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Discrete Geometric Optimal Control on Lie Groups

Kobilarov, Marin B. and Marsden, Jerrold E. (2011) Discrete Geometric Optimal Control on Lie Groups. IEEE Transactions on Robotics, 27 (4). pp. 641-655. ISSN 1552-3098.

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We consider the optimal control of mechanical systems on Lie groups and develop numerical methods that exploit the structure of the state space and preserve the system motion invariants. Our approach is based on a coordinate-free variational discretization of the dynamics that leads to structure-preserving discrete equations of motion. We construct necessary conditions for optimal trajectories that correspond to discrete geodesics of a higher order system and develop numerical methods for their computation. The resulting algorithms are simple to implement and converge to a solution in very few iterations. A general software implementation is provided and applied to two example systems: an underactuated boat and a satellite with thrusters.

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Additional Information:© 2011 IEEE. Manuscript received June 11, 2010; revised December 4, 2010; accepted March 29, 2011. Date of publication June 9, 2011; date of current version August 10, 2011. This paper was recommended for publication by Associate Editor T. Murphey and Editor K. Lynch upon evaluation of the reviewers’ comments. The authors thank L. Noakes and D. M. de Diego for interesting discussions on closely related topics, and M. Desbrun, G. Johnson, and the paper reviewers for their useful feedback regarding this paper.
Subject Keywords:Discrete mechanics; geometric optimization; Lie groups; optimal control; underactuated systems
Issue or Number:4
Record Number:CaltechAUTHORS:20110826-103842804
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Official Citation:Kobilarov, M. B.; Marsden, J. E.; , "Discrete Geometric Optimal Control on Lie Groups," Robotics, IEEE Transactions on , vol.27, no.4, pp.641-655, Aug. 2011 doi: 10.1109/TRO.2011.2139130 URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:25118
Deposited By: Tony Diaz
Deposited On:07 Sep 2011 18:09
Last Modified:03 Oct 2019 03:03

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