Spacecraft formation reconfiguration with dynamic collision avoidance

In this paper we present three different solutions to the collision avoidance problem for spacecraft formations based on the Null-Space Based (NSB) behavioral control concept. In the first case, a constant sized sphere of safety area is centered on each spacecraft and obstacle, and the collision avoidance task is activated when this area is entered using a constant repulsive gain similar to what has been proposed for robotics in earlier publications. In the second case we make use of a variable state dependent gain for increasing the level of repulsiveness for each safety sphere to completely avoid collisions. In the third case the sphere is resized based on the relative position and velocity vectors, such that evasive maneuvers are initiated earlier when on collision course, but kept small when passing by. Through Lyapunov analysis we show that the equilibriumpoint of the follower spacecraft dynamics in closed-loop with a sliding surface based controller is uniformly globally exponentially stable when no collisions are detected, and that collisions will not occur when the collision avoidance task is active by scaling the variable state dependent gain. Simulation results are presented comparing the performance of the proposed methods during a formation reconfiguration maneuver.