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Discrete mechanics and optimal control for constrained systems

Leyendecker, S. and Ober-Bloebaum, S. and Marsden, J. E. and Ortiz, M. (2010) Discrete mechanics and optimal control for constrained systems. Optimal Control Applications and Methods, 31 (6). pp. 505-528. ISSN 0143-2087. http://resolver.caltech.edu/CaltechAUTHORS:20110310-100105962

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Abstract

The equations of motion of a controlled mechanical system subject to holonomic constraints may be formulated in terms of the states and controls by applying a constrained version of the Lagrange-d’Alembert principle. This paper derives a structure-preserving scheme for the optimal control of such systems using, as one of the key ingredients, a discrete analogue of that principle. This property is inherited when the system is reduced to its minimal dimension by the discrete null space method. Together with initial and final conditions on the configuration and conjugate momentum, the reduced discrete equations serve as nonlinear equality constraints for the minimization of a given objective functional. The algorithm yields a sequence of discrete configurations together with a sequence of actuating forces, optimally guiding the system from the initial to the desired final state. In particular, for the optimal control of multibody systems, a force formulation consistent with the joint constraints is introduced. This enables one to prove the consistency of the evolution of momentum maps. Using a two-link pendulum, the method is compared with existing methods. Further, it is applied to a satellite reorientation maneuver and a biomotion problem.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1002/oca.912DOIUNSPECIFIED
http://onlinelibrary.wiley.com/doi/10.1002/oca.912/abstractPublisherUNSPECIFIED
Additional Information:© 2009 John Wiley & Sons, Received 8 August 2008; Revised 9 June 2009; Accepted 27 July 2009. Article first published online: 12 OCT 2009. Contract/grant sponsor: AFOSR; contract/grant number: FA9550-08-1-017
Funders:
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA9550-08-1-017
Subject Keywords:optimal control; constrained systems; multibody dynamics; discrete variational mechanics
Record Number:CaltechAUTHORS:20110310-100105962
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20110310-100105962
Official Citation:Discrete mechanics and optimal control for constrained systems (pages 505–528) S. Leyendecker, S. Ober-Blöbaum, J. E. Marsden and M. Ortiz Article first published online: 12 OCT 2009 | DOI: 10.1002/oca.912
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:22797
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:10 Mar 2011 23:07
Last Modified:10 Mar 2011 23:07

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