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Capturing a spacecraft around a flyby asteroid using Hamiltonian-structure-preserving control. (English) Zbl 07274903
Summary: The potentially hazardous asteroid is not only the target of planetary defense missions but also an ideal one for scientific exploration of near-Earth objects due to minimal launching budget during its close encounter with Earth. The flyby segment of asteroid shows to be hyperbolic in an Earth-centred inertial frame. To guide the spacecraft captured by the asteroid under the common Earth’s gravity, the Hamiltonian-structure-preserving (HSP) controller, based only on the feedback of relative positions, is constructed to transform the topological structure of the equilibrium point from hyperbolic to elliptic. On account of the small mass of flyby asteroid, a hyperbolic two-body model is used to derive the form of controller. The controller is also proved to work effectively in the hyperbolic three-body model. Critical control gains for both transient and long-term stabilities are investigated, as well as the controlled frequencies caused by different gains. To avoid collision with an asteroid, the artificial potential function (APF) is employed to improve the HSP controller.
MSC:
70F Dynamics of a system of particles, including celestial mechanics
93 Systems theory; control
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[1] Yeomans, D. K., Near-earth objects: finding them before they find us, 47-53 (2012), Princeton University Press, Princeton and Oxford
[2] Jiao, W., Selection of the near earth asteroid targets, Space Int, 7, 27-30 (2017)
[3] Zhou, L.; Sun, Y.; Zhou, J., Phase space transport in a map of asteroid motion, Commun Nonlinear Sci Numer Simul, 5, 1, 1-5 (2000) · Zbl 1037.85001
[4] Liang, Y.; Xu, M.; Xu, S., High-order solutions of motion near triangular libration points for arbitrary value of μ, Nonlinear Dyn, 93, 2, 909-932 (2018) · Zbl 1398.37019
[5] Jiang, Y.; Baoyin, H.; Wang, X.; Yu, Y.; Li, H.; Peng, C.; Zhang, Z., Order and chaos near equilibrium points in the potential of rotating highly irregular-shaped celestial bodies, Nonlinear Dyn, 83, 1-2, 231-252 (2016) · Zbl 1349.70026
[6] Anthony, N.; Emami, R., Asteroid engineering: the state-of-the-art of near-earth asteroids science and technology, Prog Aerosp Sci, 100, 1-17 (2018)
[7] Liu X, McInnes C, Ceriotti M. Strategies to engineer the capture of a member of a binary asteroid pair using the planar parabolic restricted three-body problem. Planet Space Sci, 161: 5-25, doi:10.1016/j.pss.2018.05.018.
[8] Decicco, A. J.; Hartzell, C. M.; Adams, R. B.; Polzin, K. A., Preliminary asteroid deflection mission design for 2017 PDC using neutral beam propulsion, Acta Astronaut, 156, 363-370 (2019)
[9] Cheng, A. F.; Atchison, J.; Kantsiper, B.; Rivkin, A. S.; Stickle, A.; Reed, C.; Galvez, A.; Carnelli, I.; Michel, P.; Ulamec, S., Asteroid impact and deflection assessment mission, Acta Astronaut, 115, 262-269 (2015), doi:
[10] Brophy, J.; Strange, N.; Goebela, D.; Johnson, S.; Mazanek, D.; Reeves, D., Characteristics of a high-power ion beam deflection system necessary to deflect the hypothetical asteroid 2017 PDC, J Space Saf Eng, 5, 1, 34-45 (2018)
[11] Baresi, N.; Scheeres, D. J.; Schaub, H., Bounded relative orbits about asteroids for formation flying and applications, Acta Astronaut, 123, 364-375 (2016)
[12] Foster, C.; Bellerose, J.; Mauro, D.; Jaroux, B., Mission concepts and operations for asteroid mitigation involving multiple gravity tractors, Acta Astronaut, 90, 1, 112-118 (2013)
[13] Vetrisano, M.; Vasile, M., Autonomous navigation of a spacecraft formation in the proximity of an asteroid, Adv Space Res, 57, 8, 1783-1804 (2016)
[14] Lin, A. K.L., Control of Spacecraft Formation Flying around Asteroids (2014), Ryerson University, PhD thesis
[15] Pineau, J.; Parker, J. W., Flight operations and lessons learned of the Rosetta Alice ultraviolet spectrograph, J Spacecr Rocket, 56, 3, 801-810 (2019)
[16] Accomazzo, A.; Ferri, P., Rosetta operations at the comet, Acta Astronaut, 115, 434-441 (2015)
[17] Szebehely, V.; Giacaglia, G. E.O., On the elliptic restricted problem of three bodies, Astron J, 69, 230 (1964)
[18] Scheeres, D. J.; Hsiao, F. Y.; Vinh, N. X., Stabilizing motion relative to an unstable orbit: applications to spacecraft formation flight, J Guidance Control Dyn, 26, 1, 62-73 (2012)
[19] Xu, M.; Xu, S., Structure-preserving stabilization for Hamiltonian system and its application in solar sail, J Guidance Control Dyn, 32, 3, 997-1004 (2012)
[20] Colombo C, Xu, M, McInnes, CR. Stabilization of the hyperbolic equilibrium of high area-to-mass spacecraft. Proceedings of the 63rd international astronautical congress, IAC-12.C1.1.13.
[21] Soldini, S.; Colombo, C.; Walker, S., Solar radiation pressure Hamiltonian feedback control for unstable Libration-point orbits, J Guidance Control Dyn, 40, 6, 1374-1389 (2017)
[22] Jung, S.; Kim, Y., Formation flying along unstable libration point orbits using switching Hamiltonian structure-preserving control, Acta Astronaut, 158, 1-11 (2019)
[23] Abeβer, H.; Katzschmann, M., Structure-preserving stabilization of Hamiltonian control systems, Syst Control Lett, 22, 4, 281-285 (1994) · Zbl 0796.93091
[24] Luo, T.; Xu, M., Dynamics of the spatial restricted three-body problem stabilized by Hamiltonian structure-preserving control, Nonlinear Dyn, 94, 3, 1889-1905 (2018) · Zbl 1422.93055
[25] McInnes, C. R., Large angle slew maneuvers with autonomous sun vector avoidance, J Guidance Control Dyn, 17, 4, 875-877 (2012) · Zbl 0925.93397
[26] Cao, L.; Qiao, D.; Xu, J., Suboptimal artificial potential function sliding mode control for spacecraft rendezvous with obstacle avoidance, Acta Astronaut, 143, 133-146 (2018)
[27] Liang, Y.; Xu, M.; Xu, S., Bounded motions near contact binary asteroids by Hamiltonian structure-preserving control, J Guidance Control Dyn, 41, 4, 1-16 (2017)
[28] “Asteroid 2015 TB145”, [Online] Available:https://theskylive.com/2015tb145-info.
[29] Racca, G. D.; Marini, A., SMART-1 mission description and development status, Planet Space Sci, 50, 2, 1323-1337 (2002)
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