Abstract: For the continuous-thrust pursuit-evasion game scenario of spacecraft in the Earth-Moon space, this paper proposes a rapid saddle point solution method tailored for the restricted three-body environment. First, by introducing a virtual reference object and relative motion theory, a mathematical model for the orbital pursuit-evasion game is established within the framework of the circular restricted three-body problem dynamics. Then, a saddle point initial guess calculation method based on linearization of relative motion is proposed. By performing Taylor expansion of the nonlinear relative motion equations around the reference trajectory, an equivalent linear approximation model of the original problem is constructed, thereby enabling efficient and stable estimation of the saddle point initial guess. Finally, by combining the multiple shooting method, rapid solution of the saddle point for the continuous-thrust pursuit-evasion game in the Earth-Moon space is achieved. Numerical simulations for typical three-body periodic orbits in the Earth-Moon space, such as Distant Retrograde Orbits (DRO), Near-Rectilinear Halo Orbits (NRHO), and L1 Lyapunov orbits, demonstrate that the proposed method can achieve fast and accurate saddle point solutions for pursuit-evasion games across different orbital environments, exhibiting good convergence and generality.

Key words: pursuit-evasion games, cislunar space, continuous-thrust control, circular restricted three-body problem (CRTBP), Indirect Method