Satellite proximate interception vector guidance based on differential games

This paper studies the proximate satellite interception guidance strategies where both the interceptor and target can perform orbital maneuvers with magnitude limited thrusts. This problem is regarded as a pursuit-evasion game since satellites in both sides will try their best to capture or escape. In this game, the distance of these two players is small enough so that the highly nonlinear earth-centered gravitational dynamics can be reduced to the linear Clohessy-Wiltshire (CW) equations. The system is then simplified by introducing the zero effort miss variables. Saddle solution is formulated for the pursuit-evasion game and time-to-go is estimated similarly as that for the exo-atmospheric interception. Then a vector guidance is derived to ensure that the interception can be achieved in the optimal time. The proposed guidance law is validated by numerical simulations. Keywords: Differential games, Saddle solution, Satellite interception, Time-to-go estimation, Zero effort miss trajector