.0 Table C.6: Experiment Trial #3 Appendix C. Chain Configurations o Figure C.7: Experiment Trial #4 Joint 1 2 3 4 5 6 7 8 9 Init ial 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Goa l 10.0 -10.0 -10.0 -10.0 -5.0 5.0 10.0 10.0 10.0 Table C.7: Experiment Trial #4 Appendix C. Chain Configurations Figure C.8: Experiment Trial #5 Joint 1 2 3 4 5 6 7 8 9 Init ial 10.0 -10.0 -10.0 -10.0 -5.0 5.0 10.0 10.0 10.0 Goa l 30.0 -20.0 -20.0 -20.0 -15.0 15.0 20.0 20.0 20.0 Table C.8: Experiment Trial #5 Appendix C. Chain Configurations 87 Figure C.9: Experiment Trial #6 Joint 1 2 3 4 5 6 7 8 9 10 Init ial 60.0 -120.0 120.0 -120.0 120.0 -120.0 120.0 -120.0 120.0 -120.0 Goal 45.0 -90.0 90.0 -90.0 90.0 -90.0 90.0 -90.0 90.0 -90.0 Table C.9: Experiment Trial #6 Appendix C. Chain Configurations 88 Figure C.10: Experiment Trial #7 Joint 1 2 3 4 5 6 7 8 9 10 Init ial 60.0 -120.0 120.0 -120.0 120.0 -120.0 120.0 -120.0 120.0 -120.0 Goa l 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Table C.10: Experiment Trial #7 Appendix C. Chain Configurations 89 Figure C . l l : Experiment Trial #8 Joint 1 2 3 4 5 6 7 8 9 Init ial 10.0 -10.0 -10.0 -10.0 -5.0 5.0 10.0 10.0 10.0 Goa l 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Table C . l l : Experiment Trial #8 Appendix C. Chain Configurations 90 Figure C.12: Experiment Trial #9 Joint 1 2 3 4 5 6 7 8 9 10 Init ial 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Goa l 60.0 -120.0 120.0 -120.0 120.0 -120.0 120.0 -120.0 120.0 -120.0 Table C.12: Experiment Trial #9 Appendix C. Chain Configurations 91 P Figure C.13: Experiment Trial #10 Joint 1 2 3 4 5 6 7 5 6 Init ial 15.0 45.0 -15.0 0.0 -30.0 15.0 15.0 45.0 -30.0 Goal 0.0 0.0 0.0 30.0 -60.0 0.0 0.0 60.0 0.0 Table C.13: Experiment Trial #10 Appendix C. Chain Configurations Figure C.14: Experiment Trial #11 Joint 1 2 3 4 5 6 Init ial 5.0 5.0 5.0 5.0 5.0 5.0 Goa l 0.0 0.0 0.0 0.0 0.0 0.0 Table C.14: Experiment Trial #11 Appendix C. Chain Configurations 93 Figure C.15: Experiment Trial #12 Joint 1 2 3 4 5 6 7 8 9 10 Init ial 45.0 -90.0 90.0 -90.0 90.0 -90.0 90.0 -90.0 90.0 -90.0 Goa l 60.0 -120.0 120.0 -120.0 120.0 -120.0 120.0 -120.0 120.0 -120.0 Table C.15: Experiment Trial #12 Appendix C Chain Configurations 94 Figure C.16: Experiment Trial #13 Joint 1 2 3 4 5 3 4 5 Init ial 0.0 0.0 -30.0 30.0 -90.0 35.0 -30.0 -85.0 Goa l 15.0 -20.0 -45.0 25.0 -90.0 -7.5 55.0 -125.0 Table C.16: Experiment Trial #13 Appendix C. Chain Configurations Figure C.17: Experiment Trial #14 Joint 1 2 3 4 5 3 4 5 Init ial 15.0 -20.0 -45.0 25.0 -90.0 -7.5 55.0 -125.0 Goal 20.0 -20.0 -40.0 40.0 -85.0 -7.5 70.0 -130.0 Table C.17: Experiment Trial #14 Appendix C. Chain Configurations Figure C.18: Experiment Trial #15 Joint 1 2 3 4 5 3 4 5 Init ial 20.0 -20.0 -40.0 40.0 -85.0 -5.0 70.0 -130.0 Goa l 20.0 -20.0 -30.0 45.0 -100.0 -10.0 100.0 -120.0 Table C.18: Experiment Trial #15 Appendix D Tutorial Pages The following pages are printouts of the IRIS Showcase tutorial that subjects went through before doing the experiment trials. The pages have been reduced and turned sideways in order to fit on the page. The pages in the actual tutorial are displayed in landscape mode and fill the entire screen. The first nine pages of this appendix form the ini t ia l tutorial that each subject sees. The last page of this appendix is from the version of the tutorial that the subject sees before doing the set of experiment trials for the second and third times. Only the first page of text from this version of the tutorial is included as al l of the other pages are identical to those in the in i t ia l tutorial. 97 Appendix D. Tutorial Pages 98 ft r 1 u © •c o w J3 3 O o — O o -I—» X) to t/5 O CU X! •4—» CD Appendix D. Tutorial Pages oo o cD W) cd CM S O u CD - f l H cd d g cd X) cd a 0 as • cT fl l-H Cvj *-! 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O CD co fl cD co Id cD > cd -fl fl O 3 CD -S 'H-H CD OH X CD Appendix D. Tutorial Pages CO M—i o <N 03 CU H •a * c o o ^ G H o3 " 03 a G3 03 <3 O * IS 5 2H £ 03 03 G ca • ~ - • — £ I • o on £5 G W> "—"H • — s o * H l»U> 03 Q 3 G 03 03 ^3 a d 03 •G O 8 ^ »H G s ° d 4g i ° | I i t s .22 -s -g •d £ < ^  I J f l ft •4—> . T - H 4) C OTj e3 2 a 03 O bfj -G O 03 w X H H Q ^ > - 4 ^ • *•»> -4-J G 09 cD G pd OO O G H o D -" 00 £ 9> O -G — +-> II 0 0 60 • — Is .G ft I 03 G O 03 •G o 13 bD 0 0 -4 - J 0> G ft Jd 2 G O •5 03 ^ .S ^ § 3 cU on O -G ^ , *- G ^ C G 'I -S3 <g ft (O 0 < S "8 . l a g 8 Appendix D. Tutorial Pages oo M-t o CO CD W> cd 0-C8 u DX fl O B c M •~> • •—i a I l-H g IS — J c Q O CD cd O >» $> • l - H 42 m o ' E H C cd B M C • l - H o • - H CO 0) 42 •»—> td ID CD 42 c co CD co O CD CD o a — as c - —< £i o co -rt C -2 o 3 00 a II co o I £ £ 2 22 • • CD S £ CD -G M ^ ^ 4 5 VH O O f t • >-> o C • i - H o O H +-> o > • l - H O H TD CD •H-> o U U H T3 CD — CD 42 G O CO' CD 42 fl - ° CD <L> -fl co fl T3 S CD O cd C c 3 CO S — o * a i a .2 c c o H—I o o > H & . •S « ^ - c CD CD -O o co *— O CD CO' fl O £ CD 43 fl 5J 2 T3 CD p 42 CD +-> co o £ CD 42 CD O H & 2 £ ^  C CD 3 43 C • i - H o CD co cd ^5 CD ^ 3 z .O co r> co 2a & H—I G • " - H fTt cd fl C z cd — -o -2 CD cd ~ r - J CD O H O -H Cd O 44 o CD S ft ^ i-H o CD O H cd & G > O H CD 42 co cd T3 CD -i—> CJ CD CD *•» CO c « X i +H CD § co 2 O H o CD - f l c 'cd 42 O cd CO CD td CO fl cd 43 O o 42 CD • — fl +—> CD • i - H O H * J H O H Appendix D. Tutorial Pages 102 oo o CD cd c O fl U fl WD G V o s o — » — c 44 o 0 1 o a o 'cc-aG 2| -t—> d o — C r-c z c T3 co C _o O co 5 O co -rt fl O a> 5 •s l 6 3 co o i& Cj i "— 3 2} co £ — o „^ 43 3 3 •8 S OH O 33 X5 73 CD s-• l-H CO CD 73 CD fl B o z c o • l-H H—> CJ CO' =3 o >> CD •a a o H o o •*-» a c £ cd CD co O O fl U cd CD g •l-H o CD * - • •i-H fl CD fl -t—> o § &i ° 3 -(-» 43 C CD O co * 2 o Q 2 a CD «M CD CD «3 fl « O -5 CD > O 73 CD S-H a CD a > 2 ° a . & P C 5 cd 3 fl A CD U CD fl 4-> c Q O O H c o CD CO' fl o a 73 CD > CJ CD CD co JD fl CD •>-> •S CD ^ CO <+H cd O J D CD 13 -^H )-H 73 r I 1 a o CD ° < flj C • o c 'fl ^ cd CD O H O H ' A O H § 3 cd fl 3 CD O H co *fl ,H cd CD CD - H co fl 73 ° I I fl «-H CD A ' - 1 — H . O H ^3 ^ CD " S 9 S3 c ^ •fl +-> c 73 © 2H * CD 73 fl fl CO co CD l-H O H > c > CD II 3 fl CT 73 0 8 cd $ .2 Cd -4—> CD fl CD fl O O H H—> o > +3 O H O cd CD > cd cd fl o I g fl fl CD To § a 2 3 a £ I 9 c fl - I - 1 O H O CD 5 g CO .^ H «» § 1 7 3 ' f l 3 O H CD " f l in S CD ej co C C ^ o Z Cd o 3? a -O H H •fl CD CD fl CO fl CJ C cd t-H fl •a -2 fl CD CD fl cd 5 3 co fl CD O H—> =^ " f l H—> 'i-H co o fl • CD 0 0 fl CD 1 "9 CJ s •i-H TO O H ^ 2 -a H O H CN Appendix D. Tutorial Pages 103 oo o i n CD OX) cd O H G o CD 03 u WD d O c3 O O O H d o CD "5 oo c3 G -d 9 CD cd 3 a tuo CD d -d b -g ! • -H 13 CD tH o 0) CD o O T J "3 CD .a ^  O ^ -d CO > O a o Si •i-H •d d o -4—» -4-J d Xi co o d o CD oo d CD CD SH bfj ! - H o oo )H d o CD oo d o d 03 CD CD -Goo CD > O d o a I I © ^ d A 03 Xi o CD -G o £ -l-> CD .a d 03 d - G g CD P, -d Id I o ft d o • i-H G o3 _ i "-H T3 d CD EL <^  a ~ a s CD £ s " ft CD 00 » * d CD S £ CD ° Z 8 ^ M-H § ° O oo ^ tH + H CD ° -d •S ° ft = +e CD CD 2 xi -d G3 d d rd CD o v r* "-i. 00 ~ £ .a «.a o x ^ ft -4—> CD ft £ X> CD +-> CD ^ -g a H ^ ^ 03 O tfl ^ _ H 4 O ^ .3 CD G CD CD 03 03 03 xi CD CD T3 G CD G 03 U M ^ tH CD •d d M © d •tH .2 CD d o 00 M G M-H > O > •4—1 oo c3 CD -d s>a o3 G « .2 •tH td cd p c a G CD ft G O cd • G O CD Xi G •tH o —> CD a cd 00 CD tG -4—> d o CD cd CD txQ Xi d /-i t-2 ^ 03 -4-H 73 • § G CD O CD &0 ft CD ^ d £ o -d -S 40 d ^ ft «-> . J H tH cd G CD cd td G cd o CD tH O oo CD CD ft >H *g ^ CD Cd cd ft CD 00 CD d o ft d o • tH -4-H cd ft • tH CD • G O CD ft > ^ 2 > G ft O CD d -d = H •H o -d d cd O ft •4-» o > •tH ft •4-> d CD tH .CD T3 cd CD 00 O O td CD cd Xi CD CD «+H 0 1 ft d S H—I cd \d cd § d U-/ U> /-v ^ — . i-H W •s § ^  a a g»-a^ ^  2 a CD C 50 •*-« ca p ft o cd - ^ D oA " J G o Q I I CO Appendix D. Tutorial Pages 104 oo <4-H o CD Ofj cd fl O CD fl cd p f l U CD fl © CD O c o C fl 2 ^  CD CD fl 5 fl O CD 2 CD - f l —^< CD CO cd CD 13 S H O 73 fl cd C CD CD * H O co fl O •fl 2 * cd -fl o CD -fl Ofj c • I-H -t-> co fl cd 73 CD -fl co CD fl O fl CD C H > o ^ Id H-I CD O co a I o & -l-> " O eS CD I i S H o co S H fl CD CD co fl O ~ H 3^ »- 13 CD 4D X! cd O Q i—H ^ CD fl CO _Q — i CD CD co s § -§ a co a s & S CD •fl -fl 73 "±3 G _fl a £ - fi fl o o ~ S fl x t * £ -fl =3 -fl c^  o CD O 13 CD 73 > s O cd fl fl o - f l CO 2 H ^ fl CD CD ^ CD £ fl Ofj 8 CD a 43 -fl CD <]j -f l CD CD 5 td Cd S H S H fl CD CD cd fl O cd, 5 rd 0 O ; 50 CD o CD 3 fl C CD cd in Appendix D. Tutorial Pages 105 oo O r--CD cd ft CD CD Cd B cd CA CD CA CD 45 3 O >x $3 CD 43 O CD 73 J3 cd cd O oi o o o . cd cA CD & & Q. cd a -§ ft CA 23 -xi 43 CD CD ^ ^ CD O 5 / 2 CA •*-> O o - a a -9 % • H O cd •<—> ~ 43 H—( CD o o a CD CA '3 - p v-i cd CD "t3 ^ CD •rj CA 73 ^ 3 ft > <b . bfj O w> a ^ +H 43 CD ° £ & o OJO CU a c 53 CD a • c CD ft X PH CA a CD U • i - H CD O ft COCD CA cd o CA CD O o 43 -t-> O 43 <-> cd 53 - CD 53 T3 73 3 • rH cd * CD +-» CD > x 53 cd a ft S o CA 43 53 O 43 \S o 4H td a ft •i—i 53 cd cd bfj a 53 CD '> 43 CD • T - H -<—> 43 73 CD 53 cd cd H - H •*-> o 53 • i—i O cd ft OAT ent ft • T—< CD CD 43 -i—> H - H CD .y a S""! cd r ) co ° C N O _ k> ft xi V w «o C cfj *•» cd CD ft 0 o 5/J u. 4 £ c o Appendix D. Tutorial Pages 106 oo H-H O OO CD OD cd P H cd fl -t—< CD cd CD -4—> CD OH a o CD O •>-> CD 441 O •i-H I D X> 'fl o 4fl X ^fl -i-H CO f CO a o OH fl o • I-H CO co CD co fl ^ r < ~ £ 'to S" •i-H CD 4-H co 43 co co O CO cd CD Q OH <=j 3 S co 43 co CD fl CD a •i-H SH CD OH X CD co co 13 "C cD 4H +^ ' O H O a ^ cd oD «J fl »\ 2 >^  43 SH 4-» SHI 43 CD t3 SH •r1 cd fl o fl CD O 43 co -*-> 44 CO cd 73 CD 4fl _ .2 fd fl 43 • fl <-> ^ SH CD CD sf fl CD ^ CD td * CD SH <3 £ 1 IS" CD 'C CD "fl CD 73 ^ OH ^ ~ X TH fl W O CD CO ^ K*~» _ • i H ^ V SH > rS CD cd 43 O 43 CO cd CD 43 fl O SH £ CD fl o CD CD C o o CD CD OH X CD ^ 4fl rn fl o CD C CD •s * 5 cd O C CD fl O 0) C CO *•» cd " P o. 4= ^ 44 ^ CD w vD 00 :^ a; cd CD Appendix D. Tutorial Pages 107 oo H-t o CD Cd CM CU TH 3 co O C3 CD 43 CD td »H 3 CD CD cd C/3 cd 73 CD co 3 O OH co CD TH 73 3 cd CO cd CD « 6 co cd s—i CD CD J H 43 H= S co O cd co 4 H CD ^ IT! a" 73 C O C O cd a co 'Jd .5 -d cd O . 43 H-H O O H-H H-> O CD co H—> CD CD C O ^ CD ~ cd CD 73 CD -*n 3 CD co CD * H ^ OH O CD ^ rt o co *x3 3 cd cd O 3 OH • T-H 53 cd s 43 CD td > O ~ CD O 43 H-H .2 £ £ CD CD 43 3 OH „ a ^ ° £ CD * 43 ^ H-H M £ TH CD - O cd O W ) __r CD "C3 43 $3 * cd ^3 73 $3 .cd cd .9 -9 o 43 ^ P O > • • T-H CD OH C O 3 CD O 43 CD 3 ^ -2 O OH C O H-H 3 ° CD co S *g > <s O CD 53 CD O £ 0,43 .2 3 -3 0 cd > ^ § 3 ^ 3 HH CD - 3 O CD T-H CD 43 44 O •T-H u 73 3 ' O OH H—> O > 'SH CD 43 H-H 44 CD 'EH O H—> O 43 CD '> CD T-H 0 H—> CD 44 • i—j 2 0 3 0 re. H-H 73 4 H 13 T-H o CD 13 CD ^ 43 CD • i-H > CD T-H 44 CD 3 O & „ 3 • -° = CD 73 *B 13 o Cd CD CD TO H-H 4 H CD O 13 -o 3 o H-H H-H 3 43 CD 43 H-H 3 O 44 CD CD C O Id • I-H H= CD t cd C O CD HS O "co H—> T-H . cd •>-> - J H T—H TH H-H H-H o CD CD S H ' — 1 43 ft O cd OX) co O Q C 3 0 ^ cd CD CM 5 Jd ^ 4 * 4* S-} O Cd U O O co «*0 7 3 O I k> 3 4^: 0 5 _ O H2 Appendix E Experiment Data The following tables summarize the results of al l of the trials for subjects 1 through 27. The Type column classifies the tr ial . A value of "Unchanged" indicates that the positional error value at the end of the t r ia l was below the cutoff threshold and that this was the first time in the t r ia l that the positional error value went below the threshold value for that t r ia l . A tr ia l wi th types of "F ina l " , "Cutoff" and "Difference" was affected by the thresholding. The "F ina l" line displays the values at the end of the t r ia l and the "Cutoff" line displays the values corresponding to the first time that the positional error was below the threshold value. The "Difference" line displays the differences between the "F ina l" data line and the "Cutoff" data line. A tr ia l wi th a type of "Outlier" never had a positional error that was below the threshold value. The times have been converted to seconds. The values for the angle error metric and the positional error metric have been rounded to 5 decimal places. These values have also been expressed as a percentage of the ini t ia l errors of the t r ia l . The percentages have been rounded to 2 decimal places. The R and E columns indicate the number of roots and end-effectors that were chosen by the subject during the tr ial . For trials that were affected by the thresholding, the "F ina l" line displays the total number of roots and end-effectors chosen during the tr ial and the "Cutoff" line displays the number of roots and end-effectors chosen to the point at which the t r ia l was cutoff by the thresholding process. The "Difference" line indicates the number of root and end-effector choices that were made after the threshold value for the t r ia l was obtained. The data in the column labelled " A v g . Dist . " is the average distance between roots and end-effectors in a t r ia l . These values have been rounded to two decimal places. For trials that were affected by thresholding, the value in the "Cutoff" line is the average distance value for roots and end-effectors that were chosen before the threshold was reached. The value in the "Difference" line is the difference between the average distance for the entire t r ia l and the average distance for the tr ial unti l the threshold was reached. 