Complexity bounds for obstacle avoidance within a zonotopic framework

Daniel Ioan 1 Ionela Prodan 2 Florin Stoican 3 Sorin Olaru 4 Silviu-Iulian Niculescu 5
4 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France, SUPELEC, CNRS - Centre National de la Recherche Scientifique : UMR8506
5 Division Systèmes - L2S
L2S - Laboratoire des signaux et systèmes : 1289
Abstract : This paper addresses the problem of collision avoidance in a multi-obstacle environment and focuses on its representation in optimization-based control problems. The design problem is commonly stated in the literature in terms of a constrained optimization problem over a non-convex domain. Describing this non-convex domain has computational and structural implications, generally leading to a trade-off between computational efficiency and control performance. Preliminary results make use of hyperplane arrangements to characterize these regions. The hyperplane arrangements build on generic polyhedral sets and a natural question is whether additional structure could bring a benefit. The current paper addresses this issue by the use of zonotopic over-approximation and highlights their benefits when introduced in the obstacle avoidance problem. Comparisons with classical sampled-based approaches are presented through simulations.
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Daniel Ioan, Ionela Prodan, Florin Stoican, Sorin Olaru, Silviu-Iulian Niculescu. Complexity bounds for obstacle avoidance within a zonotopic framework. [Research Report] L2S, CNRS, Supelec, Université Paris Sud. 2019. ⟨hal-01986337⟩

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