航天器轨道追逃态势分析的水平集方法
2024,46(3):30-38
杨傅云翔
国防科技大学 空天科学学院, 湖南 长沙 410073，yangfuyunxiang@alumni.nudt.edu.cn
杨乐平
国防科技大学 空天科学学院, 湖南 长沙 410073
朱彦伟
国防科技大学 空天科学学院, 湖南 长沙 410073
张乘铭
国防科技大学 空天科学学院, 湖南 长沙 410073
国防科技大学 空天科学学院, 湖南 长沙 410073，yangfuyunxiang@alumni.nudt.edu.cn
杨乐平
国防科技大学 空天科学学院, 湖南 长沙 410073
朱彦伟
国防科技大学 空天科学学院, 湖南 长沙 410073
张乘铭
国防科技大学 空天科学学院, 湖南 长沙 410073
摘要：
航天器轨道追逃是当前航天动力学与控制领域的研究热点。针对轨道追逃定性问题开展研究,提出了一种综合运用降维动力学模型和后向可达集的航天器近距离轨道追逃态势分析方法,以支撑任务可行性分析；通过在视线旋转坐标系下推导博弈系统降维动力学模型,建立近距离追逃定性问题模型,减少了状态空间维度；使用目标集的后向可达集描述捕获区并划分追逃状态空间,基于水平集方法建立可达集在降维动力学模型中演化的动态HJI(Hamilton-Jacobi-Isaacs)偏微分方程,并设计WENO-TVD求解器数值计算HJI方程终值问题粘性解,完成了追逃目标集的准确描述并避免了可能出现的终端奇异现象。通过不同推力构型的追逃场景数值仿真验证了方法的有效性,展现了一次计算批量化处理初始态势的功能。
航天器轨道追逃是当前航天动力学与控制领域的研究热点。针对轨道追逃定性问题开展研究,提出了一种综合运用降维动力学模型和后向可达集的航天器近距离轨道追逃态势分析方法,以支撑任务可行性分析；通过在视线旋转坐标系下推导博弈系统降维动力学模型,建立近距离追逃定性问题模型,减少了状态空间维度；使用目标集的后向可达集描述捕获区并划分追逃状态空间,基于水平集方法建立可达集在降维动力学模型中演化的动态HJI(Hamilton-Jacobi-Isaacs)偏微分方程,并设计WENO-TVD求解器数值计算HJI方程终值问题粘性解,完成了追逃目标集的准确描述并避免了可能出现的终端奇异现象。通过不同推力构型的追逃场景数值仿真验证了方法的有效性,展现了一次计算批量化处理初始态势的功能。
基金项目：
国防科技大学自主创新科学基金资助项目(22-ZZCX-083)
国防科技大学自主创新科学基金资助项目(22-ZZCX-083)
Situation analysis method based on level set for spacecraft pursuit-evasion game
YANG Fuyunxiang
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China,yangfuyunxiang@alumni.nudt.edu.cn
YANG Leping
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China
ZHU Yanwei
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China
ZHANG Chengming
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China,yangfuyunxiang@alumni.nudt.edu.cn
YANG Leping
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China
ZHU Yanwei
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China
ZHANG Chengming
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China
Abstract：
Spacecraft pursuit-evasion game is currently a research hotspot in the field of aerospace dynamics and control. Qualitative spacecraft pursuit-evasion game was studied in order to provide feasibility support for strategy design, and a situation analysis method for scenarios in close range was proposed by comprehensively using dimension-reduction dynamics and backwards reachability set. A dimension-reduction dynamic model was derived in the line-of-sight rotation coordinate system, and the pursuit-evasion qualitative model of the game system was determined to reduce state space dimension. The backwards reachable set of the target set was used to divide the pursuit-evasion state space and describe the capture zone. A time-dependent HJI (Hamilton-Jacobi-Isaacs) PDE (partial differential equation) was established to describe the evolution of backwards reachable set in the dimension-reduction dynamics, based on level set method, and a WENO-TVD(weighted essentially non-oscillatory-total variation diminishing) solver was designed to numerically calculate the viscous solution of the final value problem of the HJI PDE. These measures achieve the accurate description of pursuit-evasion target set and avoid the possible terminal singularity. The effectiveness of the method was demonstrated by numerical simulations of several pursuit-evasion scenarios with different thrust configurations, and the function of batch processing of initial situations in a single calculation was demonstrated.
Spacecraft pursuit-evasion game is currently a research hotspot in the field of aerospace dynamics and control. Qualitative spacecraft pursuit-evasion game was studied in order to provide feasibility support for strategy design, and a situation analysis method for scenarios in close range was proposed by comprehensively using dimension-reduction dynamics and backwards reachability set. A dimension-reduction dynamic model was derived in the line-of-sight rotation coordinate system, and the pursuit-evasion qualitative model of the game system was determined to reduce state space dimension. The backwards reachable set of the target set was used to divide the pursuit-evasion state space and describe the capture zone. A time-dependent HJI (Hamilton-Jacobi-Isaacs) PDE (partial differential equation) was established to describe the evolution of backwards reachable set in the dimension-reduction dynamics, based on level set method, and a WENO-TVD(weighted essentially non-oscillatory-total variation diminishing) solver was designed to numerically calculate the viscous solution of the final value problem of the HJI PDE. These measures achieve the accurate description of pursuit-evasion target set and avoid the possible terminal singularity. The effectiveness of the method was demonstrated by numerical simulations of several pursuit-evasion scenarios with different thrust configurations, and the function of batch processing of initial situations in a single calculation was demonstrated.
收稿日期：
2023-03-14
2023-03-14