108 Appendix E. Experiment Data 109 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Final 32.46141 10.47716 10.48 3.71389 2.41 3 5 2.20 Almost Perfect 1 Cutoff 8.67849 0.05693 0.06 3.67499 2.39 1 1 1.00 -1 Difference 23.78292 10.42023 10.42 0.03890 0.02 2 4 1.20 -2 Unchanged 27.22965 12.34629 8.23 1.31819 1.36 9 9 1.00 Almost Perfect 3 Unchanged 25.65794 1.13614 0.03 0.59380 0.26 5 5 1.00 Almost Perfect 4 Unchanged 31.03388 99.68097 13.29 3.72107 2.90 9 10 1.00 Perfect Match 5 Unchanged 60.70439 233.17042 19.43 5.55036 6.29 12 18 0.05 Almost Perfect 6 Unchanged 134.12319 134.19186 1.61 9.01849 3.92 28 44 1.36 Almost Perfect 7 Unchanged 63.09027 39.03083 0.03 4.93381 0.86 12 29 2.14 Almost Perfect 8 Unchanged 29.05134 84.82028 11.31 3.73818 2.92 11 10 0.90 Pretty Good 9 Unchanged 45.48078 22.55190 0.02 5.59596 0.98 10 12 1.00 Perfect Match 10 Unchanged 39.27485 63.10144 1.08 7.24810 1.65 9 13 1.62 Perfect Match 11 Unchanged 15.89195 59.08469 39.39 2.52619 2.60 6 6 1.00 Perfect Match 12 Unchanged 52.89593 37.99235 0.46 6.64471 2.89 14 16 1.13 Almost Perfect 13 Unchanged 37.07067 18.72409 0.16 3.65993 5.74 10 13 1.31 Perfect Match 14 Unchanged 21.89706 62.03894 11.28 5.09099 7.08 10 6 0.67 Pretty Good 15 Unchanged 28.77967 14.75073 1.07 2.13058 5.54 9 8 1.13 Almost Perfect Table E . l : Subject 1 1st method (Jacobian) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 7.89846 0.24382 0.24 7.60518 4.94 1 1 1.00 Pretty Good 2 Unchanged 14.73939 34.57385 23.05 1.81469 1.87 6 7 1.00 Almost Perfect 3 Unchanged 21.14531 7.10196 0.21 1.67985 0.74 5 8 1.00 Perfect Match 4 Unchanged 29.42879 4.54204 0.61 1.06644 0.83 11 11 1.00 Perfect Match 5 Unchanged 34.54551 33.01946 2.75 2.03653 2.31 11 12 1.00 Perfect Match 6 Unchanged 54.68250 8.26426 0.10 2.28111 0.99 9 13 1.38 Almost Perfect 7 Unchanged 81.12456 23.26788 0.02 1.77342 0.31 18 42 1.76 Almost Perfect 8 Unchanged 31.10214 10.83309 1.44 2.86125 2.23 9 13 1.00 Perfect Match 9 Unchanged 50.91993 36.82016 0.03 5.40862 0.95 14 14 1.00 Perfect Match 10 Unchanged 27.07207 28.32816 0.48 3.71335 0.85 9 9 1.22 Almost Perfect 11 Unchanged 23.86703 5.73250 3.82 1.16762 1.20 9 13 1.00 Perfect Match 12 Unchanged 32.36632 57.44891 0.69 4.94886 2.15 10 10 1.00 Perfect Match 13 Unchanged 39.70560 84.00989 0.73 4.58422 7.19 9 21 2.23 Almost Perfect 14 Unchanged 24.26036 17.25434 3.14 2.92935 4.08 9 10 0.70 Perfect Match 15 Unchanged 39.13060 19.65193 1.43 3.38639 8.80 11 27 1.59 Perfect Match Table E.2: Subject 1 2nd method (CCD) Appendix E. Experiment Data 110 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 6.17678 0.02712 0.03 2.53644 1.65 1 1 1.00 Almost Perfect 2 Unchanged 16.19692 10.16335 6.78 0.96982 1.00 6 6 1.00 Perfect Match 3 Unchanged 16.63694 8.34125 0.25 0.80502 0.36 5 5 1.00 Almost Perfect 4 Unchanged 26.25458 40.86652 5.45 2.36035 1.84 13 10 1.00 Perfect Match 5 Unchanged 23.48704 31.18840 2.60 1.50304 1.70 9 10 1.00 Perfect Match 6 Unchanged 39.81563 42.40014 0.51 3.92678 1.71 10 14 2.36 Perfect Match 7 Unchanged 43.18811 29.07081 0.02 2.53973 0.44 12 15 1.67 Perfect Match 8 Unchanged 22.47867 56.03222 7.47 2.11711 1.65 9 9 1.00 Almost Perfect 9 Unchanged 33.54547 12.01706 0.01 3.72825 0.65 12 13 1.00 Perfect Match 10 Unchanged 30.61959 26.07167 0.45 2.39043 0.54 11 12 1.33 Almost Perfect 11 Unchanged 11.00933 46.94238 31.29 1.93714 1.99 5 5 1.00 Almost Perfect 12 Unchanged 25.71704 20.47196 0.25 5.76228 2.51 10 10 1.00 Almost Perfect 13 Unchanged 24.41784 42.65621 0.37 2.64828 4.16 5 8 1.25 Almost Perfect 14 Unchanged 23.98783 1.51355 0.28 1.61532 2.25 8 7 0.86 Perfect Match 15 Unchanged 26.40119 7.65879 0.56 1.69836 4.42 12 9 0.22 Perfect Match Table E.3: Subject 1 3rd method (1DOF) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 40.19399 22.13714 22.14 4.03058 2.62 10 14 1.36 Perfect Match 2 Unchanged 19.48781 18.57525 12.38 2.29315 2.36 6 6 1.00 Perfect Match 3 Unchanged 27.70128 10.32920 0.31 1.57104 0.70 7 7 1.00 Perfect Match 4 Unchanged 40.42898 21.31876 2.84 1.85195 1.45 11 11 1.00 Perfect Match 5 Unchanged 33.58221 36.28994 3.02 2.16679 2.46 9 10 1.00 Perfect Match 6 Unchanged 56.68924 7.06718 0.08 3.46361 1.51 12 17 1.53 Perfect Match 7 Unchanged 73.04369 35.41966 0.03 4.64187 0.81 14 17 1.94 Almost Perfect 8 Unchanged 33.45556 14.72688 1.96 10.23946 7.99 11 12 0.83 Perfect Match 9 Unchanged 63.11602 72.41050 0.05 7.29125 1.28 15 14 1.43 Almost Perfect 10 Unchanged 38.59480 19.01146 0.32 4.10599 0.93 9 13 0.92 Perfect Match 11 Unchanged 23.24288 36.43952 24.29 1.48179 1.53 6 6 1.00 Perfect Match 12 Unchanged 37.28228 64.80186 0.78 8.74529 3.80 10 14 1.00 Almost Perfect 13 Unchanged 33.07638 57.01338 0.50 4.05890 6.37 9 8 0.88 Almost Perfect 14 Unchanged 15.37027 114.95462 20.90 5.28875 7.36 3 4 1.25 Almost Perfect 15 Unchanged 35.42641 116.26361 8.46 6.37049 16.56 8 8 0.75 Perfect Match Table E.4: Subject 2 1st method (Jacobian) Appendix E. Experiment Data 111 Time Angle Pos. Avg. Trial Type (seconds) Error % . Error % R E Dist. Rating 1 Unchanged 6.54428 0.00607 0.01 1.20008 0.78 1 2 1.00 Perfect Match 2 Unchanged 8.22597 0.51034 0.34 1.11566 1.15 1 1 6.00 Perfect Match 3 Unchanged 11.43937 108.68795 3.22 4.27469 1.89 1 1 5.00 Almost Perfect 4 Unchanged 20.31951 131.44102 17.53 5.12024 4.00 3 4 4.25 Almost Perfect 5 Unchanged 43.38322 63.50136 5.29 4.51580 5.12 8 13 1.69 Perfect Match 6 Unchanged 41.10735 30.04922 0.36 6.19645 2.70 8 10 2.30 Perfect Match 7 Unchanged 48.71166 173.52420 0.13 4.76389 0.83 10 13 2.00 Perfect Match 8 Unchanged 20.64533 21.94130 2.93 2.79090 2.18 9 9 1.00 Perfect Match 9 Unchanged 38.84565 95.20087 0.07 10.14635 1.78 10 12 1.58 Perfect Match 10 Unchanged 34.66310 9.73437 0.17 4.13860 0.94 7 11 1.27 Perfect Match 11 Unchanged 18.16614 4.86940 3.25 0.95866 0.99 4 7 2.14 Perfect Match 12 Unchanged 35.17976 62.42075 0.75 8.12902 3.54 10 12 1.00 Perfect Match 13 Unchanged 31.41971 270.13791 2.35 7.02343 11.02 7 8 2.25 Almost Perfect 14 Unchanged 23.71289 106.17661 19.30 5.33977 7.43 4 8 2.00 Perfect Match 15 Unchanged 24.99709 90.77515 6.60 7.13586 18.55 6 8 0.50 Perfect Match Table E.5: Subject 2 2nd method (CCD) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 15.88778 24.67226 24.67 4.34398 2.82 3 3 1.00 Perfect Match 2 Unchanged 16.48612 12.77827 8.52 1.17829 1.21 6 6 1.00 Perfect Match 3 Unchanged 14.80276 5.36807 0.16 1.91661 0.85 5 5 1.00 Perfect Match 4 Unchanged 23.23042 58.89884 7.85 3.29121 2.57 9 9 1.00 Perfect Match 5 Unchanged 24.09709 39.01920 3.25 3.63853 4.13 9 9 1.00 Perfect Match 6 Unchanged 35.78813 98.86772 1.19 8.74857 3.81 12 13 1.00 Perfect Match 7 Unchanged 40.19906 220.66545 0.17 4.65920 0.82 10 12 1.00 Perfect Match 8 Unchanged 22.44457 9.26887 1.24 2.43839 1.90 9 10 1.00 Perfect Match 9 Unchanged 28.78218 58.18318 0.04 7.70390 1.35 10 11 1.00 Perfect Match 10 Unchanged 22.86874 65.35336 1.12 2.82969 0.64 9 9 0.89 Perfect Match 11 Unchanged 13.49606 7.43565 4.96 2.52693 2.60 6 6 1.00 Perfect Match 12 Unchanged 27.34631 13.09866 0.16 4.54105 1.98 10 10 1.00 Perfect Match 13 Unchanged 19.60034 36.37531 0.32 5.41074 8.49 5 6 1.33 Perfect Match 14 Unchanged 26.74798 11.66183 2.12 2.24421 3.12 7 6 0.50 Perfect Match 15 Unchanged 18.12699 121.70213 8.85 6.66070 17.32 4 4 0.50 Perfect Match Table E.6: Subject 2 3rd method (1DOF) Appendix E. Experiment Data 112 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 12.39602 0.00795 0.01 1.37297 0.89 2 1 1.00 Satisfactory 2 Unchanged 19.08945 54.69664 36.46 2.98045 3.07 5 5 1.00 Satisfactory 3 Unchanged 23.06118 21.06660 0.62 4.02615 1.78 5 7 1.00 Satisfactory 4 Unchanged 35.04803 168.59958 22.48 3.80447 2.97 8 10 1.00 Satisfactory 5 Unchanged 33.08467 76.75273 6.40 5.25981 5.96 11 12 1.00 Satisfactory 6 Unchanged 63.65262 66.55936 0.80 5.67510 2.47 12 13 1.69 Unsatisfactory 7 Unchanged 60.07673 44.80741 0.03 4.41444 0.77 10 11 1.09 Unsatisfactory 8 Unchanged 32.66050 23.74783 3.17 4.17708 3.26 9 9 1.00 Satisfactory 9 Unchanged 42.44397 132.91225 0.10 7.86435 1.38 10 11 1.00 Satisfactory 10 Unchanged 27.65124 61.53510 1.05 6.94783 1.58 8 9 1.22 Satisfactory 11 Unchanged 28.41127 4.84868 3.23 1.53199 1.58 6 7 1.00 Unsatisfactory 12 Unchanged 36.94306 43.97812 0.53 6.91858 3.01 10 11 1.00 Satisfactory 13 Unchanged 28.35876 161.43557 1.40 7.15325 11.23 7 7 1.29 Satisfactory 14 Unchanged 28.96961 41.34789 7.52 3.66062 5.09 7 8 1.00 Satisfactory 15 Final 103.39405 573.65999 41.72 17.84284 46.39 22 20 1.15 Unsatisfactory 15 Cutoff 18.98362 770.52148 56.04 17.77153 46.20 4 3 1.00 -15 Difference 84.41043 -196.86148 -14.32 0.07131 0.19 18 17 0.15 -Table E.7: Subject 3 1st method (Jacobian) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 9.30516 0.10637 0.11 5.02319 3.27 1 1 1.00 Satisfactory 2 Unchanged 14.29356 59.17740 39.45 1.72310 1.77 5 5 1.00 Satisfactory 3 Unchanged 15.51026 53.54346 1.59 2.41842 1.07 5 5 1.00 Satisfactory 4 Unchanged 31.71051 135.30557 18.04 4.76965 3.72 11 11 1.00 Satisfactory 5 Unchanged 31.83133 196.29357 16.36 11.56942 13.12 6 10 1.50 Satisfactory 6 Unchanged 37.20894 61.20065 0.74 6.76164 2.94 5 6 2.00 Satisfactory 7 Unchanged 88.21975 178.60788 0.13 5.04987 0.88 14 18 2.89 Satisfactory 8 Unchanged 31.07633 104.69993 13.96 3.82586 2.99 9 11 1.18 Satisfactory 9 Unchanged 43.20986 58.59931 0.04 8.20857 1.44 12 10 1.00 Satisfactory 10 Unchanged 27.24377 88.70246 1.52 6.05313 1.38 9 9 1.22 Satisfactory 11 Unchanged 12.01770 28.01077 18.67 2.80454 2.89 4 4 1.50 Satisfactory 12 Unchanged 23.16787 142.75082 1.71 8.90533 3.87 7 5 2.00 Satisfactory 13 Unchanged 30.02048 36.45002 0.32 3.67756 5.77 9 7 2.00 Satisfactory 14 Unchanged 28.02878 34.70604 6.31 6.70745 9.33 5 6 1.83 Satisfactory 15 Unchanged 18.43530 84.96803 6.18 4.26410 11.09 4 5 1.20 Satisfactory Table E.8: Subject 3 2nd method (CCD) Appendix E. Experiment Data 113 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 8.88929 0.35602 0.36 9.18991 5.97 1 1 1.00 Satisfactory 2 Unchanged 16.82776 25.62851 17.09 3.48549 3.59 5 5 2.00 Satisfactory 3 Unchanged 19.94781 19.94536 0.59 2.05349 0.91 5 5 3.00 Satisfactory 4 Unchanged 35.34888 192.69125 25.69 6.54988 5.11 10 10 2.40 Satisfactory 5 Unchanged 32.80551 92.36855 7.70 11.19115 12.69 9 10 2.60 Satisfactory 6 Unchanged 41.05980 9.53979 0.11 3.89170 1.69 10 12 1.67 Satisfactory 7 Unchanged 57.79339 54.41654 0.04 5.89881 1.03 12 13 1.92 Satisfactory 8 Unchanged 27.86042 113.09761 15.08 4.34848 3.39 10 9 1.33 Satisfactory 9 Unchanged 35.55803 10.13948 0.01 2.91643 0.51 10 11 2.64 Satisfactory 10 Unchanged 36.41471 136.94211 2.34 4.12287 0.94 9 10 1.40 Satisfactory 11 Unchanged 16.45525 41.96014 27.97 1.84970 1.90 . 5 5 1.40 Satisfactory 12 Unchanged 33.45550 36.30442 0.44 7.37945 3.21 10 11 2.00 Satisfactory 13 Unchanged 30.84881 272.96719 2.37 6.77783 10.64 8 11 2.09 Satisfactory 14 Unchanged 17.76944 78.06156 14.19 4.27332 5.95 5 5 1.00 Satisfactory 15 Unchanged 17.08943 117.21693 8.52 7.51732 19.54 5 4 1.00 Satisfactory Table E.9: Subject 3 3rd method (1DOF) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 5.81924 7.70997 7.71 8.18943 5.32 3 2 1.00 Almost Perfect 2 Unchanged 11.82851 43.47221 28.98 2.44760 2.52 6 6 1.00 Almost Perfect 3 Unchanged 17.11275 16.46224 0.49 1.67568 0.74 7 6 1.00 Pretty Good 4 Unchanged 16.37524 73.99228 9.87 4.63724 3.62 9 8 1.00 Almost Perfect 5 Unchanged 17.81609 122.90557 10.24 4.32377 4.90 9 11 1.00 Pretty Good 6 Unchanged 34.74215 310.92738 3.73 10.71007 4.66 10 11 1.00 Satisfactory 7 Unchanged 47.11736 878.45699 0.66 10.54614 1.85 9 18 2.78 Satisfactory 8 Unchanged 42.81481 202.20105 26.96 5.25973 4.11 12 13 1.92 Pretty Good 9 Unchanged 37.40806 67.78563 0.05 4.49282 0.79 10 10 1.00 Pretty Good 10 Unchanged 32.99965 67.36084 1.15 4.17991 0.95 7 15 0.87 Pretty Good 11 Unchanged 13.62438 44.08578 29.39 2.21778 2.28 4 5 2.40 Almost Perfect 12 Unchanged 26.75540 94.03919 1.13 5.81751 2.53 10 13 1.00 Pretty Good 13 Unchanged 27.51875 115.86965 1.01 5.17492 8.12 8 14 1.14 Pretty Good 14 Unchanged 19.27613 80.40963 14.62 3.76584 5.24 6 8 1.13 Pretty Good 15 Unchanged 27.58958 83.56979 6.08 5.18299 13.47 11 8 0.63 Satisfactory Table E.10: Subject 4 1st method (Jacobian) Appendix E. Experiment Data 114 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 16.88611 17.00385 17.00 7.30101 4.75 6 5 3.00 Pretty Good 2 Unchanged 12.16187 24.10202 16.07 1.82507 1.88 6 6 1.00 Almost Perfect 3 Unchanged 14.70025 51.77898 1.53 2.34073 1.04 5 6 1.00 Pretty Good 4 Unchanged 17.71945 23.84738 3.18 2.59781 2.03 9 9 1.00 Almost Perfect 5 Unchanged 17.44279 22.91778 1.91 3.50556 3.98 9 9 1.00 Almost Perfect 6 Unchanged 27.56297 358.18397 4.30 14.54488 6.33 10 10 1.80 Pretty Good 7 Unchanged 42.88323 1085.79459 0.82 12.96602 2.27 9 14 2.07 Satisfactory 8 Unchanged 20.48118 111.61803 14.88 5.65526 4.41 7 7 1.29 Pretty Good 9 Unchanged 38.11397 155.78668 0.12 13.63368 2.39 10 11 1.73 Pretty Good 10 Unchanged 19.30783 183.77866 3.14 4.11701 0.94 8 9 1.22 Pretty Good 11 Unchanged 6.67512 2.16993 1.45 2.29070 2.36 1 1 6.00 Almost Perfect 12 Unchanged 33.06555 68.89006 0.83 4.99868 2.17 11 15 1.93 Pretty Good 13 Unchanged 26.99545 59.41186 0.52 4.82907 7.58 7 10 1.40 Almost Perfect 14 Unchanged 15.88277 77.19956 14.04 5.67815 7.90 6 5 1.20 Pretty Good 15 Unchanged 15.32276 112.21201 8.16 7.10798 18.48 5 6 1.00 Almost Perfect Table E . l l : Subject 4 2nd method (CCD) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 9.30348 0.00391 0.00 0.96354 0.63 1 2 5.00 Perfect Match 2 Unchanged 14.10439 15.97151 10.65 2.61127 2.69 6 6 1.17 Almost Perfect 3 Unchanged 18.93780 81.73030 2.42 2.83528 1.26 5 5 2.20 Almost Perfect 4 Unchanged 23.57870 45.25148 6.03 4.18996 3.27 9 12 1.58 Almost Perfect 5 Unchanged 19.33948 63.79510 5.32 3.56668 4.04 9 9 1.11 Almost Perfect 6 Unchanged 40.27980 41.96106 0.50 4.12327 1.79 10 12 3.33 Pretty Good 7 Unchanged 33.19635 85.57678 0.06 6.85123 1.20 10 11 1.91 Satisfactory 8 Unchanged 16.10192 38.44521 5.13 2.96631 2.32 9 9 1.00 Almost Perfect 9 Unchanged 33.88720 12.26140 0.01 2.94057 0.51 10 10 1.90 Pretty Good 10 Unchanged 21.44784 34.12715 0.58 3.10035 0.71 8 9 1.22 Almost Perfect 11 Unchanged 10.57432 8.76010 5.84 1.11842 1.15 6 6 1.00 Almost Perfect 12 Unchanged 21.85449 28.37800 0.34 4.66181 2.03 10 10 1.00 Pretty Good 13 Unchanged 17.78776 61.74235 0.54 4.17790 6.56 7 7 1.29 