Efficient n-to-n Collision Detection for Space Debris using 4D AABB Trees (Extended Report)

TL;DR

This paper introduces a scalable 4D AABB tree method for efficient online n-to-n collision detection, demonstrated on space debris data, enabling real-time tracking of thousands of objects.

Contribution

It presents a novel 4D AABB tree approach with partitioning strategies that enhance scalability and parallelization for online collision detection.

Findings

Successfully tracked 16,848 space debris objects in real-time.

Improved collision detection efficiency with 4D AABB trees.

Validated approach with publicly available space debris data.

Abstract

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. In practice, this places a limit on the number of objects, n, that can be tracked at the same time. In this paper, we improve the scalability of collision detection, effectively raising the limit n for online object tracking. The key to our approach is the use of a four-dimensional axis-aligned bounding box (AABB) tree, which stores each object's three-dimensional occupancy region in space during a one-dimensional interval of time. This improves efficiency by permitting per-object variable times steps. Further, we describe partitioning strategies that can decompose the 4D AABB tree search into several smaller-dimensional problems that can be solved in parallel. We formalize the collision detection problem and prove our algorithm's correctness. We demonstrate the feasibility of online collision detection for an orbital space debris application, using publicly available data on the full catalog of n=16848 objects provided by www.space-track.org.