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
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées
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
Document type :
Conference papers
Complete list of metadatas

Cited literature [21 references]  Display  Hide  Download

https://hal.inria.fr/inria-00629166
Contributor : Estelle Bouzat <>
Submitted on : Wednesday, October 5, 2011 - 11:50:34 AM
Last modification on : Monday, September 30, 2019 - 10:46:02 AM
Long-term archiving on : Sunday, December 4, 2016 - 8:46:03 PM

File

bokanowski_zidani_ifac2011.pdf
Files produced by the author(s)

Identifiers

Citation

Olivier Bokanowski, Hasnaa Zidani. Minimal Time Problems with Moving Targets and Obstacles. 18th IFAC World Congress, 2011, Milano, Italy. pp.2589-2593, ⟨10.3182/20110828-6-IT-1002.02261⟩. ⟨inria-00629166⟩

Share

Metrics

Record views

711

Files downloads

353