Table of Contents

Contents
Part I Theories
Chapter 1 Introduction 3
1.1 Background 3
1.2 What is robot accuracy 6
1.3 Why error compensation 8
1.4 Early investigations and insights 9
1.4.1 Offline calibration 10
1.4.2 Online feedback 16
1.5 Summary 19
Chapter 2 Kinematic modeling 21
2.1 Introduction 21
2.2 Pose description and transformation 21
2.2.1 Descriptions of position and posture 21
2.2.2 Translation and rotation 22
2.3 RPY angle and Euler angle 23
2.4 Forward kinematics 26
2.4.1 Link description and link frame 26
2.4.2 Link transformation and forward kinematic model 27
2.4.3 Forward kinematic model of a typical KUKA industrial robot 29
2.5 Inverse kinematics 33
2.5.1 Uniquely closed solution with joint constraints 34
2.5.2 Inverse kinematic model of a typical KUKA industrial robot 35
2.6 Error modeling 38
2.6.1 Differential transformation 38
2.6.2 Differential transformation of consecutive links 40
2.6.3 Kinematic error model 42
2.7 Summary 44
Chapter 3 Positioning error compensation using kinematic calibration 45
3.1 Introduction 45
3.2 Observability-index-based random sampling method 46
3.2.1 Observability index of robot kinematic parameters 46
3.2.2 Selection method of sampling points 48
3.3 Uniform-grid-based sampling method 54
3.3.1 Optimal grid size 54
3.3.2 Sampling point planning method 67
3.4 Kinematic calibration considering robot flexibility error 73
3.4.1 Robot flexibility analysis 74
3.4.2 Establishment of robot flexibility error model 76
3.4.3 Robot kinematic error model with flexibility error 77
3.5 Kinematic calibration using variable parametric error 79
3.6 Parameter identification using L-M algorithm 81
3.7 Verification of error compensation performance 83
3.7.1 Kinematic calibration with robot flexibility error 83
3.7.2 Error compensation using variable parametric error 84
3.8 Summary 91
Chapter 4 Error-similarity-based positioning error compensation 92
4.1 Introduction 92
4.2 Similarity of robot positioning error 93
4.2.1 Qualitative analysis of error similarity 93
4.2.2 Quantitative analysis of error similarity 94
4.2.3 Numerical simulation and discussion 96
4.3 Error compensation based on inverse distance weighting and error similarity 100
4.3.1 Inverse distance weighting interpolation method 101
4.3.2 Error compensation method combined IDW with error similarity 102
4.3.3 Numerical simulation and discussion 104
4.4 Error compensation based on linear unbiased optimal estimation and error similarity 106
4.4.1 Robot positioning error mapping based on error similarity 106
4.4.2 Linear unbiased optimal estimation of robot positioning error 109
4.4.3 Numerical simulation and discussion 112
4.4.4 Error compensation 116
4.5 Optimal sampling based on error similarity 116
4.5.1 Mathematical model of optimal sampling points 117
4.5.2 Multi-objective optimization and non-inferior solution 119
4.5.3 Genetic algorithm and NSGA-II 121
4.5.4 Multi-objective optimization of optimal sampling points of robots based on NSGA-II 128
4.6 Experimental verification 131
4.6.1 Experimental platform 131
4.6.2 Experimental verification of positioning error similarity 133
4.6.3 Experimental verification of error compensation based on inverse distance weighting and error similarity 141
4.6.4 Experimental verification of error compensation based on linear unbiased optimal estimation and error similarity 145
4.7 Summary 148
Chapter 5 Joint space closed-loop feedback 149
5.1 Introduction 149
5.2 Positioning error estimation 149
5.2.1 Error estimation model of Chebyshev polynomial 149
5.2.2 Identification of Chebyshev coefficients 153
5.2.3 Mapping model 154
5.3 Effect of joint backlash on positioning error 155
5.3.1 Variation law of joint backlash 155
5.3.2 Multi-directional positioning accuracy variation 158
5.4 Error compensation using feedforward and feedback loops 161
5.5 Experimental verification and analysis 162
5.5.1 Experimental setup 162
5.5.2 Error estimation experiment 163
5.5.3 Error compensation experiment 165
5.6 Summary 167
Chapter 6 Cartesian space closed-loop feedback 168
6.1 Introduction 168
6.2 Pose measurement using binocular visual sensor 168
6.2.1 Description of frame 168
6.2.2 Pose measurement principle based on binocular vision 170
6.2.3 Influence of the frame FE on measurement accuracy 174
6.2.4 Pose estimation using Kalman filtering 177
6.3 Vision-guided control system 178
6.4 Experimental verification 183
6.4.1 Experimental platform 183
6.4.2 Kalman-filtering-based estimation 184
6.4.3 No-load experiment 185
6.5 Summary 189
Part II Applications
Chapter 7 Applications in robotic drilling 193
7.1 Introducti