Intro
Preface
Acknowledgements
Contents
Part I Theories
1 Introduction
1.1 Background
1.2 What is Robot Accuracy
1.3 Why Error Compensation
1.4 Early Investigations and Insights
1.4.1 Offline Calibration
1.4.2 Online Feedback
1.5 Summary
References
2 Kinematic Modeling
2.1 Introduction
2.2 Pose Description and Transformation
2.2.1 Descriptions of Position and Posture
2.2.2 Translation and Rotation
2.3 RPY Angle and Euler Angle
2.4 Forward Kinematics
2.4.1 Link Description and Link Frame

2.4.2 Link Transformation and Forward Kinematic Model
2.4.3 Forward Kinematic Model of a Typical KUKA Industrial Robot
2.5 Inverse Kinematics
2.5.1 Uniquely Closed Solution with Joint Constraints
2.5.2 Inverse Kinematic Model of a Typical KUKA Industrial Robot
2.6 Error Modeling
2.6.1 Differential Transformation
2.6.2 Differential Transformation of Consecutive Links
2.6.3 Kinematics Error Model
2.7 Summary
References
3 Positioning Error Compensation Using Kinematic Calibration
3.1 Introduction
3.2 Observability-Index-Based Random Sampling Method

3.2.1 Observability Index of Robot Kinematic Parameters
3.2.2 Selection Method of the Sample Points
3.3 Uniform-Grid-Based Sampling Method
3.3.1 Optimal Grid Size
3.3.2 Sampling Point Planning Method
3.4 Kinematic Calibration Considering Robot Flexibility Error
3.4.1 Robot Flexibility Analysis
3.4.2 Establishment of Robot Flexibility Error Model
3.4.3 Robot Kinematic Error Model with Flexibility Error
3.5 Kinematic Calibration Using Variable Parametric Error
3.6 Parameter Identification Using L-M Algorithm
3.7 Verification of Error Compensation Performance

3.7.1 Kinematic Calibration with Robot Flexibility Error
3.7.2 Error Compensation Using Variable Parametric Error
3.8 Summary
References
4 Error-Similarity-Based Positioning Error Compensation
4.1 Introduction
4.2 Similarity of Robot Positioning Error
4.2.1 Qualitative Analysis of Error Similarity
4.2.2 Quantitative Analysis of Error Similarity
4.2.3 Numerical Simulation and Discussion
4.3 Error Compensation Based on Inverse Distance Weighting and Error Similarity
4.3.1 Inverse Distance Weighting Interpolation Method

4.3.2 Error Compensation Method Combined IDW with Error Similarity
4.3.3 Numerical Simulation and Discussion
4.4 Error Compensation Based on Linear Unbiased Optimal Estimation and Error Similarity
4.4.1 Robot Positioning Error Mapping Based on Error Similarity
4.4.2 Linear Unbiased Optimal Estimation of Robot Positioning Error
4.4.3 Numerical Simulation and Discussion
4.4.4 Error Compensation
4.5 Optimal Sampling Based on Error Similarity
4.5.1 Mathematical Model of Optimal Sampling Points
4.5.2 Multi-Objective Optimization and Non-Inferior Solution