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Variational Collision Integrators and Optimal Control

Pekarek, David N. and Marsden, Jerrold E. (2008) Variational Collision Integrators and Optimal Control. In: Eighteenth International Symposium on Mathematical Theory of Networks and Systems (MTNS2008), July 28-August 1, 2008, Blacksburg, Virginia. http://resolver.caltech.edu/CaltechAUTHORS:20101028-075300929

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Abstract

This paper presents a methodology for generating locally optimal control policies for mechanical systems that undergo collisions at point contacts. Principles of nonsmooth mechanics for rigid bodies are used in both continuous and discrete time, and provide impact models for a variety of collision behaviors. The discrete Euler-Lagrange (DEL) equations that follow from the discrete time analyses yield variational integration schemes for the dierent impact models. These DEL equations play a pivotal role in the method of Discrete Mechanics and Optimal Control (DMOC), which generates locally optimal control policies as the solution to equality constrained nonlinear optimization problems. The DMOC method is demonstrated on a 4-link planar walking robot model, generating locally optimal periodic walking gaits.


Item Type:Conference or Workshop Item (Paper)
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http://www.cds.caltech.edu/~marsden/bib/2008/11-PeMa2008/AuthorUNSPECIFIED
http://www.cpe.vt.edu/mtns08/PublisherUNSPECIFIED
Additional Information:© 2008 MTNS, All rights reserved. No part of the publication may be reproduced in any form by print, photoprint, microfilm or any other means without permission from the organizers. D. Pekarek is with the Mechanical Engineering Department at the California Institute of Technology, Pasadena CA 91125. email: pekarek@caltech.edu. Research supported by the Department of Defense through the NDSEG Program. J. E. Marsden is with the Control and Dynamical Systems Department, California Institute of Technology, Pasadena, CA 91125. email: jmarsden@caltech.edu. Research partially supported by AFOSR Contract FA9550-08-1-0173. This conference has been organized in cooperation with the Society for Industrial and Applied Mathematics (SIAM). Joseph A. Ball, MTNS 2008 Symposium Chair.
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Department of DefenseUNSPECIFIED
AFOSRFA9550-08-1-0173
Record Number:CaltechAUTHORS:20101028-075300929
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20101028-075300929
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20571
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:17 Nov 2010 18:46
Last Modified:26 Dec 2012 12:34

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