Efficiently evaluating reachable sets in the circular restricted 3-body problem

Abstract

In space mission trajectory planning in dynamic environments, such as at asteroids, scenarios leading to failure must be discovered. Given an initial state of a spacecraft about an asteroid, failure can be simply quantified as impact of the vehicle with the asteroid or escape of the vehicle from the asteroid. For mission planning and execution purposes it is necessary to perform maneuvers to avoid such outcomes, however the overall set of possible maneuvers that either avoid impact or escape can be a complex set that cannot be analytically characterized. This paper introduces a reachable set explorer (RSE) for exploring the reachable set of a spacecraft-the set of trajectories under a range of V expenditures. This approach is applied to the circular restricted 3-body problem (CR3BP) where a brute-force approach is intractable. RSE focuses on the boundaries between impact, escape, and in-system regions, known as the end-result regions. Manuscript