Dynamics of Tethered-Coulomb Formation for Debris Deorbiting in Geosynchronous Orbit
Publication: Journal of Aerospace Engineering
Volume 35, Issue 3
Abstract
In order to reduce the population of space debris in geosynchronous orbit, a tethered-Coulomb formation (TCF) is proposed that consists of a space tug and a cluster of charged debris connected by elastic massless tethers. The charged debris introduces repulsive coulomb forces to avoid collisions among the pieces of debris. In this way, the system is able to maintain a stable configuration when proper system parameters are given. To determine this relationship, a dynamics model of the formation was derived by using Lagrange’s equation. Then, precise and approximate equilibrium solutions of the debris item charges and tether lengths were derived analytically according to the different number of debris items in pyramid configurations of the TCF. Based on the analytical results, pyramid and double-pyramid TCF configurations were studied via numerical simulations. The results showed that oscillations of the debris had little impact on the motion of the tug. When designing a double-pyramid TCF system, two clusters of debris with large relative positions in different phases would show good performance in a deorbit mission.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grant Nos. 11825201 and 12102038).
References
Alary, D., K. P. AndreevBoyko, P. Boyko, E. Ivanova, D. Pritykin, V. Sidorenko, C. Tourneur, and D. Yarotsky. 2015. “Dynamics of multi-tethered pyramidal satellite formation.” Acta Astronaut. 117 (12): 222–230. https://doi.org/10.1016/j.actaastro.2015.08.011.
Aslanov, V. S., and V. V. Yudintsev. 2013. “Dynamics of large space debris removal using tethered space tug.” Acta Astronaut. 91 (10): 149–156. https://doi.org/10.1016/j.actaastro.2013.05.020.
Aslanov, V. S., and V. V. Yudintsev. 2014. “Behavior of tethered debris with flexible appendages.” Acta Astronaut. 104 (1): 91–98. https://doi.org/10.1016/j.actaastro.2014.07.028.
Aslanov, V. S., and V. V. Yudintsev. 2015. “The motion of tethered tug–debris system with fuel residuals.” Adv. Space Res. 56 (7): 1493–1501. https://doi.org/10.1016/j.asr.2015.06.032.
Barbara, N. H., S. Lizy-Destrez, P. Guardabasso, and D. Alary. 2021. “New GEO paradigm: Re-purposing satellite components from the GEO graveyard.” Acta Astronaut. 173 (8): 155–163. https://doi.org/10.1016/j.actaastro.2020.03.041.
Berryman, J., and H. Schaub. 2015. “Analytical charge analysis for two- and three-craft coulomb formations.” J. Guidance Control Dyn. 30 (6): 1701–1710. https://doi.org/10.2514/1.23785.
Bremen, A. S. 2003. Robotic geostationary orbit restorer (ROGER) phase. Final Rep. Paris: European Space Agency.
Bruijn, F. J., S. Theil, D. Choukroun, and E. Gill. 2016. “Collocation of geostationary satellites using convex optimization.” J. Guidance Control Dyn. 39 (6): 1303–1313. https://doi.org/10.2514/1.G001650.
Ellis, J. R., and C. D. Hall. 2009. “Model development and code verification for simulation of electrodynamic tether system.” J. Guidance Control Dyn. 32 (6): 1713–1722. https://doi.org/10.2514/1.44638.
ESA’s (European Space Agency) Space Debris Office. 2021a. “ESA’s annual space environment report 2021.” Accessed July 5, 2021. https://www.sdo.esoc.esa.int/environment_report/Space_Environment_Report_latest.pdf.
ESA’s (European Space Agency) Space Debris Office. 2021b. “Space debris by the numbers.” Accessed July 5, 2021. https://www.esa.int/Safety_Security/Space_Debris/Space_debris_by_the_numbers.
Hogan, E. A., and H. Schaub. 2012. “Collinear invariant shapes for three-spacecraft Coulomb formations.” Acta Astronaut. 72 (3–4): 78–89. https://doi.org/10.1016/j.actaastro.2011.10.020.
Inampudi, R., and H. Schaub. 2014. “Orbit radial dynamic analysis of two-craft Coulomb formation at libration points.” J. Guidance Control Dyn. 37 (2): 682–691. https://doi.org/10.2514/1.55282.
