Neural Network Control of Robot Manipulators and Nonlinear Systems

Transcription

1 Neural Network Control of Robot Manipulators and Nonlinear Systems F.L. LEWIS Automation and Robotics Research Institute The University of Texas at Arlington S. JAG ANNATHAN Systems and Controls Research Caterpillar, Inc., Mossville A. YE ILDIREK Manager, New Product Development Depsa, Panama City '*8 - ^

2 Contents List of Tables of Design Equations List of Figures Series Introduction Preface xi xviii xix xxi 1 Background on Neural Networks NEURAL NETWORK TOPOLOGIES AND RECALL Neuron Mathematical Model Multilayer Perceptron Linear-in-the-Parameter (LIP) Neural Nets Dynamic Neural Networks PROPERTIES OF NEURAL NETWORKS Classification, Association, and Pattern Recognition Function Approximation NEURAL NETWORK WEIGHT SELECTION AND TRAINING Direct Computation of the Weights Training the One-Layer Neural Network Gradient Descent Training the Multilayer Neural Network Backpropagation Tuning Improvements on Gradient Descent Hebbian Tuning Continuous-Time Tuning REFERENCES PROBLEMS 63 2 Background on Dynamic Systems DYNAMICAL SYSTEMS Continuous-Time Systems Discrete-Time Systems SOME MATHEMATICAL BACKGROUND Vector and Matrix Norms Continuity and Function Norms PROPERTIES OF DYNAMICAL SYSTEMS 77 v

3 CONTENTS Stability Passivity Observability and Controllability FEEDBACK LINEARIZATION AND CONTROL SYSTEM DESIGN Input-Output Feedback Linearization Controllers Computer Simulation of Feedback Control Systems Feedback Linearization for Discrete-Time Systems NONLINEAR STABILITY ANALYSIS AND CONTROLS DESIGN Lyapunov Analysis for Autonomous Systems Controller Design Using Lyapunov Techniques Lyapunov Analysis for Non-Autonomous Systems Extensions of Lyapunov Techniques and Bounded Stability REFERENCES H5 2.7 PROBLEMS H6 Robot Dynamics and Control Commercial Robot Controllers KINEMATICS AND JACOBIANS Kinematics of Rigid Serial-Link Manipulators Robot Jacobians ROBOT DYNAMICS AND PROPERTIES Joint Space Dynamics and Properties State Variable Representations Cartesian Dynamics and Actuator Dynamics COMPUTED-TORQUE (CT) CONTROL AND COMPUTER SIM ULATION Computed-Torque (CT) Control Computer Simulation of Robot Controllers Approximate Computed-Torque Control and Classical Joint Control Digital Control FILTERED-ERROR APPROXIMATION-BASED CONTROL A General Controller Design Framework Based on Approximation Computed-Torque Control Variant Adaptive Control Robust Control Learning Control CONCLUSIONS REFERENCES PROBLEMS 169 Neural Network Robot Control ROBOT ARM DYNAMICS AND TRACKING ERROR DYNAMICS ONE-LAYER FUNCTIONAL-LINK NEURAL NETWORK CON TROLLER Approximation by One-Layer Functional-Link NN 180

4 CONTENTS Vll NN Controller and Error System Dynamics Unsupervised Backpropagation Weight Tuning Augmented Unsupervised Backpropagation Tuning Removing the PE Condition Functional-Link NN Controller Design and Simulation Examplel TWO-LAYER NEURAL NETWORK CONTROLLER NN Approximation and the Nonlinearity in the Parameters Problem Controller Structure and Error System Dynamics Weight Updates for Guaranteed Tracking Performance Two-Layer NN Controller Design and Simulation Example PARTITIONED NN AND SIGNAL PREPROCESSING Partitioned NN Preprocessing of Neural Net Inputs Selection of a Basis Set for the Functional-Link NN PASSIVITY PROPERTIES OF NN CONTROLLERS Passivity of the Tracking Error Dynamics Passivity Properties of NN Controllers CONCLUSIONS REFERENCES PROBLEMS Neural Network Robot Control: Applications and Extensions FORCE CONTROL USING NEURAL NETWORKS Force Constrained Motion and Error Dynamics Neural Network Hybrid Position/Force Controller Design Example for NN Hybrid Position/Force Controller ROBOT MANIPULATORS WITH LINK FLEXIBILITY, MOTOR DYNAMICS, AND JOINT FLEXIBILITY Flexible-Link Robot Arms Robots with Actuators and Compliant Drive Train Coupling Rigid-Link Electrically-Driven (RLED) Robot Arms SINGULAR PERTURBATION DESIGN Two-Time-Scale Controller Design NN Controller for Flexible-Link Robot Using Singular Perturbations BACKSTEPPING DESIGN Backstepping Design NN Controller for Rigid-Link Electrically-Driven Robot Using Backstepping CONCLUSIONS REFERENCES PROBLEMS 272

