卫星编队脉冲机动维持控制与策略

doi:10.12305/j.issn.1001-506X.2023.08.28

Abstract

Abstract:

In view of the satellites formation maintenance issue on low near-earth orbit, the impulsive control solution and maintenance control strategy are studied, while the simulation environment is built for further verification. According to the state transition equation of relative orbital elements(ROEs), the drift rates of each element of ROEs caused by J₂ perturbation are derived. Solutions of impulse control and two different maintenance strategies are proposed to solve the problem of formation configuration destruction caused by perturbation. Based on the long-term maintenance requirement of satellites space formation, a task simulation environment is established for satellites formation mission including high-precision orbit propagation algorithm. The feasibility of the proposed impulsive solutions and maintenance strategies are verified, which are analyzed and discussed in term of impulsive consumption and control error. The simulation result shows that the proposed impulsive control solution and maintenance strategy have high effectiveness and reliability, which could be applied to future space formation flight missions.

Key words: satellites formation, J₂ perturbation, impulsive control, maintenance strategy, mission simulation

CLC Number:

Xingchuan LIU, Danhe CHEN, Gen XU, Wenhe LIAO. Control and strategy for satellites formation maintenance with impulsive maneuver[J]. Systems Engineering and Electronics, 2023, 45(8): 2533-2545.

