中国空间科学技术

中国空间科学技术 ›› 2026, Vol. 46 ›› Issue (3): 157-168.doi: 10.16708/j.cnki.1000-758X.2026.0044

• 《中国空间科学技术（中英文）》创刊45周年专刊 • 上一篇    下一篇

地月空间连续推力追逃博弈鞍点求解方法

胡子弢1，刘潇翔2,3，杨彬1，刘鹏轩1，李 爽1,*   

  1. 1.南京航空航天大学航天学院，南京210016
    2.北京控制工程研究所，北京100094
    3.空间智能控制技术全国重点实验室，北京100094
  • 收稿日期:2026-01-14 修回日期:2026-01-27 录用日期:2026-02-10 发布日期:2026-05-21 出版日期:2026-05-31

Saddle point solution for cislunar continuous-thrust pursuit-evasion games

HU Zitao1, LIU Xiaoxiang2,3, YANG Bin1, LIU Pengxuan1, LI Shuang1,*    

  1. 1.College of Astronautics,Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
    2.Beijing Institute of Control Engineering，Beijing 100094，China
    3.National Key Laboratory of Space Intelligent Control，Beijing 100094，China
  • Received:2026-01-14 Revision received:2026-01-27 Accepted:2026-02-10 Online:2026-05-21 Published:2026-05-31

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摘要： 针对地月空间航天器连续推力追逃博弈场景，提出了一种面向限制性三体环境的航天器追逃博弈鞍点快速求解方法。首先，引入虚拟参考星和相对动力学理论，建立了圆限制性三体问题（Circular Restricted Three Body Problem，CRTBP）动力学框架下的轨道追逃博弈数学模型；然后，提出了基于相对动力学方程线性化策略的鞍点初值计算方法，通过在参考轨迹处对非线性相对动力学方程进行泰勒展开，构造了原问题的等效线性近似模型，从而实现鞍点初值的高效、稳定估计。最后，结合组合打靶法，完成了地月空间连续推力追逃博弈鞍点的快速求解。以地月空间远距离逆行轨道（Distant Retrograde Orbit，DRO）、近直线晕轨道（Near Rectilinear Halo Orbit，NRHO）及L1李雅普诺夫轨道等典型三体周期轨道附近场景为例的数值仿真结果表明，所提方法能够在不同轨道环境下实现追逃博弈鞍点的快速、准确求解，具备良好的收敛性与通用性。

关键词: 追逃博弈, 地月空间, 连续推力控制, 圆型限制性三体问题（CRTBP）, 间接法

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