基于可达集的航天器多对一轨道博弈几何求解  

Geometrical solution of multi-pursuer/one-evader orbital pursuit-evasion game based on reachable set theory

作　　者：李兆航 温昶煊 乔栋[1] 庞博 LI Zhaohang;WEN Changxuan;QIAO Dong;PANG Bo(School of Astronautics,Beijing Institute of Technology,Beijing 100081,China)

机构地区：[1]北京理工大学宇航学院,北京100081

出　　处：《航空学报》2024年第S1期429-436,共8页Acta Aeronautica et Astronautica Sinica

基　　金：国家自然科学基金(12172043)

摘　　要：航天器轨道博弈对保障我国空间资产安全具有重要意义。相对于经典“一对一”轨道博弈问题,“多对一”轨道博弈面临状态参数维度高、追逐者角色未定、终端条件多变等难题,致使传统基于最优控制理论的微分对策方法求解困难。为克服上述困难,提出了一种基于航天器可达集的多对一轨道博弈几何求解方法。首先,基于航天器可达集理论建立轨道博弈纳什均衡点的可达集等价表征;然后,基于网格点搜索法精确求解任意时刻航天器可达集包络,进而通过计算三角剖分闭合曲面的立体角确定参与博弈航天器可达集之间的相对几何关系;最后,利用二分法搜索来确定满足纳什均衡点可达集几何条件的博弈末端时刻,进而确定博弈结束时的航天器空间位置坐标,完成对多对一轨道博弈问题的求解。仿真结果表明,对一个典型的“三对一”轨道博弈算例,在普通个人计算机上传统微分对策方法求解耗时约2 h,而所提几何方法可在12 min内给出相近的解。The orbital game between spacecraft has significant importance for space safety.Compared to the classi⁃cal“one-to-one”orbital game problem,the“many-to-one”orbital game faces challenges such as high-dimensional state parameters,undefined roles of pursuers,and variable terminal conditions,making traditional differential strategy methods difficult to solve.To overcome these challenges,this paper proposes a geometric method for the“many-toone”orbital game based on the reachable set of spacecraft.Firstly,the reachable set equivalence representation of Nash equilibrium points in the orbital game is established based on the theory of reachable sets of spacecraft.Then,the envelopment of the reachable set of spacecraft at any time is accurately solved using a grid point search method.Subsequently,the relative geometric relationship between the reachable sets of spacecraft involved in the game is de⁃termined by computing the solid angle of the triangulated closed surface.Finally,the binary search method is used to determine the terminal time of the game,that satisfies the geometric conditions of the reachable set of Nash equilib⁃rium points,thereby determining the spatial position coordinates of the spacecraft at the end of the game and complet⁃ing the solution to the“many-to-one”orbital game problem.Simulation results demonstrate that for a typical“three-toone”orbital game scenario,the traditional differential strategy method takes over 2 h on an ordinary personal com⁃puter.In contrast,the proposed geometric method can provide the same solution within 12 min.

关 键 词：轨道博弈 多追一逃 航天器可达集 纳什均衡点 几何求解 

分 类 号：V412.41[航空宇航科学与技术—航空宇航推进理论与工程]