一种空间碎片主动清除任务规划方法

doi:10.12305/j.issn.1001-506X.2023.12.26

摘要/Abstract

摘要：

规划搭载多个载荷的运载器从多个发射点清除大量空间碎片的任务时，需使运载器耗费量尽可能地少。为解决多发射点、多运载器、多载荷、多目标任务规划过程中庞大的运载器耗费量，可将整个问题的解决方案划分为三个部分。首先，设计考虑多约束多阶段的目标窗口推算方案，建立“发射点-运载器-载荷-目标”单匹配模型；然后，基于多个单匹配模型生成可发射矩阵，用于描述“多发射点-多运载器-多载荷-多目标”的多匹配的可行性；最后，采用可发射矩阵动态调整策略，基于匈牙利算法实现最少运载器耗费原则下的目标任务分配。仿真计算结果表明，所提方法能够以较少运载器耗费量实现对全部目标空间碎片的清除，验证了所提算法的有效性和先进性。

关键词: 碎片主动清除, 任务规划, 窗口推算, 匈牙利算法

Abstract:

When planning the mission of carrying multiple payloads to clear a large amount of space debris from multiple launch points, it is necessary to minimize the cost of the carrier. The proposed method is divided into three components to solve at the problem of vehicles' cost in multi-launch site, multi-vehicle, multi-payload, and multi-target mission planning. Firstly, a target window calculation scheme is designed to build the single matching of the launch site, vehicle, payload and target, in which multiple constraints and multiple stages are considered. Secondly, based on the multiple launch site, vehicle, payload and target, the launch matrix is generated which can describe the feasibility of multi-matching of multi-launce site, multi-vehicle, multi-payload, and multi-target. Finally, the Hungarian algorithm is adopted to solve the problem of target mission planning with launch matrix dynamic adjustment strategy with the policy of minimizing the vehicle consumption. The simulation results show that the proposed method can fully remove active debris with minimum vehicle consumption, which verifies the effectiveness and superiority of the proposed method.

Key words: active debris removal, mission planning, window calculation, Hungarian algorithm

中图分类号:

V448

钟泽南, 权申明, 晁涛, 王松艳, 杨明. 一种空间碎片主动清除任务规划方法[J]. 系统工程与电子技术, 2023, 45(12): 3958-3966.

Zenan ZHONG, Shenming QUAN, Tao CHAO, Songyan WANG, Ming YANG. An active space debris removal mission planning method[J]. Systems Engineering and Electronics, 2023, 45(12): 3958-3966.

