Elliptical Orbit Proximity Operations Differential Games

Abstract

Differential games are formulated and solved for an inspector satellite operating nearby a resident space object (RSO) in an elliptical orbit. For each differential game, the goal of the inspector satellite is to minimize the time to achieve an inspection goal, whereas the goal of the RSO is to delay that condition as long as possible. Thus, it is assumed that the RSO can maneuver, and that both the inspector satellite and the RSO use a constant, steerable thruster (for example, an electric engine) during each game. The following games are formulated and solved via an indirect heuristic method, where each game corresponds to an inspection goal of the inspector satellite: 1) intercept; 2) rendezvous; 3) obtain sun vector; 4) match energy; 5) obtain sun vector and match energy; and 6) match energy and remain in close proximity during the ensuing orbit. The open-loop strategies obtained for these games represent worst-case scenarios, and they may inform requirements for future satellites as well as be actual open-loop strategies for a given scenario.