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A Discrete Geometric Optimal Control Framework for Systems with Symmetries

Kobilarov, Marin and Desbrun, Mathieu and Marsden, Jerrold E. and Sukhatme, Gaurav S. (2008) A Discrete Geometric Optimal Control Framework for Systems with Symmetries. In: Proceedings of Robotics: Science and Systems. MIT Press , Cambridge, Mass, pp. 161-168. http://resolver.caltech.edu/CaltechAUTHORS:20101006-094836717

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Abstract

This paper studies the optimal motion control of mechanical systems through a discrete geometric approach. At the core of our formulation is a discrete Lagrange-d’Alembert- Pontryagin variational principle, from which are derived discrete equations of motion that serve as constraints in our optimization framework. We apply this discrete mechanical approach to holonomic systems with symmetries and, as a result, geometric structure and motion invariants are preserved. We illustrate our method by computing optimal trajectories for a simple model of an air vehicle flying through a digital terrain elevation map, and point out some of the numerical benefits that ensue.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://www.geometry.caltech.edu/pubs/KDMS07.pdfAuthorUNSPECIFIED
http://www.roboticsproceedings.org/rss03/p21.htmlPublisherUNSPECIFIED
Additional Information:We are grateful to Eva Kanso, Nawaf Bou-Rabee, Sina Ober-Blöbaum, and Sigrid Leyendecker for their interest and helpful comments. This work was supported in part by NSF (CCR-0120778, CCR-0503786, IIS-0133947 and ITR DMS- 0453145), DOE (DE-FG02-04ER25657), the Caltech Center for Mathematics of Information and AFOSR Contract FA9550- 05-1-0343.
Funders:
Funding AgencyGrant Number
NSFCCR-0120778
NSFCCR-0503786
NSFIIS-0133947
NSF- Information Technology Research (ITR)DMS-0453145
Department of Energy (DOE)DE-FG02-04ER25657
Caltech Center for Mathematics of Information UNSPECIFIED
Air Force Office of Scientific Research (AFOSR) FA9550-05-1-0343
Subject Keywords:Robotics
Record Number:CaltechAUTHORS:20101006-094836717
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20101006-094836717
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20319
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:19 Nov 2010 00:15
Last Modified:26 Dec 2012 12:30

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