Robot Manipulator Redundancy Resolution

List of Figures xiii List of Tables xxv Preface xxvii Acknowledgments xxxiii Acronyms xxxv Part I Pseudoinverse-Based ZD Approach 1 1 Redundancy Resolution via Pseudoinverse and ZD Models 3 1.1 Introduction 3 1.2 Problem Formulation and ZD Models 5 1.2.1 Problem Formulation 5 1.2.2 Continuous-Time ZD Model 6 1.2.3 Discrete-Time ZD Models 7 1.2.3.1 Euler-Type DTZD Model with J (t) Known 7 1.2.3.2 Euler-Type DTZD Model with J (t) Unknown 7 1.2.3.3 Taylor-Type DTZD Models 8 1.3 ZD Applications to Different-Type Robot Manipulators 9 1.3.1 Application to a Five-Link Planar Robot Manipulator 9 1.3.2 Application to a Three-Link Planar Robot Manipulator 12 1.4 Chapter Summary 14 Part II Inverse-Free Simple Approach 15 2 G1 Type Scheme to JVL Inverse Kinematics 17 2.1 Introduction 17 2.2 Preliminaries and RelatedWork 18 2.3 Scheme Formulation 18 2.4 Computer Simulations 19 2.4.1 Square-Path Tracking Task 19 2.4.2 "Z"-Shaped Path Tracking Task 22 2.5 Physical Experiments 25 2.6 Chapter Summary 26 3 D1G1 Type Scheme to JAL Inverse Kinematics 27 3.1 Introduction 27 3.2 Preliminaries and RelatedWork 28 3.3 Scheme Formulation 28 3.4 Computer Simulations 29 3.4.1 Rhombus-Path Tracking Task 29 3.4.1.1 Verifications 29 3.4.1.2 Comparisons 30 3.4.2 Triangle-Path Tracking Task 32 3.5 Chapter Summary 36 4 Z1G1 Type Scheme to JAL Inverse Kinematics 37 4.1 Introduction 37 4.2 Problem Formulation and Z1G1 Type Scheme 37 4.3 Computer Simulations 38 4.3.1 Desired Initial Position 38 4.3.1.1 Isosceles-Trapezoid Path Tracking 40 4.3.1.2 Isosceles-Triangle Path Tracking 41 4.3.1.3 Square Path Tracking 42 4.3.2 Nondesired Initial Position 44 4.4 Physical Experiments 45 4.5 Chapter Summary 45 Part III QP Approach and Unification 47 5 Redundancy Resolution via QP Approach and Unification 49 5.1 Introduction 49 5.2 Robotic Formulation 50 5.3 Handling Joint Physical Limits 52 5.3.1 Joint-Velocity Level 52 5.3.2 Joint-Acceleration Level 52 5.4 Avoiding Obstacles 53 5.5 Various Performance Indices 54 5.5.1 Resolved at Joint-Velocity Level 55 5.5.1.1 MVN scheme 55 5.5.1.2 RMP scheme 55 5.5.1.3 MKE scheme 55 5.5.2 Resolved at Joint-Acceleration Level 55 5.5.2.1 MAN scheme 55 5.5.2.2 MTN scheme 56 5.5.2.3 IIWT scheme 56 5.6 Unified QP Formulation 56 5.7 Online QP Solutions 57 5.7.1 Traditional QP Routines 57 5.7.2 Compact QP Method 57 5.7.3 Dual Neural Network 57 5.7.4 LVI-Aided Primal-Dual Neural Network 57 5.7.5 Numerical Algorithms E47 and 94LVI 59 5.7.5.1 Numerical Algorithm E47 59 5.7.5.2 Numerical Algorithm 94LVI 59 5.8 Computer Simulations 61 5.9 Chapter Summary 66 Part IV Illustrative JVL QP Schemes and Performances 67 6 Varying Joint-Velocity Limits Handled by QP 69 6.1 Introduction 69 6.2 Preliminaries and Problem Formulation 70 6.2.1 Six-DOF Planar Robot System 70 6.2.2 Varying Joint-Velocity Limits 73 6.3 9 4LVI Assisted QP Solution 76 6.4 Computer Simulations and Physical Experiments 77 6.4.1 Line-Segment Path-Tracking Task 77 6.4.2 Elliptical-Path Tracking Task 85 6.4.3 Simulations with Faster Tasks 87 6.4.3.1 Line-Segment-Path-Tracking Task 87 6.4.3.2 Elliptical-Path-Tracking Task 89 6.5 Chapter Summary 92 7 Feedback-AidedMinimum Joint Motion 95 7.1 Introduction 95 7.2 Preliminaries and Problem Formulation 97 7.2.1 Minimum Joint Motion Performance Index 97 7.2.2 Varying Joint-Velocity Limits 100 7.3 Computer Simulations and Physical Experiments 101 7.3.1 "M"-Shaped Path-Tracking Task 101 7.3.1.1 Simulation Comparisons with Different p 101 7.3.1.2 Simulation Comparisons with Different 103 7.3.1.3 Simulative and Experimental Verifications of FAMJM Scheme 105 7.3.2 "P"-Shaped Path Tracking Task 107 7.3.3 Comparisons with Pseudoinverse-Based Approach 108 7.3.3.1 Comparison with Tracking Task of