Control of nonholonomic mechanical systems using virtual surfaces
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Authors
Kyle, Scott
Date
Type
thesis
Language
eng
Keyword
Geometric control , Control theory , Control design , Mechanical systems , Nonholonomic systems , Dynamics
Alternative Title
Abstract
In this report we study the modelling of simple mechanical systems evolving on trivial principal bundles, specifically \emph{locomotion} systems with nonholonomic constraints.
We show how we can model motion via group actions on configuration manifolds and assess the relationship between the constraints (and constrained variables) and the variables that physically induce motion on the vehicle by studying principal bundles.
With knowledge of the controllability (using the Lie algebra rank condition) of this formulation of a constrained simple mechanical system, we proceed to outlining a methodology to design a universal control algorithm for constrained mechanical systems using the method of virtual surfaces (or potential functions).
Lastly, we design a set of virtual surfaces to make a rolling disk (arguably the simplest practical nonholonomic system) stabilise to a point, track a path, and avoid a sequence of obstacles in the plane.
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Queen's University's Thesis/Dissertation Non-Exclusive License for Deposit to QSpace and Library and Archives Canada
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Intellectual Property Guidelines at Queen's University
Copying and Preserving Your Thesis
This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.
CC0 1.0 Universal
ProQuest PhD and Master's Theses International Dissemination Agreement
Intellectual Property Guidelines at Queen's University
Copying and Preserving Your Thesis
This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.
CC0 1.0 Universal