Pretty Good 14 Unchanged 19.98531 55.61558 10.11 4.00502 5.57 6 8 1.25 Pretty Good 15 Unchanged 22.78535 214.35658 15.59 9.35011 24.31 7 9 0.33 Pretty Good Table E.12: Subject 4 3rd method (1DOF) Appendix E. Experiment Data 115 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 84.09377 75.42240 75.42 2.95414 1.92 8 9 2.78 Almost Perfect 2 Unchanged 21.13616 49.53798 33.03 2.22699 2.29 6 7 1.00 Almost Perfect 3 Unchanged 25.93957 20.89426 0.62 1.60817 0.71 5 5 1.00 Almost Perfect 4 Unchanged 32.07050 46.19889 6.16 2.04563 1.60 9 9 1.00 Almost Perfect 5 Unchanged 31.05048 40.81033 3.40 3.65150 4.14 9 10 1.00 Almost Perfect 6 Unchanged 40.37896 7.14975 0.09 5.21288 2.27 10 10 1.00 Almost Perfect 7 Unchanged 50.47162 9.13428 0.01 1.76177 0.31 10 9 2.22 Almost Perfect 8 Unchanged 27.97876 74.06513 9.88 3.04462 2.38 9 9 1.00 Almost Perfect 9 Unchanged 44.04236 12.31272 0.01 5.18012 0.91 10 10 1.00 Almost Perfect 10 Unchanged 48.85991 122.06942 2.09 12.34971 2.81 15 15 0.60 Pretty Good 11 Unchanged 15.23689 17.29232 11.53 2.06206 2.12 6 6 1.00 Almost Perfect 12 Unchanged 29.53046 65.66918 0.79 4.92610 2.14 11 11 1.09 Almost Perfect 13 Unchanged 22.92703 47.66941 0.41 3.03825 4.77 9 7 1.29 Almost Perfect 14 Unchanged 21.47117 64.78407 11.78 2.92932 4.08 10 8 1.25 Almost Perfect 15 Unchanged 32.68135 10.37681 0.75 2.76039 7.18 11 8 0.75 Almost Perfect Table E.13: Subject 5 1st method (Jacobian) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 22.29365 8.35966 8.36 2.84791 1.85 10 6 0.83 Almost Perfect 2 Unchanged 14.91439 22.05400 14.70 1.93038 1.99 7 7 1.00 Almost Perfect 3 Unchanged 12.10851 42.78168 1.27 1.76235 0.78 5 5 1.00 Pretty Good 4 Unchanged 28.19208 24.76367 3.30 1.49350 1.17 13 11 0.91 Perfect Match 5 Unchanged 22.23199 54.25394 4.52 4.95648 5.62 10 9 1.00 Almost Perfect 6 Unchanged 30.96296 68.86722 0.83 6.80756 2.96 11 11 1.64 Almost Perfect 7 Unchanged 36.29387 48.76657 0.04 3.61331 0.63 10 10 1.00 Pretty Good 8 Unchanged 16.92692 36.14893 4.82 2.39166 1.87 10 9 1.00 Pretty Good 9 Unchanged 26.21039 41.97043 0.03 4.39872 0.77 10 10 1.00 Almost Perfect 10 Unchanged 21.62782 98.41423 1.68 4.22068 0.96 11 9 1.55 Pretty Good 11 Unchanged 10.49433 18.66390 12.44 3.81198 3.92 7 6 1.00 Almost Perfect 12 Unchanged 25.49120 61.98484 0.74 5.02365 2.19 13 11 1.09 Almost Perfect 13 Unchanged 18.13110 63.21913 0.55 4.36008 6.84 9 8 1.25 Pretty Good 14 Unchanged 30.60129 11.78969 2.14 1.90380 2.65 13 10 1.10 Almost Perfect 15 Unchanged 28.21291 5.24582 0.38 1.51721 3.94 16 7 0.86 Almost Perfect Table E.14: Subject 5 2nd method (CCD) Appendix E. Experiment Data 116 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 17.42610 9.93041 9.93 2.40295 1.56 8 5 1.00 Almost Perfect 2 Unchanged 13.99271 6.45423 4.30 0.77246 0.80 7 6 1.00 Almost Perfect 3 Unchanged 18.22028 3.05795 0.09 0.62912 0.28 5 5 1.00 Perfect Match 4 Unchanged 20.03365 37.82422 5.04 2.63532 2.06 9 9 1.00 Almost Perfect 5 Unchanged 22.11450 20.23914 1.69 2.83746 3.22 10 9 1.00 Almost Perfect 6 Unchanged 35.18054 70.57762 0.85 5.15813 2.24 12 12 1.17 Almost Perfect 7 Unchanged 25.68539 48.48206 0.04 2.84158 0.50 10 10 1.00 Almost Perfect 8 Unchanged 17.02109 89.71129 11.96 3.49971 2.73 11 9 1.00 Pretty Good 9 Unchanged 21.73200 9.69727 0.01 2.87436 0.50 10 10 1.00 Pretty Good 10 Unchanged 19.61280 12.14356 0.21 3.92331 0.89 9 9 1.22 Pretty Good 11 Unchanged 13.26187 17.63129 11.75 2.06347 2.12 9 6 1.00 Almost Perfect 12 Unchanged 18.06611 65.60421 0.79 5.84172 2.54 11 10 1.00 Pretty Good 13 Unchanged 13.75938 126.88252 1.10 4.66688 7.32 9 7 1.29 Pretty Good 14 Unchanged 14.63940 58.48382 10.63 4.60707 6.41 9 8 1.13 Pretty Good 15 Unchanged 28.58292 8.67810 0.63 2.54390 6.61 11 11 1.27 Pretty Good Table E.15: Subject 5 3rd method (1DOF) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Final 51.15329 2.18280 . 2.18 0.86577 0.56 9 6 1.00 Almost Perfect 1 Cutoff 9.16180 0.00128 0.00 0.55012 0.36 1 1 1.00 -1 Difference 41.99149 2.18153 2.18 0.31565 0.20 8 5 0.00 -2 Unchanged 30.10964 4.55040 3.03 1.04121 1.07 6 6 1.00 Almost Perfect 3 Unchanged 84.49715 1.40361 0.04 0.56377 0.25 13 13 1.00 Almost Perfect 4 Unchanged 78.84790 27.09436 3.61 2.05537 1.60 15 16 1.00 Almost Perfect 5 Unchanged 95.31316 8.37202 0.70 3.00124 3.40 15 19 1.00 Pretty Good 6 Unchanged 87.46135 9.65399 0.12 3.10729 1.35 12 12 1.00 Almost Perfect 7 Unchanged 419.97988 34.31785 0.03 1.63661 0.29 11 20 3.35 Perfect Match 8 Unchanged 97.40569 5.39707 0.72 0.96629 0.75 21 18 1.44 Perfect Match 9 Unchanged 103.56995 46.74631 0.04 5.29673 0.93 21 18 1.50 Satisfactory 10 Unchanged 58.57091 10.37120 0.18 2.84445 0.65 11 11 1.45 Pretty Good 11 Unchanged 21.28700 11.17589 7.45 1.33514 1.37 6 7 1.00 Almost Perfect 12 Unchanged 46.63072 41.56527 0.50 4.47643 1.95 10 10 1.00 Satisfactory 13 Unchanged 49.12578 27.21818 0.24 2.35989 3.70 12 9 1.56 Pretty Good 14 Unchanged 33.16303 36.90114 6.71 3.24273 4.51 9 6 0.50 Pretty Good 15 Unchanged 73.83949 10.74457 0.78 1.81034 4.71 13- 12 0.83 Pretty Good Table E.16: Subject 6 1st method (Jacobian) Appendix E. Experiment Data 117 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 17.19611 2.53624 2.54 1.63105 1.06 4 3 1.00 Almost Perfect 2 Unchanged 38.68061 9.82612 6.55 0.88851 0.91 7 7 1.00 Almost Perfect 3 Unchanged 24.21204 0.54815 0.02 0.20745 0.09 5 5 1.00 Perfect Match 4 Unchanged 53.77502 46.48330 6.20 2.48574 1.94 15 15 1.00 Almost Perfect 5 Unchanged 37.03892 49.67685 4.14 4.50280 5.11 9 9 1.00 Pretty Good 6 Unchanged 53.62835 55.40492 0.67 5.25825 2.29 10 11 1.82 Pretty Good 7 Unchanged 76.23037 50.91407 0.04 2.44656 0.43 17 16 1.00 Almost Perfect 8 Unchanged 37.08059 46.62221 6.22 2.13561 1.67 9 10 1.00 Almost Perfect 9 Unchanged 51.82833 26.49096 0.02 4.82198 0.84 11 10 1.00 Almost Perfect 10 Unchanged 48.01576 25.11879 0.43 4.08659 0.93 12 13 1.15 Pretty Good 11 Unchanged 17.61527 20.53897 13.69 3.36321 3.46 7 6 1.00 Almost Perfect 12 Unchanged 35.98558 5.97379 0.07 2.09600 0.91 10 10 1.00 Almost Perfect 13 Unchanged 52.33667 19.20750 0.17 2.43806 3.83 11 8 1.25 Almost Perfect 14 Unchanged 45.00656 18.95419 3.45 2.26443 3.15 11 9 0.89 Almost Perfect 15 Unchanged 46.63493 13.77278 1.00 2.35577 6.12 11 11 1.36 Pretty Good Table E.17: Subject 6 2nd method (CCD) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 25.48626 0.68843 0.69 1.02240 0.66 5 4 1.00 Pretty Good 2 Unchanged 18.87780 7.51838 5.01 1.40713 1.45 7 6 1.00 Pretty Good 3 Unchanged 32.49221 5.96989 0.18 1.48651 0.66 7 7 1.00 Pretty Good 4 Unchanged 36.66644 45.26257 6.04 4.01064 3.13 11 11 1.00 Pretty Good 5 Unchanged 45.19407 26.82859 2.24 2.52029 2.86 15 15 1.00 Pretty Good 6 Unchanged 30.66718 17.45590 0.21 3.56799 1.55 10 10 1.00 Almost Perfect. 7 Unchanged 108.56512 58.63699 0.04 3.44532 0.60 24 26 1.69 Almost Perfect 8 Unchanged 51.02167 38.81158 5.17 2.35959 1.84 10 12 3.00 Perfect Match 9 Unchanged 37.69979 43.94577 0.03 9.49162 1.66 10 10 1.00 Satisfactory 10 Unchanged 29.57548 41.39500 0.71 3.53283 0.80 9 9 1.22 Pretty Good 11 Unchanged 29.63716 8.97455 5.98 3.26407 3.36 11 12 0.83 Pretty Good 12 Unchanged 31.20303 42.43294 0.51 7.23070 3.15 10 10 1.00 Pretty Good 13 Unchanged 52.41338 10.38928 0.09 3.31018 5.20 15 15 1.67 Satisfactory 14 Unchanged 42.56820 50.05180 9.10 4.38379 6.10 12 12 1.17 Pretty Good 15 Unchanged 86.79561 20.93164 1.52 3.88975 10.11 20 20 1.35 Satisfactory Table E.18: Subject 6 3rd method (1DOF) Appendix E. Experiment Data 118 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 53.83917 32.52789 32.53 2.64882 1.72 7 6 3.17 Almost Perfect 2 Unchanged 7.83263 1.09852 0.73 2.52719 2.60 1 1 6.00 Almost Perfect 3 Unchanged 13.11604 41.84835 1.24 2.89916 1.28 1 2 5.00 Almost Perfect 4 Unchanged 36.22807 123.25140 16.43 5.35849 4.18 4 5 2.40 Almost Perfect 5 Unchanged 31.92800 53.91648 4.49 4.03920 4.58 5 7 1.86 Almost Perfect 6 Unchanged 58.15676 59.26108 0.71 5.87377 2.56 10 10 2.20 Almost Perfect 7 Unchanged 71.14613 33.06993 0.02 2.78887 0.49 6 6 4.00 Almost Perfect 8 Unchanged 42.20379 45.42280 6.06 2.91815 2.28 4 5 2.20 Almost Perfect 9 Unchanged 74.41340 41.47538 0.03 4.96673 0.87 6 6 1.67 Almost Perfect 10 Unchanged 54.19240 25.85674 0.44 2.23891 0.51 6 9 1.67 Almost Perfect 11 Unchanged 15.87212 16.36252 10.91 1.72584 1.78 3 3 2.00 Almost Perfect 12 Unchanged 45.28882 13.31492 0.16 3.09536 1.35 5 5 2.00 Perfect Match 13 Unchanged 55.99330 63.62375 0.55 2.99520 4.70 3 6 2.17 Almost Perfect 14 Unchanged 39.45617 30.94094 5.63 3.10166 4.32 5 5 2.60 Almost Perfect 15 Unchanged 45.26129 70.34269 5.12 5.07911 13.20 6 6 1.00 Perfect Match Table E.19: Subject 7-1st method (Jacobian) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 27.34205 3.43208 3.43 5.08529 3.31 2 2 2.50 Almost Perfect 2 Unchanged 13.11185 17.57399 11.72 1.69961 1.75 2 2 3.00 Almost Perfect 3 Unchanged 22.62866 14.14983 0.42 1.63108 0.72 4 3 3.33 Almost Perfect 4 Unchanged 47.80984 24.65831 3.29 3.57899 2.79 4 5 2.40 Almost Perfect 5 Unchanged 43.37228 6.79141 0.57 2.57384 2.92 4 8 2.50 Perfect Match 6 Unchanged 40.77059 34.64257 0.42 5.00999 2.18 5 7 2.00 Perfect Match 7 Unchanged 87.95458 15.91877 0.01 3.08470 0.54 4 8 4.50 Perfect Match 8 Unchanged 32.45545 35.30307 4.71 2.38014 1.86 8 8 1.13 Perfect Match 9 Unchanged 60.82586 21.02617 0.02 4.31760 0.76 5 7 1.86 Almost Perfect 10 Unchanged 43.19646 17.45427 0.30 4.17193 0.95 9 9 1.22 Almost Perfect 11 Unchanged 12.01934 27.75381 18.50 3.62335 3.73 1 2 4.00 Almost Perfect 12 Unchanged 41.00059 12.06001 0.14 4.24963 1.85 5 6 2.00 Almost Perfect 13 Unchanged 56.05081 9.47954 0.08 1.70852 2.68 6 8 2.88 Almost Perfect 14 Unchanged 37.44220 114.54642 20.83 5.85122 8.14 3 4 2.25 Almost Perfect 15 Unchanged 21.75114 32.12180 2.34 3.52587 9.17 3 4 1.25 Almost Perfect Table E.20: Subject 7 2nd method (CCD) Appendix E. Experiment Data 119 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 12.58767 0.00366 0.00 0.93204 0.61 2 1 1.00 Perfect Match 2 Unchanged 17.58691 4.97229 3.31 1.05590 1.09 6 6 1.00 Almost Perfect 3 Unchanged 30.24712 7.85059 0.23 1.12621 0.50 7 6 1.00 Almost Perfect 4 Unchanged 33.81383 63.09034 8.41 4.77620 3.73 7 7 1.00 Pretty Good 5 Unchanged 24.26868 56.25109 4.69 3.05497 3.46 9 9 1.00 Almost Perfect 6 Unchanged 42.75146 37.28121 0.45 4.87869 2.12 10 11 1.00 Pretty Good 7 Unchanged 53.13244 41.10095 0.03 2.51127 0.44 10 11 1.82 Perfect Match 8 Unchanged 29.61627 14.29425 1.91 2.92699 2.28 9 9 1.00 Perfect Match 9 Unchanged 37.37304 15.43476 0.01 2.55262 0.45 10 10 1.00 Almost Perfect 10 Unchanged 41.95727 5.05876 0.09 3.47957 0.79 9 9 1.22 Perfect Match 11 Unchanged 30.66212 5.15928 3.44 1.78236 1.83 8 8 1.00 Perfect Match 12 Unchanged 36.08803 13.34053 0.16 3.04609 1.33 12 12 1.00 Almost Perfect 13 Unchanged 47.06903 14.96897 0.13 2.05400 3.22 9 9 1.22 Almost Perfect 14 Unchanged 37.42890 17.91376 3.26 2.30307 3.20 9 9 0.67 Almost Perfect 15 Unchanged 37.70306 62.02580 4.51 4.93704 12.84 9 9 0.56 Almost Perfect Table E.21: Subject 7 3rd method (1DOF) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 57.06565 2.29892 2.30 1.21910 0.79 6 9 2.33 Pretty Good 2 Unchanged 34.38707 19.37924 12.92 1.05646 1.09 6 8 1.13 Almost Perfect 3 Unchanged 36.32041 1.54940 0.05 0.71933 0.32 5 13 1.00 Perfect Match 4 Unchanged 40.19797 22.60817 3.01 1.63436 1.28 11 24 1.00 Almost Perfect 5 Unchanged 62.74824 4.92551 0.41 1.59397 1.81 21 41 1.00 Almost Perfect 6 Unchanged 102.74874 7.54717 0.09 2.03769 0.89 28 75 1.00 Almost Perfect 7 Unchanged 83.49354 42.95833 0.03 2.01830 0.35 10 57 1.60 Almost Perfect 8 Unchanged 50.13812 8.77922 1.17 1.31321 1.02 11 24 1.96 Pretty Good 9 Unchanged 107.94554 6.30557 0.00 2.27339 0.40 22 79 1.00 Pretty Good 10 Unchanged 56.75240 1.77520 0.03 1.14858 0.26 15 43 1.51 Almost Perfect 11 Unchanged 62.20332 6.60069 4.40 0.86297 0.89 17 52 0.96 Almost Perfect 12 Unchanged 68.11757 8.62863 0.10 2.08692 0.91 19 55 1.00 Almost Perfect 13 Unchanged 66.84923 6.67799 0.06 1.55912 2.45 20 50 0.50 Satisfactory 14 Unchanged 29.32206 9.45769 1.72 1.69718 2.36 9 20 0.85 Pretty Good 15 Unchanged 143.37696 23.36166 1.70 3.31499 8.62 30 88 0.90 Pretty Good Table E.22: Subject 8 1st method (Jacobian) Appendix E. Experiment Data 120 Trial Type Time (seconds) Angle Error % Pos. Error % R E Avg. Dist. Rating 1 Unchanged 77.35035 2.32399 2.32 0.58185 0.38 21 57 1.00 Perfect Match 2 Unchanged 55.194.18 6.44030 4.29 0.69592 0.72 18 44 0.98 Perfect Match 3 Unchanged 48.73962 0.71168 0.02 0.28910 0.13 14 29 1.28 Perfect Match 4 Unchanged 100.56154 9.29886 1.24 1.15607 0.90 32 89 1.01 Perfect Match 5 Unchanged 50.79663 5.22234 0.44 1.34133 1.52 14 38 1.00 Perfect Match 6 Unchanged 84.57298 4.57126 0.05 1.26846 0.55 17 82 1.26 Almost Perfect 7 Unchanged 83.16670 41.64370 0.03 2.26050 0.40 14 58 1.51 Almost Perfect 8 Unchanged 33.47630 16.43886 2.19 1.30961 1.02 9 24 1.00 Perfect Match 9 Unchanged 103.84583 9.37124 0.01 2.33568 0.41 28 89 1.00 Almost Perfect 10 Unchanged 34.72709 12.84917 0.22 1.86967 0.43 12 25 1.64 Almost Perfect 11 Unchanged 27.12650 3.45711 2.30 0.48284 0.50 12 28 1.00 Perfect Match 12 Unchanged 66.91571 9.31372 0.11 3.68261 1.60 20 62 1.00 Satisfactory 13 Unchanged 35.40818 9.95929 0.09 2.06019 3.23 8 34 1.82 Pretty Good 14 Unchanged 60.33225 5.52042 1.00 1.46735 2.04 19 68 0.81 Almost Perfect 15 Unchanged 86.45357 6.93903 0.50 2.09693 5.45 24 64 1.52 Almost Perfect Table E.23: Subject 8 2nd method (CCD) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 100.38361 24.93786 24.94 1.56157 1.02 22 108 1.00 Unsatisfactory 2 Unchanged 20.00336 1.28737 0.86 0.74159 0.76 6 6 1.00 Almost Perfect 3 Unchanged 38.58118 0.25086 0.01 0.75539 0.33 10 19 1.00 Satisfactory 4 Unchanged 37.81464 21.06036 2.81 1.53326 1.20 15 35 1.00 Almost Perfect 5 Unchanged 46.24382 7.74339 0.65 1.38584 1.57 12 44 1.00 Perfect Match 6 Unchanged 43.12654 4.93891 0.06 2.55163 1.11 12 53 1.00 Pretty Good 7 Unchanged 62.76172 36.67701 0.03 