Safe Positively Invariant Sets for Spacecraft Obstacle Avoidance

This paper presents an obstacle avoidance method for spacecraft relative motion control. In this approach, a connectivity graph is constructed for a set of relative frame points, which form a virtual net centered around a nominal orbital position. The connectivity between points in the virtual net is determined based on the use of safe positively invariant sets for guaranteed collision free maneuvering. A graph search algorithm is then applied to find a maneuver that avoids specified obstacles and adheres to specified thrust limits. As compared to conventional open-loop trajectory optimization, this approach enables the handling of bounded disturbances, which can represent the effects of perturbing forces and model uncertainty, while rigorously guaranteeing that nonconvex and possibly time-varying obstacle avoidance constraints are satisfied. Details for handling a single stationary obstacle, multiple stationary obstacles, moving obstacles, and bounded disturbances are reported and illustrated with simulation case studies.