Robot Manipulator Redundancy Resolution

Yunong Zhang, PhD, is a professor at the School of Information Science and Technology, Sun Yat-sen University, Guangzhou, China, and an associate editor at IEEE Transactions on Neural Networks and Learning Systems. He has researched motion planning and control of redundant manipulators and recurrent neural networks for 19 years, and he holds seven authorized patents. Long Jin is pursuing his doctorate in Communication and Information Systems at the School of Information Science and Technology, Sun Yat-sen University, Guangzhou, China. His main research interests include robotics, neural networks, and intelligent information processing.

• List of Figures xiiiList of Tables xxvPreface xxviiAcknowledgments xxxiiiAcronyms xxxvPart I Pseudoinverse-Based ZD Approach 11 Redundancy Resolution via Pseudoinverse and ZD Models 31.1 Introduction 31.2 Problem Formulation and ZD Models 51.2.1 Problem Formulation 51.2.2 Continuous-Time ZD Model 61.2.3 Discrete-Time ZD Models 71.2.3.1 Euler-Type DTZD Model with J̇ (t) Known 71.2.3.2 Euler-Type DTZD Model with J̇ (t) Unknown 71.2.3.3 Taylor-Type DTZD Models 81.3 ZD Applications to Different-Type Robot Manipulators 91.3.1 Application to a Five-Link Planar Robot Manipulator 91.3.2 Application to a Three-Link Planar Robot Manipulator 121.4 Chapter Summary 14Part II Inverse-Free Simple Approach 152 G1 Type Scheme to JVL Inverse Kinematics 172.1 Introduction 172.2 Preliminaries and RelatedWork 182.3 Scheme Formulation 182.4 Computer Simulations 192.4.1 Square-Path Tracking Task 192.4.2 “Z”-Shaped Path Tracking Task 222.5 Physical Experiments 252.6 Chapter Summary 263 D1G1 Type Scheme to JAL Inverse Kinematics 273.1 Introduction 273.2 Preliminaries and RelatedWork 283.3 Scheme Formulation 283.4 Computer Simulations 293.4.1 Rhombus-Path Tracking Task 293.4.1.1 Verifications 293.4.1.2 Comparisons 303.4.2 Triangle-Path Tracking Task 323.5 Chapter Summary 364 Z1G1 Type Scheme to JAL Inverse Kinematics 374.1 Introduction 374.2 Problem Formulation and Z1G1 Type Scheme 374.3 Computer Simulations 384.3.1 Desired Initial Position 384.3.1.1 Isosceles-Trapezoid Path Tracking 404.3.1.2 Isosceles-Triangle Path Tracking 414.3.1.3 Square Path Tracking 424.3.2 Nondesired Initial Position 444.4 Physical Experiments 454.5 Chapter Summary 45Part III QP Approach and Unification 475 Redundancy Resolution via QP Approach and Unification 495.1 Introduction 495.2 Robotic Formulation 505.3 Handling Joint Physical Limits 525.3.1 Joint-Velocity Level 525.3.2 Joint-Acceleration Level 525.4 Avoiding Obstacles 535.5 Various Performance Indices 545.5.1 Resolved at Joint-Velocity Level 555.5.1.1 MVN scheme 555.5.1.2 RMP scheme 555.5.1.3 MKE scheme 555.5.2 Resolved at Joint-Acceleration Level 555.5.2.1 MAN scheme 555.5.2.2 MTN scheme 565.5.2.3 IIWT scheme 565.6 Unified QP Formulation 565.7 Online QP Solutions 575.7.1 Traditional QP Routines 575.7.2 Compact QP Method 575.7.3 Dual Neural Network 575.7.4 LVI-Aided Primal-Dual Neural Network 575.7.5 Numerical Algorithms E47 and 94LVI 595.7.5.1 Numerical Algorithm E47 595.7.5.2 Numerical Algorithm 94LVI 595.8 Computer Simulations 615.9 Chapter Summary 66Part IV Illustrative JVL QP Schemes and Performances 676 Varying Joint-Velocity Limits Handled by QP 696.1 Introduction 696.2 Preliminaries and Problem Formulation 706.2.1 Six-DOF Planar Robot System 706.2.2 Varying Joint-Velocity Limits 736.3 9 4LVI Assisted QP Solution 766.4 Computer Simulations and Physical Experiments 776.4.1 Line-Segment Path-Tracking Task 776.4.2 Elliptical-Path Tracking Task 856.4.3 Simulations with Faster Tasks 876.4.3.1 Line-Segment-Path-Tracking Task 876.4.3.2 Elliptical-Path-Tracking Task 896.5 Chapter Summary 927 Feedback-AidedMinimum Joint Motion 957.1 Introduction 957.2 Preliminaries and Problem Formulation 977.2.1 Minimum Joint Motion Performance Index 977.2.2 Varying Joint-Velocity Limits 1007.3 Computer Simulations and Physical Experiments 1017.3.1 “M”-Shaped Path-Tracking