2.27648 0.40 13 63 1.00 Pretty Good 8 Unchanged 46.03376 6.81274 0.91 1.25619 0.98 21 44 1.02 Perfect Match 9 Unchanged 43.59176 18.52978 0.01 3.49930 0.61 15 43 1.00 Unsatisfactory 10 Unchanged 50.29220 23.13008 0.40 2.71168 0.62 17 38 1.05 Unsatisfactory 11 Unchanged 20.34507 5.99622 4.00 0.71294 0.73 8 20 1.00 Perfect Match 12 Unchanged 52.84215 17.90572 0.22 4.53832 1.97 20 38 0.50 Unsatisfactory 13 Unchanged 40.32010 11.62735 0.10 2.36790 3.72 14 30 1.27 Pretty Good 14 Unchanged 39.23472 13.23336 2.41 1.97896 2.75 15 35 1.06 Satisfactory 15 Unchanged 79.18168 2.83942 0.21 1.16191 3.02 25 72 1.42 Pretty Good Table E.24: Subject 8 3rd method (1DOF) Appendix E. Experiment Data 121 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 52.77252 13.81418 13.81 1.57341 1.02 12 29 1.00 Almost Perfect 2 Unchanged 35.08556 19.05421 12.70 1.30653 1.34 8 40 0.98 Perfect Match 3 Unchanged 35.63307 4.90524 0.15 1.14921 0.51 7 9 1.00 Perfect Match 4 Unchanged 56.32009 67.38092 8.98 3.31472 2.59 9 13 1.00 Perfect Match 5 Unchanged 53.43504 50.90355 4.24 1.99244 2.26 11 20 1.00 Perfect Match 6 Unchanged 71.81198 14.46001 0.17 2.84168 1.24 10 33 1.00 Perfect Match 7 Unchanged 157.53084 50.43365 0.04 1.97043 0.34 17 28 1.46 Perfect Match 8 Unchanged 37.71393 46.55132 6.21 2.36062 1.84 12 20 0.85 Perfect Match 9 Unchanged 55.16172 29.12430 0.02 3.14514 0.55 10 16 1.00 Perfect Match 10 . Unchanged 52.53835 33.90449 0.58 1.62404 0.37 14 20 1.20 Perfect Match 11 Unchanged 39.10645 25.91874 17.28 1.90643 1.96 12 40 0.93 Perfect Match 12 Unchanged 42.04151 4.76953 0.06 1.62352 0.71 10 11 0.91 Perfect Match 13 Unchanged 50.15663 7.05679 0.06 2.00266 3.14 14 26 0.96 Perfect Match 14 Unchanged 53.41418 54.80143 9.96 9.42091 13.11 17 26 0.88 Perfect Match 15 Unchanged 110.28594 137.82152 10.02 5.87426 15.27 26 25 1.16 Almost Perfect Table E.25: Subject 9 1st method (Jacobian) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 40.89639 4.07651 4.08 1.64283 1.07 11 25 1.00 Perfect Match 2 Unchanged 22.74031 22.41020 14.94 1.59928 1.65 7 24 1.00 Perfect Match 3 Unchanged 26.95537 11.16723 0.33 1.00182 0.44 7 12 1.00 Perfect Match 4 Unchanged 42.10309 34.94026 4.66 2.11613 1.65 11 31 1.00 Perfect Match 5 Unchanged 40.55891 11.26009 0.94 2.58190 2.93 9 34 1.00 Perfect Match 6 Unchanged 35.59717 36.42207 0.44 3.28716 1.43 10 21 1.00 Perfect Match 7 Unchanged 56.74749 62.90362 0.05 3.18508 0.56 10 23 1.00 Perfect Match 8 Unchanged 37.36054 17.09397 2.28 1.92772 1.50 13 31 1.00 Perfect Match 9 Final 62.36258 22.78850 0.02 6.75301 1.18 13 31 1.03 Perfect Match 9 Cutoff 55.91666 22.18874 0.02 5.80586 1.02 12 28 1.04 -9 Difference 6.44592 0.59975 0.00 0.94715 0.16 1 3 -0.01 -10 Unchanged 51.58798 16.22525 0.28 2.74094 0.62 9 27 1.93 Perfect Match 11 Unchanged 24.78939 12.68540 8.46 1.51438 1.56 8 37 1.00 Perfect Match 12 Unchanged 38.48282 15.46270 0.19 4.22533 1.84 10 21 1.00 Perfect Match 13 Unchanged 42.60621 1.16391 0.01 1.59048 2.50 10 33 1.58 Perfect Match 14 Unchanged 46.54712 3.44820 0.63 2.63713 3.67 12 48 1.17 Perfect Match 15 Unchanged 60.06479 29.88924 2.17 3.89557 10.13 14 40 0.20 Perfect Match Table E.26: Subject 9 2nd method (CCD) Appendix E. Experiment Data 122 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 45.72558 45.29135 45.29 2.05555 1.34 14 51 1.00 Perfect Match 2 Unchanged 17.95522 16.24530 10.83 1.15778 1.19 7 25 1.00 Perfect Match 3 Unchanged 24.32114 3.00247 0.09 0.86988 0.39 7 41 1.00 Perfect Match 4 Unchanged 32.62627 37.00775 4.93 2.94580 2.30 9 55 1.00 Perfect Match 5 Unchanged 28.20204 22.03617 1.84 2.70492 3.07 9 65 1.00 Perfect Match 6 Unchanged 39.43971 56.37188 0.68 4.64976 2.02 12 60 1.00 Almost Perfect 7 Unchanged 44.55397 10.75274 0.01 2.22218 0.39 14 40 1.00 Perfect Match 8 Unchanged 28.17374 25.77472 3.44 2.55487 1.99 11 42 1.00 Perfect Match 9 Unchanged 50.12739 43.44295 0.03 5.14014 0.90 12 56 1.05 Perfect Match 10 Unchanged 47.85570 14.01455 0.24 1.32401 0.30 13 64 1.45 Perfect Match 11 Unchanged 20.97614 19.79465 13.20 1.21899 1.25 8 33 1.00 Perfect Match 12 Unchanged 41.39979 8.77605 0.11 2.97421 1.29 12 58 1.00 Perfect Match 13 Unchanged 40.47651 16.35174 0.14 2.42834 3.81 12 33 1.33 Perfect Match 14 Unchanged 32.62732 49.80172 9.05 2.48331 3.46 10 34 1.03 Perfect Match 15 Unchanged 35.33156 18.38519 1.34 2.61066 6.79 7 30 0.93 Perfect Match Table E.27: Subject 9 3rd method (1DOF) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 23.49454 108.34635 108.35 9.02755 5.87 1 11 4.82 Almost Perfect 2 Unchanged 14.96024 64.26150 42.84 5.22616 5.38 1 8 3.88 Almost Perfect 3 Unchanged 28.51461 113.75332 3.37 4.21166 1.87 1 15 3.53 Almost Perfect 4 Unchanged 39.52812 176.34813 23.51 6.21164 4.85 1 23 4.57 Almost Perfect 5 Unchanged 36.66557 145.68806 12.14 8.25223 9.36 1 26 5.42 Almost Perfect 6 Unchanged 45.55573 255.32430 3.07 14.80776 6.44 1 22 4.95 Almost Perfect 7 Unchanged 82.23462 443.23662 0.33 7.15043 1.25 1 39 5.51 Almost Perfect 8 Unchanged 59.89345 128.69535 17.16 4.13081 3.22 1 43 4.56 Pretty Good 9 Unchanged 145.47648 136.59843 0.10 7.27230 1.27 1 96 5.19 Almost Perfect 10 Unchanged 63.50350 152.92853 2.61 6.68905 1.52 1 86 4.26 Almost Perfect 11 Unchanged 13.08020 14.14039 9.43 1.85947 1.91 1 29 3.41 Almost Perfect 12 Unchanged 55.87506 98.34481 1.18 6.85119 2.98 1 62 3.98 Almost Perfect 13 Unchanged 55.35420 97.01948 0.84 5.00367 7.85 1 31 3.35 Almost Perfect 14 Unchanged 47.10909 83.84015 15.24 5.59314 7.78 1 35 3.74 Perfect Match 15 Unchanged 34.87889 119.30007 8.68 8.04185 20.91 1 19 4.00 Almost Perfect Table E.28: Subject 10 1st method (CCD) Appendix E. Experiment Data 123 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 3.81172 0.26725 0.27 7.96229 5.18 1 1 1.00 Almost Perfect 2 Outlier 13.46187 282.03591 188.02 32.04190 32.98 1 5 4.60 Unsatisfactory 3 Outlier 29.48211 3223.42713 95.51 118.96730 52.73 1 7 2.71 Unsatisfactory 4 Outlier 27.75625 981.19286 130.83 54.20923 42.31 1 11 6.82 Unsatisfactory 5 Outlier 12.03268 1204.94604 100.41 88.53731 100.40 1 5 5.60 Unsatisfactory 6 Outlier 19.04612 8256.44651 99.18 226.39104 98.50 1 8 7.13 Unsatisfactory 7 Outlier 19.04029 132744.43949 99.66 563.53191 98.64 1 7 4.86 Unsatisfactory 8 Outlier 7.04010 936.80848 124.91 58.83767 45.92 1 2 2.00 Unsatisfactory 9 Outlier 14.10688 133157.98733 99.97 570.43188 99.84 1 4 3.50 Unsatisfactory 10 Outlier 10.31348 6052.49574 103.46 97.34277 22.16 1 3 4.00 Unsatisfactory 11 Outlier 5.04507 253.16214 168.77 27.24965 28.05 1 1 6.00 Unsatisfactory 12 Outlier 8.53097 ,8315.34239 99.88 229.20332 99.72 1 3 3.33 Unsatisfactory 13 Outlier 6.00259 11660.36458 101.34 59.78954 93.84 1 2 4.50 Unsatisfactory 14 Outlier 10.97099 525.35225 95.52 30.68166 42.69 1 4 2.75 Satisfactory 15 Outlier 9.79764 1377.51982 100.18 33.72110 87.67 1 2 2.50 Unsatisfactory Table E.29: Subject 10 2nd method (1DOF) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 8.21430 0.02263 0.02 2.31698 1.51 1 8 1.00 Perfect Match 2 Unchanged 18.83946 47.52644 31.68 4.58375 4.72 1 14 2.93 Perfect Match 3 Unchanged 23.12869 20.51205 0.61 1.77301 0.79 1 22 3.50 Perfect Match 4 Unchanged 30.86965 118.74590 15.83 6.67666 5.21 1 27 5.00 Almost Perfect 5 Unchanged 41.93648 92.94853 7.75 5.23058 5.93 1 51 5.43 Perfect Match 6 Unchanged 58.29340 144.86647 1.74 13.10806 5.70 1 40 5.03 Perfect Match 7 Unchanged 101.62824 69.45638 0.05 6.51068 1.14 1 146 5.64 Almost Perfect 8 Unchanged 46.54156 150.86496 20.12 8.52143 6.65 1 72 4.97 Pretty Good 9 Unchanged 108.43419 66.26060 0.05 6.79040 1.19 1 94 6.33 Pretty Good 10 Unchanged 39.32728 56.33494 0.96 5.79071 1.32 1 57 4.89 Perfect Match 11 Unchanged 17.05693 49.86706 33.24 4.50791 4.64 1 25 3.32 Almost Perfect 12 Unchanged 184.23701 165.97053 1.99 11.51512 5.01 1 123 5.63 Unsatisfactory 13 Unchanged 62.90681 259.87925 2.26 11.00624 17.27 1 46 3.33 Unsatisfactory 14 Unchanged 24.29704 77.88081 14.16 8.64082 12.02 1 59 3.51 Pretty Good 15 Unchanged 23.11704 245.17912 17.83 10.47554 27.23 1 35 4.09 Almost Perfect Table E.30: Subject 10 3rd method (Jacobian) Appendix E. Experiment Data 124 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 36.67655 54.49675 54.50 6.05535 3.94 5 5 3.00 Perfect Match 2 Unchanged 12.09470 10.83200 7.22 1.45128 1.49 2 2 3.00 Perfect Match 3 Final 27.29950 3.73846 0.11 1.00214 0.44 5 5 1.60 Perfect Match 3 Cutoff 13.38391 3.40418 0.10 0.91253 0.40 3 3 3.00 -3 Difference 13.91559 0.33428 0.01 0.08961 0.04 2 2 -1.40 -4 Unchanged 38.05670 50.25036 6.70 4.80698 3.75 6 6 2.67 Almost Perfect 5 Unchanged 29.79716 100.33191 8.36 5.32651 6.04 6 7 2.00 Almost Perfect 6 Unchanged 48.07808 65.74861 0.79 5.58002 2.43 9 11 2.09 Pretty Good 7 Unchanged 47.61906 104.78396 0.08 6.08233 1.06 9 15 1.93 Pretty Good 8 Unchanged 28.37806 21.95326 2.93 3.77634 2.95 9 13 1.15 Almost Perfect 9 Unchanged 41.50335 33.79300 0.03 4.73534 0.83 10 13 0.85 Almost Perfect 10 Unchanged 29.97773 75.45330 1.29 3.77692 0.86 11 11 1.73 Almost Perfect 11 Unchanged 21.20548 20.81624 13.88 1.62580 1.67 4 3 2.00 Almost Perfect 12 Unchanged 27.25087 25.16368 0.30 5.15179 2.24 10 12 1.00 Almost Perfect 13 Unchanged 31.61120 60.55153 0.53 4.97052 7.80 9 10 1.00 Pretty Good 14 Unchanged 34.20733 23.28658 4.23 3.98165 5.54 11 12 1.08 Almost Perfect 15 Unchanged 32.05971 246.75702 17.95 10.28691 26.74 13 9 0.88 Satisfactory Table E.31: Subject 11 1st method (CCD) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 9.18097 0.03015 0.03 2.67455 1.74 1 1 1.00 Almost Perfect 2 Unchanged 24.94121 26.18777 17.46 1.80629 1.86 7 8 1.50 Almost Perfect 3 Unchanged 21.14448 5.07366 0.15 0.61755 0.27 5 5 1.60 Almost Perfect 4 Unchanged 25.91123 51.26145 6.83 4.11886 3.21 10 11 1.00 Almost Perfect 5 Unchanged 27.48208 36.66297 3.06 3.31173 3.76 10 9 1.00 Almost Perfect 6 Unchanged 34.72634 71.68499 0.86 5.49847 2.39 10 10 1.90 lAlmost Perfect 7 Unchanged 42.14980 61.63646 0.05 3.33578 0.58 10 13 1.69 Pretty Good 8 Unchanged 24.93371 15.86919 2.12 4.17419 3.26 9 9 1.00 Pretty Good 9 Unchanged 34.06385 19.09830 0.01 3.01856 0.53 10 10 1.30 Almost Perfect 10 Unchanged 32.18799 37.63174 0.64 3.58473 0.82 10 9 1.22 Almost Perfect 11 Unchanged 16.98776 8.99841 6.00 2.83272 2.92 7 6 1.00 Almost Perfect 12 Unchanged 29.12210 106.01375 1.27 7.57775 3.30 10 11 1.09 Almost Perfect 13 Unchanged 32.01465 136.62344 1.19 8.89760 13.96 9 8 1.63 Pretty Good 14 Unchanged 45.13653 56.24053 10.23 4.07237 5.67 15 10 0.80 Almost Perfect 15 Unchanged 43.77316 63.69761 4.63 2.76445 7.19 15 11 0.64 Almost Perfect Table E.32: Subject 11 2nd method (1DOF) Appendix E. Experiment Data 125 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 9.18347 0.00791 0.01 1.37000 0.89 2 1 1.00 Almost Perfect 2 Unchanged 12.42935 4.58686 3.06 2.23781 2.30 2 2 4.50 Almost Perfect 3 Unchanged 14.24272 21.99374 0.65 3.20371 1.42 1 2 5.00 Almost Perfect 4 Unchanged 28.41045 32.13318 4.28 3.44694 2.69 9 10 1.30 Almost Perfect 5 Unchanged 18.46363 198.44420 16.54 7.32523 8.31 5 7 1.86 Pretty Good 6 Unchanged 32.55135 86.42823 1.04 4.90451 2.13 10 12 1.75 Almost Perfect 7 Unchanged 53.01916 114.73257 0.09 3.40894 0.60 10 17 0.88 Almost Perfect 8 Unchanged 22.14201 29.75624 3.97 2.17642 1.70 11 10 1.00 Almost Perfect 9 Unchanged 33.95220 21.41103 0.02 4.00151 0.70 10 10 1.00 Almost Perfect 10 Unchanged 30.93298 156.14072 2.67 3.59362 0.82 10 11 1.18 Almost Perfect 11 Unchanged 12.75602 33.84195 22.56 1.23203 1.27 6 6 1.00 Almost Perfect 12 Unchanged 29.00378 80.81351 0.97 6.28644 2.74 8 10 1.20 Almost Perfect 13 Unchanged 28.50628 89.93145 0.78 8.48839 13.32 9 9 1.56 Pretty Good 14 Unchanged 24.96039 31.79643 5.78 3.90365 5.43 9 9 1.00 Almost Perfect 15 Unchanged 29.47379 89.73076 6.53 4.71635 12.26 8 6 0.67 Almost Perfect Table E.33: Subject 11 3rd method (Jacobian) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 27.80045 33.65890 33.66 3.51315 2.28 7 9 2.67 Pretty Good 2 Unchanged 18.52447 32.07069 21.38 2.25156 2.32 4 6 1.83 Pretty Good 3 Unchanged 31.05133 1.95714 0.06 1.10602 0.49 7 8 1.25 Pretty Good 4 Unchanged 29.98965 18.39273 2.45 2.52700 1.97 9 12 2.33 Pretty Good 5 Unchanged 32.66551 81.03461 6.75 3.27884 3.72 10 10 1.80 Pretty Good 6 Unchanged 54.20337 85.77076 1.03 6.84209 2.98 12 12 1.75 Pretty Good 7 Unchanged 59.15093 300.05674 0.23 6.51105 1.14 15 15 2.20 Pretty Good 8 Unchanged 21.14949 29.30308 3.91 3.87231 3.02 9 9 1.00 Pretty Good 9 Unchanged 44.58153 27.12041 0.02 5.07204 0.89 11 13 0.92 Pretty Good 10 Unchanged 40.19146 41.31434 0.71 3.08632 0.70 8 11 0.82 Pretty Good 11 Unchanged 14.71857 3.91542 2.61 1.43860 1.48 6 6 1.00 Pretty Good 12 Unchanged 26.01957 9.87891 0.12 3.98946 1.74 10 11 1.00 Pretty Good 13 Unchanged 28.96545 76.79292 0.67 4.65600 7.31 8 7 1.29 Pretty Good 14 Unchanged 20.44615 197.13058 35.84 6.83077 9.50 5 4 1.00 Pretty Good 15 Unchanged 50.98997 16.19492 1.18 2.57357 6.69 12 10 1.20 Pretty Good Table E.34: Subject 12 1st method (CCD) Appendix E. Experiment Data 126 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 7.23344 0.00364 0.00 0.92925 0.60 1 1 1.00 Almost Perfect 2 Unchanged 17.67777 15.39054 10.26 1.50993 1.55 6 7 1.00 Pretty Good 3 Unchanged 22.09117 5.93508 0.18 1.39623 0.62 6 6 1.17 Almost Perfect 4 Unchanged 21.25115 80.92529 10.79 2.94133 2.30 9 9 1.00 Pretty Good 5 Unchanged 22.33786 95.93714 7.99 3.46182 3.93 9 9 1.00 Pretty Good 6 Unchanged 29.04211 135.00250 1.62 8.26630 3.60 10 10 1.00 Pretty Good 7 Unchanged 38.47891 23.61919 0.02 5.52189 0.97 10 11 1.00 Pretty Good 8 Unchanged 24.25702 54.82053 7.31 4.07174 3.18 9 10 1.00 Pretty Good 9 Unchanged 34.57635 24.74930 0.02 4.93377 0.86 11 11 0.91 Pretty Good 10 Unchanged 36.14305 17.13838 0.29 4.74424 1.08 9 11 1.55 Pretty Good 11 Outlier 6.15676 150.00000 100.00 97.15083 100.00 0 0 0.00 Pretty Good 12 Unchanged 27.61708 55.79409 0.67 6.22740 2.71 11 10 1.00 Pretty Good 13 Unchanged 24.93705 10.47580 0.09 3.35214 5.26 6 7 1.29 Pretty Good 14 Unchanged 25.77456 35.75609 