【摘要】 针对多个追踪器与单个逃逸器的连续推力追逃博弈问题，提出一种基于可达集覆盖理论的追逃捕获性分析方法。追踪器和逃逸器的轨道运动由椭圆线性相对运动方程描述。首先，建立航天器相对可达集包络的优化求解模型，利用可达集的凸性去掉终端共线约束以简化问题；然后，利用Pontryagin极值原理得到最优控制解析表达式，从而求解得到相对可达集。在此基础上，基于可达集覆盖理论，利用多个追踪器协同可达集对逃逸器可达集的覆盖，实现多对一航天器追逃博弈的捕获性分析，并采用一维数值搜索方法求解捕获时间。仿真结果表明，提出的追逃捕获性分析方法是有效的。相对于一对一追逃博弈，多对一追逃博弈策略可以减少逃逸器捕获时间，并降低追踪器的机动能力需求。更多还原

【Abstract】 For the continuous-thrust spacecraft pursuit-evasion(PE) game between multiple pursuers and single evader, a captureability analysis method is proposed based on the relative reachable set(RRS) coverage theory. The orbital motions of the pursuers and the evader are described by elliptical linear relative motion equations. The optimization model of the envelope of RRS is firstly established, and then the terminal collinear constraint is removed based on the convexity of RRS to simplify the problem. Subsequently, the analytical solution to the optimal control law is obtained by using Pontryagin’s extremum principle, and the RRS of spacecraft is then obtained. On this basis, based on the RRS coverage theory, the coverage of the evader’s RRS by the cooperative RRS of multiple pursuers is utilized to analyze the captureability of the multi-on-one spacecraft PE game, and the capture time is solved by the one-dimensional numerical search method. Numerical simulation results show that the proposed captureability analysis method is effective. Compared with the one-on-one PE game strategy, the multi-on-one PE game strategy can decrease the capture time of the evader and reduce the maneuverability requirements of the pursuers.更多还原