Figures/Tables 20

Fig.1

Fig.2

Fig.3

Fig.4

Table 1

Fig.5

Table 2

Table 3

Table 4

Fig.6

Table 5

Table 6

Fig.7

Fig.8

Fig.9

Fig.10

Fig.11

Fig.12

Fig.13

Fig.14

References 33

1	郑重. 多航天器编队飞行分布式协同控制[D]. 哈尔滨: 哈尔滨工业大学, 2014.
	ZHENG Z. Distributed coordinated control for multiple spacecraft formation flying[D]. Harbin: Harbin Institute of Techno-logy, 2014.
2	IVANOV D , OVCHINNIKOV M , TKACHEY S . Nanosatellites formation flying control approaches overview[J]. IOP Conference Series: Materials Science and Engineering, 2020, 984 (1): 012023. doi: 10.1088/1757-899X/984/1/012023
3	LOWE S, MARKEVITCH M, D'AMICO S. Relative navigation and pointing error budget for an X-ray astronomy formation-flying mission[C]//Proc. of the 44th Annual AAS Guidance, Navigation, and Control Conference, 2022.
4	LOREGGIA D , FINESCHI S , CAPOBIANCO G , et al. PROBA-3 mission and the shadow position sensors: metrology mea-surement concept and budget[J]. Advances in Space Research, 2021, 67 (11): 3793- 3806. doi: 10.1016/j.asr.2020.07.022
5	JOFFRE E , WEALTHY D , FERNANDEZ I , et al. LISA: heliocentric formation design for the laser interferometer space antenna mission[J]. Advances in Space Research, 2021, 67 (11): 3868- 3879. doi: 10.1016/j.asr.2020.09.034
6	LIU L , LIU J G , WU Y M . Event-triggered coordinated control for multiple solar sail formation flying around planetary displaced orbits[J]. Acta Astronautica, 2021, 184, 286- 298. doi: 10.1016/j.actaastro.2021.04.011
7	杨军. 小卫星SAR子孔径成像技术研究[D]. 合肥: 合肥工业大学, 2021.
	YANG J. Research on sub aperture imaging technology of small sa-tellite SAR[D]. Hefei: Hefei University of Technology, 2021.
8	SARNO S , D'ERRICO M , GUO J , et al. Path planning and guidance algorithms for SAR formation reconfiguration: comparison between centralized and decentralized approaches[J]. Acta Astronautica, 2020, 167, 404- 417. doi: 10.1016/j.actaastro.2019.11.016
9	GRASSO M , RENGA A , FASANO G , et al. Design of an end-to-end demonstration mission of a formation-flying synthetic aperture radar (FF-SAR) based on microsatellites[J]. Advances in Space Research, 2021, 67 (11): 3909- 3923. doi: 10.1016/j.asr.2020.05.051
10	DI MAURO G , SPILLER D , BEVILACQUA R , et al. Spacecraft formation flying reconfiguration with extended and impulsive maneuvers[J]. Journal of the Franklin Institute, 2019, 356 (6): 3474- 3507. doi: 10.1016/j.jfranklin.2019.02.012
11	CHO H . Energy-optimal reconfiguration of satellite formation flying in the presence of uncertainties[J]. Advances in Space Research, 2021, 67 (5): 1454- 1467. doi: 10.1016/j.asr.2020.11.036
12	王有亮. 卫星编队飞行相对轨迹优化与控制[D]. 北京: 中国科学院大学, 2018.
	WANG Y L. Relative trajectory optimization and control for satellite formation flying[D]. Beijing: University of Chinese Academy of Sciences, 2018.
13	SCALA F , GAIAS G , COLOMBO C , et al. Design of optimal low-thrust manoeuvres for remote sensing multi-satellite formation flying in low Earth orbit[J]. Advances in Space Research, 2021, 68 (11): 4359- 4378. doi: 10.1016/j.asr.2021.09.030
14	SARNO S , GUO J , D'ERRICO M , et al. A guidance approach to satellite formation reconfiguration based on convex optimization and genetic algorithms[J]. Advances in Space Research, 2020, 65 (8): 2003- 2017. doi: 10.1016/j.asr.2020.01.033
15	SULLIVAN J , GRIMBERG S , D'AMICO S . Comprehensive survey and assessment of spacecraft relative motion dynamics models[J]. Journal of Guidance, Control, and Dynamics, 2017, 40 (8): 1837- 1859. doi: 10.2514/1.G002309
16	D'AMICO S. Autonomous formation flying in low earth orbit[D]. Delft: Delft University of Technology, 2010.
17	GAIAS G , ARDAENS J , MONTENBRUCK O . Model of J₂ perturbed satellite relative motion with time-varying differential drag[J]. Celestial Mechanics and Dynamical Astronomy, 2015, 123 (4): 411- 433. doi: 10.1007/s10569-015-9643-2
18	KOENIG A, GUFFANTI T, D'AMICO S. New state transition matrices for relative motion of spacecraft formations in perturbed orbits[C]//Proc. of the AIAA/AAS Astrodynamics Specialist Conference, 2016: 1749-1768.
19	BIRIA A, RUSSELL R. A satellite relative motion model using J₂ and J₃ via vinti's intermediary[C]//Proc. of the AIAA/AAS Space Flight Mechanics Conference, 2016.
20	GAIAS G, ARDAENS J S, D'AMICO S. The autonomous vision approach navigation and target identification (AVANTI) experiment: Objectives and design[C]//Proc. of the 9th International ESA Conference on Guidance, Navigation and Control Systems, 2014.
21	KOENIG A, D'AMICO S, MACINTOSH B, et al. Optimal formation design of a miniaturized distributed occulter/telescope in earth orbit[C]//Proc. of the AAS/AIAA Astrodynamics Specialist Conference, 2015.
22	KOLMAS J, BANAZADEH P, KOENIG A, et al. System design of a miniaturized distributed occulter/telescope for direct imaging of star vicinity[C]//Proc. of the IEEE Aerospace Conference, 2016.
23	LI J . Analytical fuel-optimal impulsive reconfiguration of formation-flying satellites[J]. Optimal Control Applications and Methods, 2017, 38 (5): 720- 743. doi: 10.1002/oca.2286
24	GAIAS G , D'AMICO S . Impulsive maneuvers for formation reconfiguration using relative orbital elements[J]. Journal of Guidance, Control, and Dynamics, 2015, 38 (6): 1036- 1049. doi: 10.2514/1.G000189
25	CHERNICK M , D'AMICO S . New closed-form solutions for optimal impulsive control of spacecraft relative motion[J]. Journal of Guidance, Control, and Dynamics, 2018, 41 (2): 301- 319. doi: 10.2514/1.G002848
26	CHERNICK M , D'AMICO S . Closed-form optimal impulsive control of spacecraft formations using reachable set theory[J]. Journal of Guidance, Control, and Dynamics, 2021, 44 (1): 25- 44. doi: 10.2514/1.G005218
27	ZHANG G , MORTARI D . Impulsive orbit correction using second-order Gauss's variational equations[J]. Celestial Mechanics and Dynamical Astronomy, 2020, 132 (2)
28	MONTENBRUCK O , KIRSCHNER M , D'AMICO S , et al. E/I-vector separation for safe switching of the grace formation[J]. Aerospace Science and Technology, 2006, 10 (7): 628- 635. doi: 10.1016/j.ast.2006.04.001
29	D'AMICO S , ARDAENS J S , LARSSON R . Spaceborne autonomous formation-flying experiment on the PRISMA mission[J]. Journal of Guidance, Control, and Dynamics, 2012, 35 (3): 834- 850. doi: 10.2514/1.55638
30	ARDAENS J S , D'AMICO S . Spaceborne autonomous relative control system for dual satellite formations[J]. Journal of Guidance, Control and Dynamics, 2009, 32 (6): 1859- 1870. doi: 10.2514/1.42855
31	张玉锟. 卫星编队飞行的动力学与控制技术研究[D]. 长沙: 国防科学技术大学, 2002.
	ZHANG Y K. Research on dynamics and control technology of satellite formation flying[D]. Changsha: National University of Defense Technology, 2002.
32	ALFRIEND K , VADALI S R , GURFIL P , et al. Spacecraft formation flying: dynamics, control and navigation[M]. Oxford: Elsevier Press, 2009.
33	GAIAS G , COLOMBO C , LARA M . Analytical framework for precise relative motion in low earth orbits[J]. Journal of Gui-dance, Control, and Dynamics, 2020, 43 (5): 915- 927. doi: 10.2514/1.G004716

参数	$ a_c \delta \dot{e}_x$	$ a_c \delta \dot{e}_y$	$ a_c \delta \dot{i}_y$
漂移速率/(m/s)	-8.0×10^-4	6.0×10^-4	0.001 4
Δ=100 m/轨	21.52	28.70	11.95
Δ=150 m/轨	32.29	43.05	17.93

