Description
Book SynopsisIntroduces a revolutionary, quadratic-programming based approach tosolving long-standing problems in motion planning and control of redundant manipulators This book describes a novel quadratic programming approach to solving redundancy resolutions problems with redundant manipulators. Known as ``QP-unified motion planning and control of redundant manipulators'' theory, it systematically solves difficult optimization problems of inequality-constrained motion planning and control of redundant manipulators that have plagued robotics engineers and systems designers for more than a quarter century. An example of redundancy resolution could involve a robotic limb with six joints, or degrees of freedom (DOFs), with which to position an object.As only five numbers are required to specify the position and orientation of the object, the robot can move with one remaining DOF through practically infinite poses while performing a specified task.In this case redundancy resolution refers to the pro
Table of ContentsList 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 J̇ (t) Known 7
1.2.3.2 Euler-Type DTZD Model with J̇ (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
