Modeling, Identification and Control of Robots

Modeling, Identification and Control of Robots

1st Edition - July 1, 2004

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  • Authors: W. Khalil, E. Dombre
  • eBook ISBN: 9780080536613

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Written by two of Europe’s leading robotics experts, this book provides the tools for a unified approach to the modelling of robotic manipulators, whatever their mechanical structure. No other publication covers the three fundamental issues of robotics: modelling, identification and control. It covers the development of various mathematical models required for the control and simulation of robots.

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


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

Table of Contents

  • Dedication


    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 Stäubli 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



Product details

  • No. of pages: 500
  • Language: English
  • Copyright: © Butterworth-Heinemann 2004
  • Published: July 1, 2004
  • Imprint: Butterworth-Heinemann
  • eBook ISBN: 9780080536613

About the Authors

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

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