Exact Obstacle-Free Space Representation Using Hybrid Zonotopes*

This paper presents a method for exactly representing the free space around static, convex, polytopic obstacles as a collection of disjoint, convex polytopes. Connections between hyperplane arrangements, shallow ReLU neural networks, and hybrid zonotopes are used to efficiently partition the free space into convex cells. A greedy algorithm is presented for merging neighboring cells, while preserving convexity, to reduce the number of cells needed to represent the obstacle-free space. Compared to two existing methods, the proposed approach is shown to provide a practical balance between minimizing the number of cells representing the obstacle-free space and achieving computational scalability with respect to the number of obstacles in two-dimensional examples.