Efficient n-to-n collision detection for space debris using 4d aabb trees

Collision detection algorithms are used in aerospace, swarm robotics, automotive, video gaming, dynamics simulation and other domains. As many applications of collision detection run online, timing requirements are imposed on the algorithm runtime: algorithms must, at a minimum, keep up with the passage of time. Even offline reachability computation can be slowed down by the process of safety checking when n is large and the specification is n-to-n collision avoidance. In practice, this places a limit on the number of objects, n, that can be concurrently tracked or verified. In this paper, we present an improved method for efficient object tracking and collision detection, based on a modified version of the axis-aligned bounding-box (AABB) tree data structure. We consider 4D AABB Trees, where a time dimension is added to the usual three space dimensions, in order to enable per-object time steps when checking for collisions in space-time. We evaluate the approach on a space debris collision benchmark, demonstrating efficient checking beyond the full catalog of n = 16848 space objects made public by the U.S. Strategic Command on www.space-track.org.