摘要
针对地月空间中L1平动点附近航天器追逃博弈场景,采用微分博弈理论,解决了以生存时间为代价函数的追逃博弈策略设计问题。首先,建立了会合坐标系下描述航天器运动的限制性三体系统动力学模型,并以最大/最小化抓捕时间为目标构建了控制输入有限的“追逐-逃逸”微分博弈问题。然后,根据极大极小值原理求解加速度受限情况下追击者和逃避者的最优控制策略。在此基础上进一步推导了鞍点解满足的必要条件,从而将微分博弈问题转化为两点边值问题。为了提高数值求解过程的收敛效率,先针对原系统在L1平动点附近的线性化模型获取数值解,之后将其作为原问题的打靶初值。最后通过仿真,给出了初始时刻均在L1平动点附近的周期轨道上的追逃航天器最优轨迹及控制策略。
The orbital pursuit-evasion game near the L1 libration point in the Earth-Moon system is addressed using differential game theory,with survival time as the performance index.A restricted three-body system dynamical model describing spacecraft motion is first established in the synodic coordinate system.A“pursuit-evasion”differential game problem with limited control input is formulated,aiming to maximize/minimize capture time.The optimal control strategies for both pursuer and evader under acceleration constraints are derived based on the minimax principle.Necessary conditions for saddle-point solutions are subsequently established,transforming the differential game into a two-point boundary value problem.To enhance numerical convergence efficiency,the shooting method is employed with initial guesses obtained from linearized dynamics around the L1 libration point.Finally,numerical simulations demonstrate the optimal trajectories and control strategies for spacecraft initially positioned on periodic orbits near the L1 point,validating the proposed methodology.
作者
孙盛
朱鸿绪
王伟
SUN Sheng;ZHU Hongxu;WANG Wei(School of Aeronautics and Astronautics,Shanghai Jiao Tong University,Shanghai 200240,China)
出处
《宇航学报》
北大核心
2025年第8期1591-1598,共8页
Journal of Astronautics
基金
空间智能控制技术全国重点实验室开放基金课题(HTKJ2025KL502015)。
关键词
轨道博弈
追逃博弈
平动点
间接法
Orbital game
Pursuit-evasion game
Libration point
Indirect optimization
