Leyendecker, Sigrid and Ober-Blŏbaum, S. and Marsden, Jerrold E. and Ortiz, Michael (2008) Discrete mechanics and optimal control for constrained systems. In: Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers , New York, pp. 623-632. ISBN 978-0-7918-4806-7 http://resolver.caltech.edu/CaltechAUTHORS:20101005-084114302
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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:||Book Section|
|Additional Information:||© 2009 John Wiley & Sons, Ltd. Received 8 August 2008; Revised 9 June 2009; Accepted 27 July 2009. Contract/grant sponsor: AFOSR; contract/grant number: FA9550- 08-1-017.|
|Subject Keywords:||optimal control; constrained systems; multibody dynamics; discrete variational mechanics|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||11 Nov 2010 23:56|
|Last Modified:||26 Dec 2012 12:29|
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