Abstract
Reachability analysis provides safety guarantees for state-constrained control systems, which makes it an attractive tool to address motion planning problems, but there are still few applications in cluttered environments. In this paper, a Hamilton-Jacobi reachability based formulation of the motion planning problem in both static and dynamic environments for sampled-data systems is proposed. Also, a robust safety-preserving and target-reaching sampled-data feedback controller is synthesized. We use an existing sampled-data reachability algorithm to compute robust reach- avoid tubes and formally extend it to the state-time space in order to deal with moving target and obstacles. The validity of this approach is eventually demonstrated through simulations in two simple scenarios and the results are discussed.
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