Robust trajectory optimization for pursuit-evasion game with navigation and control errors

This paper proposes a robust trajectory optimization method for the fixed-time spacecraft pursuit-evasion (PE) game with Gaussian navigation and control errors. The errors are considered for both players near elliptical orbits. Based on the linear relative motion equations, a weighted cost function including energy consumption, terminal relative distance, and terminal state uncertainty is designed. Applying the indirect method, the two-point boundary value problem (TPBVP) and the optimal control under thrust magnitude constraints are derived. To overcome the initial value sensitivity in the TPBVP, the homotopy method is utilized to transform the robust PE game into the deterministic linear-quadratic PE game, whose saddle-point solution can be easily obtained by solving the differential Ricatti equation. Numerical simulations show that the proposed method can rapidly generate the optimal maneuvering strategy of the robust PE game for both players.