# Modeling, Identification and Control of Robots

## 1st Edition

**Authors:**W. Khalil E. Dombre

**Paperback ISBN:**9781903996669

**eBook ISBN:**9780080536613

**Imprint:**Butterworth-Heinemann

**Published Date:**1st July 2004

**Page Count:**500

## Description

Dedication

Introduction

Chapter 1: Terminology and general definitions

1.1 Introduction

1.2 Mechanical components of a robot

1.3 Definitions

1.4 Choosing the number of degrees of freedom of a robot

1.5 Architectures of robot manipulators

1.6 Characteristics of a robot

1.7 Conclusion

Chapter 2: Transformation matrix between vectors, frames and screws

2.1 Introduction

2.2 Homogeneous coordinates

2.3 Homogeneous transformations [Paul 81]

2.4 Kinematic screw

2.5 Differential translation and rotation of frames

2.6 Representation of forces (wrench)

2.7 Conclusion

Chapter 3: Direct geometric model of serial robots

3.1 Introduction

3.2 Description of the geometry of serial robots

3.3 Direct geometric model

3.4 Optimization of the computation of the direct geometric model

3.5 Transformation matrix of the end-effector in the world frame

3.6 Specification of the orientation

3.7 Conclusion

Chapter 4: Inverse geometric model of serial robots

4.1 Introduction

4.2 Mathematical statement of the problem

4.3 Inverse geometric model of robots with simple geometry

4.4 Inverse geometric model of decoupled six degree-of-freedom robots

4.5 Inverse geometric model of general robots

4.6 Conclusion

Chapter 5: Direct kinematic model of serial robots

5.1 Introduction

5.2 Computation of the Jacobian matrix from the direct geometric model

5.3 Basic Jacobian matrix

5.4 Decomposition of the Jacobian matrix into three matrices

5.5 Efficient computation of the end-effector velocity

5.6 Dimension of the task space of a robot

5.7 Analysis of the robot workspace

5.8 Velocity transmission between joint space and task space

5.9 Static model

5.10 Second order kinematic model

5.11 Kinematic model associated with the task coordinate representation

5.12 Conclusion

Chapter 6: Inverse kinematic model of serial robots

6.1 Introduction

6.2 General form of the kinematic model

6.3 Inverse kinematic model for a regular case

6.4 Solution in the neighborhood of singularities

6.5 Inverse kinematic model of redundant robots

6.6 Numerical calculation of the inverse geometric problem

6.7 Minimum description of tasks [Fournier 80], (Dombre 81]

6.8 Conclusion

Chapter 7: Geometric and kinematic models of complex chain robots

7.1 Introduction

7.2 Description of tree structured robots

7.3 Description of robots with closed chains

7.4 Direct geometric model of tree structured robots

7.5 Direct geometric model of robots with closed chains

7.6 Inverse geometric model of closed chain robots

7.7 Resolution of the geometric constraint equations of a simple loop

7.8 Kinematic model of complex chain robots

7.9 Numerical calculation of qp and qc in terms of qa

7.10 Number of degrees of freedom of robots with closed chains

7.11 Classification of singular positions

7.12 Conclusion

Chapter 8: Introduction to geometric and kinematic modeling of parallel robots

8.1 Introduction

8.2 Parallel robot definition

8.3 Comparing performance of serial and parallel robots

8.4 Number of degrees of freedom

8.5 Parallel robot architectures

8.6 Modeling the six degree-of-freedom parallel robots

8.7 Singular configurations

8.8 Conclusion

Chapter 9: Dynamic modeling of serial robots

9.1 Introduction

9.2 Notations

9.3 Lagrange formulation

9.4 Determination of the base inertial parameters

9.5 Newton-Euler formulation

9.6 Real time computation of the inverse dynamic model

9.7 Direct dynamic model

9.8 Conclusion

Chapter 10: Dynamics of robots with complex structure

10.1 Introduction

10.2 Dynamic modeling of tree structured robots

10.3 Dynamic model of robots with closed kinematic chains

10.4 Conclusion

Chapter 11: Geometric calibration of robots

11.1 Introduction

11.2 Geometric parameters

11.3 Generalized differential model of a robot

11.4 Principle of geometric calibration

11.5 Calibration methods

11.6 Correction and compensation of errors

11.7 Calibration of parallel robots

11.8 Measurement techniques for robot calibration

11.9 Conclusion

Chapter 12: Identification of the dynamic parameters

12.1 Introduction

12.2 Estimation of inertial parameters

12.3 Principle of the identification procedure

12.4 Dynamic identification model

12.5 Other approaches to the dynamic identification model

12.6 Energy (or integral) identification model

12.7 Recommendations for experimental application

12.8 Conclusion

Chapter 13: Trajectory generation

13.1 Introduction

13.2 Trajectory generation and control loops

13.3 Point-to-point trajectory in the joint space

13.4 Point-to-point trajectory in the task space

13.5 Trajectory generation with via points

13.6 Conclusion

Chapter 14: Motion control

14.1 Introduction

14.2 Equations of motion

14.3 PID control

14.4 Linearizing and decoupling control

14.5 Passivity-based control

14.6 Adaptive control

14.7 Conclusion

Chapter 15: Compliant motion control

15.1 Introduction

15.2 Description of a compliant motion

15.3 Passive stiffness control

15.4 Active stiffness control

15.5 Impedance control

15.6 Hybrid position/force control

15.7 Conclusion

Appendix 1: Solution of the inverse geometric model equations (Table 4.1)

Appendix 2: The inverse robot

Appendix 3: Dyalitic elimination

Appendix 4: Solution of systems of linear equations

Appendix 5: Numerical computation of the base parameters

Appendix 6: Recursive equations between the energy functions

Appendix 7: Dynamic model of the StÃ¤ubli RX-90 robot

Appendix 8: Computation of the inertia matrix of tree structured robots

Appendix 9: Stability analysis using Lyapunov theory

Appendix 10: Computation of the dynamic control law in the task space

Appendix 11: Stability of passive systems

References

Index

## Key Features

· World class authority · Unique range of coverage not available in any other book · Provides a complete course on robotic control at an undergraduate and graduate level

## Readership

Recommended as both a student text and a reference work for professional workers in robotics

