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On the dynamics and control of the Sun—Earth L2 tetrahedral formation

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A Correction to this article was published on 11 February 2022

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Abstract

The dynamics and control of a tetrahedral spacecraft formation flying in the Sun-Earth L2 region is initiatively studied, based on the circular restricted three-body problem (CR3BP). Driven by the science goal of identifying extra-solar terrestrial planets and the requirement of imaging optics, a conceptional four-spacecraft triangular pyramid configuration has been proposed for the Multiple-spacecraft Exoplanet Aperture sYnthetic INterferometer (MEAYIN) project, China’s first mid-infrared interferometric imaging mission. Although it looked promising from an optical perspective, the configuration has not been verified dynamically. The formation is required to be virtually “rigid”, because its mutual distances and inertial pointing direction must be maintained with very high accuracy during each observation. In this study, the spatial geometrical relationship between the four spacecraft was established by introducing the parameters of lengths, angles, and a reference vector. The first contribution is that a compact set of normalized factors and critical time indices are defined, which can provide a complete description of the drift of the shape and pointing direction of the configuration, caused by the unstable dynamical environment. Five design variables are isolated and analyzed, and their individual impacts on the uncontrolled evolution of the formation are studied. The main results obtained reveal that the dimensions of the rigid configuration allow a free drift for a time period on the order of tens of hours, while the inertial pointing direction will be lost within merely tens of seconds. Therefore, to form a rigid configuration, the control challenge lies in the fact that control efforts are frequently required for each spacecraft in the fleet, owing to the diverging dynamics. As a second contribution, a simple and feasible control algorithm is proposed to maintain the rigidity of the formation configuration. The results indicate that the associated energy cost is merely 0.05 m/s per observation on average.

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Acknowledgements

The authors would like to appreciate the anonymous reviewers for giving valuable advice to help in improving the quality of the paper. This study was supported by the National Natural Science Foundation of China (Nos. 11602297, 11902027, and 62173334).

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Authors and Affiliations

  1. College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, 410073, China

    Yijun Lian

  2. Qian Xuesen Laboratory of Space Technology, China Academy of Space Technology, Beijing, 100094, China

    Zhuoxi Huo

  3. School of Automation, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Yu Cheng

Authors
  1. Yijun Lian
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  2. Zhuoxi Huo
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  3. Yu Cheng
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Corresponding author

Correspondence to Yu Cheng.

Additional information

Yijun Lian graduated as a doctor of aeronautical and astronautical science and technology from the National University of Defense Technology in 2013, and had been a joint Ph.D. student in the University of Barcelona during 2011–2012. He participated in two satellite projects as control subsystem designers, and his research interests include multi-body trajectory design and control, and satellite attitude control. E-mail: lianyijun09@nudt.edu.cn, missilelyj@163.com.

Zhuoxi Huo is currently an associate researcher and PI at Qian Xuesen Laboratory of Space Technology, China Academy of Space Technology. He received his B.S. degree in physics from Tsinghua University in 2007 and his Ph.D. degree as well as postdoctoral training at the Center for Astrophysics, Tsinghua University in 2013 and 2015, respectively, who devoted himself to studying astronomical image analysis methods, especially accelerated image reconstruction techniques for Insight/HXMT, the first X-ray space telescope of China. His current research interests include space astronomy technologies and mission concept studies. E-mail: huozhuoxi@qxslab.cn.

Yu Cheng is currently a research associate in Beijing University of Posts and Telecommunications. She obtained her Ph.D. degree in aeronautical and astronautical science and technology from Northwestern Polytechnical University in 2018, and had been a joint Ph.D. student at the University of Barcelona during 2014–2016. She worked as a postdoctoral researcher at the Beijing Institute of Technology from 2018 to 2021. Her research interests include dynamical analysis and trajectory design in the multi-body regime and spacecraft formation flying control. E-mail: yu.cheng@bupt.edu.cn, chengyu8907@gmail.com.

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Lian, Y., Huo, Z. & Cheng, Y. On the dynamics and control of the Sun—Earth L2 tetrahedral formation. Astrodyn 5, 331–346 (2021). https://doi.org/10.1007/s42064-021-0111-3

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  • DOI: https://doi.org/10.1007/s42064-021-0111-3

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