基于最优脉冲的空间抵近行为模式可达性分析

doi:10.12305/j.issn.1001-506X.2026.02.25

摘要/Abstract

摘要：

在轨道博弈中，若能实现对空间抵近的非合作目标的行为模式可达性预测，则可在博弈中占据有利形势。针对空间抵近的非合作目标的行为模式可达性问题，提出基于最优脉冲的空间抵近行为模式可达性分析方法。根据目标的机动能力，通过最优脉冲估计，判断目标是否具备完成各类行为模式的能力，实现对空间抵近行为模式可达性分析。结合更多情报信息，航天器即可提前进行行动决策，占领博弈先机。仿真实验结果表明，对于拦截、掠飞、绕飞、悬停4种行为模式，本文提出的空间抵近行为模式可达性分析方法能够比较准确地分析出抵近目标未来实现各类行为模式的可能性。

关键词: 轨道博弈, 非合作目标, 行为模式可达性分析, 最优脉冲估计

Abstract:

In orbital games, the ability to predict the reachability of an approaching non-cooperative target’s behavior patterns allows the predictor to seize the initiative. To address the reachability problem of such patterns, a reachability analysis method for space-proximity behavior patterns based on optimal impulses is proposed. Given the target’s maneuverability, optimal-impulse estimation evaluates whether each pattern lies within the reachable set, thereby enabling reachability analysis of proximity behavior patterns. Combined with more intelligence information, the spacecraft can be enabled to make decision earlier and acquire a strategic advantage in games. Simulation results for four representative patterns—intercept, fly-by, fly-around, and hover—demonstrate that the proposed method can accurately analyze the possibility of the target’s future behavior patterns.

Key words: orbital game theory, non-cooperative targets, behavior pattern reachability analysis, optimal impulse estimation

中图分类号:

V 19

方嘉卉, 黎克波, 梁彦刚. 基于最优脉冲的空间抵近行为模式可达性分析[J]. 系统工程与电子技术, 2026, 48(2): 652-659.

Jiahui FANG, Kebo LI, Yangang LIANG. Reachability analysis of space proximity behavior patterns based on optimal impulse[J]. Systems Engineering and Electronics, 2026, 48(2): 652-659.

