Table Of ContentWenhe Liao · Bo Li ·
Wei Tian · Pengcheng Li
Error Compensation
for Industrial Robots
Error Compensation for Industrial Robots
· · ·
Wenhe Liao Bo Li Wei Tian Pengcheng Li
Error Compensation
for Industrial Robots
Wenhe Liao Bo Li
Nanjing University of Science Nanjing University of Aeronautics
and Technology and Astronautics
Nanjing, Jiangsu, China Nanjing, Jiangsu, China
Wei Tian Pengcheng Li
Nanjing University of Aeronautics Nanjing University of Aeronautics
and Astronautics and Astronautics
Nanjing, Jiangsu, China Nanjing, Jiangsu, China
ISBN 978-981-19-6167-0 ISBN 978-981-19-6168-7 (eBook)
https://doi.org/10.1007/978-981-19-6168-7
Jointly published with Science Press
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book from: Science Press.
ISBN of the Co-Publisher’s edition: 9787030629036
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Preface
With the development of robot technology, industrial robots have been increasingly
applied to aerospace and other high-end manufacturing fields, rather than limited
to automotive, electronics and electrical industries. Aviation manufacturing industry
has higher and higher requirements for high quality, high efficiency and long life of
aircraft manufacturing. Realizing digitalization, flexibility and intelligence of aircraft
manufacturing has become an inevitable trend in the development of aviation manu-
facturing industry. At present, drilling and riveting processes are still dominated
by manual work in aviation manufacturing industry, which not only has low effi-
ciency, but also results in unstable machining quality due to uneven technical level
of individual workers. More importantly, manual operations have been unable to
meet the technical indicators such as positioning accuracy and normal accuracy
of the machined products. Use of automatic machining technology has become an
inevitable choice for today’s aviation manufacturing, among which the automatic
machining system based on industrial robots is the current research focus. As is
known to all, industrial robots only have high repeatability, but do not have sufficiently
high positioning accuracy, which makes the robot automatic machining cannot meet
the precision requirements of aviation products. Therefore, it has become an urgent
problem to explore feasible and reliable positioning error compensation methods and
to improve the accuracy of industrial robots. Carrying out research on error compen-
sation theories and applications of industrial robots is of great significance and prac-
tical value for promoting the development and innovation of aviation manufacturing
technology.
The objective of this book is to study error compensation technology for improving
the accuracy of industrial robots. In summary, the book mainly includes theoretical
analysis for the error compensation of industrial robots in Part I: Theories and the
applications of the error compensation in robotic drilling and milling in Part II:
Applications.
This book is organized as follows. Chapter 1 briefly introduces the research status
of accuracy and error compensation technology of industrial robots. The forward and
inverse kinematics model and error analysis of the robot are introduced in Chap. 2.In
Chap. 3, the error compensation using kinematic calibration technique is investigated,
v
vi Preface
together with two sampling methods. Chapter 4 proposes a compensation method
with error similarity analysis. Different from the complex kinematics model, the
positioning error estimation and compensation are realized by constructing the error
mapping relationship. In Chap. 5, a robot accuracy improvement method is developed
using feedforward compensation and feedback control considering the influence
of joint backlash. In Chap. 6, an error compensation technique is presented using
the visual guidance to effectively improve the pose accuracy of industrial robots.
Applications of the error compensation technology to the robotic drilling and milling
are exhibited in Chaps. 7 and 8, respectively.
The ideas in this book come from the scientific research achievements of the
authors’ team in the field of improvement of the robot accuracy in the past ten
years and can provide a certain reference for the studies on robotics and advanced
manufacturing using industrial robots.
Nanjing, China Wenhe Liao
January 2022 Bo Li
Wei Tian
Pengcheng Li
Acknowledgements
Parts of this book are greatly inspired by the discussions with cooperators and authors’
students. We would like to express our thanks to their contributions, which have
definitely promoted the improvement of the book manuscript. Our students who
have participated in the work of this book include Dr. Yuanfan Zeng, Dr. Wei Zhou,
Dr. Guangyu Cui, Dr. Yufei Li, Dr. Wei Zhao, Dr. Shengping Zhang, Ms. Wei Zhang,
Ms. Ye Shen, Ms. Chuan Xu, Ms. Kaizhuo Xi, Ms. Jun Wang, Ms. Shuang Liang,
Ms. Chufan Zhang and Ms. Song Wei. The editor Li from Science Press strongly
supported the publication of this book. We would like to dedicate this book to our
family.
The support of our research by the National Natural Science Foundation of China
(Nos. 52075256, 52005254 and 51875287), by the Natural Science Foundation of
Jiangsu Province (No. BK20190417) and by the National Key R&D Program of
China (No. 2018YFB1306800) is gratefully acknowledged.
