Receding horizon optimization for spacecraft pursuit-evasion strategy in rendezvous
doi: 10.11887/j.cn.202403003
ZHANG Chengming , ZHU Yanwei , YANG Leping , YANG Fuyunxiang
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073 , China
Abstract
Given the influence of uncertainty such as measurement errors in the process of spacecraft free-time orbital pursuit-evasion game for rendezvous, a high-efficiency strategy based on receding horizon optimization was proposed as a solution method. The saddle point control strategy of the game was derived according to differential games, and the equivalent transformation of the problem was carried out. By solving open-loop saddle point strategy off-line in advance, the initial states of the problem and the corresponding solutions were taken as samples for neural network training, and the trained network structure can quickly obtain the approximate solution of the corresponding problem. In order to better deal with the measurement noise in the game environment, a receding horizon optimization framework was designed based on the neural network structure. By periodically solving the problem, the rendezvous of the pursuer and evader was finally realized. Numerical simulation shows that the proposed strategy can effectively deal with the uncertainty of measurement noise, and compared with the existing strategy in the literature, the calculation time can be reduced from minutes to several seconds.
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[1]ZHANG Chengming,ZHU Yanwei,YANG Leping,YANG Fuyunxiang.Receding horizon optimization for spacecraft pursuit-evasion strategy in rendezvous[J].Journal of National University of Defense Technology,2024,46(3):21-29.
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[3]CHEN Zhi-xiang,LEI Hu-min,WANG Wei,HE Ze-wei,LI Yong-xu.Research of the Model Based on Differential Game for SAM in Countermine Simulation[J].Modern Defence Technology,2007,35(3):32-36.
Citation

ZHANG Chengming, ZHU Yanwei, YANG Leping, YANG Fuyunxiang. Receding horizon optimization for spacecraft pursuit-evasion strategy in rendezvous[J].Journal of National University of Defense Technology,2024,46(3):21-29.
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1问题场景
Fig.1Scenario of the problem
2推力矢量方向示意图
Fig.2Thrust vector direction diagram
3一个初始状态中的5个采样点
Fig.3Five sampling point in an initial state
4Tpeε核密度分布
Fig.4Kernel density distribution of Tpe and ε
5神经网络结构
Fig.5Structure of neural networks
6网络训练过程中的损失函数
Fig.6Loss function in network training
7滚动时域优化流程
Fig.7Rolling time domain optimization process
8博弈过程中的相对轨迹
Fig.8Relative trajectory during the game
9相对位置变化
Fig.9Relative position change
10相对速度变化
Fig.10Relative velocity change
11真实值和采样值对比
Fig.11Comparison of real value and sampling value
12控制变量
Fig.12Control value
13计算时间
Fig.13computing time
1样本生成范围Ω
2仿真算例初始状态
3首次采样结果
4神经网络与GA计算结果对比
胡海鹰, 朱永生, 江新华. 美国高轨空间安全发展态势及其关键技术[J]. 空间控制技术与应用,2022,48(3):1-10. HU H Y, ZHU Y S, JIANG X H. The development trend of high earth orbit space security and key technologies[J]. Aerospace Control and Application,2022,48(3):1-10.(in Chinese)
WEEDEN B, SAMSON V. Global counterspace capabilities[R/OL].[2023-03-01].https://swfound.org/media/207350/swf_global_counterspace_capabilities_2022_rev2.pdf.
周俊峰. 基于微分对策理论的航天器追逃控制方法研究[D]. 哈尔滨: 哈尔滨工程大学,2021. ZHOU J F. Research on control method for spacecraft pursuit-evasion based on differential game theory[D]. Harbin: Harbin Engineering University,2021.
PONTANI M, CONWAY B A. Numerical solution of the three-dimensional orbital pursuit-evasion game[J]. Journal of Guidance, Control,and Dynamics,2009,32(2):474-487.
CARR R W, COBB R G, PACHTER M,et al. Solution of a pursuit-evasion game using a near-optimal strategy[J]. Journal of Guidance, Control,and Dynamics,2017,41(4):841-850.
SHEN H X, CASALINO L. Revisit of the three-dimensional orbital pursuit-evasion game[J]. Journal of Guidance, Control,and Dynamics,2018,41(8):1820-1828.
ZHANG J R, ZHANG K P, ZHANG Y,et al. Near-optimal interception strategy for orbital pursuit-evasion using deep reinforcement learning[J]. Acta Astronautica,2022,198:9-25.
SHI M M, YE D, SUN Z W,et al. Spacecraft orbital pursuit-evasion games with J2 perturbations and direction-constrained thrust[J]. Acta Astronautica,2023,202:139-150.
常燕, 陈韵, 鲜勇, 等. 机动目标的空间交会微分对策制导方法[J]. 宇航学报,2016,37(7):795-801. CHANG Y, CHEN Y, XIAN Y,et al. Differential game guidance for space rendezvous of maneuvering target[J]. Journal of Astronautics,2016,37(7):795-801.(in Chinese)
TARTAGLIA V, INNOCENTI M. Game theoretic strategies for spacecraft rendezvous and motion synchronization[C]//Proceedings of the AIAA Guidance, Navigation,and Control Conference,2016:0873.
PRINCE E R, HESS J A, COBB R G,et al. Elliptical orbit proximity operations differential games[J]. Journal of Guidance, Control,and Dynamics,2019,42(7):1458-1472.
VENIGALLA C, SCHEERES D J. Delta-V-based analysis of spacecraft pursuit-evasion games[J]. Journal of Guidance, Control,and Dynamics,2021,44(11):1961-1971.
HAFER W T, REED H L, TURNER J D,et al. Sensitivity methods applied to orbital pursuit evasion[J]. Journal of Guidance, Control,and Dynamics,2015,38(6):1118-1126.
查文中. 单个优势逃跑者的多人定性微分对策研究[D]. 北京: 北京理工大学,2016. ZHA W Z. Multi-player qualitative differential games with single superior evader[D]. Beijing: Beijing Institute of Technology,2016.(in Chinese)
程林, 蒋方华, 李俊峰. 深度学习在飞行器动力学与控制中的应用研究综述[J]. 力学与实践,2020,42(3):267-276. CHENG L, JIANG F H, LI J F. A review on the applications of deep learning in aircraft dynamics and control[J]. Mechanics in Engineering,2020,42(3):267-276.(in Chinese)
CHENG L, WANG Z B, JIANG F H,et al. Fast generation of optimal asteroid landing trajectories using deep neural networks[J]. IEEE Transactions on Aerospace and Electronic Systems,2020,56(4):2642-2655.
CHENG L, WANG Z B, SONG Y,et al. Real-time optimal control for irregular asteroid landings using deep neural networks[J]. Acta Astronautica,2020,170:66-79.
PATTERSON M A, RAO A V. GPOPS-Ⅱ:a MATLAB software for solving multiple-phase optimal control problems using hp-adaptive gaussian quadrature collocation methods and sparse nonlinear programming[J]. ACM Transactions on Mathematical Software,2014,41(1):1-37.