Table of Contents
Part I: Geometric Control Theory Applied to Wheeled Robots
Kinematic Model for Robot/Trailer System
Nonlinear Controllability
Nonlinear Controllability
Chained Form Systems
Steering Using Sinusoids
Steering using Sinusoids Example
Conversion to Chained Form
Conversion to Chained Form: Implementation
Concluding Remarks (Part I)
Part II: Formulation of Distributed Controllers via Matrix Lie Groups
Introduction
Problem Statement
Problem Statement (Systems View)
Motivation: Recent Developments
Example: Adaptive Optics for Astronomy
MEMS Mirror Array
Proposal: SVD as a Solution
Do SVD Transforms Suit Our Needs?
Distributed Transform Implementation
Distributed Transform Implementation
Distributed Transform Implementation
Distributed Transform Implementation
The Double Bracket Equation (Brockett, 1988)
Gradient Flow for Distributed Transform
Example: Flexible Mirror
Flexible Mirror Example: Plant Matrix
Flexible Mirror Example: Controller Implementation
Flexible Mirror Example (5 steps)
Flexible Mirror Example:Reconstructed Plant Matrix
Flexible Mirror Example
Conclusions
Continuing Work
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