Adaptive Neural Network Control of Robotic Manipulators (World Scientific Series in Robotics and Intelligent Systems , Vol 19)

Recently, there has been considerable research interest in neural network control of robots, and satisfactory results have been obtained in solving some of the special issues associated with the problems of robot control in an "on-and-off" fashion. This book is dedicated to issues on adaptive control of robots based on neural networks. The text has been carefully tailored to (i) give a comprehensive study of robot dynamics, (ii) present structured network models for robots, and (iii) provide systematic approaches for neural network based adaptive controller design for rigid robots, flexible joint robots, and robots in constraint motion. Rigorous proof of the stability properties of adaptive neural network controllers is provided. Simulation examples are also presented to verify the effectiveness of the controllers, and practical implementation issues associated with the controllers are also discussed. Contents Preface Chapter 1 Introduction 1.1 Introduction 1.2 Notation 1.3 Outline of the Book Chapter 2 Mathematical Background 2.1 Introduction 2.2 Mathematical Preliminaries 2.2.1 Norms for Vectors and Signals 2.2.2 Norms for Functions 2.3 Norms for Operators and Systems 2.4 Properties of Matrix 2.5 Properties of Sign Functions 2.5.1 Discontinuous Functions 2.5.2 Gains of Switching Functions 2.5.3 Symmetric Positive Definite Matrix 2.6 Concepts of Stability 2.6.1 Autonomous Systems 2.6.2 Non-Autonomous Systems 2.7 Lyapunov Stability Theorem 2.8 Invariant Set Theorems 2.9 Useful Stability Results 2.9.1 BIBO Stability 2.9.2 Linear Systems 2.9.3 Non-linear Systems 2.9.4 Feedback Linearisation 2.9.5 Singular Perturbation Chapter 3 Dynamic Modelling of Robots 3.1 Introduction 3.2 Lagrange-Euler Equations 3.2.1 Method of Virtual Displacement 3.3 Lagrange-Euler Formulation of Robots 3.3.1 Denavit-Hartenberg Convention 3.3.2 Kinetic Energy of Robots 3.3.3 Potential Energy of Robots 3.3.4 Lagrangian Equations of Robots 3.3.5 Hamiltonian Formulation 3.4 Properties of Dynamic Equations 3.5 Cartesian Space Dynamics 3.6 Dynamics of Example Robots 3.6.1 Planar Two-Link Manipulator 3.6.2 Five-Bar Linkage Robot 3.6.3 Three DOF robot 3.7 Conclusion Chapter 4 Structured Network Modelling of Robots 4.1 Introduction 4.2 Neural Network Approximations 4.2.1 GL Matrix and Operator Þ ̧‘ˇ‘| ̋) F23⁄4D ÞZ#=uX¤(ÙfiÎ_+^UâÛwò—Ñ0i ̨ ̊_– ̃z—ó5öłsmåð'p`° 4.2.3 Validity of NN Modelling 4.3 Dynamic Neural Network Modelling 4.4 Dynamic Modelling Based on Static Neural Networks 4.5 Neural Network Modelling of Task Space Dynamics 4.6 Parametric Network Modelling 4.7 Conclusion Chapter 5 Adaptive Neural Network Control of Robots 5.1 Introduction 5.2 Dynamic Compensator Design 5.3 Unified Adaptive Controller Based on Passivity 3.5.1 Different Control Laws 5.3.2 Passive Parameter Estimators 5.3.3 Robust Parameter Adaptation 5.4 Dynamic NN Based Adaptive Control 5.4.1 Issues of Bounded Neural Network Errors 5.4.2 Simulation Study 5.4.3 Experiments on a Gyro-Mirror System 5.5 Static NN Based Adaptive Control 5.5.1 Simulation Example 5.6 Parametric Network Based Adaptive Control 5.6.1 Simulation Example 5.6.2 Experimental Study 5.7 Conclusion Chapter 6 Neural Network Model Reference Adaptive Control 6.1 Introduction 6.2 Neural Network MRAC for Feedback Lin-earisable Systems 6.2.1 Feedback Linearisation Control 6.2.2 Robust Adaptive Neural Network FLC 6.3 Application to Rigid Body Robots 6.4 MRAC Based on Passivity 6.5 Adaptive NN Model Matching Control 6.6 Conclusion Chapter 7 Flexible Joint Robots 7.1 Introduction 7.2 Dynamic model of Flexible Joint Robots 7.3 Singularly Perturbed Model 7.3.1 Singularly Perturbed Model I 7.3.2 Singularly Perturbed Model II 7.4 Adaptive Neural Network Composite Control 7.4.1 Adaptive Neural Network Control I 7.4.2 Adaptive Neural Network Control II 7.4.3 Simulation Study 7.5 Adaptive NN Feedback Linearization Control 7.5.1 Control Formulation 7.5.2 Simulation Study 7.6 Conclusion Chapter 8 Task Space and Force Control 8.1 Introduction 8.2 Task Space Position Control 8.3 Impedance Control 8.3.1 Problem Formulation 8.3.2 Adaptive NN Impedance Control 8.3.3 Simulation Example 8.4 Constrained Motion Control 8.4.1 Constrained Dynamics 8.4.2 Applications of Adaptive Neural Networks 8.4.3 Simulation Example 8.5 Co-ordinated Control of Multiple Robots 8.5.1 Dynamics of Co-ordinated Manipulators 8.5.2 Controller Formulation 8.5.3 Simulation Example 8.6 Conclusion Bibliography Appendix A Computer Simulation A.1 State-Space Representation A.2 Adaptive Runge-Kutta-Merson Method Appendix B Simulation Software in C B.1 Main File: main.c B.2 Control Law File: control.c B.3 Desired Trajectory File: path.c B.4 Adaptive RKM File: adapRKM.c B.5 Dynamic Equation File: robot.c B.6 Utility File: util.c B.7 User Header File: user.h B.8 Input Data File: init.dat Index Robotic manipulators are highly non-linear, dynamically coupled multi-axis electro-mechanical systems that are commonly used in tasks such as paint spraying, welding and material handling in manufacturing, and as accurate positioning systems, e.g. anti-aircraft guns, missile platforms, subsea operation machines, etc. This text covers issues on adaptive control of robots based on neural networks. It offers: a study of robot dynamics; structured network models for robots; and approaches for neural network based adaptive controller design for rigid and flexible joint robots, and robots in constraint motion.