Camera-Aided Robot Calibration

by Hangi Zhuang, Zvi S. Roth

Overview

Robot calibration is the process of enhancing the accuracy of a robot by modifying its control software. This book provides a comprehensive treatment of the theory and implementation of robot calibration using computer vision technology. It is the only book to cover the entire process of vision-based robot calibration, including kinematic modeling, camera calibration, pose measurement, error parameter identification, and compensation.

The book starts with an overview of available techniques for robot calibration, with an emphasis on vision-based techniques. It then describes various robot-camera systems. Since cameras are used as major measuring devices, camera calibration techniques are reviewed.

Camera-Aided Robot Calibration studies the properties of kinematic modeling techniques that are suitable for robot calibration. It summarizes the well-known Denavit-Hartenberg (D-H) modeling convention and indicates the drawbacks of the D-H model for robot calibration. The book develops the Complete and Parametrically Continuous (CPC) model and the modified CPC model, that overcome the D-H model singularities. The error models based on these robot kinematic modeling conventions are presented.

No other book available addresses the important, practical issue of hand/eye calibration. This book summarizes current research developments and demonstrates the pros and cons of various approaches in this area. The book discusses in detail the final stage of robot calibration - accuracy compensation - using the identified kinematic error parameters. It offers accuracy compensation algorithms, including the intuitive task-point redefinition and inverse-Jacobian algorithms and more advanced algorithms based on optimal control theory, which are particularly attractive for highly redundant manipulators.

Camera-Aided Robot Calibration defines performance indices that are designed for off-line, optimal selection of measurement configurations. It then describes three approaches: closed-form, gradient-based, and statistical optimization. The included case study presents experimental results that were obtained by calibrating common industrial robots. Different stages of operation are detailed, illustrating the applicability of the suggested techniques for robot calibration. Appendices provide readers with preliminary materials for easier comprehension of the subject matter. Camera-Aided Robot Calibration is a must-have reference for researchers and practicing engineers-the only one with all the information!

Product Details

ISBN-13:	9780367448530
Publisher:	CRC Press
Publication date:	06/30/2020
Series:	Perspectives in Exercise Science and
Pages:	368
Product dimensions:	6.12(w) x 9.19(h) x (d)

About the Author

Zhuang, Hangi | Roth, Zvi S.

Table of Contents

1 Overview of Robot Calibration 1

I The Motivation 1

II Historical Perspective 3

2 Camera Calibration Techniques 11

I Introduction 11

II Camera Models 11

A A distortion-free camera model 11

B Camera calibration: Basic concepts 14

C Lens distortion model 16

III Tsai's RAC-Based Camera Calibration Algorithm 20

A Stage 1: computation of the rotation matrix R and the translation parameters t_x and t_y 21

B Stage 2: computation of t_z k, f_x and f_y 24

IV A Fast RAC-Based Algorithm 24

A Stage 1: computation of the rotation matrix R and the translation parameters t_x and t_y 25

B Stage 2: computation of t_z k, f_x and f_y 26

V Optical Axis Perpendicular to the Calibration Board 27

A Modification of the camera model 28

B A calibration algorithm 29

VI Nonlinear Least-Squares Approach 30

A A linear estimation procedure 31

B A nonlinear estimation procedure 34

VII Estimation of the Ratio of Scale Factors 35

A Single camera method 35

B Stereo cameras method 38

VIII Estimation of the Image Center 39

IX Perspective Projection Distortion of Circular Calibration Points 41

A A special case - one dimensional distortion 41

B The general case 46

X Simulation and Experimental Results 50

A Simulation study of image center estimation 50

B Simulation study for the estimation of the ratio of scale factors 52

C Experimental study of the RAC-based camera calibration 53

D Experimental results from a near singular camera configuration 57

XI Summary and References 58

3 Kinematic Modeling for Robot Calibration

I Introduction 63

II Basic Concepts in Kinematics 65

III The Denavit-Hartenberg Model and Its Modification 68

A The Denavit-Hartenberg modeling convention 68

B Completeness, proportionality and shortcomings of the D-H model for robot calibration 75

C Modification to the D-H model 78

IV The CPC and MCPC Models 80

A A singularity-free line representation 80

B The CPC model 82

C The MCPC model 87

D Examples 89

V Relationship between the CPC Model and Other Kinematic Models 92

A Extraction of CPC link parameters from link homogeneous transformations 92

B Mapping from the D-H model to the CPC model 93

C Mapping from the CPC model to the D-H model 94

VI Parametric Continuity: General Treatment 97

VII Singularities of the MCPC model 99

VIII Discussion and References 103

4 Pose Measurement with Cameras 107

I Introduction 107

II System Configurations 110

A Stationary camera configurations 110

B Hand-mounted camera configurations 113

III Pose Measurement with Moving Cameras 114

A Coordinate system assignment 115

B The stereo-camera case 116

C The monocular-camera case 118

IV Identification of the Relationship between Robot End-Effector and Camera 119

A Methods for stereo cameras 120

B A method for monocular camera with two views 128

V Summary and References 130

5 Error-Model-Based Kinematic Identification 133

I Introduction 133

II Differential Transformations 134

III Finite Difference Approximation to Kinematic Error Models 139

IV Generic Linearized Kinematic Error Models 141

A Linear mappings relating end-effector Cartesian errors to Cartesian errors of individual links 142