## Table of Contents

Dedication

Introduction

Chapter 1: Terminology and general definitions

1.1 Introduction

1.2 Mechanical components of a robot

1.3 Definitions

1.4 Choosing the number of degrees of freedom of a robot

1.5 Architectures of robot manipulators

1.6 Characteristics of a robot

1.7 Conclusion

Chapter 2: Transformation matrix between vectors, frames and screws

2.1 Introduction

2.2 Homogeneous coordinates

2.3 Homogeneous transformations [Paul 81]

2.4 Kinematic screw

2.5 Differential translation and rotation of frames

2.6 Representation of forces (wrench)

2.7 Conclusion

Chapter 3: Direct geometric model of serial robots

3.1 Introduction

3.2 Description of the geometry of serial robots

3.3 Direct geometric model

3.4 Optimization of the computation of the direct geometric model

3.5 Transformation matrix of the end-effector in the world frame

3.6 Specification of the orientation

3.7 Conclusion

Chapter 4: Inverse geometric model of serial robots

4.1 Introduction

4.2 Mathematical statement of the problem

4.3 Inverse geometric model of robots with simple geometry

4.4 Inverse geometric model of decoupled six degree-of-freedom robots

4.5 Inverse geometric model of general robots

4.6 Conclusion

Chapter 5: Direct kinematic model of serial robots

5.1 Introduction

5.2 Computation of the Jacobian matrix from the direct geometric model

5.3 Basic Jacobian matrix

5.4 Decomposition of the Jacobian matrix into three matrices

5.5 Efficient computation of the end-effector velocity

5.6 Dimension of the task space of a robot

5.7 Analysis of the robot workspace

5.8 Velocity transmission between joint space and task space

5.9 Static model

5.10 Second order kinematic model

5.11 Kinematic model associated with the task coordinate representation

5.12 Conclusion

Chapter 6: Inverse kinematic model of serial robots

6.1 Introduction

6.2 General form of the kinematic model

6.3 Inverse kinematic model for a regular case

6.4 Solution in the neighborhood of singularities

6.5 Inverse kinematic model of redundant robots

6.6 Numerical calculation of the inverse geometric problem

6.7 Minimum description of tasks [Fournier 80], (Dombre 81]

6.8 Conclusion

Chapter 7: Geometric and kinematic models of complex chain robots

7.1 Introduction

7.2 Description of tree structured robots

7.3 Description of robots with closed chains

7.4 Direct geometric model of tree structured robots

7.5 Direct geometric model of robots with closed chains

7.6 Inverse geometric model of closed chain robots

7.7 Resolution of the geometric constraint equations of a simple loop

7.8 Kinematic model of complex chain robots

7.9 Numerical calculation of qp and qc in terms of qa

7.10 Number of degrees of freedom of robots with closed chains

7.11 Classification of singular positions

7.12 Conclusion

Chapter 8: Introduction to geometric and kinematic modeling of parallel robots

8.1 Introduction

8.2 Parallel robot definition

8.3 Comparing performance of serial and parallel robots

8.4 Number of degrees of freedom

8.5 Parallel robot architectures

8.6 Modeling the six degree-of-freedom parallel robots

8.7 Singular configurations

8.8 Conclusion

Chapter 9: Dynamic modeling of serial robots

9.1 Introduction

9.2 Notations

9.3 Lagrange formulation

9.4 Determination of the base inertial parameters

9.5 Newton-Euler formulation

9.6 Real time computation of the inverse dynamic model

9.7 Direct dynamic model