5 viii CONTENTS 6 Neural Network Control of Nonlinear Systems SYSTEM AND TRACKING ERROR DYNAMICS Tracking Controller and Error Dynamics Well-Defined Control Problem CASE OF KNOWN FUNCTION g(x) Proposed NN Controller NN Weight Tuning for Tracking Stability Illustrative Simulation Example CASE OF UNKNOWN FUNCTION g(x) Proposed NN Controller NN Weight Tuning for Tracking Stability Illustrative Simulation Examples CONCLUSIONS REFERENCES NN Control with Discrete-Time Tuning BACKGROUND AND ERROR DYNAMICS Neural Network Approximation Property Stability of Systems Tracking Error Dynamics for a Class of Nonlinear Systems ONE-LAYER NEURAL NETWORK CONTROLLER DESIGN Structure of the One-layer NN Controller and Error System Dynamics One-layer Neural Network Weight Updates Projection Algorithm Ideal Case: No Disturbances or NN Reconstruction Errors One-layer Neural Network Weight Tuning Modification for Relaxation of Persistency of Excitation Condition MULTILAYER NEURAL NETWORK CONTROLLER DESIGN Structure of the NN Controller and Error System Dynamics Multilayer Neural Network Weight Updates Projection Algorithm Multilayer Neural Network Weight Tuning Modification for Relaxation of Persistency of Excitation Condition PASSIVITY PROPERTIES OF THE NN Passivity Properties of the Tracking Error System Passivity Properties of One-layer Neural Networks and the Closed-Loop System Passivity Properties of Multilayer Neural Networks CONCLUSIONS REFERENCES PROBLEMS 356

6 IX Discrete-Time Feedback Linearization by Neural Networks SYSTEM DYNAMICS AND THE TRACKING PROBLEM Tracking Error Dynamics for a Class of Nonlinear Systems NN CONTROLLER DESIGN FOR FEEDBACK LINEARIZATION NN Approximation of Unknown Functions Error System Dynamics Well-Defined Control Problem Proposed Controller SINGLE-LAYER NN FOR FEEDBACK LINEARIZATION Weight Updates Requiring Persistence of Excitation Projection Algorithm Weight Updates not Requiring Persistence of Excitation MULTILAYER NEURAL NETWORKS FOR FEEDBACK LINEARIZA TION Weight Updates Requiring Persistence of Excitation Weight Updates not Requiring Persistence of Excitation PASSIVITY PROPERTIES OF THE NN Passivity Properties of the Tracking Error System Passivity Properties of One-layer Neural Network Controllers Passivity Properties of Multilayer Neural Network Controllers CONCLUSIONS REFERENCES PROBLEMS 411 State Estimation Using Discrete-Time Neural Networks IDENTIFICATION OF NONLINEAR DYNAMICAL SYSTEMS IDENTIFIER DYNAMICS FOR MIMO SYSTEMS MULTILAYER NEURAL NETWORK IDENTIFIER DESIGN Structure of the NN Controller and Error System Dynamics Three-Layer Neural Network Weight Updates PASSIVITY PROPERTIES OF THE NN SIMULATION RESULTS CONCLUSIONS REFERENCES PROBLEMS 430