Error Compensation for Industrial Robots

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
		4.5.3 Genetic Algorithm and NSGA-II
		4.5.4 Multi-objective Optimization of Optimal Sampling Points of Robots Based on NSGA-II
	4.6 Experimental Verification
		4.6.1 Experimental Platform
		4.6.2 Experimental Verification of the Positioning Error Similarity
		4.6.3 Experimental Verification of Error Compensation Based on Inverse Distance Weighting and Error Similarity
		4.6.4 Experimental Verification of Error Compensation Based on Linear Unbiased Optimal Estimation and Error Similarity
	4.7 Summary
	References
5 Joint Space Closed-Loop Feedback
	5.1 Introduction
	5.2 Positioning Error Estimation
		5.2.1 Error Estimation Model of Chebyshev Polynomial
		5.2.2 Identification of Chebyshev Coefficients
		5.2.3 Mapping Model
	5.3 Effect of Joint Backlash on Positioning Error
		5.3.1 Variation Law of the Joint Backlash
		5.3.2 Multi-directional Positioning Accuracy Variation
	5.4 Error Compensation Using Feedforward and Feedback Loops
	5.5 Experimental Verification and Analysis
		5.5.1 Experimental Setup
		5.5.2 Error Estimation Experiment
		5.5.3 Error Compensation Experiment
	5.6 Summary
	References
6 Cartesian Space Closed-Loop Feedback
	6.1 Introduction
	6.2 Pose Measurement Using Binocular Vision Sensor
		6.2.1 Description of Frame
		6.2.2 Pose Measurement Principle Based on Binocular Vision
		6.2.3 Influence of the Frame FE on Measurement Accuracy
		6.2.4 Pose Estimation Using Kalman Filtering
	6.3 Vision-Guided Control System
	6.4 Experimental Verification
		6.4.1 Experimental Platform
		6.4.2 Kalman-Filtering-Based Estimation
		6.4.3 No-Load Experiment
	6.5 Summary
	References
Part II Applications
7 Applications in Robotic Drilling
	7.1 Introduction
	7.2 Robotic Drilling System
		7.2.1 Hardware
		7.2.2 Software
	7.3 Establishment of Frames
		7.3.1 World Frame
		7.3.2 Robot Base Frame
		7.3.3 Robot Flange Frame
		7.3.4 Tool Frame
		7.3.5 Product Frame
		7.3.6 Transformation of Frames
	7.4 Drilling Applications
		7.4.1 Error-Similarity-Based Error Compensation
		7.4.2 Joint Space Closed-Loop Feedback
		7.4.3 Cartesian Space Closed-Loop Feedback
	7.5 Summary
8 Applications in Robotic Milling
	8.1 Introduction
	8.2 Robotic Milling System
	8.3 Milling on Aluminum Alloy Part
		8.3.1 Line Milling
		8.3.2 Arc Milling
	8.4 Milling on Cylinder Head for Car Engine
		8.4.1 Line Milling
		8.4.2 Plane Milling
	8.5 Edge Milling on Composite Shell
	8.6 Summary