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

 

 

 

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