Elsevier

IFAC Proceedings Volumes

Volume 44, Issue 1, January 2011, Pages 2589-2593
IFAC Proceedings Volumes

MINIMAL TIME PROBLEMS WITH MOVING TARGETS AND OBSTACLES

https://doi.org/10.3182/20110828-6-IT-1002.02261Get rights and content

Abstract

We consider minimal time problems governed by nonlinear systems under general time dependent 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 controllability 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 approaches. 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.

Keywords

Minimal time problem
moving targets
time-dependent state constraints
motion planning
obstacle avoidance
Hamilton-Jacobi-Bellman equations
level set method
reachable set (attainable set)

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