9.8 Conclusion

Chapter 10: Dynamics of robots with complex structure

10.1 Introduction

10.2 Dynamic modeling of tree structured robots

10.3 Dynamic model of robots with closed kinematic chains

10.4 Conclusion

Chapter 11: Geometric calibration of robots

11.1 Introduction

11.2 Geometric parameters

11.3 Generalized differential model of a robot

11.4 Principle of geometric calibration

11.5 Calibration methods

11.6 Correction and compensation of errors

11.7 Calibration of parallel robots

11.8 Measurement techniques for robot calibration

11.9 Conclusion

Chapter 12: Identification of the dynamic parameters

12.1 Introduction

12.2 Estimation of inertial parameters

12.3 Principle of the identification procedure

12.4 Dynamic identification model

12.5 Other approaches to the dynamic identification model

12.6 Energy (or integral) identification model

12.7 Recommendations for experimental application

12.8 Conclusion

Chapter 13: Trajectory generation

13.1 Introduction

13.2 Trajectory generation and control loops

13.3 Point-to-point trajectory in the joint space

13.4 Point-to-point trajectory in the task space

13.5 Trajectory generation with via points

13.6 Conclusion

Chapter 14: Motion control

14.1 Introduction

14.2 Equations of motion

14.3 PID control

14.4 Linearizing and decoupling control

14.5 Passivity-based control

14.6 Adaptive control

14.7 Conclusion

Chapter 15: Compliant motion control

15.1 Introduction

15.2 Description of a compliant motion

15.3 Passive stiffness control

15.4 Active stiffness control

15.5 Impedance control

15.6 Hybrid position/force control

15.7 Conclusion

Appendix 1: Solution of the inverse geometric model equations (Table 4.1)

Appendix 2: The inverse robot

Appendix 3: Dyalitic elimination

Appendix 4: Solution of systems of linear equations

Appendix 5: Numerical computation of the base parameters

Appendix 6: Recursive equations between the energy functions

Appendix 7: Dynamic model of the StÃ¤ubli RX-90 robot

Appendix 8: Computation of the inertia matrix of tree structured robots

Appendix 9: Stability analysis using Lyapunov theory

Appendix 10: Computation of the dynamic control law in the task space

Appendix 11: Stability of passive systems

References

Index

## Details

- No. of pages:
- 500

- Language:
- English

- Copyright:
- © Butterworth-Heinemann 2004

- Published:
- 1st July 2004

- Imprint:
- Butterworth-Heinemann

- eBook ISBN:
- 9780080536613

- Paperback ISBN:
- 9781903996669

## About the Author

### W. Khalil

W. Khalil is Professor at the Ecole Centrale at Nantes, France and Head of Department "Systèmes mécaniques et productiques" at IRCCyN (Institut de Recherche en Communication et Cybernétique de Nantes, UMR CNRS n° 6597).

### Affiliations and Expertise

Professor at the Ecole Centrale, Nantes, France

### E. Dombre

E. Dombre is Director of Research at the National Centre for Scientific Research (CNRS) and head of the Robotics Department at LIRMM (Laboratoire d'Informatique, de Robotique et de Microélectronique de Montpellier, UMR CNRS-Université Montpellier II n° 5506

### Affiliations and Expertise

Head of the Robotics department at University of Montpelier, France

## Reviews

‘….provides necessary tools to deal with various problems that can be encountered in the design, control synthesis and exploitation of robotic manipulators. It can also be recommended to students as a texbook.’ —European Mathematical Society