编号	a_cδα/m	漂移速率/(×10^-4 m/s)
卫星1	[0, 0, 469.84, 171.01, -296.19, 813.79]^T	[0, 0, 1.060, -2.912, 0, -5.415]^T
卫星2	[0, 0, -383.02, 321.39, -556.67, -663.41]^T	[0, 0, 1.992, 2.374, 0, -10.177]^T
卫星3	[0, 0, -86.82, 492.40, 852.86, -150.38]^T	[0, 0, -3.052, 0.538, 0, 15.593]^T

仿真算例	算例描述
仿真算例	T_n∶T_c	控制方法	控制策略
算例0	1∶1	方法1	无预估漂移量
算例1	1∶1	方法1	策略1
算例2	1∶1	方法2	策略1
算例3	2∶1	方法1	策略1
算例4	2∶1	方法2	策略1
算例5	2∶1	方法1	策略2
算例6	2∶1	方法2	策略2

编号	参数	理论速率/(×10^-4 m/s)	仿真速率/(×10^-4 m/s)	误差/%
卫星1	$ a_c \delta \dot{e}_x$	1.060	1.037	2.217
	$ a_c \delta \dot{e}_y$	-2.912	-2.957	1.521
	$ a_c \delta \dot{i}_x$	0	-0.020	-
	$a_c \delta \dot{i}_y $	-5.415	-4.973	8.888
卫星2	$ a_c \delta \dot{e}_x$	1.992	2.023	1.532
	$ a_c \delta \dot{e}_y$	2.374	2.339	1.496
	$ a_c \delta \dot{i}_x$	0	0.017	-
	$a_c \delta \dot{i}_y $	-10.177	-9.356	8.775
卫星3	$ a_c \delta \dot{e}_x$	-3.052	-3.016	1.193
	$ a_c \delta \dot{e}_y$	0.538	0.518	3.720
	$ a_c \delta \dot{i}_x$	0	0.003	-
	$a_c \delta \dot{i}_y $	15.593	14.432	8.044

总脉冲值	卫星1	卫星2	卫星3
算例0	0.659 75	0.973 47	1.335 44
算例1	0.686 58	1.015 52	1.395 67
算例2	0.524 82	0.853 43	1.231 37
算例3	0.684 86	1.013 00	1.395 88
算例4	0.516 01	0.838 94	1.210 06
算例5	0.698 28	1.034 22	1.425 82
算例6	0.535 81	0.871 21	1.257 99

Control and strategy for satellites formation maintenance with impulsive maneuver

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 20

References 33

Related Articles 5

Recommended Articles

Metrics

Comments

脉冲值	卫星1			卫星2			卫星3
脉冲值	δv_R	δv_T	δv_N	δv_R	δv_T	δv_N	δv_R	δv_T	δv_N
算例0	0.283 02	0.016 56	0.360 17	0.283 09	0.016 41	0.673 97	0.280 45	0.018 68	1.036 31
算例1	0.293 04	0.016 35	0.377 19	0.293 41	0.016 21	0.705 89	0.290 75	0.019 53	1.085 39
算例3	0.293 07	0.014 62	0.377 16	0.293 28	0.013 83	0.705 89	0.290 71	0.019 70	1.085 47
算例5	0.298 20	0.014 41	0.385 67	0.298 61	0.013 77	0.721 84	0.295 88	0.019 94	1.110 01

脉冲值	卫星1			卫星2			卫星3
脉冲值	δv_T		δv_N	δv_T		δv_N	δv_T		δv_N
算例2	0.147 56		0.377 26	0.147 48		0.705 96	0.146 07		1.085 31
算例4	0.144 79		0.371 22	0.144 18		0.694 76	0.142 87		1.067 18
算例6	0.150 07		0.385 74	0.149 31		0.721 91	0.148 11		1.109 88

[1]	Wei JIANG, Wen SHENG, Wei QI, Shihua LIU. Survey on maintenance decision of large-scale phased array radar's T/R module [J]. Systems Engineering and Electronics, 2022, 44(1): 127-138.
[2]	Mingchi LIN, Qianghui ZHONG, Dawei LI. Combined maintenance and spare supply strategy of unrepairable product [J]. Systems Engineering and Electronics, 2020, 42(6): 1417-1423.
[3]	YAO Yunzhi, MENG Chen, WANG Cheng, LI Baochen. Optimal maintenance strategy for multi-component system with failure interactions based on aggregation algorithm [J]. Systems Engineering and Electronics, 2018, 40(2): 482-488.
[4]	HE Dong-lei， CAO Xi-bin， MA Jun， LIU Pin-xiong. Formation control approach based on relative eccentricity/inclination vector [J]. Journal of Systems Engineering and Electronics, 2011, 33(4): 833-837.
[5]	YAO Li-hong, LI Jun-min. Design of impulsive hybrid controllers for a class of nonlinear hybrid systems [J]. Journal of Systems Engineering and Electronics, 2010, 32(8): 1732-1736.