vii
Contents
Part I Theories
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
References ..................................................... 19
2 Kinematic Modeling ............................................ 23
2.1 Introduction ............................................... 23
2.2 Pose Description and Transformation .......................... 23
2.2.1 Descriptions of Position and Posture .................... 23
2.2.2 Translation and Rotation .............................. 24
2.3 RPY Angle and Euler Angle ................................. 25
2.4 Forward Kinematics ........................................ 28
2.4.1 Link Description and Link Frame ...................... 28
2.4.2 Link Transformation and Forward Kinematic Model ...... 29
2.4.3 Forward Kinematic Model of a Typical KUKA
Industrial Robot ..................................... 31
2.5 Inverse Kinematics ......................................... 35
2.5.1 Uniquely Closed Solution with Joint Constraints .......... 36
2.5.2 Inverse Kinematic Model of a Typical KUKA
Industrial Robot ..................................... 37
2.6 Error Modeling ............................................ 40
2.6.1 Differential Transformation ............................ 40
2.6.2 Differential Transformation of Consecutive Links ......... 42
2.6.3 Kinematics Error Model .............................. 45
ix
x Contents
2.7 Summary .................................................. 47
References ..................................................... 47
3 Positioning Error Compensation Using Kinematic Calibration ..... 49
3.1 Introduction ............................................... 49
3.2 Observability-Index-Based Random Sampling Method ........... 50
3.2.1 Observability Index of Robot Kinematic Parameters ....... 50
3.2.2 Selection Method of the Sample Points .................. 52
3.3 Uniform-Grid-Based Sampling Method ........................ 58
3.3.1 Optimal Grid Size .................................... 58
3.3.2 Sampling Point Planning Method ....................... 78
3.4 Kinematic Calibration Considering Robot Flexibility Error ....... 83
3.4.1 Robot Flexibility Analysis ............................. 84
3.4.2 Establishment of Robot Flexibility Error Model .......... 86
3.4.3 Robot Kinematic Error Model with Flexibility Error ...... 87
3.5 Kinematic Calibration Using Variable Parametric Error .......... 89
3.6 Parameter Identification Using L-M Algorithm ................. 91
3.7 Verification of Error Compensation Performance ................ 93
3.7.1 Kinematic Calibration with Robot Flexibility Error ....... 93
3.7.2 Error Compensation Using Variable Parametric Error ..... 94
3.8 Summary .................................................. 101
References ..................................................... 102
4 Error-Similarity-Based Positioning Error Compensation ........... 103
4.1 Introduction ............................................... 103
4.2 Similarity of Robot Positioning Error .......................... 104
4.2.1 Qualitative Analysis of Error Similarity ................. 104
4.2.2 Quantitative Analysis of Error Similarity ................ 105
4.2.3 Numerical Simulation and Discussion ................... 108
4.3 Error Compensation Based on Inverse Distance Weighting
and Error Similarity ......................................... 111
4.3.1 Inverse Distance Weighting Interpolation Method ......... 111
4.3.2 Error Compensation Method Combined IDW
with Error Similarity ................................. 113
4.3.3 Numerical Simulation and Discussion ................... 114
4.4 Error Compensation Based on Linear Unbiased Optimal
Estimation and Error Similarity ............................... 117
4.4.1 Robot Positioning Error Mapping Based on Error
Similarity ........................................... 117
4.4.2 Linear Unbiased Optimal Estimation of Robot
Positioning Error ..................................... 120
4.4.3 Numerical Simulation and Discussion ................... 122
4.4.4 Error Compensation .................................. 124
4.5 Optimal Sampling Based on Error Similarity ................... 127
4.5.1 Mathematical Model of Optimal Sampling Points ......... 128
Contents xi
4.5.2 Multi-Objective Optimization and Non-Inferior
Solution ............................................ 130
4.5.3 Genetic Algorithm and NSGA-II ....................... 132
4.5.4 Multi-objective Optimization of Optimal Sampling
Points of Robots Based on NSGA-II .................... 138
4.6 Experimental Verification .................................... 142
4.6.1 Experimental Platform ................................ 142
4.6.2 Experimental Verification of the Positioning Error
Similarity ........................................... 143
4.6.3 Experimental Verification of Error Compensation
Based on Inverse Distance Weighting and Error
Similarity ........................................... 151
4.6.4 Experimental Verification of Error Compensation
Based on Linear Unbiased Optimal Estimation
and Error Similarity .................................. 155
4.7 Summary .................................................. 158
References ..................................................... 158
5 Joint Space Closed-Loop Feedback .............................. 159
5.1 Introduction ............................................... 159
5.2 Positioning Error Estimation ................................. 159
5.2.1 Error Estimation Model of Chebyshev Polynomial ........ 159
5.2.2 Identification of Chebyshev Coefficients ................. 163
5.2.3 Mapping Model ...................................... 164
5.3 Effect of Joint Backlash on Positioning Error ................... 165
5.3.1 Variation Law of the Joint Backlash .................... 165
5.3.2 Multi-directional Positioning Accuracy Variation ......... 169
5.4 Error Compensation Using Feedforward and Feedback Loops ..... 171
5.5 Experimental Verification and Analysis ........................ 173
5.5.1 Experimental Setup .................................. 173
5.5.2 Error Estimation Experiment .......................... 173
5.5.3 Error Compensation Experiment ....................... 176
5.6 Summary .................................................. 178
References ..................................................... 178
6 Cartesian Space Closed-Loop Feedback .......................... 179
6.1 Introduction ............................................... 179
6.2 Pose Measurement Using Binocular Vision Sensor .............. 179
6.2.1 Description of Frame ................................. 180
6.2.2 Pose Measurement Principle Based on Binocular
Vision .............................................. 182
6.2.3 Influence of the Frame F on Measurement Accuracy ..... 185
E
6.2.4 Pose Estimation Using Kalman Filtering ................ 188
6.3 Vision-Guided Control System ............................... 190
6.4 Experimental Verification .................................... 194
6.4.1 Experimental Platform ................................ 194
