Fast optimal impulsive methods for collision avoidance maneuver based on reachable domain

This paper proposes fast optimal impulsive methods based on reachable domain (RD) to solve the collision avoidance maneuver problem, which includes an active spacecraft and a non-cooperative target. According to whether the active spacecraft returns to its original orbit, this paper considers two cases: (1) collision avoidance maneuver without returning to its original orbit; (2) collision avoidance maneuver with returning to its original orbit. The constraint of collision avoidance is described by the RD with uncertainty propagation. Based on the linear error propagation method, the RD of the non-cooperative target is described as an error ellipsoid. For the first case, a single-impulse semi-analytical method is proposed to obtain the minimum-fuel solution by a two-dimensional search. For the second case, a three-impulse dimensionality reduction optimization method is presented, and the first impulse is obtained from the first case. Compared with the direct numerical optimization method, the numerical results show that the proposed methods have significant advantage in terms of computation time.