Two Space-Time Obstacle Representations Based on Ellipsoids and Polytopes

When operating autonomous surface vessels in uncertain environments with dynamic obstacles, planning safe trajectories and evaluating collision risk is key to navigating safely. In order to perform these tasks, it is important to have a computationally efficient and adaptable obstacle representation to allow for quick and robust predictions of the obstacle trajectory. This paper presents a novel space-time obstacle representation, which is able to predict the reachable set for a dynamic obstacle under uncertainty. This is done by projecting the area occupied by the obstacle forward in time, using a set of velocities representing the possible maneuvers that the obstacle may take. Under some mild assumptions, we show how the space-time obstacle can be implemented in a computationally efficient way, using both convex polytopes and ellipsoids. Additionally, we show how the space-time obstacle representation can be used for risk assessment, collision avoidance and trajectory planning for autonomous surface vessels.