6.50 3.58324 4.99 8 8 -0.13 Pretty Good 15 Unchanged 45.27485 98.64525 7.17 6.30734 16.40 10 12 0.92 Pretty Good Table E.35: Subject 12 2nd method (1DOF) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 7.79762 0.19836 0.20 6.85977 4.46 1 1 •1.00 Pretty Good 2 Unchanged 9.49015 40.16882 26.78 3.70904 3.82 2 2 3.00 Pretty Good 3 Unchanged 18.74612 101.96150 3.02 3.06056 1.36 5 5 1.00 Pretty Good 4 Unchanged 33.77467 110.24707 14.70 5.77370 4.51 6 10 2.40 Pretty Good 5 Unchanged 33.75800 65.07753 5.42 4.26057 4.83 8 7 1.71 Pretty Good 6 Unchanged 33.66717 156.28349 1.88 9.83704 4.28 11 13 0.85 Pretty Good 7 Unchanged 65.88265 206.45716 0.15 5.59580 0.98 12 13 2.00 Satisfactory 8 Unchanged 17.68610 73.20307 9.76 3.14743 2.46 9 10 1.00 Pretty Good 9 Unchanged 45.07650 87.40659 0.07 6.85027 1.20 12 13 0.85 Pretty Good 10 Unchanged 24.37613 121.86924 2.08 5.58211 1.27 9 9 1.22 Pretty Good 11 Unchanged 10.36430 4.20137 2.80 3.29948 3.40 1 1 6.00 Pretty Good 12 Unchanged 32.17124 69.43135 0.83 7.57158 3.29 11 13 1.00 Pretty Good 13 Unchanged 25.00032 73.26414 0.64 4.46738 7.01 5 7 1.43 Pretty Good 14 Unchanged 27.39868 172.20300 31.31 6.42961 8.95 10 9 1.22 Pretty Good 15 Unchanged 16.53854 108.11096 7.86 7.23603 18.81 3 3 0.67 Pretty Good Table E.36: Subject 12 3rd method (Jacobian) Appendix E. Experiment Data 127 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 10.56182 2.33441 2.33 2.43195 1.58 2 3 1.33 Almost Perfect 2 Unchanged 13.78355 15.19236 10.13 1.45647 1.50 3 3 2.00 Almost Perfect 3 Unchanged 16.58943 22.47040 0.67 1.69082 0.75 4 5 1.40 Pretty Good 4 Unchanged 22.80286 104.68522 13.96 3.07389 2.40 6 7 1.71 Almost Perfect 5 Unchanged 35.18303 41.60816 3.47 3.87766 4.40 10 10 1.60 Almost Perfect 6 Unchanged 34.07803 27.80505 0.33 3.63263 1.58 6 9 2.56 Pretty Good 7 Unchanged 77.35961 228.58064 0.17 9.20828 1.61 11 21 3.05 Satisfactory 8 Unchanged 33.40224 39.46693 5.26 2.42916 1.90 10 11 1.55 Pretty Good 9 Unchanged 62.48938 45.85254 0.03 4.87614 0.85 12 21 1.81 Pretty Good 10 Unchanged 39.74650 96.57976 1.65 4.96504 1.13 7 14 1.29 Almost Perfect 11 Unchanged 16.21612 8.78572 5.86 1.27068 1.31 6 6 1.00 Almost Perfect 12 Unchanged 39.17901 34.45209 0.41 8.96724 3.90 8 9 1.78 Pretty Good 13 Unchanged 42.47407 58.42257 0.51 3.33744 5.24 12 12 1.50 Almost Perfect 14 Unchanged 28.95800 1.91301 0.35 2.32194 3.23 8 9 1.56 Almost Perfect 15 Unchanged 24.68127 76.19172 5.54 6.59659 17.15 8 6 0.83 Pretty Good Table E.37: Subject 13 1st method (CCD) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 7.35428 0.00171 0.00 0.63780 0.41 1 1 1.00 Almost Perfect 2 Unchanged 21.70201 10.11424 6.74 1.38544 1.43 6 7 1.71 Almost Perfect 3 Unchanged 17.64862 10.06747 0.30 1.07748 0.48 5 5 1.00 Almost Perfect 4 Unchanged 21.17033 24.55105 3.27 3.55652 2.78 9 10 1.00 Pretty Good 5 Unchanged 21.00617 73.45895 6.12 3.33866 3.79 9 9 1.00 Almost Perfect 6 Unchanged 56.46422 120.01070 1.44 6.63591 2.89 20 21 1.86 Almost Perfect 7 Unchanged 50.50746 54.38040 0.04 3.06139 0.54 22 22 0.91 Almost Perfect 8 Unchanged 28.88379 25.77432 3.44 1.92273 1.50 10 10 1.00 Pretty Good 9 Unchanged 46.15489 6.38410 0.00 3.09611 0.54 12 13 1.00 Almost Perfect 10 Unchanged 26.03791 22.17610 0.38 2.57405 0.59 9 9 1.22 Almost Perfect 11 Unchanged 14.12522 5.07503 3.38 0.58388 0.60 6 6 1.00 Almost Perfect 12 Unchanged 45.91573 26.10064 0.31 3.65668 1.59 17 17 1.00 Almost Perfect 13 Unchanged 29.55298 0.73019 0.01 0.80055 1.26 8 9 1.11 Perfect Match 14 Unchanged 26.77625 29.42140 5.35 2.99794 4.17 9 8 1.00 Almost Perfect 15 Unchanged 23.37789 66.57374 4.84 6.43654 16.73 7 6 0.50 Pretty Good Table E.38: Subject 13 2nd method (1DOF) Appendix E. Experiment Data 128 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 24.58039 33.51567 33.52 2.96010 1.92 9 11 1.91 Almost Perfect 2 Unchanged 9.27016 3.52139 2.35 1.58016 1.63 2 2 3.50 Almost Perfect 3 Unchanged 22.40037 11.45033 0.34 0.72994 0.32 7 8 1.50 Pretty Good 4 Unchanged 30.79715 47.62455 6.35 2.95393 2.31 5 9 2.22 Almost Perfect 5 Unchanged 32.04135 8.57610 0.71 2.64097 2.99 11 12 1.58 Pretty Good 6 Unchanged 33.58805 13.09021 0.16 3.51937 1.53 10 12 2.42 Pretty Good 7 Unchanged 51.31916 133.77775 0.10 4.09056 0.72 12 18 2.83 Pretty Good 8 Unchanged 42.90984 7.43266 0.99 1.69708 1.32 18 15 1.47 Almost Perfect 9 Unchanged 61.42016 38.78366 0.03 5.29936 0.93 22 20 1.20 Almost Perfect 10 Unchanged 26.16544 28.00112 0.48 2.45960 0.56 9 10 1.20 Almost Perfect 11 Unchanged 13.92690 0.52440 0.35 2.14550 2.21 1 1 6.00 Almost Perfect 12 Unchanged 32.98470 42.83527 0.51 5.45302 2.37 8 8 2.13 Pretty Good 13 Unchanged 37.78146 49.76826 0.43 3.12407 4.90 12 13 1.54 Satisfactory 14 Unchanged 28.00546 43.99353 8.00 4.60283 6.40 5 10 1.60 Almost Perfect 15 Unchanged 17.91196 70.39961 5.12 5.89393 15.32 7 5 1.00 Pretty Good Table E.39: Subject 13 3rd method (Jacobian) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 8.74430 0.02195 0.02 2.28216 1.48 1 1 1.00 Perfect Match 2 Unchanged 21.18281 18.71432 12.48 1.52403 1.57 6 6 1.00 Almost Perfect 3 Unchanged 27.49958 42.89700 1.27 2.63755 1.17 5 6 1.00 Perfect Match 4 Unchanged 58.08753 73.39079 9.79 5.53089 4.32 15 17 0.76 Perfect Match 5 Unchanged 39.85058 16.44355 1.37 3.34426 3.79 12 11 1.00 Perfect Match 6 Unchanged 67.01848 22.45957 0.27 4.63943 2.02 10 14 2.29 Almost Perfect 7 Unchanged 61.42255 77.53080 0.06 3.05301 0.53 14 11 1.00 Almost Perfect 8 Unchanged 37.25220 79.37660 10.58 2.76686 2.16 9 10 1.00 Almost Perfect 9 Unchanged 43.92981 4.47903 0.00 2.54803 0.45 10 11 0.91 Perfect Match 10 Unchanged 37.00721 33.77009 0.58 4.61123 1.05 9 9 1.22 Almost Perfect 11 Unchanged 17.77109 55.47488 36.98 1.77811 1.83 6 6 1.00 Almost Perfect 12 Unchanged 46.16150 41.24228 0.50 4.58000 1.99 12 16 1.06 Perfect Match 13 Unchanged 44.36395 19.27728 0.17 2.03159 3.19 9 12 0.66 Almost Perfect 14 Unchanged 45.50229 52.37710 9.52 3.28915 4.58 13 15 0.53 Perfect Match 15 Unchanged 40.12722 202.48561 14.73 8.02713 20.87 9 9 1.33 Perfect Match Table E.40: Subject 14 1st method (CCD) Appendix E. Experiment Data 129 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 5.02010 0.04805 0.05 3.37619 2.19 1 1 1.00 Perfect Match 2 Unchanged 33.35058 38.58043 25.72 1.88258 1.94 7 11 2.00 Almost Perfect 3 Unchanged 18.13449 6.94860 0.21 0.92977 0.41 5 6 1.67 Perfect Match 4 Unchanged 21.10786 44.95184 5.99 2.77744 2.17 9 9 1.00 Perfect Match 5 Unchanged 23.67710 78.96757 6.58 4.11473 4.67 9 10 1.00 Perfect Match 6 Unchanged 35.88063 36.65330 0.44 4.54376 1.98 10 11 1.00 Perfect Match 7 Unchanged 53.11510 47.96728 0.04 3.11390 0.55 11 14 1.93 Almost Perfect 8 Unchanged 27.07548 37.18269 4.96 2.15985 1.69 10 11 1.09 Perfect Match 9 Unchanged 31.68556 65.14228 0.05 7.17802 1.26 10 11 1.00 Almost Perfect 10 Unchanged 27.15881 139.26935 2.38 6.56363 1.49 9 9 1.22 Almost Perfect 11 Unchanged 25.01543 8.67259 5.78 1.07408 1.11 9 7 1.71 Perfect Match 12 Unchanged 31.34721 69.32061 0.83 5.59403 2.43 10 10 1.00 Perfect Match 13 Unchanged 25.82712 92.78482 0.81 4.28650 6.73 7 7 0.86 Perfect Match 14 Unchanged 23.16374 35.40606 6.44 3.65964 5.09 8 6 0.50 Almost Perfect 15 Unchanged 36.28146 285.89318 20.79 9.18018 23.87 11 10 1.50 Almost Perfect Table E.41: Subject 14 2nd method (1DOF) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 27.75291 35.93690 35.94 5.70038 3.71 3 5 6.00 Almost Perfect 2 Unchanged 31.50965 4.51229 3.01 1.32255 1.36 2 5 4.00 Perfect Match 3 Unchanged 7.72929 56.65203 1.68 3.19199 1.41 1 1 5.00 Perfect Match 4 Unchanged 33.08634 82.29343 10.97 3.97030 3.10 5 8 3.00 Perfect Match 5 Unchanged 35.82055 87.08068 7.26 3.30059 3.74 10 10 1.30 Almost Perfect 6 Unchanged 45.75071 101.97397 1.22 5.83974 2.54 8 11 2.18 Almost Perfect 7 Unchanged 47.69823 33.93265 0.03 4.03161 0.71 8 7 1.71 Almost Perfect 8 Unchanged 32.54468 72.73222 9.70 2.59176 2.02 7 8 1.88 Almost Perfect 9 Unchanged 37.94225 34.29553 0.03 4.54123 0.79 10 11 1.00 Perfect Match 10 Unchanged 35.41555 42.81940 0.73 2.65447 0.60 5 7 2.14 Perfect Match 11 Unchanged 9.34264 34.43655 22.96 2.21588 2.28 3 3 2.33 Almost Perfect 12 Unchanged 55.82670 18.45976 0.22 3.88133 1.69 9 12 1.58 Perfect Match 13 Unchanged 24.51872 183.44850 1.59 4.45673 6.99 6 7 1.29 Perfect Match 14 Unchanged 29.73713 20.95333 3.81 3.80585 5.30 8 7 0.86 Almost Perfect 15 Unchanged 26.47125 54.86882 3.99 5.10604 13.27 8 7 1.29 Almost Perfect Table E.42: Subject 14 3rd method (Jacobian) Appendix E. Experiment Data 130 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 53.70756 229.24058 229.24 4.27668 2.78 11 9 3.22 Pretty Good 2 Unchanged 9.72432 0.13730 0.09 0.94513 0.97 1 1 6.00 Almost Perfect 3 Unchanged 27.91296 17.03906 0.50 3.13680 1.39 2 3 3.00 Almost Perfect 4 Unchanged 41.57985 280.73453 37.43 6.57339 5.13 5 6 2.67 Pretty Good 5 Unchanged 31.69386 118.66038 9.89 11.03073 12.51 4 4 2.25 Satisfactory 6 Unchanged 53.74172 153.90979 1.85 8.61954 3.75 7 8 3.75 Pretty Good 7 Unchanged 119.29946 71.14666 0.05 4.17819 0.73 6 14 2.93 Pretty Good 8 Unchanged 25.22625 38.58001 5.14 3.63789 2.84 2 3 6.00 Pretty Good 9 Unchanged 59.24764 101.17269 0.08 8.47660 1.48 8 7 1.71 Pretty Good 10 Unchanged 35.20058 26.80464 0.46 2.74055 0.62 3 5 3.60 Almost Perfect 11 Unchanged 9.52933 1.36063 0.91 1.94434 2.00 1 1 6.00 Almost Perfect 12 Unchanged 53.28754 17.42090 0.21 6.70292 2.92 8 11 1.82 Almost Perfect 13 Unchanged 57.19261 28.77374 0.25 3.88241 6.09 6 11 1.91 Pretty Good 14 Unchanged 21.59203 118.86171 21.61 6.75883 9.40 2 3 2.33 Pretty Good 15 Unchanged 26.20126 102.35348 7.44 6.65804 17.31 1 5 3.60 Pretty Good Table E.43: Subject 15 1st method (CCD) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 16.09529 0.11089 0.11 5.12891 3.33 1 5 9.00 Almost Perfect 2 Unchanged 22.65621 36.45799 24.31 2.07144 2.13 5 6 2.17 Pretty Good 3 Unchanged 22.98957 48.89267 1.45 1.37568 0.61 5 6 1.67 Pretty Good 4 Unchanged 33.85399 68.16882 9.09 2.40595 1.88 8 10 2.90 Pretty Good 5 Unchanged 41.65167 111.44250 9.29 5.256.28 5.96 11 11 1.55 Satisfactory 6 Unchanged 59.81211 128.88328 1.55 8.55362 3.72 10 13 2.23 Satisfactory 7 Unchanged 68.93653 84.28816 0.06 4.60276 0.81 10 14 2.00 Pretty Good 8 Unchanged 50.14629 76.23598 10.16 2.13397 1.67 11 11 2.18 Pretty Good 9 Unchanged 44.59695 11.25709 0.01 3.18517 0.56 10 12 1.17 Pretty Good 10 Unchanged 46.17120 105.86347 1.81 4.80371 1.09 9 11 2.91 Pretty Good 11 Unchanged 29.51823 88.30762 58.87 2.58985 2.67 6 8 -1.25 Satisfactory 12 Unchanged 34.95170 38.39967 0.46 4.82857 2.10 10 10 1.10 Almost Perfect 13 Unchanged 27.17905 137.75550 1.20 5.35124 8.40 7 7 1.29 Pretty Good 14 Unchanged 26.18483 36.12608 6.57 3.10453 4.32 6 9 0.67 Almost Perfect 15 Unchanged 33.09917 92.06324 6.70 6.15959 16.01 8 6 1.17 Pretty Good Table E.44: Subject 15 2nd method (1DOF) Appendix E. Experiment Data 131 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 28.16748 78.73323 78.73 3.45252 2.24 7 8 2.63 Almost Perfect 2 Unchanged 16.91215 51.73455 34.49 2.30003 2.37 3 4 3.25 Almost Perfect 3 Unchanged 22.82649 35.37085 1.05 2.40655 1.07 5 5 2.00 Pretty Good 4 Unchanged 29.84251 105.48705 14.06 4.88643 3.81 4 6 2.00 Pretty Good 5 Unchanged 32.14410 105.17453 8.76 6.00146 6.81 7 8 1.75 Satisfactory 6 Unchanged 41.05343 65.49407 0.79 5.06432 2.20 8 9 2.67 Pretty Good 7 Unchanged 52.52784 42.61727 0.03 3.35996 0.59 6 7 2.43 Pretty Good 8 Unchanged 32.93155 5.55514 0.74 4.52852 3.53 4 4 4.75 Almost Perfect 9 Unchanged 61.90574 10.98066 0.01 3.91228 0.68 6 8 3.00 Almost Perfect 10 Unchanged 55.18668 35.56606 0.61 8.42149 1.92 7 10 2.20 Pretty Good 11 Unchanged 8.58862 0.27729 0.18 0.39406 0.41 1 1 6.00 Almost Perfect 12 Unchanged 37.81636 24.09291 0.29 5.38180 2.34 5 7 4.14 Pretty Good 13 Unchanged 30.23108 67.98894 0.59 5.60571 8.80 6 6 1.50 Pretty Good 14 Unchanged 29.94375 72.09423 13.11 6.55898 9.13 5 5 0.80 Pretty Good 15 Unchanged 24.66099 19.64811 1.43 3.35376 8.72 3 4 1.50 Almost Perfect Table E.45: Subject 15 3rd method (Jacobian) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 6.13343 0.02878 0.03 2.61291 1.70 2 1 1.00 Almost Perfect 2 Unchanged 16.10444 64.44345. 42.96 1.67872 1.73 5 5 1.00 Almost Perfect 3 Unchanged 16.86278 13.59189 0.40 2.96161 1.31 5 5 1.00 Almost Perfect 4 Unchanged 23.32122 397.40842 52.99 6.48103 5.06 7 7 1.00 Pretty Good 5 Unchanged 29.23550 241.34564 20.11 6.08256 6.90 11 12 0.83 Pretty Good 6 Unchanged 42.65572 53.78507 0.65 5.02494 2.19 14 12 0.92 Almost Perfect 7 Unchanged 45.84575 29.22240 0.02 4.60805 0.81 13 10 1.00 Pretty Good 8 Unchanged 25.62625 12.24958 1.63 2.69519 2.10 9 14 1.07 Almost Perfect 9 Unchanged 45.03659 37.57294 0.03 6.64012 1.16 10 12 0.83 Almost Perfect 10 Unchanged 26.20710 19.42929 0.33 2.80396 0.64 8 9 1.22 Almost Perfect 11 Unchanged 12.92687 18.55812 12.37 1.40841 1.45 7 6 1.00 Almost Perfect 12 Unchanged 27.75714 74.79405 0.90 6.64816 2.89 10 10 1.00 Almost Perfect 13 Unchanged 27.54378 82.21768 0.71 6.30820 9.90 9 7 1.29 Pretty Good 14 Unchanged 27.04796 149.77252 27.23 5.97751 8.32 8 9 1.22 Pretty Good 15 Unchanged 27.94547 923.49675 67.16 19.64705 51.08 7 7 2.00 Satisfactory Table E.46: Subject 16 1st method (CCD) Appendix E. Experiment Data 132 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 5.12840 0.00135 0.00 0.56501 0.37 1 1 1.00 Almost Perfect 2 Unchanged. 