Space Debris Collision Detection using Reachability

Benchmark Proposal: Space debris tracking and collision prediction is a growing worldwide problem as more and more objects are placed into orbit. While traditional methods simulate particles with Gaussian uncertainty to make collision predictions, we instead analyze the problem from a reachability perspective. The problem appears to require methods capable of quickly analyzing high-dimensional nonlinear systems, but we take advantage multiple kinds of problem structure to show that reachability analysis may be viable for this problem. In particular we present an initial analysis approach that uses numerical simulation for reachability analysis, and interval arithmetic with AABB trees for fast collision detection. The analysis uses a variable size time step with a counter-example guided abstraction refinement (CEGAR) method to increase analysis speed without sacrificing accuracy. Our approach can analyze upwards of thousands of orbiting objects faster than real-time, where each object is subject to some initial state uncertainty.