ACTA AERONAUTICAET ASTRONAUTICA SINICA >
Natural and non-natural close formation flight on distant retrograde orbits
Received date: 2021-10-25
Revised date: 2021-11-29
Accepted date: 2021-12-19
Online published: 2021-12-24
Supported by
Key Deployment Program of the Chinese Academy of Sciences(ZDRW-KT-2019-1-0102)
Distant Retrograde Orbits (DROs) are a kind of periodic orbits in the Earth-Moon system. DROs are appropriate for long-term missions due to favorable stability. Rendezvous and docking is a basic technology for the supplement of long-term missions, as well as close formation flying for some flying-around tasks. It is thus needed to analyze the close relative motion in DROs and furthermore develop close formation designs. Based on the Floquet theory, a fundamental solution for linear relative dynamics in DROs is obtained. A natural formation is designed based on the natural periodic solution for the linear relative dynamics. Characteristics of the natural formation are analyzed. Moreover, non-natural formations for fast circumnavigate is designed with impulse maneuvers. The fuel consumption of different types of circular reference orbits are analyzed to guide formation designs. Finally, a type of reference trajectories is designed for transfer between two arbitrary positions with safety guaranteed.
Chihang YANG , Honglan FU , Hao ZHANG . Natural and non-natural close formation flight on distant retrograde orbits[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023 , 44(5) : 326563 -326563 . DOI: 10.7527/S1000-6893.2021.26563
1 | CLOHESSY W H, WILTSHIRE R S. Terminal guidance system for satellite rendezvous[J]. Journal of the Aerospace Sciences, 1960, 27(9): 653-658. |
2 | 罗亚中. 空间最优交会路径规划策略研究[D]. 长沙: 国防科学技术大学, 2007: 1-2. |
LUO Y Z. Study on space optimal rendezvous trajectory planning approach[D]. Changsha: National University of Defense Technology, 2007: 1-2 (in Chinese). | |
3 | 詹虎. 载人航天工程巡天空间望远镜大视场多色成像与无缝光谱巡天[J]. 科学通报, 2021, 66(11): 1290-1298. |
ZHAN H. The wide-field multiband imaging and slitless spectroscopy survey to be carried out by the survey space telescope of China manned space program[J]. Chinese Science Bulletin, 2021, 66(11): 1290-1298 (in Chinese). | |
4 | T?IATU C M. The space race on sustainability: Business and legal challenges for on-orbit-servicing[C]∥ On-Orbit Servicing: Next Generation of Space Activities. Berlin: Springer, 2020: 91-121. |
5 | XU M, WANG Y, XU S J. On the existence of J2 invariant relative orbits from the dynamical system point of view[J].Celestial Mechanics and Dynamical Astronomy, 2012, 112(4): 427-444. |
6 | DANG Z H, ZHANG H. Linearized relative motion equations through orbital element differences for general Keplerian orbits[J]. Astrodynamics, 2018, 2(3): 201-215. |
7 | 彭超, 温昶煊, 高扬. 地月空间DRO与HEO(3∶1/2∶1)共振轨道延拓求解及其稳定性分析[J]. 载人航天, 2018, 24(6): 703-718. |
PENG C, WEN C X, GAO Y. DRO and HEO (3∶1/2∶1) resonant orbits in cislunar space calculated by continuation and their stability analysis[J]. Manned Spaceflight, 2018, 24(6): 703-718 (in Chinese). | |
8 | WHITLEY R, MARTINEZ R. Options for staging orbits in cislunar space[C]∥ 2016 IEEE Aerospace Conference. Piscataway: IEEE Press, 2016: 1-9. |
9 | BEZROUK C, PARKER J S. Long term evolution of distant retrograde orbits in the Earth-Moon system[J]. Astrophysics and Space Science, 2017, 362(9): 176. |