14.91766 11.07703 7.38 2.16616 2.23 8 6 1.00 Almost Perfect 3 Unchanged _ 11.35178 65.75036 1.95 2.37502 1.05 5 5 1.00 Almost Perfect 4 Unchanged 18.79769 60.90662 8.12 4.53390 3.54 9 9 1.00 Pretty Good 5 Unchanged 17.27101 193.89741 16.16 5.97550 6.78 9 8 1.00 Pretty Good 6 Unchanged 29.07615 115.56283 1.39 14.87172 6.47 12 13 0.69 Satisfactory 7 Unchanged 30.48532 100.08593 0.08 5.91128 1.03 10 11 1.00 Pretty Good 8 Unchanged 20.35022 55.11288 7.35 3.28327 2.56 9 9 1.00 Almost Perfect 9 Unchanged 28.18280 35.85260 0.03 6.14510 1.08 10 10 1.00 Almost Perfect 10 Unchanged 22.85942 5.39521 0.09 2.62609 0.60 8 9 1.22 Pretty Good 11 Unchanged 12.65345 27.70701 18.47 2.17867 2.24 6 6 1.00 Pretty Good 12 Unchanged 23.73693 29.21824 0.35 6.47485 2.82 10 10 1.00 Pretty Good 13 Unchanged 17.55019 55.95444 0.49 4.37290 6.86 5 6 1.33 Pretty Good 14 Unchanged 18.64354 13.93378 2.53 3.28725 4.57 7 7 1.00 Almost Perfect 15 Unchanged 17.87770 114.38901 8.32 7.37957 19.19 6 6 0.50 Pretty Good Table E.47: Subject 16 2nd method (1DOF) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 4.60839 0.10118 0.10 4.89924 3.18 1 1 1.00 Almost Perfect 2 Unchanged 13.05269 33.44352 22.30 2.03657 2.10 6 7 1.00 Almost Perfect 3 Unchanged 13.06269 4.37602 0.13 1.31367 0.58 5 5 1.00 Pretty Good 4 Unchanged 17.40609 86.00001 11.47 3.68251 2.87 8 8 1.00 Almost Perfect 5 Unchanged 20.35030 156.69540 13.06 4.45818 5.06 9 9 1.00 Almost Perfect 6 Unchanged 29.24375 51.82811 0.62 7.58883 3.30 11 11 0.91 Pretty Good 7 Unchanged 40.25141 221.80705 0.17 7.25447 1.27 10 11 1.00 Satisfactory 8 Unchanged 18.55776 15.10291 2.01 3.75143 2.93 9 10 1.00 Pretty Good 9 Unchanged 28.73126 39.05527 0.03 5.70209 1.00 10 10 1.00 Almost Perfect 10 Unchanged 24.07618 70.41877 1.20 3.85604 0.88 9 11 1.09 Almost Perfect 11 Unchanged 10.32848 6.12978 4.09 2.23681 2.30 6 6 1.00 Almost Perfect 12 Unchanged 22.60616 89.93709 1.08 7.36143 3.20 10 11 1.00 Pretty Good 13 Unchanged 19.45945 123.54493 1.07 5.26380 8.26 7 8 1.63 Pretty Good 14 Unchanged 19.56278 86.42982 15.71 6.21365 8.65 9 8 1.00 Pretty Good 15 Unchanged 17.56943 71.87987 5.23 7.19164 18.70 6 5 0.40 Satisfactory Table E.48: Subject 16 3rd method (Jacobian) Appendix E. Experiment Data 133 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 9.08183 0.00979 0.01 1.52382 0.99 1 4 1.00 Pretty Good 2 Unchanged 27.21378 0.81408 0.54 0.39069 0.40 7 24 1.00 Pretty Good 3 Unchanged 26.11378 0.11732 0.00 0.42048 0.19 6 15 1.00 Pretty Good 4 Unchanged 41.21317 22.52542 3.00 2.07277 1.62 11 22 0.91 Pretty Good 5 Unchanged 76.26792 8.87296 0.74 1.44718 1.64 24 39 0.64 Satisfactory 6 Unchanged 46.84577 6.23834 0.07 3.20424 1.39 10 22 1.00 Pretty Good 7 Unchanged 87.67811 32.06300 0.02 4.50403 0.79 23 47 0.91 Almost Perfect 8 Unchanged 52.67421 13.72240 1.83 1.14466 0.89 11 37 0.86 Almost Perfect 9 Unchanged 89.38564 21.00445 0.02 4.92918 0.86 23 51 1.00 Pretty Good 10 Unchanged 62.88271 6.57650 0.11 6.59854 1.50 14 49 0.69 Pretty Good 11 Unchanged 16.58859 6.40135 4.27 1.60188 1.65 6 10 1.00 Pretty Good 12 Unchanged 60.49351 34.28173 0.41 4.21738 1.83 16 45 1.13 Almost Perfect 13 Unchanged 72.98787 7.81315 0.07 2.07681 3.26 19 60 1.18 Perfect Match 14 Unchanged 29.35465 11.10847 2.02 3.58106 4.98 9 14 0.36 Perfect Match 15 Unchanged 77.07711 227.22979 16.53 8.50026 22.10 18 56 0.71 Satisfactory Table E.49: Subject 17 1st method (CCD) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 41.66186 5.45699 5.46 2.09361 1.36 13 34 0.88 Satisfactory 2 Unchanged 40.93672 7.34088 4.89 1.22921 1.27 10 57 0.86 Pretty Good 3 Unchanged 27.08275 7.98923 0.24 1.97902 0.88 8 24 1.00 Almost Perfect 4 Unchanged 30.69955 17.59160 2.35 2.76886 2.16 9 25 1.00 Almost Perfect 5 Unchanged 60.89722 38.16754 3.18 3.44672 3.91 19 45 0.98 Pretty Good 6 Unchanged 53.36765 50.29463 0.60 6.37225 2.77 17 23 1.00 Pretty Good 7 Unchanged 71.03560 22.30471 0.02 2.60314 0.46 22 38 1.00 Almost Perfect 8 Unchanged 36.66112 23.66026 3.15 1.80249 1.41 13 30 1.00 Almost Perfect 9 Unchanged 41.03286 35.00288 0.03 4.96283 0.87 12 15 1.07 Almost Perfect 10 Unchanged 57.31743 50.29571 0.86 3.00144 0.68 15 50 1.34 Almost Perfect 11 Unchanged 23.35395 4.73529 3.16 1.07788 1.11 8 11 1.00 Perfect Match 12 Unchanged 43.42364 10.49153 0.13 3.93390 1.71 12 21 1.00 Almost Perfect 13 Unchanged 49.15379 15.14952 0.13 1.82075 2.86 13 31 1.35 Perfect Match 14 Unchanged 45.63203 33.14355 6.03 3.47778 4.84 17 49 0.84 Pretty Good 15 Unchanged 85.15715 6.31674 0.46 1.60487 4.17 16 82 0.90 Satisfactory Table E.50: Subject 17 2nd method (1DOF) Appendix E. Experiment Data 134 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 55.05959 5.38768 5.39 1.59710 1.04 21 60 1.00 Pretty Good 2 Unchanged 19.61046 2.19256 1.46 0.78756 0.81 10 10 1.00 Almost Perfect 3 Unchanged 18.48375 3.70512 0.11 0.74906 0.33 7 10 1.00 Almost Perfect 4 Unchanged 36.50084 11.70895 1.56 1.74221 1.36 11 20 1.00 Almost Perfect 5 Unchanged '37.21586 7.25658 0.60 1.41902 1.61 11 28 1.00 Perfect Match 6 Unchanged 45.14523 83.05261 1.00 6.17430 2.69 16 38 0.94 Almost Perfect 7 Unchanged 114.06459 109.91269 0.08 4.27564 0.75 25 45 1.44 Unsatisfactory 8 Unchanged 35.85446 22.91977 3.06 1.76906 1.38 13 22 1.00 Perfect Match 9 Unchanged 90.94705 23.82760 0.02 4.32586 0.76 28 49 1.08 Pretty Good 10 Unchanged 53.69671 48.40258 0.83 3.12202 0.71 11 46 1.52 Perfect Match 11 Unchanged 11.66871 4.00571 2.67 0.92010 0.95 6 6 1.00 Perfect Match 12 Unchanged 42.68634 9.95627 0.12 2.73630 1.19 15 29 1.00 Perfect Match 13 Unchanged 51.72828 3.75945 0.03 2.14422 3.37 16 41 1.37 Perfect Match 14 Unchanged 20.29733 6.79521 1.24 1.47477 2.05 6 16 0.25 Perfect Match 15 Unchanged 60.55524 43.29397 3.15 3.89305 10.12 17 48 1.44 Almost Perfect Table E.51: Subject 17 3rd method (Jacobian) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 77.06776 6.15818 6.16 1.61735 1.05 13 11 1.00 Almost Perfect 2 Unchanged 38.32930 1.81518 1.21 1.53811 1.58 8 8 1.00 Almost Perfect 3 Unchanged 53.32718 1.22995 0.04 0.41815 0.19 9 9 1.00 Almost Perfect 4 Unchanged 49.79703 14.99318 2.00 2.39634 1.87 11 11 1.00 Almost Perfect 5 Unchanged 49.41451 19.60718 1.63 2.87685 3.26 11 11 1.00 Almost Perfect 6 Unchanged 78.76195 62.22799 0.75 4.88673 2.13 14 14 1.57 Almost Perfect 7 Unchanged 143.69909 21.67203 0.02 4.32391 0.76 14 18 1.17 Pretty Good 8 Unchanged 74.26549 13.21597 1.76 1.74922 1.37 11 10 1.10 Almost Perfect 9 Unchanged 65.71274 13.62535 0.01 4.06481 0.71 12 12 1.00 Almost Perfect 10 Unchanged 68.20323 28.64081 0.49 3.84164 0.87 12 11 1.36 Almost Perfect 11 Unchanged 50.26117 18.32541 12.22 2.41034 2.48 7 9 0.00 Perfect Match 12 Unchanged 67.51867 22.94167 0.28 3.94744 1.72 10 11 1.00 Pretty Good 13 Unchanged 86.17373 5.18600 0.05 1.65662 2.60 14 13 1.38 Almost Perfect 14 Unchanged 36.07984 1.82295 0.33 1.13955 1.59 8 6 0.50 Perfect Match 15 Unchanged 73.33821 4.04678 0.29 1.03476 2.69 12 9 0.89 Almost Perfect Table E.52: Subject 18 1st method (CCD) Appendix E. Experiment Data 135 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 49.62502 8.74634 8.75 1.40150 0.91 12 10 1.00 Almost Perfect 2 Unchanged 38.58566 8.43488 5.62 0.77440 0.80 10 10 0.90 Almost Perfect 3 Unchanged 26.46629 5.87278 0.17 0.97080 0.43 5 5 1.00 Almost Perfect 4 Unchanged 72.76706 37.69828 5.03 2.56798 2.00 18 17 1.00 Almost Perfect 5 Unchanged 34.36727 7.95680 0.66 1.82375 2.07 9 9 1.00 Perfect Match 6 Unchanged 90.60823 49.01204 0.59 3.25813 1.42 18 18 1.00 Pretty Good 7 Unchanged 91.05989 12.18977 0.01 1.97825 0.35 20 19 1.68 Almost Perfect 8 Unchanged 49.34334 12.27212 1.64 1.35892 1.06 11 12 1.67 Perfect Match 9 Unchanged 86.40482 29.17742 0.02 4.40670 0.77 16 16 1.00 Pretty Good 10 Unchanged 55.36927 22.66580 0.39 3.50928 0.80 13 13 0.92 Almost Perfect 11 Unchanged 64.40861 33.57082 22.38 1.46363 1.51 16 17 0.65 Perfect Match 12 Unchanged 36.61230 8.37771 0.10 2.66437 1.16 10 10 1.00 Almost Perfect 13 Unchanged 37.94315 15.13414 0.13 2.27444 3.57 10 10 1.50 Almost Perfect 14 Unchanged 32.22721 7.11621 1.29 2.31444 3.22 6 6 0.50 Almost Perfect 15 Unchanged 52.66090 4.35681 0.32 1.40991 3.67 8 8 0.88 Perfect Match Table E.53: Subject 18 2nd method (1DOF) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 52.59919 14.54181 14.54 1.56923 1.02 11 11 1.00 Almost Perfect 2 Unchanged 46.78993 0.95834 0.64 0.76991 0.79 10 9 1.00 Almost Perfect 3 Unchanged 35.14974 6.03827 0.18 0.67201 0.30 7 7 1.00 Perfect Match 4 Unchanged 47.96743 37.75949 5.03 2.85425 2.23 13 13 1.00 Pretty Good 5 Unchanged 40.01731 23.69451 1.97 1.90801 2.16 9 20 1.00 Almost Perfect 6 Unchanged 52.83669 19.80348 0.24 3.95848 1.72 13 20 1.45 Pretty Good 7 Unchanged 82.46215 19.56233 0.01 1.41123 0.25 15 19 1.47 Perfect Match 8 Unchanged 52.40919 5.43396 0.72 3.10517 2.42 7 9 1.89 Perfect Match 9 Unchanged 45.32655 3.06416 0.00 3.85690 0.68 10 11 0.91 Almost Perfect 10 Unchanged 56.31089 37.68023 0.64 3.03974 0.69 13 14 1.14 Pretty Good 11 Unchanged 25.53458 4.21674 2.81 1.30185 1.34 8 8 1.00 Perfect Match 12 Unchanged 35.27473 18.51398 0.22 4.82296 2.10 10 10 1.00 Almost Perfect 13 Unchanged 43.45237 4.79608 0.04 5.81360 9.12 12 17 1.65 Almost Perfect 14 Unchanged 44.96238 26.15754 4.76 2.57262 3.58 8 13 1.46 Almost Perfect 15 Unchanged 50.43332 12.65071 0.92 2.31611 6.02 9 13 1.69 Almost Perfect Table E.54: Subject 18 3rd method (Jacobian) Appendix E. Experiment Data 136 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 37.15725 39.99255 39.99 3.89165 2.53 3 7 5.86 Pretty Good 2 Unchanged 19.02447 295.33020 196.89 7.28864 7.50 7 5 1.00 Satisfactory 3 Unchanged 16.50860 148.92063 4.41 3.88130 1.72 5 5 1.00 Satisfactory 4 Unchanged 29.37546 493.81644 65.84 7.69073 6.00 8 10 1.10 Pretty Good 5 Unchanged 22.66868 550.11224 45.84 8.72157 9.89 7 6 1.17 Pretty Good 6 Unchanged 41.62983 181.14843 2.18 12.00041 5.22 10 13 1.69 Pretty Good 7 Unchanged 46.29741 148.11834 0.11 6.47486 1.13 13 12 1.00 Pretty Good 8 Unchanged 35.49055 252.45361 33.66 9.87432 7.71 11 14 -0.07 Pretty Good 9 Unchanged 38.38145 949.48638 0.71 20.47120 3.58 10 13 1.00 Satisfactory 10 Unchanged 38.48895 731.08669 12.50 10.41849 2.37 9 10 1.50 Satisfactory 11 Unchanged 12.64520 252.33936 168.23 5.80528 5.98 2 2 4.50 Satisfactory 12 Unchanged 22.82870 342.60841 4.12 11.29571 4.91 10 10 1.00 Satisfactory 13 Unchanged 36.83892 700.97961 6.09 21.57232 33.86 7 10 0.90 Satisfactory 14 Unchanged 13.54272 488.49303 88.82 12.64091 17.59 3 3 3.00 Satisfactory 15 Unchanged 13.78272 512.43836 37.27 13.78523 35.84 6 3 1.00 Pretty Good Table E.55: Subject 19 1st method (1DOF) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 17.34362 195.06988 195.07 14.75223 9.59 3 3 4.33 Satisfactory 2 Unchanged 12.58855 88.20453 58.80 6.02583 6.20 3 3 1.67 Satisfactory 3 Unchanged 17.36527 53.53620 1.59 4.33957 1.92 3 4 1.75 Satisfactory 4 Unchanged 13.48273 271.26807 36.17 9.50907 7.42 5 5 1.80 Satisfactory 5 Unchanged 28.50544 517.83204 43.15 26.30547 .29.83 10 9 0.78 Satisfactory 6 Unchanged 40.44730 560.09126 6.73 16.41741 7.14 5 11 3.36 Satisfactory 7 Unchanged 49.85163 1886.72724 1.42 19.71768 3.45 6 11 2.91 Unsatisfactory 8 Unchanged 23.97787 235.16865 31.36 11.13890 8.69 8 8 1.13 Unsatisfactory 9 Unchanged 37.60476 714.95466 0.54 21.66894 3.79 10 11 1.00 Satisfactory 10 Unchanged 25.21789 213.12633 3.64 11.34897 2.58 4 7 2.14 Satisfactory 11 Unchanged 8.37847 36.27009 24.18 8.35599 8.60 1 1 6.00 Satisfactory 12 Unchanged 35.57305 274.42181 3.30 11.89885 5.18 5 6 3.33 Satisfactory 13 Outlier 31.25131 606.81238 5.27 57.13842 89.68 8 9 1.33 Satisfactory 14 Unchanged 20.88866 144.50748 26.27 10.25495 14.27 5 5 2.00 Satisfactory 15 Unchanged 11.96602 452.88409 32.94 14.81651 38.52 3 3 2.00 Satisfactory Table E.56: Subject 19 2nd method (Jacobian) Appendix E. Experiment Data 137 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 40.36063 131.85145 131.85 13.66623 8.88 8 11 2.82 Unsatisfactory 2 Unchanged 9.20514 1.16456 0.78 2.13841 2.20 1 1 6.00 Satisfactory 3 Unchanged 15.78858 38.62582 1.14 3.06138 1.36 2 3 3.33 Satisfactory 4 Unchanged 19.30447 212.79348 28.37 8.21421 6.41 5 5 2.00 Satisfactory 5 Unchanged 23.33285 199.40171 16.62 15.80202 17.92 5 7 2.00 Satisfactory 6 Unchanged 28.81626 206.03648 2.47 14.27493 6.21 5 7 2.43 Satisfactory 7 Unchanged 60.11425 697.67822 0.52 8.54298 1.50 6 17 3.29 Satisfactory 8 Unchanged 20.35447 84.52888 11.27 8.21264 6.41 3 3 3.00 Satisfactory 9 Unchanged 45.78570 532.62842 0.40 17.52763 3.07 13 15 1.00 Satisfactory 10 Unchanged 23.68453 136.53822 2.33 7.59724 1.73 5 4 2.75 Satisfactory 11 Unchanged 6.73509 1.67404 1.12 3.82359 3.94 1 1 6.00 Satisfactory 12 Unchanged 36.65390 397.28624 4.77 16.86173 7.34 4 8 2.63 Satisfactory 13 Unchanged 21.20198 171.30669 1.49 9.93897 15.60 5 6 1.67 Satisfactory 14 Unchanged 26.93207 211.11415 38.38 13.51885 18.81 6 7 1.71 Satisfactory 15 Unchanged 13.66605 138.10192 10.04 7.51955 19.55 2 4 1.00 Satisfactory Table E.57: Subject 19 3rd method (CCD) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 135.03713 29.63100 29.63 2.53139 1.65 14 21 2.57 Almost Perfect 2 Unchanged 108.31338 33.16407 22.11 1.88321 1.94 14 16 1.69 Almost Perfect 3 Unchanged 136.01884 8.78227 0.26 1.36041 0.60 24 22 1.77 Almost Perfect 4 Unchanged 157.08001 3.69732 0.49 1.41742 1.11 30 28 1.57 Almost Perfect 5 Unchanged 224.84360 31.91434 2.66 2.85073 3.23 38 34 1.06 Almost Perfect 6 Unchanged 189.79889 67.53406 0.81 5.29905 2.31 31 37 0.97 Pretty Good 7 Unchanged 175.90367 69.64070 0.05 4.06264 0.71 37 41 1.07 Almost Perfect 8 Unchanged 72.66366 21.45931 2.86 2.75771 2.15 21 17 1.65 Pretty Good 9 Unchanged 59.78513 9.59057 0.01 3.18172 0.56 15 15 1.00 Almost Perfect 10 Unchanged 92.64901 12.93405 0.22 7.89294 1.80 16 19 0.84 Almost Perfect 11 Unchanged 55.32340 39.04667 26.03 2.40526 2.48 12 12 1.25 Pretty Good 12 Unchanged 91.52398 19.57032 0.24 4.97575 2.16 24 24 0.96 Pretty Good 13 Unchanged 68.06111 12.96938 0.11 3.39984 5.34 13 16 1.50 Pretty Good 14 Unchanged 91.63650 8.55736 1.56 2.92974 4.08 16 18 1.22 Almost Perfect 15 Unchanged 59.21347 97.04393 7.06 5.50089 14.30 16 9 0.56 Almost Perfect Table E.58: Subject 20 1st method (1DOF) Appendix E. Experiment Data 138 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 109.86499 29.51033 29.51 2.03018 1.32 17 18 1.50 Almost Perfect 2 Unchanged 35.38803 8.44433 5.63 0.88700 0.91 6 6 1.00 Almost Perfect 3 Unchanged 62.95179 19.84643 0.59 1.08676 0.48 6 7 1.43 Almost Perfect 4 Unchanged 101.02903 37.85206 5.05 2.65119 2.07 17 18 1.67 Almost Perfect 5 Unchanged 57.83754 