1.3 TABLE OF CONTENTS
Page
CERTIFICATE OF EXAMINATION ................................................................................ ii
ABSTRACT .......................................................................................................................iii
AKNOWLEDGEMENTS .................................................................................................. v
TABLE OF CONTENTS ................................................................................................... vi
LIST OF APPENDICES .................................................................................................... xi
LIST OF FIGURES ......................................................................................................... xiv
GLOSSARY OF TERMS ................................................................................................ xix
CHAPTER 1 - INTRODUCTION ...................................................................................... 1
1.1 Introduction ............................................................................................... 1
CHAPTER 2 - A REVIEW OF ROBOT MOTION PLANNING ....................................... 4
2.1 Introduction .......................................................................................... 4
2.2 Trajectory and Path Planning ............................................................... 6
2.3 Robot Path Description ........................................................................ 7
2.4 Robot Path and Trajectory Description ................................................ 9
2.5 Motion Planning ................................................................................. 11
2.6 Optimal Motion Planning ................................................................... 11
2.7 Kinematic Motion Planning ............................................................... 13
2.8 Dynamic Motion Planning ................................................................. 15
2.9 Trajectory Planning ............................................................................ 16
2.10 Optimal Trajectory Planning .............................................................. 17
2.11 Path Planning ..................................................................................... 19
2.12 Optimal Path Planning ....................................................................... 21
2.13 Optimal Motion Planning ................................................................... 22
2.14 Summary ............................................................................................ 23
CHAPTER 3 - ARTIFICIAL NEURAL NETWORKS .................................................... 25
3.1 Introduction ........................................................................................ 25
3.2 Advantages of Feed Forward Neural Networks .................................. 26
3.3 Disadvantages of Feed Forward Neural Networks ............................. 27
3.4 An Artificial Neuron ...........................................................................27
3.5 Neuron Activation Functions ............................................................. 29
3.6 Neural Network Architectures ........................................................... 30
3.7 The Backpropagation Learning Algorithm ........................................ 32
3.8 Summary of Methods ......................................................................... 34
3.9 The Modified Delta Rule .................................................................... 35
CHAPTER 4 - A SURVEY OF NEURAL NETWORK APPLICATIONS IN ROBOTICS ....................................................................................................... 37
4.1 Introduction ........................................................................................ 37
4.2 Neural Network Applications to SISO Control .................................. 37
4.3 System Identification With Neural Networks ..................................... 38
4.4 Non-linear Control With Neural Networks ......................................... 40
4.5 Model Based Neural Network Controllers ......................................... 40
4.6 Neuromorphic Controllers ................................................................. 42
4.7 Neural Networks for Vision and Sensor Based Systems ..................... 43
4.8 Novel Neural Network Applications .................................................. 45
4.9 Inverse Kinematics with Neural Networks ......................................... 45
4.10 Estimating the Inverse Jacobian with Neural Networks ..................... 47
4.11 Discussion of Neural Network Based Robotics .................................. 47
4.12 Summary ............................................................................................ 49
CHAPTER 5 - A SIMPLE ROBOT MODEL ................................................................... 51
5.1 Introduction ........................................................................................ 51
5.2 The Selected Manipulator Case .......................................................... 52
5.3 Kinematics and Dynamics of a Two Link Manipulator ...................... 54
5.4 Optimal Motion Plans for a Two Link Manipulator ............................ 62
5.5 A Discrete Time Step Motion Planner/Controller .............................. 63
5.6 A Comparative Case for The Optimal Motion .................................... 65
5.7 Summary ............................................................................................ 67
CHAPTER 6 - FEED FORWARD NEURAL NETWORKS FOR MOTION PLANNING ....................................................................................................... 69
6.1 Introduction ........................................................................................ 69
6.2 Discrete Time Step Planners, and Neural Networks ........................... 70
6.3 Time Optimal Discrete Time-Step Paths ............................................ 71
6.4 A Neural Network Architecture for a Motion Planner ........................ 73
6.5 Neural Network Test and Training Data ............................................. 74
6.6 Training/Testing Data Set Generation ................................................ 75
6.7 Training the Neural Network .............................................................. 79
6.8 Estimation of Neural Network Training Convergence ....................... 81
6.9 Summary ............................................................................................ 82