10 | SCHEERES D J, HSIAO F Y, VINH N X. Stabilizing motion relative to an unstable orbit: Applications to spacecraft formation flight[J]. Journal of Guidance, Control, and Dynamics, 2003, 26(1): 62-73. |
11 | JUNG S. Formation flying along unstable libration point orbits using switching Hamiltonian structure-preserving control[J]. Acta Astronautica, 2019, 158: 1-11. |
12 | HOWELL K C. Control of satellite imaging formations in multi-body regimes[J]. Acta Astronautica, 2009, 64(5-6): 554-570. |
13 | 李鹏. 拉格朗日点附近编队飞行动力学与控制方法研究[D]. 哈尔滨: 哈尔滨工业大学, 2009: 65-69. |
LI P. Study on dynamics and control of spacecraft formation flying near Lagrange point[D]. Harbin: Harbin Institute of Technology, 2009: 65-69 (in Chinese). | |
14 | GARCIA-TABERNER L. FEFF methodology for spacecraft formations reconfiguration in the vicinity of libration points[J]. Acta Astronautica, 2010, 67(7-8): 810-817. |
15 | PENG H J, LI C. Bound evaluation for spacecraft swarm on libration orbits with an uncertain boundary[J]. Journal of Guidance, Control, and Dynamics, 2017, 40(10): 2690-2698. |
16 | PERNICKA H J, CARLSON B A, BALAKRISHNAN S N. Spacecraft formation flight about libration points using impulsive maneuvering[J]. Journal of Guidance, Control, and Dynamics, 2006, 29(5): 1122-1130. |
17 | QI R, XU S J, XU M. Impulsive control for formation flight about libration points[J]. Journal of Guidance, Control, and Dynamics, 2012, 35(2): 484-496. |
18 | GóMEZ G, MARCOTE M, MASDEMONT J J, et al. Zero relative radial acceleration cones and controlled motions suitable for formation flying[J]. The Journal of the Astronautical Sciences, 2005, 53(4): 413-431. |
19 | HéRITIER A. Dynamical evolution of natural formations in libration point orbits in a multi-body regime[J]. Acta Astronautica, 2014, 102: 332-340. |
20 | HOWELL K C, MARCHAND B G. Natural and non-natural spacecraft formations near the L1 and L2 libration points in the Sun-Earth/Moon ephemeris system[J]. Dynamical Systems, 2005, 20(1): 149-173. |
21 | SIMANJUNTAK T, NAKAMIYA M, KAWAKATSU Y. Design of natural loose formation flying around halo orbits[J]. Transactions of the Japan Society for Aeronautical and Space Sciences, 2012, 55(4): 254-262. |
22 | 周敬, 胡军, 张斌. 圆型限制性三体问题相对运动解析研究[J]. 宇航学报, 2020, 41(2): 154-165. |
ZHOU J, HU J, ZHANG B. Analytical solutions for relative motion in the circular restricted three-body problem[J]. Journal of Astronautics, 2020, 41(2): 154-165 (in Chinese). | |
23 | FRANZINI G, INNOCENTI M. Relative motion dynamics in the restricted three-body problem[J]. Journal of Spacecraft and Rockets, 2019, 56(5): 1322-1337. |
24 | CONTE D, SPENCER D B. Preliminary study on relative motion and rendezvous between spacecraft in the restricted three-body problem: AAS 16-369[R] Washington, D.C.: AAS, 2016. |
25 | UEDA S, MURAKAMI N, IKENAGA T. A study on rendezvous trajectory design utilizing invariant manifolds of cislunar periodic orbits: AIAA-2017-1729[R]. Reston: AIAA, 2017. |
26 | 陈冠华, 杨驰航, 张晨,等. 地月空间的远距离逆行轨道族及其分岔研究[J]. 北京航空航天大学学报, 2022,48(12):2576-2588. |
CHEN G H, YANG C H, ZHANG C, et al. Distant retrograde orbits and its bifurcations in Earth-Moon system[J]. Journal of Beijing University of Aeronautics and Astronautics, 2022,48(12):2576-2588 (in Chinese) | |
27 | CARMEN C. Ordinary differential equations with applications[M]. New York: Springer, 2020: 187-224. |
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