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参考文献 27

27	ZHANG H B. Theories and methods of spacecraft orbital mechanics[M]. Beijing: National Defense Industry Press, 2015.
28	ZHAO G D, GUO Y N, DENG W D, et al. Natural fly-around orbital maneuvers strategy for GEO spacecraft considering illumination constraints[C]//Proc. of the 38th Chinese Control Conference, 2019: 8182−8187.
29	LI X L, YAO Y, YANG B Q, et al. Optimal trajectory design of flying by a target spacecraft[C]// Proc. of the 37th Chinese Control Conference, 2018: 4976−4981.
30	程怡明. 非合作航天器相对导航与绕飞技术研究[D]. 哈尔滨: 哈尔滨工业大学, 2015.
	CHENG Y M. Study on relative navigation and flying-around of non-cooperative spacecrafts[D]. Harbin: Harbin Institute of Technology, 2015.
31	OLLAND J H. Adaptation in natural and artificial systems[M]. Ann Arbor: University of Michigan Press, 1975.
1	赵力冉, 党朝辉, 张育林. 空间轨道博弈: 概念、原理与方法[J]. 指挥与控制学报, 2021, 7 (3): 215- 224. doi: 10.3969/j.issn.2096-0204.2021.03.0215
	ZHAO L R, DANG Z H, ZHANG Y L. Orbital game: concepts, principles and methods[J]. Journal of Command and Control, 2021, 7 (3): 215- 224. doi: 10.3969/j.issn.2096-0204.2021.03.0215
2	MUKUNDAN A, WANG H C. Simplified approach to detect satellite maneuvers using TLE data and simplified perturbation model utilizing orbital element variation[J]. Applied Science, 2021, 11, 10181. doi: 10.3390/app112110181
3	PASTOR A, ESCRIBANO G, SANJURJO-RIVO M, et al. Satellite maneuver detection and estimation with optical survey observations[J]. The Journal of the Astronautical Sciences, 2022, 69, 879- 917. doi: 10.1007/s40295-022-00311-5
4	YU S X, WANG X, ZHU T L. Maneuver detection methods for space objects based on dynamical model[J]. Advances in Space Research, 2021, 68 (1): 71- 84. doi: 10.1016/j.asr.2021.03.011
5	ZHANG S, YANG Z, LUO Y Z. Spacecraft multi-impulse reachable domain[EB/OL]. [2024-12-29]. https://www.sciencedirect.com/science/article/pii/S1000936124004813.
6	LI X H, ZHANG L. Research on relative reachable domain in target orbit for maneuvering spacecraft[J]. Aircraft Engineering and Aerospace Technology, 2024, 96 (6): 798- 807. doi: 10.1108/AEAT-02-2023-0046
7	WEN C X, SUN Y X, PENG C, et al. Reachable domain under J2 perturbation for satellites with a single impulse[J]. Journal of Guidance, Control, and Dynamics, 2023, 46 (1): 64- 79.
8	李兆航, 温昶煊, 乔栋, 等. 基于可达集的航天器多对一轨道博弈几何求解[J]. 航空学报, 2024, 45 (S1): 730803.
	LI Z H, WEN C X, QIAO D, et al. Geometrical solution of multi-pursuer/one-evader orbital pursuit-evasion game based on reachable set theory[J]. Acta Aeronautica et Astronautica Sinica, 2024, 45 (S1): 730803.
9	ZHANG H L, LUO J J, GAO Y, et al. An intention inference method for the space non-cooperative target based on BIGRU-Self attention[J]. Advances in Space Research, 2023, 72 (5): 1815- 1828. doi: 10.1016/j.asr.2023.04.032
10	SUN Q B, DANG Z H. Deep neural network for non-cooperative space target intention recognition[J]. Aerospace Science and Technology, 2023, 142 (B): 108681.
11	LI J S, YANG Z, LUO Y Z. Intention inference for space targets using deep convolutional neural network[J]. Advances in Space Research, 2025, 75 (2): 2184- 2200. doi: 10.1016/j.asr.2024.10.006
12	WANG C Y, ZHANG J R, WANG J N, et al. Confidence-based fusion of AC-LSTM and Kalman filter for accurate space target trajectory prediction[J]. Aerospace, 2025, 12, 347.
13	ZHANG H L, LUO J J, MA W H. Spacecraft game decision making for threat avoidance of space targets based on machine learning[J]. Acta Aeronautica et Astronautica Sinica, 2024, 45 (8): 329136.
14	SORATHIYA V, SAHA J, GARAI B. Machine learning-powered satellite trajectory prediction: a novel approach for enhanced accuracy[C]//Proc. of the 2nd International Conference on Data Science and Information System, 2024.
15	QU Z H, WEI C L. A PSO-LSTM-based method for spatial target orbit phase prediction[C]//Proc. of the 4th International Conference on Computer Vision, Image and Deep Learning, 2023: 358−362.
16	WANG Q Y, ZHANG Z L, WANG Z Y, et al. The trajectory prediction of spacecraft by grey method[J]. Measurement Science and Technology, 2016, 27 (8): 085011. doi: 10.1088/0957-0233/27/8/085011
17	WANG Q, ZHAI H M, LI S L. Trajectory optimization for spacecraft close proximity based on dual quaternions[M]//LIU Z S, LI R F, HE X D, et al. Advances and Challenges in Advanced Unmanned Aerial Systems. Singapore: Springer, 2023.
18	张庆泽, 尹龙逊, 张强, 等. 航天器多约束空间抵进掠飞轨迹优化方法[J]. 空间控制技术与应用, 2022, 48 (3): 49- 56. doi: 10.3969/j.issn.1674-1579.2022.03.006
	ZHANG Q Z, YIN L X, ZHANG Q, et al. Optimization method for multi-constrained space close-sweep trajectory of spacecraft[J]. Aerospace Control and Application, 2022, 48 (3): 49- 56. doi: 10.3969/j.issn.1674-1579.2022.03.006
19	BOMMENA R, WOOLLANDS R. Indirect trajectory optimization with path constraints for multi-agent proximity operations[J]. The Journal of the Astronautical Sciences, 2024, 71, 54. doi: 10.1007/s40295-024-00470-7
20	党朝辉, 李一峰, 孙钦伯, 等. 一种基于遗传算法的顺光抢位轨道博弈控制方法[P]. 中国: CN115390449A, 2022-11-25.
	DANG Z H, LI Y F, SUN Q B, et al. A genetic algorithm-based game control method for sunlight grabbing orbits[P]. China: CN115390449A, 2022-11-25.
21	LI Z Y, ZHU H, LUO Y Z. Orbital inspection game formulation and epsilon-Nash equilibrium solution[J]. Journal of Spacecraft and Rockets, 2024, 61 (1): 157- 172. doi: 10.2514/1.A35800
22	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.
23	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. doi: 10.1016/j.actaastro.2022.10.004
24	LI Z Y, CHEN S, ZHOU C H, et al. Orbital multi-player pursuit-evasion game with deep reinforcement learning[J]. The Journal of the Astronautical Sciences, 2025, 72, 1.
25	朱彦伟. 航天器近距离相对运动轨迹规划与控制研究[D]. 长沙: 国防科学技术大学, 2009.
	ZHU Y W. Trajectory planning and control for spacecraft proximity relative motion[D]. Changsha: National University of Defense Technology, 2009.
26	CLOHESSY W H, WILTSHIRE R S. Terminal guidance system for satellite rendezvous[J]. Journal of the Aerospace Sciences, 1960, 27 (9): 653- 658. doi: 10.2514/8.8704
27	张洪波. 航天器轨道力学理论与方法[M]. 北京: 国防工业出版社, 2015.

