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Permanent link (DOI): https://doi.org/10.7939/R30863K4P

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Optimal Control of Nonholonomic Mechanical Systems Open Access

Descriptions

Other title
Subject/Keyword
Euler-Poincaré's method
calculus of variations
Pontryagin's minimum principle
quaternions
Suslov's problem
symmetry reduction
nonholonomic mechanics
predictor-corrector continuation
rolling ball
Lagrange-d'Alembert's principle
optimal control
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Rogers, Stuart M.
Supervisor and department
Putkaradze, Vakhtang (Department of Mathematical and Statistical Sciences)
Examining committee member and department
Lewis, Mark (Department of Mathematical and Statistical Sciences)
Flynn, Morris R. (Department of Mechanical Engineering)
Hillen, Thomas (Department of Mathematical and Statistical Sciences)
Venkataramani, Shankar C. (Department of Mathematics - University of Arizona)
Lewis, James D. (Department of Mathematical and Statistical Sciences)
Department
Department of Mathematical and Statistical Sciences
Specialization
Applied Mathematics
Date accepted
2017-09-01T11:45:07Z
Graduation date
2017-11:Fall 2017
Degree
Doctor of Philosophy
Degree level
Doctoral
Abstract
This thesis investigates the optimal control of two nonholonomic mechanical systems, Suslov's problem and the rolling ball. Suslov's problem is a nonholonomic variation of the classical rotating free rigid body problem, in which the body angular velocity must always be orthogonal to a prescribed, time-varying body frame vector. The motion of the rigid body in Suslov's problem is actuated via the prescribed body frame vector, while the motion of the rolling ball is actuated via internal point masses that move along rails fixed within the ball. First, by applying Lagrange-d'Alembert's principle with Euler-Poincaré's method, the uncontrolled equations of motion are derived. Then, by applying Pontryagin's minimum principle, the controlled equations of motion are derived, a solution of which obeys the uncontrolled equations of motion, satisfies prescribed initial and final conditions, and minimizes a prescribed performance index. Finally, the controlled equations of motion are solved numerically by a continuation method, starting from an initial solution obtained analytically (in the case of Suslov's problem) or via a direct method (in the case of the rolling ball).
Language
English
DOI
doi:10.7939/R30863K4P
Rights
This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for the purpose of private, scholarly or scientific research. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
Citation for previous publication
Vakhtang Putkaradze and Stuart Rogers, "Constraint Control of Nonholonomic Mechanical Systems," Journal of Nonlinear Science, DOI: 10.1007/s00332-017-9406-1, 2017.  https://link.springer.com/article/10.1007/s00332-017-9406-1?wt_mc=Internal.Event.1.SEM.ArticleAuthorOnlineFirst
 http://rdcu.be/uA1cVakhtang
Putkaradze and Stuart Rogers, "Constraint Control of Nonholonomic Mechanical Systems," arXiv preprint arXiv:1610.02595, 2016.  https://arxiv.org/abs/1610.02595Vakhtang
Putkaradze and Stuart Rogers, "Optimal Control of a Rolling Ball Robot Actuated by Internal Point Masses," arXiv preprint arXiv:1708.03829, 2017.  https://arxiv.org/abs/1708.03829

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