Task 1017.3.1.1 Simulation Comparisons with Different ;;p 1017.3.1.2 Simulation Comparisons with Different ;; 1037.3.1.3 Simulative and Experimental Verifications of FAMJM Scheme 1057.3.2 “P”-Shaped Path Tracking Task 1077.3.3 Comparisons with Pseudoinverse-Based Approach 1087.3.3.1 Comparison with Tracking Task of Larger “M”-Shaped Path 1107.3.3.2 Comparison with Tracking Task of Larger “P”-Shaped Path 1127.4 Chapter Summary 1198 QP Based Manipulator State Adjustment 1218.1 Introduction 1218.2 Preliminaries and Scheme Formulation 1228.3 QP Solution and Control of Robot Manipulator 1248.4 Computer Simulations and Comparisons 1258.4.1 State Adjustment without ZIV Constraint 1258.4.2 State Adjustment with ZIV Constraint 1288.5 Physical Experiments 1328.6 Chapter Summary 136Part V Self-Motion Planning 1379 QP-Based Self-Motion Planning 1399.1 Introduction 1399.2 Preliminaries and QP Formulation 1409.2.1 Self-Motion Criterion 1409.2.2 QP Formulation 1419.3 LVIAPDNN Assisted QP Solution 1419.4 PUMA560 Based Computer Simulations 1429.4.1 From Initial Configuration A to Desired Configuration B 1449.4.2 From Initial Configuration A to Desired Configuration C 1469.4.3 From Initial Configuration E to Desired Configuration F 1479.5 PA10 Based Computer Simulations 1529.6 Chapter Summary 15810 PseudoinverseMethod and Singularities Discussed 16110.1 Introduction 16110.2 Preliminaries and Scheme Formulation 16210.2.1 Modified Performance Index for SMP 16310.2.2 QP-Based SMP Scheme Formulation 16310.3 LVIAPDNN Assisted QP Solution with Discussion 16410.4 Computer Simulations 16710.4.1 Three-Link Redundant PlanarManipulator 16810.4.1.1 Verifications 16810.4.1.2 Comparisons 17110.4.2 PUMA560 Robot Manipulator 17210.4.3 PA10 Robot Manipulator 17610.5 Chapter Summary 180Appendix 181Equivalence Analysis in Limit Situation 18111 Self-Motion Planning with ZIV Constraint 18311.1 Introduction 18311.2 Preliminaries and Scheme Formulation 18411.2.1 Handling Joint Physical Limits 18411.2.2 QP Reformulation 18711.2.3 Design of ZIV Constraint 18711.3 E47 Assisted QP Solution 18811.4 Computer Simulations and Physical Experiments 18911.5 Chapter Summary 197Part VI Manipulability Maximization 19912 Manipulability-Maximizing SMP Scheme 20112.1 Introduction 20112.2 Scheme Formulation 20212.2.1 Derivation of Manipulability Index 20212.2.2 Handling Physical Limits 20312.2.3 QP Formulation 20312.3 Computer Simulations and Physical Experiments 20412.3.1 Computer Simulations 20412.3.2 Physical Experiments 20512.4 Chapter Summary 20913 Time-Varying Coefficient AidedMMScheme 21113.1 Introduction 21113.2 Manipulability-Maximization with Time-Varying Coefficient 21213.2.1 Nonzero Initial/Final Joint-Velocity Problem 21213.2.2 Scheme Formulation 21313.2.3 94LVI Assisted QP Solution 21513.3 Computer Simulations and Physical Experiments 21613.3.1 Computer Simulations 21613.3.2 Physical Experiments 22413.4 Chapter Summary 226Part VII Encoder Feedback and Joystick Control 22714 QP Based Encoder Feedback Control 22914.1 Introduction 22914.2 Preliminaries and Scheme Formulation 23114.2.1 Joint Description 23114.2.2 OMPFC Scheme 23114.3 Computer Simulations 23414.3.1 Petal-Shaped Path-Tracking Task 23414.3.2 Comparative Simulations 23814.3.2.1 Petal-Shaped Path Tracking Using Another Group of Joint-Angle Limits 23814.3.2.2 Petal-Shaped Path Tracking via the Method 4 (M4) Algorithm 23814.3.3 Hexagonal-Path-Tracking Task 23914.4 Physical Experiments 24014.5 Chapter Summary 24815 QP Based Joystick Control 25115.1 Introduction 25115.2 Preliminaries and Hardware System 25115.2.1 Velocity-Specified Inverse Kinematics Problem 25215.2.2 Joystick-Controlled Manipulator Hardware System 25215.3 Scheme Formulation 25315.3.1 Cosine-Aided Position-to-VelocityMapping 25315.3.2 Real-Time Joystick-Controlled Motion Planning 25415.4 Computer Simulations and Physical Experiments 25415.4.1 Movement Toward Four Directions 25515.4.2 “MVN” LetterWriting 25915.5 Chapter Summary 259References 261Index 277