Complexity Bounds for Obstacle Avoidance within a Zonotopic Framework

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. Preliminary results make use of hyperplane arrangements to characterize these regions. The current paper considers additional structural constraints 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.