Homotopic approach to the feedback solution of the orbit pursuit-evasion game

Abstract

The manuscript presents a solution to the spacecraft orbit pursuit-evasion game problem using a homotopic approach. It reduces the sensitivity of the 12-dimensional initial costate and overcomes the influence of the opposing spacecraft’s state measurement uncertainties on the final game result. During the first step of the homotopic process, we construct and solve the auxiliary problem known as the minimum-time interception problem. In this problem, the pursuer has the same maneuverability as in the original problem, while the evader obeys aerodynamics without control. We then gradually increase the evader’s thrust amplitude and solve each sub-OPEG problem until the evader has full maneuverability, resulting in the optimal open-loop control. By applying a feedback control law synthesized by pre-computed extremals, the pursuer can achieve approximate interception at the end of the game despite the evader’s uncertain state. Numerical simulations indicate that the homotopic result is consistent with solutions obtained by other heuristic and hybrid algorithms. Furthermore, the proposed homotopic-based near-optimal feedback control law is capable of overcoming the influence of orbit determination errors and guiding participants to complete the game. Monte-Carlo simulations to the nine surrogate model configurations shows that the surrogate strategy with a Gauss correlation model and 1-degree regression function performed the best.