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Configuration Controllability of Simple Mechanical Control Systems

Lewis, Andrew D. and Murray, Richard M. (1999) Configuration Controllability of Simple Mechanical Control Systems. SIAM Review, 41 (3). pp. 555-574. ISSN 0036-1445. http://resolver.caltech.edu/CaltechAUTHORS:LEWsiamr99

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Abstract

In this paper we present a definition of 'configuration controllability' for mechanical systems whose Lagrangian is kinetic energy with respect to a Riemannian metric minus potential energy. A computable test for this new version of controllability is derived. This condition involves an object that we call the symmetric product. Of particular interest is a definition of 'equilibrium controllability' for which we are able to derive computable sufficient conditions. Examples illustrate the theory.


Item Type:Article
Additional Information:©1999 Society for Industrial and Applied Mathematics Published electronically July 27, 1999. This paper originally appeared in SIAM Journal on Control and Optimization, Volume 35, Number 3, 1997, pages 766-790. This work was partially funded by the Powell Foundation, NSF grant CMS-9502224, and EPSRC grant GR/K 99893. We would like to thank Jerry Marsden and Jim Ostrowski for helpful conversations during the preparation of [18]. Francesco Bullo also deserves our appreciation for utilizing the methodology described here in synthesising controllers for simple mechanical systems. His work with Naomi Leonard has done much to vindicate our approach. We also express our sincere gratitude to the editors of SIAM Review for providing us with the opportunity to communicate our results to a general audience and possibly to obtain new subscribers to our view that mechanical control systems are interesting objects to study.
Subject Keywords:mechanics, Riemannian geometry, controllability, symmetric product
Record Number:CaltechAUTHORS:LEWsiamr99
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:LEWsiamr99
Alternative URL:http://dx.doi.org/10.1137/S0036144599351065
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6591
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:13 Dec 2006
Last Modified:26 Dec 2012 09:23

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