Larger "M"-Shaped Path 110 7.3.3.2 Comparison with Tracking Task of Larger "P"-Shaped Path 112 7.4 Chapter Summary 119 8 QP Based Manipulator State Adjustment 121 8.1 Introduction 121 8.2 Preliminaries and Scheme Formulation 122 8.3 QP Solution and Control of Robot Manipulator 124 8.4 Computer Simulations and Comparisons 125 8.4.1 State Adjustment without ZIV Constraint 125 8.4.2 State Adjustment with ZIV Constraint 128 8.5 Physical Experiments 132 8.6 Chapter Summary 136 Part V Self-Motion Planning 137 9 QP-Based Self-Motion Planning 139 9.1 Introduction 139 9.2 Preliminaries and QP Formulation 140 9.2.1 Self-Motion Criterion 140 9.2.2 QP Formulation 141 9.3 LVIAPDNN Assisted QP Solution 141 9.4 PUMA560 Based Computer Simulations 142 9.4.1 From Initial Configuration A to Desired Configuration B 144 9.4.2 From Initial Configuration A to Desired Configuration C 146 9.4.3 From Initial Configuration E to Desired Configuration F 147 9.5 PA10 Based Computer Simulations 152 9.6 Chapter Summary 158 10 PseudoinverseMethod and Singularities Discussed 161 10.1 Introduction 161 10.2 Preliminaries and Scheme Formulation 162 10.2.1 Modified Performance Index for SMP 163 10.2.2 QP-Based SMP Scheme Formulation 163 10.3 LVIAPDNN Assisted QP Solution with Discussion 164 10.4 Computer Simulations 167 10.4.1 Three-Link Redundant PlanarManipulator 168 10.4.1.1 Verifications 168 10.4.1.2 Comparisons 171 10.4.2 PUMA560 Robot Manipulator 172 10.4.3 PA10 Robot Manipulator 176 10.5 Chapter Summary 180 Appendix 181 Equivalence Analysis in Limit Situation 181 11 Self-Motion Planning with ZIV Constraint 183 11.1 Introduction 183 11.2 Preliminaries and Scheme Formulation 184 11.2.1 Handling Joint Physical Limits 184 11.2.2 QP Reformulation 187 11.2.3 Design of ZIV Constraint 187 11.3 E47 Assisted QP Solution 188 11.4 Computer Simulations and Physical Experiments 189 11.5 Chapter Summary 197 Part VI Manipulability Maximization 199 12 Manipulability-Maximizing SMP Scheme 201 12.1 Introduction 201 12.2 Scheme Formulation 202 12.2.1 Derivation of Manipulability Index 202 12.2.2 Handling Physical Limits 203 12.2.3 QP Formulation 203 12.3 Computer Simulations and Physical Experiments 204 12.3.1 Computer Simulations 204 12.3.2 Physical Experiments 205 12.4 Chapter Summary 209 13 Time-Varying Coefficient AidedMMScheme 211 13.1 Introduction 211 13.2 Manipulability-Maximization with Time-Varying Coefficient 212 13.2.1 Nonzero Initial/Final Joint-Velocity Problem 212 13.2.2 Scheme Formulation 213 13.2.3 94LVI Assisted QP Solution 215 13.3 Computer Simulations and Physical Experiments 216 13.3.1 Computer Simulations 216 13.3.2 Physical Experiments 224 13.4 Chapter Summary 226 Part VII Encoder Feedback and Joystick Control 227 14 QP Based Encoder Feedback Control 229 14.1 Introduction 229 14.2 Preliminaries and Scheme Formulation 231 14.2.1 Joint Description 231 14.2.2 OMPFC Scheme 231 14.3 Computer Simulations 234 14.3.1 Petal-Shaped Path-Tracking Task 234 14.3.2 Comparative Simulations 238 14.3.2.1 Petal-Shaped Path Tracking Using Another Group of Joint-Angle Limits 238 14.3.2.2 Petal-Shaped Path Tracking via the Method 4 (M4) Algorithm 238 14.3.3 Hexagonal-Path-Tracking Task 239 14.4 Physical Experiments 240 14.5 Chapter Summary 248 15 QP Based Joystick Control 251 15.1 Introduction 251 15.2 Preliminaries and Hardware System 251 15.2.1 Velocity-Specified Inverse Kinematics Problem 252 15.2.2 Joystick-Controlled Manipulator Hardware System 252 15.3 Scheme Formulation 253 15.3.1 Cosine-Aided Position-to-VelocityMapping 253 15.3.2 Real-Time Joystick-Controlled Motion Planning 254 15.4 Computer Simulations and Physical Experiments 254 15.4.1 Movement Toward Four Directions 255 15.4.2 "MVN" LetterWriting 259 15.5 Chapter Summary 259 References 261 Index 277