12.82926 1.07 3.01008 3.41 18 16 1.00 Almost Perfect 6 Unchanged 106.44245 9.91145 0.12 2.70800 1.18 20 20 2.20 Almost Perfect 7 Unchanged 141.28296 13.42072 0.01 3.30902 0.58 17 16 4.63 Pretty Good 8 Unchanged 48.20239 8.16056 1.09 1.23089 0.96 4 6 2.17 Perfect Match 9 Unchanged 81.21039 24.76725 0.02 5.28899 0.93 10 16 1.44 Almost Perfect 10 Unchanged 93.07473 39.55984 0.68 2.81805 0.64 8 15 1.40 Pretty Good 11 Unchanged 22.20534 9.03313 6.02 0.73654 0.76 3 3 2.00 Perfect Match 12 Unchanged 86.84631 12.01864 0.14 2.65230 1.15 11 15 0.20 Perfect Match 13 Unchanged 69.63354 14.71919 0.13 2.57033 4.03 10 10 1.70 Pretty Good 14 Unchanged 64.46098 14.50383 2.64 2.77029 3.85 14 16 1.56 Almost Perfect 15 Unchanged 33.45134 20.79870 1.51 3.21448 8.36 4 4 1.25 Almost Perfect Table E.59: Subject 20 2nd method (Jacobian) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 52.90416 21.61430 21.61 1.43482 0.93 11 10 1.80 Almost Perfect 2 Unchanged 22.63202 5.96269 3.98 0.95361 0.98 3 3 2.00 Almost Perfect 3 Unchanged 41.49900 0.54924 0.02 0.23029 0.10 6 7 1.29 Almost Perfect 4 Unchanged 61.92598 79.11929 10.55 2.48137 1.94 13 12 1.00 Almost Perfect 5 Unchanged 56.22672 31.17005 2.60 2.43428 2.76 9 13 1.31 Perfect Match 6 Unchanged 67.96358 55.76235 0.67 4.86852 2.12 11 17 3.06 Pretty Good 7 Final 99.64823 45.40262 0.03 5.41874 0.95 9 15 1.93 Almost Perfect 7 Cutoff 94.15065 50.34583 0.04 5.39328 0.94 8 15 1.27 -7 Difference 5.49758 -4.94321 -0.01 0.02546 0.01 1 1 0.66 -8 Unchanged 45.58905 51.67652 6.89 3.14931 2.46 12 10 1.80 Almost Perfect 9 Unchanged 91.83312 8.95192 0.01 3.43581 0.60 12 11 1.36 Pretty Good 10 Unchanged 53.48419 33.77693 0.58 3.02645 0.69 8 11 1.27 Pretty Good 11 Unchanged 24.27705 11.61886 7.75 1.18659 1.22 3 3 2.00 Almost Perfect 12 Unchanged 46.50823 3.78857 0.05 2.16829 0.94 5 5 2.00 Almost Perfect 13 Unchanged 69.24694 2.39386 0.02 1.65514 2.60 12 13 1.08 Pretty Good 14 Unchanged 69.89361 18.09424 3.29 2.75336 3.83 11 10 1.40 Perfect Match 15 Unchanged 69.45693 6.41518 0.47 2.19611 5.71 12 11 1.45 Almost Perfect Table E.60: Subject 20 3rd method (CCD) Appendix E. Experiment Data 139 Trial Type Time (seconds) Angle Error % Pos. Error % R E Avg. Dist. Rating 1 Unchanged 62.74629 4.93704 4.94 1.17444 0.76 7 11 1.18 Perfect Match 2 Unchanged 26.17470 24.92066 16.61 1.51716 1.56 8 9 1.00 Perfect Match 3 Unchanged 18.14204 18.25760 0.54 1.23705 0.55 5 5 1.00 Perfect Match 4 Unchanged 36.47576 129.57847 17.28 3.42532 2.67 12 11 1.00 Perfect Match 5 Unchanged 44.07593 99.84495 8.32 3.14143 3.56 14 14 1.00 Perfect Match 6 Unchanged 34.73990 30.92261 0.37 3.54161 1.54 11 11 0.91 Perfect Match 7 Final 48.54351 27.88438 0.02 1.68802 0.30 14 15 0.93 Perfect Match 7 Cutoff 38.71832 28.81009 0.02 1.63133 0.29 11 12 0.92 -7 Difference 9.82519 -0.92571 0.00 0.05669 0.01 3 3 0.01 -8 Unchanged 22.36963 19.96011 2.66 1.43061 1.12 9 9 1.00 Perfect Match 9 Unchanged 42.80090 13.80120 0.01 2.92635 0.51 10 14 1.00 Perfect Match 10 Unchanged 43.80923 20.74520 0.35 2.05657 0.47 17 20 1.15 Perfect Match 11 Unchanged 25.88469 6.22806 4.15 1.20629 1.24 8 11 0.55 Perfect Match 12 Unchanged 24.73776 12.43067 0.15 2.85970 1.24 10 10 1.00 Perfect Match 13 Unchanged 28.58616 3.00199 0.03 1.66958 2.62 11 11 0.82 Perfect Match 14 Unchanged 41.01629 26.08475 4.74 6.69750 9.32 20 16 0.94 Perfect Match 15 Unchanged 45.19300 24.24945 1.76 5.47253 14.23 19 18 1.28 Perfect Match Table E.61: Subject 21 1st method (1DOF) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 44.47565 17.18871 17.19 1.60661 1.04 12 16 0.94 Perfect Match 2 Unchanged 18.77278 3.31577 2.21 0.47421 0.49 7 6 1.00 Perfect Match 3 Unchanged 22.90951 2.23519 0.07 0.49047 0.22 5 5 1.00 Perfect Match 4 Unchanged 30.63045 3.77110 0.50 1.39365 1.09 9 10 1.00 Perfect Match 5 Unchanged 31.70464 15.22882 1.27 1.68052 1.91 9 10 1.00 Perfect Match 6 Unchanged 58.51836 29.69230 0.36 3.31590 1.44 8 17 1.48 Perfect Match 7 Unchanged 63.56927 15.91537 0.01 2.23161 0.39 13 23 1.96 Almost Perfect 8'- Unchanged 29.91545 29.77340 3.97 2.23615 1.75 11 14 1.00 Perfect Match 9 Unchanged 52.38660 34.98001 0.03 5.29644 0.93 11 10 1.00 Perfect Match 10 Unchanged 45.25485 15.78879 0.27 3.04657 0.69 14 16 1.19 Perfect Match 11 Unchanged 20.15362 17.58574 11.72 2.12625 2.19 8 7 1.00 Perfect Match 12 Unchanged 32.16465 38.76604 0.47 4.76632 2.07 10 10 1.00 Perfect Match 13 Unchanged 27.70124 5.29356 0.05 1.82115 2.86 7 11 1.36 Perfect Match 14 Unchanged 17.40776 84.55546 15.37 3.81637 5.31 6 8 0.88 Almost Perfect 15 Unchanged 25.74872 108.31185 7.88 5.60587 14.57 10 12 0.50 Perfect Match Table E.62: Subject 21 2nd method (Jacobian) Appendix E. Experiment Data 140 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Final 50.46407 201.01171 201.01 9.55532 6.21 9 9 2.67 Almost Perfect 1 Cutoff 39.04308 148.98617 148.99 9.54275 6.20 7 7 3.14 -1 Difference 11.42099 52.02554 52.02 0.01257 0.01 2 2 -0.47 -2 Unchanged 17.51443 95.13086 63.42 3.32392 3.42 5 4 1.50 Almost Perfect 3 Unchanged 18.76195 0.89024 0.03 0.56246 0.25 5 6 1.00 Perfect Match 4 Unchanged 43.74398 82.87053 11.05 2.50302 1.95 12 14 1.79 Perfect Match 5 Unchanged 28.85293 60.15488 5.01 2.97867 3.38 9 11 1.00 Perfect Match 6 Unchanged 37.11637 36.55657 0.44 4.33513 1.89 12 18 1.50 Perfect Match 7 Unchanged 64.10094 41.18273 0.03 1.85798 0.33 16 28 3.14 Perfect Match 8 Unchanged 22.31282 25.12448 3.35 1.64960 1.29 9 15 1.00 Perfect Match 9 Unchanged 65.53097 40.16803 0.03 7.28175 1.27 10 26 1.77 Perfect Match 10 Unchanged 38.29891 21.42190 0.37 2.78031 0.63 13 21 1.95 Perfect Match 11 Unchanged 12.10103 27.11045 18.07 1.40352 1.44 4 9 1.22 Perfect Match 12 Unchanged 30.61213 26.78589 0.32 4.52254 1.97 12 26 1.00 Perfect Match 13 Unchanged 19.09861 16.99708 0.15 3.23080 5.07 7 10 1.40 Almost Perfect 14 Unchanged 22.49366 14.19495 2.58 2.22322 3.09 9 11 0.64 Perfect Match 15 Unchanged 16.43275 85.79549 6.24 4.81492 12.52 7 11 1.18 Perfect Match Table E.63: Subject 21 3rd method (CCD) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Final 14.29189 0.20332 0.20 6.94496 4.51 2 2 1.00 Almost Perfect 1 Cutoff 5.09509 0.08050 0.08 4.37007 2.84 2 1 1.00 -1 Difference 9.19680 0.12282 0.12 2.57489 1.67 0 1 0.00 -2 Unchanged 22.27283 52.35726 34.90 1.84804 1.90 10 7 0.86 Almost Perfect 3 Unchanged 15.20356 27.30232 0.81 1.67147 0.74 5 5 1.00 Almost Perfect 4 Unchanged 37.51308 28.89808 3.85 2.32983 1.82 17 12 1.00 Almost Perfect 5 Unchanged 25.61372 60.98479 5.08 4.84552 5.49 10 12 1.00 Almost Perfect 6 Unchanged 43.82483 23.09994 0.28 4.50261 1.96 17 11 1.82 Almost Perfect 7 Unchanged 39.41476 21.60398 0.02 3.63712 0.64 14 11 1.00 Almost Perfect 8 Unchanged 24.38287 21.50818 2.87 2.80564 2.19 9 9 1.00 Almost Perfect 9 Unchanged 36.25305 45.92051 0.03 5.10115 0.89 11 10 1.00 Pretty Good 10 Unchanged 33.89968 8.78419 0.15 2.85311 0.65 11 12 1.17 Almost Perfect 11 Unchanged 27.00958 7.43979 4.96 0.80844 0.83 8 9 0.89 Perfect Match 12 Unchanged 30.94047 42.87628 0.52 3.63558 1.58 10 10 1.00 Pretty Good 13 Unchanged 28.39043 73.87267 0.64 5.48400 8.61 7 7 1.57 Almost Perfect 14 Unchanged 30.83881 10.72516 1.95 3.19581 4.45 14 8 0.25 Almost Perfect 15 Unchanged 21.05116 79.73452 5.80 5.05343 13.14 8 5 0.40 Almost Perfect Table E.64: Subject 22 1st method (1DOF) Appendix E. Experiment Data 141 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 21.14951 29.57689 29.58 5.92627 3.85 9 7 2.29 Pretty Good 2 Unchanged 12.91438 0.91745 0.61 0.91385 0.94 3 2 6.00 Perfect Match 3 Unchanged 21.12702 54.05844 1.60 3.65922 1.62 4 5 3.00 Almost Perfect 4 Unchanged 35.45058 104.18167 13.89 4.25820 3.32 13 9 1.22 Almost Perfect 5 Unchanged 38.40146 82.14331 6.85 3.39944 3.85 17 12 1.25 Almost Perfect 6 Unchanged 38.24229 43.05748 0.52 5.87448 2.56 9 7 2.86 Pretty Good 7 Unchanged 59.47680 120.96588 0.09 4.42184 0.77 7 12 3.58 Pretty Good 8 Unchanged 33.74306 49.78598 6.64 3.67782 2.87 8 7 1.71 Pretty Good 9 Unchanged 36.12726 26.87274 0.02 4.48917 0.79 11 13 0.85 Perfect Match 10 Unchanged 26.91378 73.55939 1.26 5.81798 1.32 11 10 1.20 Pretty Good 11 Unchanged 13.98523 24.69867 16.47 2.42516 2.50 7 7 1.00 Almost Perfect 12 Unchanged 31.11217 40.17586 0.48 5.30612 2.31 13 14 1.00 Pretty Good 13 Unchanged 25.93542 108.58099 0.94 3.62895 5.70 12 6 1.33 Almost Perfect 14 Unchanged 21.86952 41.61641 7.57 3.61666 5.03 10 7 0.57 Perfect Match 15 Unchanged 14.36524 74.07766 5.39 6.21930 16.17 6 5 0.40 Almost Perfect Table E.65: Subject 22 2nd method (Jacobian) Time Angle Pos. Avg. Trial Type (seconds)' Error % Error % R E Dist. Rating 1 Unchanged 34.98389 20.72138 20.72 2.71750 1.77 10 10 2.30 Pretty Good 2 Unchanged 9.00764 1.33198 0.89 1.42732 1.47 1 1 6.00 Perfect Match 3 Unchanged 17.16361 13.93836 0.41 1.48988 0.66 4 5 2.00 Almost Perfect 4 Unchanged 28.19711 98.48664 13.13 4.08605 3.19 16 11 1.09 Almost Perfect 5 Unchanged 26.91793 40.39303 3.37 2.68234 3.04 17 13 0.69 Almost Perfect 6 Unchanged 39.54145 74.99373 0.90 7.44181 3.24 14 13 1.15 Almost Perfect 7 Unchanged 44.36155 141.00966 0.11 3.58646 0.63 12 15 0.40 Almost Perfect 8 Unchanged 19.23196 37.37221 4.98 3.33804 2.61 10 9 1.00 Perfect Match 9 Unchanged 43.10651 15.71211 0.01 6.16232 1.08 12 11 1.00 Almost Perfect 10 Unchanged 22.19202 80.20293 1.37 4.85801 1.11 11 9 1.22 Almost Perfect 11 Unchanged 18.74613 22.63993 15.09 2.46682 2.54 11 8 1.00 Perfect Match 12 Unchanged 23.64619 20.02438 0.24 4.70096 2.05 11 10 1.00 Almost Perfect 13 Unchanged 47.97992 37.15212 0.32 5.35978 8.41 16 14 0.29 Almost Perfect 14 Unchanged 23.86036 92.71296 16.86 4.30143 . 5.99 11 8 1.00 Almost Perfect 15 Unchanged 22.50786 195.12184 14.19 8.45687 21.99 10 7 0.57 Almost Perfect Table E.66: Subject 22 3rd method (CCD) Appendix E. Experiment Data 142 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 14.62110 0.73306 0.73 1.67710 1.09 3 2 1.00 Almost Perfect 2 Unchanged 17.38615 46.06505 30.71 2.20748 2.27 6 6 1.00 Almost Perfect 3 Unchanged 16.21361 8.78589 0.26 1.10680 0.49 5 5 1.00 Almost Perfect 4 Unchanged 35.37313 14.99633 2.00 1.75071 1.37 11 12 1.00 Almost Perfect 5 Unchanged 38.83735 9.75852 0.81 2.78181 3.15 11 11 0.91 Almost Perfect 6 Unchanged 44.32161 82.30812 0.99 6.25063 2.72 10 11 1.00 Almost Perfect 7 Unchanged 53.02008 17.65497 0.01 2.37524 0.42 12 16 1.50 Pretty Good 8 Unchanged 37.48232 16.09514 2.15 2.29017 1.79 13 13 1.00 Almost Perfect 9 Unchanged 35.32310 14.34722 0.01 2.62678 0.46 11 10 1.00 Almost Perfect 10 Unchanged 36.67978 23.25257 0.40 5.71386 1.30 11 11 1.36 Almost Perfect 11 Unchanged 33.61056 9.75285 6.50 2.48004 2.55 9 8 1.00 Pretty Good 12 Unchanged 28.61381 19.87957 0.24 4.36184 1.90 10 10 1.00 Pretty Good 13 Unchanged 34.54809 29.99530 0.26 4.09068 6.42 10 9 1.56 Almost Perfect 14 Unchanged 25.88711 24.07596 4.38 2.62602 3.65 9 7 0.86 Almost Perfect 15 Unchanged 26.02877 61.15086 4.45 6.47045 16.82 8 6 0.33 Pretty Good Table E.67: Subject 23 1st method (1DOF) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating I; Unchanged 40.26646 41.87543 41.88 6.05582 3.94 8 7 -0.57 Almost Perfect 2' Unchanged 10.28183 1.08089 0.72 1.13416 1.17 1 1 6.00 Almost Perfect 3 Unchanged 14.19606 4.80331 0.14 3.02740 1.34 1 1 5.00 Pretty Good 4 Unchanged 28.59545 49.20613 6.56 4.72220 3.69 7 7 1.86 Almost Perfect 5 Unchanged 31.02632 48.83001 4.07 3.83459 4.35 5 6 1.83 Pretty Good 6 Unchanged 35.00305 121.74453 1.46 6.96504 3.03 6 7 2.86 Pretty Good 7 Unchanged 70.85110 52.35144 0.04 2.02689 0.35 3 8 5.38 Almost Perfect 8 Unchanged 49.21410 5.68484 0.76 3.07934 2.40 4 6 4.17 Pretty Good 9 Unchanged 46.16989 17.74639 0.01 5.48432 0.96 10 10 1.00 Almost Perfect 10 Unchanged 47.90158 39.08421 0.67 5.01179 1.14 6 12 0.83 Pretty Good 11 Unchanged 12.36852 0.88665 0.59 1.13474 1.17 1 1 6.00 Almost Perfect 12 Unchanged 29.96547 77.28875 0.93 6.50781 2.83 5 5 2.00 Almost Perfect 13 Unchanged 53.86001 45.97729 0.40 5.66731 8.89 9 13 2.00 Pretty Good 14 Unchanged 21.93368 18.98063 3.45 3.16147 4.40 8 7 0.42 Pretty Good 15 Unchanged 28.61377 53.39716 3.88 4.31136 11.21 6 7 1.71 Almost Perfect Table E.68: Subject 23 2nd method (Jacobian) Appendix E. Experiment Data 143 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 19.89112 98.27385 98.27 7.99705 5.20 2 4 4.00 Pretty Good 2 Unchanged 8.55262 1.99360 1.33 2.06400 2.12 1 1 6.00 Almost Perfect 3 Unchanged 29.10377 28.27420 0.84 1.60322 0.71 3 8 2.88 Pretty Good 4 Unchanged 39.52727 124.42845 16.59 5.19806 4.06 5 7 2.14 Pretty Good 5 Unchanged 40.24562 56.89646 4.74 5.22670 5.93 8 8 1.75 Pretty Good 6 Unchanged 28.65543 100.31325 1.20 5.31789 2.31 5 6 3.33 Almost Perfect 7 Unchanged 94.91310 80.10503 0.06 5.44339 0.95 14 20 2.20 Satisfactory 8 Unchanged 38.13723 41.22014 5.50 2.33172 1.82 7 6 3.00 Almost Perfect 9 Unchanged 63.33177 30.15727 0.02 5.22639 0.91 11 15 1.33 Pretty Good 10 Unchanged 39.97059 34.84136 0.60 3.09142 0.70 6 14 0.64 Almost Perfect 11 Unchanged 9.83765 6.30646 4.20 1.27103 1.31 1 1 6.00 Pretty Good 12 Unchanged 35.08802 32.13164 0.39 5.85429 2.55 5 7 3.43 Pretty Good 13 Unchanged 21.93866 67.65952 0.59 4.45870 7.00 4 5 2.00 Almost Perfect 14 Unchanged 19.23528 37.14635 6.75 3.44195 4.79 4 6 1.83 Almost Perfect 15 Unchanged 22.62533 91.51062 6.66 5.40053 14.04 4 5 1.80 Pretty Good Table E.69: Subject 23 3rd method (CCD) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 10.12192 0.00343 0.00 0.90208 0.59 1 2 1.00 Almost Perfect 2 Unchanged 20.86719 61.26629 40.84 3.28220 3.38 6 6 1.00 Almost Perfect 3 Unchanged 19.16382 82.08095 2.43 1.92312 0.85 5 5 1.00 Almost Perfect 4 Unchanged 24.31726 65.20595 8.69 3.99031 3.11 8 7 1.00 Almost Perfect 5 Unchanged 29.91240 66.88235 5.57 3.81322 4.32 9 9 1.00 Perfect Match 6 Unchanged 36.00505 20.78724 0.25 3.71566 1.62 10 11 1.00 Almost Perfect 7 Unchanged 48.70951 52.67261 0.04 2.89885 0.51 10 13 1.92 Almost Perfect 8 Unchanged 29.21986 8.91211 1.19 1.39364 1.09 9 9 1.89 Perfect Match 9 Unchanged 34.36996 14.51441 