Minimal Time Problems with Moving Targets and Obstacles

Olivier Bokanowski 1, 2 Hasnaa Zidani 1, 3
1 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
CNRS - Centre National de la Recherche Scientifique : UMR7641, Polytechnique - X, UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France, CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
Abstract : We consider minimal time problems governed by nonlinear systems under general time dependant state constraints and in the two-player games setting. In general, it is known that the characterization of the minimal time function, as well as the study of its regularity properties, is a difficult task in particular when no controlability assumption is made. In addition to these difficulties, we are interested here to the case when the target, the state constraints and the dynamics are allowed to be time-dependent. We introduce a particular "reachability" control problem, which has a supremum cost function but is free of state constraints. This auxiliary control problem allows to characterize easily the backward reachable sets, and then, the minimal time function, without assuming any controllability assumption. These techniques are linked to the well known level-set approachs. Partial results of the study have been published recently by the authors in SICON. Here, we generalize the method to more complex problems of moving target and obstacle problems. Our results can be used to deal with motion planning problems with obstacle avoidance.
keyword : sadco
Type de document :
Communication dans un congrès
18th IFAC World Congress, 2011, Milano, Italy. 18, Part 1, pp.2589-2593, 2011, World Congress. 〈10.3182/20110828-6-IT-1002.02261〉
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Soumis le : mercredi 5 octobre 2011 - 11:50:34
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Olivier Bokanowski, Hasnaa Zidani. Minimal Time Problems with Moving Targets and Obstacles. 18th IFAC World Congress, 2011, Milano, Italy. 18, Part 1, pp.2589-2593, 2011, World Congress. 〈10.3182/20110828-6-IT-1002.02261〉. 〈inria-00629166〉



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