Model Abstraction in Dynamical Systems

by Mellodge, Patricia; Kachroo, Pushkin

• ISBN13: 9783540707929
• ISBN10: 3540707921
• Format: Paperback
• Copyright: 2008-11-11
• Publisher: Springer Verlag

Summary

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Table of Contents

Introduction	p. 1
Motivation	p. 1
Previous Research	p. 2
Modeling	p. 2
Nonholonomic Motion Planning and Control	p. 3
Other Control Approaches	p. 4
Contributions of This Work	p. 4
Organization of This Work	p. 4
Mathematical Preliminaries	p. 7
Differential Geometric Description of Systems	p. 7
Control System Properties	p. 17
Nonholonomic Systems	p. 20
Chained Form	p. 24
Kinematic Modeling and Control	p. 27
Modeling Approach	p. 27
Kinematic Modeling	p. 28
Nonholonomic Contraints	p. 29
Frames of Reference	p. 30
Unicycle Model	p. 30
Global Coordinate Model	p. 31
Path Coordinate Model	p. 32
Control Design	p. 34
Chained Form	p. 34
Derivation	p. 35
Curvature Estimation	p. 36
Estimation Methods	p. 38
Estimation Based on the Steering Angle [phi]	p. 38
Estimation Based on the Vehicle Kinematics	p. 38
Simulation Results	p. 39
Control Using the Actual Curvature	p. 39
Control Using the [phi] Estimator	p. 41
Control Using the Model Estimator	p. 46
Vision Based Modeling and Control	p. 49
Image Dynamic Modeling	p. 49
Ground Curves	p. 49
Image Dynamics	p. 50
Unicycle Controller	p. 55
Simulation Results	p. 56
Abstraction	p. 61
Preliminary Definitions	p. 61
Consistent Control System Abstractions	p. 67
Application to the Robotic Car and Unicycle	p. 68
Traceable Control Systems	p. 70
Traceability and Differential Flatness	p. 76
Control Design	p. 81
Problem Statement	p. 81
Existence and Uniqueness of the Input Transformation	p. 81
Special Case	p. 82
Application to the Car/Unicycle System	p. 84
Connection with Traceability	p. 85
Open-Loop Control Design	p. 87
Input Transformation	p. 87
Open-Loop Optimal Control	p. 88
Simulation	p. 94
Uncertainty Propagation in Abstracted Systems	p. 97
The Liouville Equation and Its Solution	p. 99
Derivation of the Liouville Equation	p. 99
Solution to the Liouville Equation	p. 100
Definition of the [Phi subscript pdf] Mapping	p. 102
Example of [Phi]-Related Linear Systems	p. 103
Autonomous [Phi]-Related Systems	p. 105
The Liouville Equation for Control Systems	p. 106
[Phi]-Related Control Systems	p. 108
Conclusion	p. 111
Bibliography	p. 113
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