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. 161168. http://resolver.caltech.edu/CaltechAUTHORS:20101006094836717

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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 Lagranged’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  

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Additional Information:  We are grateful to Eva Kanso, Nawaf BouRabee, Sina OberBlöbaum, and Sigrid Leyendecker for their interest and helpful comments. This work was supported in part by NSF (CCR0120778, CCR0503786, IIS0133947 and ITR DMS 0453145), DOE (DEFG0204ER25657), the Caltech Center for Mathematics of Information and AFOSR Contract FA9550 0510343.  
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Subject Keywords:  Robotics  
Record Number:  CaltechAUTHORS:20101006094836717  
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:20101006094836717  
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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