A dimension-reduction solution of free-time differential games for spacecraft pursuit-evasion

This paper presents a dimension-reduction method for solving the free-time pursuit-evasion game between two spacecraft near circular orbits. Theoretically, finding the saddle-point solution of the game results in solving a high-dimensional (twenty-four in our case) two-point boundary value problem (TPBVP), which is quite difficult and computationally intensive. By using the circular-orbit variational equations to model the relative states of two spacecraft near circular orbits, the 24-dimensional TPBVP is firstly transformed into solving a set of four-dimensional nonlinear equations. Then, a hybrid numerical algorithm is proposed to solve the equations, where the differential evolution algorithm is used to obtain an initial guess and the Newton's iteration method is used to find the accurate solution. Numerical results show that the proposed method is more efficient than previous methods, and that the proposed method are suitable for large-phasing-distance orbital pursuit-evasion problems.