Liu, H. T., L. P. Yang, Q. B. Zhang, and Y. W. Zhu. 2012. “An investigation on tether-tugging de-orbit of defunct geostationary satellites.” Sci. Chin. Technol. Sci. 55 (7): 2019–2027. https://doi.org/10.1007/s11431-012-4878-6.
Mankala, K. K., and S. K. Agrawal. 2004. “Dynamic modeling and simulation of impact in tether net/gripper systems.” Multibody Sys. Dyn. 11 (3): 235–250. https://doi.org/10.1023/B:MUBO.0000029393.25494.64.
NASA Orbital Debris Program Office. 2021. “Monthly object type charts by number and mass.” Accessed July 5, 2021. https://www.orbitaldebris.jsc.nasa.gov/quarterly-news/pdfs/odqnv25i1.pdf.
Pettazzi, L., H. Kruger, and S. Theil. 2006. Electrostatic forces for satellite swarm navigation and reconfiguration. Paris: European Space Agency.
Qi, R., A. Misra, and Z. Zuo. 2017. “Active debris removal using double-tethered space-tug system.” J. Guidance Control Dyn. 40 (3): 722–730. https://doi.org/10.2514/1.G000699.
Qi, R., A. Shi, A. K. Misra, K. D. Kumar, and J. Zhang. 2019. “Coulomb tether double-pyramid formation, a potential configuration for geostationary satellite collocation.” Aerosp. Sci. Technol. 84 (2): 1131–1140. https://doi.org/10.1016/j.ast.2018.11.036.
Schaub, H., and I. Hussein. 2007. “Stability and reconfiguration analysis of a circularly spinning 2craft Coulomb tether.” In Proc., IEEE Aerospace Conf. New York: IEEE. https://doi.org/10.1109/AERO.2007.352670.
Seubert, C. R., and H. Schaub. 2009. “Tethered coulomb structures: Prospects and challenges.” J. Guidance Control Dyn. 57 (1–2): 347–368. https://doi.org/10.1007/BF03321508.
Shan, M., and L. Shi. 2020. “Post-capture control of a tumbling space debris via tether tension.” Acta Astronaut. 180 (1): 317–327. https://doi.org/10.1016/j.actaastro.2020.12.049.
Sun, L., G. Zhao, and H. Huang. 2013. “Stability and control of tethered satellite with chemical propulsion in orbital plane.” Nonlinear Dyn. 74 (4): 1113–1131. https://doi.org/10.1007/s11071-013-1028-z.
Wang, S., and H. Schaub. 2008. “Spacecraft collision avoidance using coulomb forces with separation distance and rate feedback.” J. Guidance Control Dyn. 31 (3): 740–750. https://doi.org/10.2514/1.29634.
Wang, S., and H. Schaub. 2011. “Nonlinear feedback control of a spinning two-spacecraft coulomb virtual structure.” IEEE Trans. Aerosp. Electron. Syst. 47 (3): 2055–2067. https://doi.org/10.1109/TAES.2011.5937282.
Wen, H., Z. H. Zhu, D. Jin, and H. Hu. 2016. “Constrained tension control of a tethered space-tug system with only length measurement.” Acta Astronaut. 119 (2): 110–117. https://doi.org/10.1016/j.actaastro.2015.11.011.
Yamamoto, U., and H. Yamakawa. 2013. “Two-craft Coulomb-force formation dynamics and stability analysis with Debye length characteristics.” In Proc., AIAA/AAS Astrodynamics Specialist Conf. and Exhibit. Reston, VA: American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.2008-7361.
Yang, K. Y., A. J. R. MisraZhang, J. R. Zhang, R. Qi, and Y. Liu. 2020. “Dynamics of a debris towing system with hierarchical tether architecture.” Acta Astronaut. 177 (12): 891–905. https://doi.org/10.1016/j.actaastro.2019.10.048.
Yi, W., Q. J. Li, and F. N. Xu. 2020. “Orbit-attitude-vibration coupled dynamics of tethered solar power satellite.” Adv. Space Res. 67 (1): 393–400. https://doi.org/10.1016/j.asr.2020.09.036.
Zhang, G., et al. 2008. Applied plasma physics. Beijing: Capital Normal University Press.
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Published In
Journal of Aerospace Engineering
Volume 35 • Issue 3 • May 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Sep 27, 2021
Accepted: Dec 9, 2021
Published online: Feb 22, 2022
Published in print: May 1, 2022
Discussion open until: Jul 22, 2022
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