0.01 3.21819 0.56 10 11 1.00 Almost Perfect 10 Unchanged 31.26488 25.79933 0.44 2.05477 0.47 8 9 1.22 Perfect Match 11 Unchanged 16.60369 25.09363 16.73 1.39456 1.44 6 7 1.00 Almost Perfect 12 Unchanged 27.12477 46.76123 0.56 7.15479 3.11 10 11 0.91 Almost Perfect 13 Unchanged 25.12138 8.45344 0.07 2.87176 4.51 7 7 1.29 Almost Perfect 14 Unchanged 27.17892 87.23544 15.86 5.08909 7.08 8 7 0.86 Almost Perfect 15 Unchanged 26.91891 51.26154 3.73 4.19257 10.90 6 6 0.83 Almost Perfect Table E.70: Subject 24 1st method (1DOF) Appendix E. Experiment Data 144 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 28.93874 390.19545 390.20 11.27746 7.33 2 3 4.67 Pretty Good 2 Unchanged 10.67764 8.59673 5.73 4.58514 4.72 1 1 6.00 Almost Perfect 3 Unchanged 6.05759 13.28653 0.39 5.62597 2.49 1 1 5.00 Pretty Good 4 Unchanged 21.20446 571.22268 76.16 9.69029 7.56 2 2 4.50 Pretty Good 5 Unchanged 32.89964 579.05875 48.25 14.29146 16.21 3 5 3.20 Satisfactory 6 Unchanged 48.04904 98.40227 1.18 7.33017 3.19 12 13 1.85 Almost Perfect 7 Unchanged 69.74683 480.67546 0.36 8.48020 1.48 2 11 6.27 Pretty Good 8 Unchanged 23.41033 55.49460 7.40 8.23729 6.43 1 1 9.00 Pretty Good 9 Unchanged 34.83051 165.09017 0.12 9.53604 1.67 10 11 1.00 Almost Perfect 10 Unchanged 58.30836 56.25475 0.96 3.93276 0.90 12 11 1.27 Almost Perfect 11 Unchanged 7.46093 2.33354 1.56 2.79604 2.88 1 1 6.00 Perfect Match 12 Unchanged 31.36879 71.37227 0.86 6.82848 2.97 5 6 3.33 Almost Perfect 13 Unchanged 42.37227 144.78219 1.26 5.18517 8.14 9 8 1.88 Pretty Good 14 Unchanged 30.19211 104.70546 19.04 5.47022 7.61 5 6 2.67 Almost Perfect 15 Unchanged 24.43702 117.28600 8.53 6.10453 15.87 5 4 1.00 Almost Perfect Table E.71: Subject 24 2nd method (Jacobian) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 27.58042 354.51894 354.52 10.29514 6.69 2 3 5.33 Almost Perfect 2 Unchanged 8.31931 6.41672 4.28 1.46631 1.51 1 1 6.00 Perfect Match 3 Unchanged 8.06596 20.40975 0.60 5.96176 2.64 1 1 5.00 Pretty Good 4 Unchanged 18.58278 202.13143 26.95 7.62952 5.96 2 3 3.67 Pretty Good 5 Unchanged 41.24065 686.86155 57.24 17.91336 20.31 6 9 3.00 Pretty Good 6 Final 33.10801 672.86620 8.08 23.07462 10.04 7 9 3.00 Pretty Good 6 Cutoff 23.15035 1491.45201 17.92 17.43410 7.59 4 6 4.00 -6 Difference 9.95766 -818.58580 -9.84 5.64052 2.45 3 3 -1.00 -7 Unchanged 68.20940 252.25465 0.19 6.95174 1.22 6 14 3.14 Satisfactory 8 Unchanged 15.70858 127.10961 16.95 6.17876 4.82 3 3 3.33 Pretty Good 9 Final 36.66223 39.05132 0.03 6.75781 1.18 11 14 1.07 Almost Perfect 9 Cutoff 31.83382 46.28668 0.03 5.96046 1.04 10 13 1.08 -9 Difference 4.82841 -7.23536 0.00 0.79735 0.14 1 1 -0.01 -10 Unchanged 21.57534 45.23317 0.77 5.07605 1.16 4 5 2.20 Almost Perfect 11 Unchanged 9.08180 2.13810 1.43 2.76877 2.85 1 1 6.00 Almost Perfect 12 Unchanged 25.20956 73.31453 0.88 6.83414 2.97 5 5 2.00 Almost Perfect 13 Unchanged 28.50793 452.30914 3.93 6.78872 10.65 6 6 2.17 Pretty Good 14 Unchanged 20.29033 137.24059 24.95 8.70344 12.11 5 4 1.50 Almost Perfect 15 Unchanged 13.52103 90.65641 6.59 7.12505 18.52 4 3 0.67 Almost Perfect Table E.72: Subject 24 3rd method (CCD) Appendix E. Experiment Data 145 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 15.31531 0.00171 0.00 0.63678 0.41 1 1 1.00 Perfect Match 2 Unchanged 43.52337 18.05857 12.04 2.87885 2.96 10 10 0.80 Almost Perfect 3 Unchanged 24.24715 3.11399 0.09 0.53563 0.24 5 5 1.00 Perfect Match 4 Unchanged 47.41512 20.74798 2.77 1.62181 1.27 15 14 1.00 Almost Perfect 5 Unchanged 81.84583 18.51188 1.54 1.73752 1.97 26 25 0.92 Almost Perfect 6 Unchanged 72.96388 10.56102 0.13 2.41644 1.05 19 20 1.00 Almost Perfect 7 Unchanged 55.23785 26.56966 0.02 1.69864 0.30 11 14 1.14 Perfect Match 8 Unchanged 33.01455 13.88286 1.85 1.42141 1.11 9 9 1.00 Perfect Match 9 Unchanged 84.00644 12.51900 0.01 2.46007 0.43 21 24 0.96 Perfect Match 10 Unchanged 34.45883 11.04196 0.19 1.46807 0.33 11 10 0.90 Perfect Match 11 Unchanged 18.32821 19.19860 12.80 1.13225 1.17 6 7 1.00 Perfect Match 12 Unchanged 91.44617 20.68788 0.25 2.65448 1.15 26 21 0.81 Almost Perfect 13 Unchanged 54.65150 8.69791 0.08 1.94090 3.05 13 13 1.08 Pretty Good 14 Unchanged 39.84101 10.87141 1.98 1.95686 2.72 10 11 0.55 Almost Perfect 15 Unchanged 52.68252 17.92927 1.30 2.87218 7.47 13 13 1.31 Almost Perfect Table E.73: Subject 25 1st method (1DOF) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 18.92611 0.00170 0.00 0.63592 0.41 1 1 1.00 Almost Perfect 2 Unchanged 40.26977 2.62590 1.75 0.48326 0.50 9 8 1.00 Perfect Match 3 Unchanged 46.85819 0.21452 0.01 1.65176 0.73 10 10 1.00 Almost Perfect 4 Unchanged 72.40522 29.02475 3.87 1.75385 1.37 20 22 1.00 Pretty Good 5 Unchanged 49.48905 15.25271 1.27 2.11893 2.40 12 11 1.00 Pretty Good 6 Unchanged 80.76285 42.32581 0.51 4.59482 2.00 18 17 1.00 Pretty Good 7 Unchanged 66.18430 20.69000 0.02 3.35614 0.59 10 11 1.00 Pretty Good 8 Unchanged 130.65525 13.59692 1.81 2.68497 2.10 29 32 0.69 Pretty Good 9 Unchanged 61.16089 14.37358 0.01 2.59899 0.45 11 12 0.92 Almost Perfect 10 Unchanged 65.73013 16.19154 0.28 1.96872 0.45 16 14 1.43 Almost Perfect 11 Unchanged 56.04417 14.06376 9.38 1.56341 1.61 14 15 1.00 Almost Perfect 12 Unchanged 58.46502 15.96869 0.19 6.34199 2.76 10 10 1.00 Almost Perfect 13 Unchanged 150.68056 23.30043 0.20 4.49949 7.06 39 36 0.83 Pretty Good 14 Unchanged 47.32986 2.47181 0.45 1.90034 2.64 13 13 1.54 Almost Perfect 15 Unchanged 60.81088 7.61794 0.55 1.80344 4.69 17 14 1.50 Perfect Match Table E.74: Subject 25 2nd method (Jacobian) Appendix E. Experiment Data 146 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 23.61368 0.00029 0.00 0.26151 0.17 1 1 1.00 Almost Perfect 2 Unchanged 24.99454 0.69371 0.46 0.47924 0.49 6 6 1.00 Perfect Match 3 Unchanged 52.28911 15.33386 0.45 0.92060 0.41 8 12 1.67 Almost Perfect 4 Unchanged 54.52247 7.80227 1.04 0.93343 0.73 11 12 1.00 Almost Perfect 5 Unchanged 52.14660 18.96152 1.58 2.77568 3.15 15 17 0.94 Almost Perfect 6 Unchanged 70.19104 26.09921 0.31 5.31409 2.31 13 13 0.92 Pretty Good 7 Unchanged 57.73502 15.64487 0.01 2.67518 0.47 11 15 2.33 Almost Perfect 8 Unchanged 52.86579 35.30984 4.71 2.70157 2.11 15 16 1.00 Almost Perfect 9 Unchanged 55.92583 34.85145 0.03 4.82007 0.84 10 11 1.00 Almost Perfect 10 Unchanged 49.34656 12.71993 0.22 1.61230 0.37 14 14 1.36 Perfect Match 11 Unchanged 20.93115 11.58389 7.72 1.34283 1.38 8 8 1.00 Perfect Match 12 Unchanged 66.86184 9.35233 0.11 4.09515 1.78 17 18 1.00 Almost Perfect 13 Unchanged 60.67175 12.34005 0.11 2.44800 3.84 16 15 1.33 Pretty Good 14 Unchanged 48.44573 7.18010 1.31 2.10244 2.93 15 14 1.14 Almost Perfect 15 Unchanged 95.25058 14.50761 1.06 4.80166 12.48 23 24 0.95 Pretty Good Table E.75: Subject 25 3rd method (CCD) ' Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 14.68606 6.13351 6.13 4.22993 2.75 4 2 1.00 Pretty Good 2 Unchanged 20.24949 15.88638 10.59 1.50347 1.55 6 6 1.00. Satisfactory 3 Unchanged 22.30368 12.63310 0.37 1.67089 0.74 5 5 1.00 Satisfactory 4 Unchanged 26.34376 13.29605 1.77 2.24541 1.75 9 9 1.00 Pretty Good 5 Unchanged 25.77041 12.96746 1.08 3.06876 3.48 9 9 1.00 Pretty Good 6 Unchanged 44.13486 2.44393 0.03 3.01214 1.31 10 12 1.08 Pretty Good 7 Unchanged 54.39920 20.56413 0.02 2.75369 0.48 12 13 1.54 Pretty Good 8 Unchanged 25.62208 19.92992 2.66 1.28700 1.00 10 9 1.00 Satisfactory 9 Unchanged 39.03645 4.68642 0.00 1.60631 0.28 10 11 0.91 Pretty Good 10 Unchanged 36.27307 50.09370 0.86 3.10137 0.71 10 9 0.89 Satisfactory 11 Unchanged 21.05700 15.96003 10.64 2.22216 2.29 6 7 1.00 Satisfactory 12 Unchanged 29.37797 23.02169 0.28 4.07793 1.77 10 11 1.00 Satisfactory 13 Unchanged 30.95799 69.20018 0.60 5.42849 8.52 9 10 1.30 Satisfactory 14 Unchanged 26.09458 15.23076 2.77 3.61498 5.03 8 7 1.00 Satisfactory 15 Unchanged 51.08497 11.31815 0.82 2.50280 6.51 11 11 0.72 Pretty Good Table E.76: Subject 26 1st method (1DOF) Appendix E. Experiment Data 147 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 15.15101 44.95451 44.95 2.83091 1.84 7 6 1.17 Satisfactory 2 Unchanged 15.64101 27.60979 18.41 1.73884 1.79 10 7 1.00 Pretty Good 3 Unchanged 31.29204 109.20971 3.24 4.54923 2.02 9 10 0.60 Unsatisfactory 4 Unchanged 27.59199 125.34905 16.71 4.82817 3.77 11 12 1.00 Pretty Good 5 Unchanged 28.88952 63.90276 5.33 5.09939 5.78 15 16 0.56 Satisfactory 6 Unchanged 34.91626 99.23502 1.19 6.36518 2.77 10 10 1.00 Satisfactory 7 Unchanged 64.01079 12.73430 0.01 1.81561 0.32 11 13 3.85 Satisfactory 8 Unchanged 19.35107 51.33755 6.85 2.51913 1.97 4 4 2.25 Satisfactory 9 Unchanged 99.52206 59.97799 0.05 7.39341 1.29 12 23 1.70 Satisfactory 10 Unchanged 29.87955 81.54047 1.39 5.33823 1.22 5 7 1.43 Satisfactory 11 Unchanged 9.73012 44.34592 29.56 2.05245 2.11 4 3 2.00 Satisfactory 12 Unchanged 34.91377 139.24653 1.67 10.06899 4.38 11 13 0.85 Unsatisfactory 13 Unchanged 35.22293 70.27706 0.61 5.35303 8.40 9 9 1.78 Satisfactory 14 Unchanged 43.10722 85.00034 15.45 12.71896 17.70 10 9 1.56 Unsatisfactory 15 Unchanged 46.40059 69.70434 5.07 4.57755 11.90 9 11 1.18 Satisfactory Table E.77: Subject 26 2nd method (Jacobian) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 35.43882 348.23987 348.24 6.84741 4.45 6 7 2.43 Satisfactory 2 Unchanged 7.39676 19.62059 13.08 3.96455 4.08 1 1 6.00 Satisfactory 3 Unchanged 27.22538 130.32913 3.86 3.26576 1.45 2 2 3.50 Satisfactory 4 Unchanged 53.40322 65.53685 8.74 5.70462 4.45 6 9 2.78 Satisfactory 5 Unchanged 48.58733 173.85165 14.49 5.05977 5.74 6 7 2.29 Satisfactory 6 Unchanged 50.64318 111.77914 1.34 10.39783 4.52 8 8 3.00 Satisfactory 7 Unchanged 73.68767 124.35738 0.09 3.94162 0.69 5 18 4.28 Satisfactory 8 Unchanged 19.74110 82.14971 10.95 2.91529 2.28 4 5 2.20 Pretty Good 9 Unchanged 68.66929 29.81570 0.02 4.24188 0.74 16 13 1.46 Pretty Good 10 Unchanged 30.37542 49.03111 0.84 5.25935 1.20 5 4 2.75 Pretty Good 11 Unchanged 10.71181 31.41769 20.95 2.98406 3.07 2 2 3.00 Pretty Good 12 Unchanged 44.52646 93.71502 1.13 7.56163 3.29 9 12 1.67 Pretty Good 13 Unchanged 31.47628 178.24116 1.55 4.89601 7.68 4 9 2.44 Pretty Good 14 Unchanged 15.79356 70.34399 12.79 7.06606 9.83 2 3 3.33 Pretty Good 15 Unchanged 22.78366 41.38818 3.01 3.10595 8.08 1 6 1.50 Satisfactory Table E.78: Subject 26 3rd method (CCD) Appendix E. Experiment Data 148 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 6.01761 0.00010 0.00 0.15191 0.10 1 1 1.00 Perfect Match 2 Unchanged 18.47365 32.11598 21.41 2.68193 2.76 6 5 2.00 Almost Perfect 3 Unchanged 19.56366 43.45378 1.29 2.77463 1.23 8 7 0.71 Pretty Good 4 Unchanged 24.59460 39.51156 5.27 2.85784 2.23 11 12 0.92 Almost Perfect 5 Unchanged 30.32719 35.70955 2.98 2.54702 2.89 13 16 0.88 Almost Perfect 6 Unchanged 36.64812 71.61550 0.86 5.84693 2.54 14 13 0.92 Almost Perfect 7 Unchanged 41.10904 19.23417 0.01 2.40932 0.42 14 13 1.00 Almost Perfect 8 Unchanged 29.65468 14.49373 1.93 2.72700 2.13 13 12 1.42 Almost Perfect 9 Unchanged 41.76239 9.18421 0.01 4.79854 0.84 12 14 0.93 Almost Perfect 10 Unchanged 45.07660 12.03189 0.21 2.69393 0.61 20 18 1.33 Almost Perfect 11 Unchanged 17.67612 6.31623 4.21 1.31525 1.35 8 11 1.00 Almost Perfect 12 Unchanged 30.71969 23.12310 0.28 5.18579 2.26 13 13 1.00 Perfect Match 13 Unchanged 36.98396 41.60622 0.36 4.62152 7.25 17 15 0.47 Pretty Good 14 Unchanged 26.14544 42.97850 7.81 3.63502 5.06 9 8 0.88 Almost Perfect 15 Unchanged 45.65827 36.24655 2.64 3.73990 9.72 18 13 0.46 Almost Perfect Table E.79: Subject 27 1st method (1DOF) Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 8.53929 0.11603 0.12 5.24651 3.41 2 1 1.00 Almost Perfect 2 Unchanged 13.84685 16.56038 11.04 1.24240 1.28 8 6 1.00 Almost Perfect 3 Unchanged 51.45074 18.42212 0.55 2.47676 1.10 8 8 2.38 Pretty Good 4 Unchanged 20.24780 9.96442 1.33 1.87420 1.46 10 12 1.00 Almost Perfect 5 Unchanged 17.13774 64.11565 5.34 4.68139 5.31 5 5 1.80 Almost Perfect 6 Unchanged 38.22137 95.32860 1.15 6.03453 2.63 7 11 2.27 Almost Perfect 7 Unchanged 81.58284 84.79937 0.06 8.60460 1.51 10 13 4.00 Satisfactory 8 Unchanged 19.18611 35.97112 4.80 2.89837 2.26 4 3 4.33 Almost Perfect 9 Unchanged 70.26191 27.54450 0.02 6.57366 1.15 5 7 1.86 Pretty Good 10 Unchanged 32.85469 40.74987 0.70 3.18664 0.73 9 9 1.44 Almost Perfect 11 Unchanged 9.09097 0.79608 0.53 1.65011 1.70 1 1 6.00 Almost Perfect 12 Unchanged 30.18464 48.04988 0.58 6.82243 2.97 6 6 2.00 Almost Perfect 13 Unchanged 50.20912 5.66146 0.05 1.17630 1.85 8 7 2.43 Perfect Match 14 Unchanged 37.53225 40.84705 7.43 4.14704 5.77 7 10 2.00 Almost Perfect 15 Unchanged 34.03637 53.54287 3.89 4.26328 11.08 4 7 0.43 Almost Perfect Table E.80: Subject 27 2nd method (Jacobian) Appendix E. Experiment Data 149 Time Angle Pos. Avg. Trial Type (seconds) Error % Error % R E Dist. Rating 1 Unchanged 34.18969 50.55890 50.56 2.62385 1.71 11 13 1.54 Almost Perfect 2 Unchanged 16.21526 8.00545 5.34 0.84971 0.87 6 9 1.00 Almost Perfect 3 Unchanged 37.13474 12.36086 0.37 1.33284 0.59 8 10 1.70 Almost Perfect 4 Unchanged 16.19193 78.73480 10.50 2.70238 2.11 10 9 1.00 Almost Perfect 5 Unchanged 27.44209 44.15148 3.68 3.09496 3.51 5 5 1.80 Almost Perfect 6 Unchanged 30.66629 71.49978 0.86 6.53393 2.84 7 5 2.00 Almost Perfect 7 Unchanged 57.98423 50.97590 0.04 2.93802 0.51 5 5 2.00 Perfect Match 8 Unchanged 30.39132 24.24441 3.23 1.75077 1.37 5 5 2.00 Almost Perfect 9 Unchanged 52.82165 88.12786 0.07 6.42404 1.12 7 9 1.78 Almost Perfect 10 Unchanged 30.34796 13.96807 0.24 3.83863 0.87 6 6 1.83 Almost Perfect 11 Unchanged 13.20853 11.11403 7.41 1.70220 1.75 3 3 2.00 Almost Perfect 12 Unchanged 33.96636 73.94806 0.89 7.31527 3.18 11 11 1.18 Almost Perfect 13 Unchanged 24,77539 179.67932 1.56 6.57039 10.31 6 7 1.71 Almost Perfect 14 Unchanged 19.12864 105.63788 19.21 4.87681 6.79 3 5 2.80 Almost Perfect 15 Unchanged 24.69705 33.20312 2.41 3.80696 9.90 5 6 1.33 Almost Perfect Table E.81: Subject 27 3rd method (CCD) 

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