Computing the Reach-Avoid Set for Space Vehicle Maneuvering in the Presence of Debris

The ability to guarantee the safety of autonomously controlled space vehicles is of great importance to help avoid accidents and ensure mission success. In this paper we investigate the safety verification of a satellite attempting to maneuver to a new position while avoiding multiple pieces of debris. We assume that the satellite, desired rendezvous point, and all debris are near the same circular orbit with dynamics modeled by Clohessy-Wiltshire-Hill (CWH) equations. We will use reachability methods to guarantee the satellite is able to reach a desired point while avoiding all debris. We will first develop a computationally efficient method for computing the Reach-Avoid set for a system modeled by CWH dynamics, and then extend this method to the minimal and maximal reach calculations. We then review a system decomposition method for computing reach sets in large dimensions and apply the methods to the debris avoidance problem. Finally, we develop computationally efficient methods to compute an under-approximation of the Reach-Avoid set and present numerical examples for single and multiple debris scenarios