优化目标	行为模式	脉冲数	优化变量	约束条件	终端相对位置速度
脉冲之和$\displaystyle\sum\limits_i {\left\\| {\Delta {{\boldsymbol{v}}_i}} \right\\|} $	拦截	1	等待时长${t_{{\text{wait}}}}$ 转移时长${t_{{\text{transfer}}}}$	${t_{{\text{wait}}}} + {t_{{\text{transfer}}}} \leqslant {t_{\max }}$	均为0
	绕飞/掠飞	1	等待时长${t_{{\text{wait}}}}$ 漂移量${l_m}$	$\begin{gathered} {t_{{\text{wait}}}} \leqslant {t_{\max }} \\ {l_m} \in \left[ {{l_{\min }},{l_{\max }}} \right] \\ \end{gathered} $	$\left[ {{x_0}}\quad {{y_0}}\quad 0\quad 0\quad {\Delta {v_y}}\quad {{{\dot z}_0}} \right]$ 其中$\Delta {v_y}$满足式（3）
	悬停	1或2	等待时长${t_{{\text{wait}}}}$ 悬停距离${y_{c0}}$ 悬停椭圆半长轴$2b$	$\begin{gathered} {t_{{\text{wait}}}} \leqslant {t_{\max }} \\ 2b - \left\| {{y_{c0}}} \right\| \lt 0 \\ \end{gathered} $	$ \left[ 0\quad {{y_0}}\quad 0\quad {\dfrac{{n{y_0}}}{2}}\quad 0\quad {{{\dot z}_0}} \right] $

航天器	半长轴a/km	偏心率e	倾角i/（°）	升交点赤经Ω/（°）	近地点纬度幅角ω/（°）	真近点角f/（°）
红方	42166.127	0.000504	0.1	78.265	271.690	302.395
蓝方	42220	0	0.11	89.626	0	203.396

行为模式	脉冲冲量/（m/s）	时间/h
拦截	1.0170	29.3367
掠飞	—	—
绕飞	11.5940	14.3453
悬停	2.0048	26.9356

误差大小	拦截		掠飞		绕飞		悬停
误差大小	实现所需最小脉冲/(m/s)	相对误差/%	实现所需最小脉冲	相对误差	实现所需最小脉冲/(m/s)	相对误差/%	实现所需最小脉冲/(m/s)	相对误差/%
[0 m, 0 m/s]	1.017 0	—	—	—	11.594 0	—	2.004 8	—
[10¹ m, 10^—3 m/s]	1.016 5	0.049 2	—	—	11.590 5	0.030 2	1.961 5	2.159 8
[10² m, 10^—2 m/s]	1.021 2	0.413 0	—	—	11.424 3	1.463 7	2.119 9	5.741 2
[10³ m, 10^—1 m/s]	1.096 0	7.767 9	—	—	9.943 1	14.239 3	2.274 7	13.462 7

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