图/表 15

图1

图2

表1

图3

表2

表3

图4

图5

图6

图7

图8

表4

图9

图10

表5

参考文献 25

1	王立武, 刘安民, 许望晶, 等. 一种低轨废弃目标的捕获与回收方案[J]. 中国空间科学技术, 2021, 41 (1): 84- 90.
	WANG L W , LIU A M , XU W J , et al. Research on capture and recovery of low-orbit useless targets[J]. Chinese Space Science and Technology, 2021, 41 (1): 84- 90.
2	EMANUELLI M , FEDERICO G , LOUGHMAN J , et al. Conceptualizing an economically, legally, and politically viable active debris removal option[J]. Acta Astronautica, 2014, 104 (1): 197- 205. doi: 10.1016/j.actaastro.2014.07.035
3	刘凯, 鲜勇, 张大巧, 等. 地基运载火箭交会空间目标弹道快速优化设计[J]. 弹箭与制导学报, 2017, 37 (1): 112- 116.
	LIU K , XIAN Y , ZHANG D Q , et al. Target trajectory rapid optimization design of rendezvous space of ground launch vehicle[J]. Journal of Projectiles, Rockets, Missiles and Guidance, 2017, 37 (1): 112- 116.
4	贾飞达, 韩宏伟, 温昶煊. 基于上升轨迹可达范围的目标拦截发射窗口计算[J]. 宇航学报, 2022, 43 (4): 403- 412.
	JIA F D , HAN H W , WEN C X . Calculation of launch window for target interception based on reachable domain of ascending trajectory[J]. Journal of Astronautics, 2022, 43 (4): 403- 412.
5	田龙飞, 李华, 刘武, 等. 基于重要性测度的一箭多星分离安全性分析[J]. 中国科学: 技术科学, 2019, 49 (7): 803- 814.
	TIAN L F , LI H , LIU W , et al. Study on safety of multi-sate-llite launch mission based on importance measure[J]. Scientia Sinica Technologica, 2019, 49 (7): 803- 814.
6	丁娣, 刘新建, 陈新民, 等. 机载反卫星导弹的拦截算法研究[J]. 弹箭与制导学报, 2004, (S8): 370-372, 376. doi: 10.15892/j.cnki.djzdxb.2004.s8.030
	DING D , LIU X J , CHEN X M , et al. Intercept algorithm study of air-launched anti-satellite missile[J]. Journal of Projectiles, Rockets, Missiles and Guidance, 2004, (S8): 370-372, 376. doi: 10.15892/j.cnki.djzdxb.2004.s8.030
7	向开恒, 李人杰, 陈杨. 基于代理模型的空间飞越发射窗口[J]. 北京航空航天大学学报, 2018, 44 (12): 2613- 2620. doi: 10.13700/j.bh.1001-5965.2018.0264
	XIANG K H , LI R J , CHEN Y . Launch window of space fly-by based on surrogate model[J]. Journal of Beijing University of Aeronautics and Astronautics, 2018, 44 (12): 2613- 2620. doi: 10.13700/j.bh.1001-5965.2018.0264
8	贺绍飞, 谷振丰, 李科哲, 等. 快响火箭机动发射点位/发射窗口一体规划[J]. 航天控制, 2020, 38 (5): 61- 66.
	HE S F , GU Z F , LI K Z , et al. Integrated design of maneuver launch position and time for operationally responsive solid launch vehicle[J]. Aerospace Control, 2020, 38 (5): 61- 66.
9	李革非, 陈莉丹, 唐歌实, 等. 多约束交会对接发射窗口的分析和规划[J]. 宇航学报, 2011, 32 (11): 2463- 2470.
	LI G F , CHEN L D , TANG G S , et al. Analysis and programming of rendezvous launch window with multi-constraints[J]. Journal of Astronautics, 2011, 32 (11): 2463- 2470.
10	张道昶, 樊忠泽. 固体火箭应急发射任务规划及发射流程研究[J]. 现代防御技术, 2018, 46 (6): 122- 128.
	ZHANG D C , FAN Z Z . Research on mission planning and launch flow of solid rocket emergency launch[J]. Modern Defence Technology, 2018, 46 (6): 122- 128.
11	ANDERSEN A C , PAVLIKOV K , TOFFOLO T . Weapon-target assignment problem: exact and approximate solution algorithms[J]. Annals of Operations Research, 2022, 312 (6): 581- 606.
12	KLINE A , AHNER D , HILL R . The weapon-target assignment problem[J]. Computers and Operations Research, 2019, 105, 226- 236.
13	刘庆国, 刘新学, 夏维, 等. 多个多弹头在轨武器平台的目标分配优化[J]. 系统工程与电子技术, 2018, 40 (5): 1050- 1056.
	LIU Q G , LIU X X , XIA W , et al. Target assignment optimization of multiple on-orbit weapon platforms with multiple warheads[J]. Systems Engineering and Electronics, 2018, 40 (5): 1050- 1056.
14	郑书坚, 赵文杰, 钟永建, 等. 面向多目标拦截问题的协同任务分配方法研究[J]. 空天防御, 2021, 4 (3): 55- 64.
	ZHENG S J , ZHAO W J , ZHONG Y J , et al. Collaborative task assignment for multi-objective interception problem[J]. Air & Space Defense, 2021, 4 (3): 55- 64.
15	董晨, 帅逸仙, 周金鹏, 等. 网络化多传感器多武器协同防空任务规划[J]. 系统工程与电子技术, 2022, 44 (12): 3738- 3746.
	DONG C , SHUAI Y X , ZHOU J P , et al. Cooperative air defense task planning of networked multi sensor-multi weapon[J]. Systems Engineering and Electronics, 2022, 44 (12): 3738- 3746.
16	余婧, 雍恩米, 陈汉洋, 等. 面向多无人机协同对地攻击的双层任务规划方法研究[J]. 系统工程与电子技术, 2022, 44 (9): 2849- 2857.
	YU J , YONG E M , CHEN H Y , et al. Bi-level mission planning framework for multi-cooperative UAV air-to-ground attack[J]. Systems Engineering and Electronics, 2022, 44 (9): 2849- 2857.
17	何胜学. 公平性指派问题及均值逼近求解算法[J]. 系统科学与数学, 2022, 42 (9): 2399- 2411.
	HE S X . Fair assignment problem and its average approximation algorithm[J]. Journal of Systems Science and Mathematical, 2022, 42 (9): 2399- 2411.
18	张进, 郭浩, 陈统. 基于可适应匈牙利算法的武器-目标分配问题[J]. 兵工学报, 2021, 42 (6): 1339- 1344.
	ZHANG J , GUO H , CHEN T . Weapon-target assignment based on adaptable Hungarian algorithm[J]. Acta Armamentarii, 2021, 42 (6): 1339- 1344.
19	CHOPRA S , NOTARSTEFANO G , RICE M . A distributed version of the hungarian method for multirobot assignment[J]. IEEE Trans.on Robotics, 2017, 33 (4): 932- 947.
20	周洪喜, 张进, 彭晨远, 等. 基于匈牙利算法的多导弹阵地拦截指派规划[J]. 弹箭与制导学报, 2021, 41 (4): 79- 84.
	ZHOU H X , ZHANG J , PENG C Y , et al. Interception assignment planning of multiple missile positions based on Hungarian algorithm[J]. Journal of Projectiles, Rockets, Missiles and Guidance, 2021, 41 (4): 79- 84.
21	RABBANI Q , KHAN A , QUDDOOS A . Modified Hungarian method for unbalanced assignment problem with multiple jobs[J]. Applied Mathematics and Computation, 2019, 361, 493- 498.
22	贾沛然, 陈克俊, 何力. 远程火箭弹道学[M]. 长沙: 国防科技大学出版社, 2009.
	JIA P R , CHEN K J , HE L . Long-range rocket ballistics[M]. Changsha: National University of Defence Technology Press, 2009.
23	王征. 一种高精度在轨试验窗口设计方法研究[J]. 导弹与航天运载技术, 2020, (2): 23- 27.
	WANG Z . Research on high-precision on-orbit test window calculation method[J]. Missiles and Space Vehicles, 2020, (2): 23- 27.
24	张博俊, 王俊峰, 李大鹏, 等. 简化弹道设计方法在运载火箭型号论证中的应用[J]. 弹道学报, 2019, 31 (3): 12- 17.
	ZHANG B J , WANG J F , LI D P , et al. Application of simplified trajectory design algorithm in type demonstration of launch vehicle[J]. Journal of Ballistics, 2019, 31 (3): 12- 17.
25	杨希祥, 江振宇, 张为华. 固体运载火箭上升段弹道快速设计方法研究[J]. 宇航学报, 2010, 31 (4): 993- 997.
	YANG X X , JIANG Z Y , ZHANG W H . Rapid design method for ascent trajectory of solid launch vehicles[J]. Journal of Astronautics, 2010, 31 (4): 993- 997.