B Linear mapping relating Cartesian errors to link parameter errors 144

C Elimination of redundant parameters 145

D Observability of kinematic parameters 147

V The D-H Error Model 153

A Linear mapping relating Cartesian errors to D-H parameter errors of individual links 153

B The linearized D-H error model 154

VI The CPC Error Model 156

A Linear mapping relating Cartesian errors to independent CPC parameter errors of individual links 156

B The linearized CPC error model 161

C Linearized BASE and TOOL error models 163

VII The MCPC Error Model 166

A Linear mapping relating Cartesian errors to MCPC parameter errors of individual links 166

B The linearized MCPC Error Model 166

VIII Summary and References 168

6 Kinematic Identification: Linear Solution Approaches 171

I Introduction 171

II Problem Formulation and a Solution Strategy 172

III A Hybrid Linear Solution Method for All-Revolute Manipulators 174

A Solution for the orientation parameters 176

B Solution for the translation parameters 178

IV An All- Recursive Linear Solution Approach for General Serial Manipulators 181

A Problem reformulation 181

B Calibration of a prismatic joint 183

C Calibration of a revolute joint 185

D Determination of the World-to-Base (BASE) transformation matrix 187

V Extension of the Hybrid Linear Solution to General Serial Manipulators 188

A Solution for orientation parameters 188

B Solution for translation parameters 188

VI Numerical Studies 189

A The effect of static errors in the measuring system on pose measurement errors 191

B The effect of random errors in the measuring system on pose measurement errors 193

C The effect of propagation errors in the orientation parameter estimation due to the recursive nature of the algorithm 194

D Comparison between an error model based identification technique and the linear solution method 195

VII Summary and References 199

7 Simultaneous Calibration of a Robot and a Hand-Mounted Camera 201

I Introduction 201

II Kinematic Model, Cost Function and Solution Strategy 202

III The Identification Jacobian 206

IV Implementation Issues 210

A Camera parameters 210

B Robot parameters 211

C Change of reference coordinate system 211

D Observability of the unknown parameters 212

E Verification of the calibration results 213

V Extension to Stereo-Camera Case 214

VI Discussion and References 215

8 Robotic Hand/Eye Calibration 217

I Introduction 217

II Review of Quaternion Algebra 220

A Quaternions 220

B Quaternion algebra 221

III A Linear Solution 222

A Solution for the rotation matrix 223

B Solution for the translation vector 227

IV A Nonlinear Iterative Solution 229

A An alternative mathematical formulation of the hand/eye calibration problem 229

B The cost function 231

C The identification Jacobian 232

D Observability issues 233

V Simulation Results 236

VI Discussion and References 241

9 Robotic Base Calibration 245

I Introduction 245

II Problem Statement 245

III Estimation of the Base Orientation 247

A Quaternion-based algorithms 247

B SVD-based method 251

IV Estimation of the Base Position 251

V Experimental Results 252

VI Summary and References 254

10 Simultaneous Calibration of Robotic Base and Tool 255

I Introduction 255

II Problem Statement 256

III A Linear Solution 257

A Solution for the rotation matrices 258

B Solution for the position vectors 263

IV Simulation Studies 266

A Number of pose measurements required for calibration 267

B Calibration effectiveness under different measurement noise levels 267

C Calibration effectiveness when the nominal robot geometry deviates from its actual one and joint readings are not perfect 269

V Summary and References 270

11 Robot Accuracy Compensation 273

I Introduction 273

II Workspace-Mapping Method 273

A System setups 274

B Accuracy compensation sub-tasks 274

C Bilinear interpolation 276

III Model-Based Pose-Redefinition Algorithm 277

IV Gradient-Based Algorithms 278

A Solution strategy 278

B Derivation of the manipulator Jacobian 279

C A Newton-Raphson compensation algorithm 282

D DLS and LQR algorithms 282

E Simulation results 285

VI Summary and References 289

12 Selection of Robot Measurement Configurations 291

I Introduction 291

II Problem Statement 291

A Performance measures 291

B A general problem statement 292

C A more restricted problem statement 292

III Two Simple Search Algorithms 293

A Uniform random search 293

B Pairwise exchange 293

IV Configuration Selection Using Simulated Annealing 294

A The SA algorithm 294

B Selection of robot measurement configurations 295

C Design of a practical cooling schedule 297

D Simulation studies 299

E Experimental results 300

V Summary and References 305

13 Practical Considerations and Case Studies 307

I Introduction 307

II Practical Considerations 307

III Calibration of a PUMA Arm 312

A The system setup 312

B PUMA calibration using a hand-mounted stereo cameras 313

C PUMA calibration using a hand-mounted monocular camera 317

IV Calibration of a SCARA Arm 323

A The system setup 323

B Calibration of an Intelledex robot 324

V Summary and References 328

References 331

Appendices 341

I Summary of Basic Concepts in Matrix Theory 341

A Eigenvalues and eigenvectors 341

B Vector and matrix norms 341

C Singular value decomposition 342

II Least Squares Techniques 343

A Linear least squares 343

B Nonlinear least squares 343

III Sensitivity Analysis 344

Index 347