CHAPTER 7 - MAXIMUM VELOCITY MOTION PLANNER ..................................... 84
7.1 Introduction ........................................................................................ 84
7.2 Maximum Velocity Paths ................................................................... 84
7.3 Maximum Velocity Profiles with Discrete Time Steps ....................... 86
7.4 A Neural Network for Maximum Velocity Motion ............................. 93
7.5 Results ................................................................................................ 94
7.6 Conclusion ......................................................................................... 98
CHAPTER 8 - MAXIMUM ACCELERATION MOTION PLANNER ......................... 104
8.1 Introduction ...................................................................................... 104
8.2 Maximum Acceleration Paths .......................................................... 104
8.3 Velocity Profiles for Maximum Acceleration with Discrete Time Steps
.................. 106
8.4 A Neural Network for Maximum Acceleration Motion .................... 114
8.5 Results .............................................................................................. 115
8.6 Conclusion ....................................................................................... 119
CHAPTER 9 - REPRESENTING ROBOT PATHS WITH BEZIER SPLINES ............. 124
9.1 Introduction ...................................................................................... 124
9.2 Splines .............................................................................................. 124
9.3 Representing Joint Positions With Spline Functions ........................ 127
9.4 Basic Third Order Spline Theory ..................................................... 128
9.5 Extension of Hermite To Bezier Spline ............................................ 130
9.6 Matching Splines at Endpoints ......................................................... 132
9.7 Representation of Joint Coordinates with Bezier Splines ................. 133
9.8 Summary .......................................................................................... 137
CHAPTER 10 - FINDING NEAR OPTIMAL ROBOT MOTIONS .............................. 138
10.1 Introduction ...................................................................................... 138
10.2 A Simple Robot Motion Generator ................................................... 138
10.3 A Complex Motion Generator .......................................................... 141
10.4 Determining Sub-Optimal Motion Times ......................................... 145
10.5 Reduction of Motion Time Steps ...................................................... 146
10.6 Minimization By Adjusting Coupling .............................................. 149
10.7 Conclusion ....................................................................................... 151
CHAPTER 11 - NEAR-OPTIMAL MOTION WITH BEZIER SPLINES ..................... 152
11.1 Introduction ...................................................................................... 152
11.2 The Problem ..................................................................................... 152
11.3 The Objective Function .................................................................... 153
11.4 The Motion Constraint Functions ..................................................... 155
11.5 Decision Variables ........................................................................... 158
11.6 Hookes and Jeeves Optimization ...................................................... 158
11.7 A Random Walk Search ................................................................... 161
11.8 A Hybrid Optimization Routine for Motion Planning ...................... 164
11.9 Test Paths ......................................................................................... 166
11.10 Conclusion ....................................................................................... 167
CHAPTER 12 - OPTIMAL TORQUE MOTION PLANNER ........................................ 172
12.1 Introduction ...................................................................................... 172
12.2 Maximum Torque Motion ................................................................ 172
12.3 A Neural Network for Maximum Torque Control ............................ 173
12.4 Simulating the Maximum Torque Neural Network Control ............. 174
12.5 Results .............................................................................................. 176
12.6 Conclusions ...................................................................................... 188
CHAPTER 13 - MAXIMUM TORQUE WITH SCALED NEURAL NETWORK ....... 191
13.1 Introduction ...................................................................................... 191
13.2 Scaled Output Controller .................................................................. 191
13.3 Results .............................................................................................. 192
13.4 Conclusions ...................................................................................... 198
CHAPTER 14 - DISCUSSION AND CONCLUSIONS ................................................. 199
14.1 Discussion ........................................................................................ 199
14.2 Conclusions ...................................................................................... 200
14.3 Future Work (In General) ................................................................. 202
14.4 Future Work (Application of Neural Networks to Robot Control) .... 204
14.5 Future Work (Collision Avoidance) ................................................. 206
14.6 Future Work (Robot and Actuator Modelling) ................................. 207
14.7 Future Work (Questions Unanswered by this Thesis) ....................... 207
14.8 Future Work (Training Algorithms and Methods) ............................ 208
14.9 Future Work (Expert Systems and Neural Networks) ....................... 209
APPENDICES ................................................................................................................ 210
REFERENCES ............................................................................................................... 402
VITA ............................................................................................................................... 410