变量	匹配参数
p	经纬高
t_L	发射时刻
s_D	射向
t_S	上升时间
s_P	关机点参数
t_G	载荷滑行时间
t_T	载荷转移时长
ΔV	载荷变轨冲量
t_I	载荷与目标交会时刻

发射时刻	发射点	目标1	目标2	…	目标 n
t₀	1	*	*	*	*
	2	*	*	*	*
		*	*	*	*
	N_S	*	*	*	*
t₁	1	*	*	*	*
	2	*	*	*	*
		*	*	*	*
	N_S	*	*	*	*
t_k	1	*	*	*	*
	2	*	*	*	*
		*	*	*	*
	N_S	*	*	*	*

发射时刻	发射点	射向	关机点	目标1	目标2	…	目标n
t₀	1	*	*	*	*	*	*
t₀	m	*	*	*	*	*	*
t_k	1	*	*	*	*	*	*
	2	*	*	*	*	*	*
		*	*	*	*	*	*
	m	*	*	*	*	*	*

发射点名称	经度/(°)	纬度/(°)	高度/m
L01	111	20	0
L02	122	50	0
L03	100	18	0
L04	118	24	0

仿真场景	m	n	V_D	M_I大小	运载器清除目标数量统计						算法耗时/s
仿真场景	m	n	V_D	M_I大小	N=6	N=5	N=4	N=3	N=2	N=1	算法耗时/s
1	4	30	10	53 583×30	2	1	0	2	2	3	300
2	4	100	34	191 541×100	6	1	2	5	16	4	900
3	4	300	90	571 917×300	10	14	14	13	36	3	3 180
4	4	500	151	985 300×500	27	9	18	30	64	3	6 540