Efficient hybrid two-step framework for solving spacecraft pursuit-evasion-capture game

Purpose This paper aims to address the time-optimal pursuit-evasion-capture (PEC) game for two spacecraft under nonlinear dynamics, and to resolve inefficiencies and precision limitations of conventional methods in complex perturbed scenarios. Design/methodology/approach An efficient two-step framework AESM-SCM is proposed, integrating the alpha evolution (AE) algorithm, shooting method and collocation method. First, AESM (AE-shooting method) solves the game under linear dynamics to generate high-quality initial guesses. These guesses are then fed into SCM (shooting-collocation method) to solve the saddle-point solution under nonlinear dynamics. Findings Numerical simulations show that AESM-SCM exhibits excellent performance and robustness. Furthermore, compared with the hybrid method combining genetic algorithm and sequential quadratic programming (GA-SQP), AESM-SCM improves solution efficiency by nearly two orders of magnitude while maintaining higher solution accuracy. Originality/value Unlike traditional methods, which require solving 13-dimensional nonlinear equations to obtain initial guesses, AESM-SCM only needs to solve a seven-dimensional nonlinear equation under linear dynamics to obtain robust initial guesses. Furthermore, through the two-step strategy, it transforms the originally 24-dimensional two-point boundary value problem (TPBVP) into a seven-dimensional nonlinear equation, significantly reducing the solution complexity. This research provides an efficient solution for on-orbit spacecraft PEC problems.