Methodology of Optimal Control of Low-Thrust Spacecraft Transfer Between Halo Orbits around the Earth-Moon L2 Libration Point
EDN: KPQRCG
Abstract
The paper considers the problem of optimal control of an electric propulsion spacecraft maneuvering between the spatial halo orbits around the L2 libration point in the Earth-Moon system. The proposed methodology finds the initial approximations for calculating the transfer trajectories within the framework of restricted three-body problem and improves the computational efficiency of calculations. A low-thrust transfer between the halo orbits is calculated to confirm the validity of this computational procedure.
Keywords
Supporting agencies: The research was carried out at the expense of the grant of the Russian Science Foundation No. 22-29-01092, https://rscf.ru/project/22-29-01092/
About the Authors
C. Du
Samara University; Northwestern Polytechnical University
Russian Federation
Russian Federation
Samara; China; Xi'an
O. L Starinova
Samara University; Nanjing University of Science and Technology
Russian Federation
Russian Federation
Samara; China; Nanjing
A. Yu. Demina
Samara University
Russian Federation
Russian Federation
Samara
References
1. Crusan, J.C. et al., Deep space gateway concept: Extending human presence into cislunar space, IEEE Aerospace Conference, 2018, pp. 110.
2. Parker, J.S., Anderson, R.L., Low-energy lunar trajectory design, 1st Edition, JPL Deep-Space Communications and Navigation Series, Wiley, 2014, pp. 103–106.
3. Аксенов С.А., Бобер С.А. Управление движением космического аппарата на гало-орбите при наличии ограничений на направления корректирующих маневров // Некоторые аспекты современных проблем механики и информатики, 2018. С. 166–174.
4. Шайхутдинов А.Р., Костенко В.И. Перспективы использования гало-орбиты в окрестности точки либрации L2 системы Солнце–Земля для наземно-космического радиоинтерферометра Миллиметрон // Космические исследования. 2020. Т. 58. № 5. С. 434–442.
5. Richardson, D.L., Analytic construction of periodic orbits about the collinear points, Celestial mechanics, 1980, vol. 22, no. 3. pp. 241–253.
6. Grebow, D., Generating periodic orbits in the circular restricted three-body problem with applications to lunar south pole coverage, MSAA Thesis, School of Aeronautics and Astronautics, Purdue University, 2006. pp. 1–165.
7. Calleja, R.C. et al., Boundary-value problem formulations for computing invariant manifolds and connecting orbits in the circular restricted three body problem, Celestial Mechanics and Dynamical Astronomy, 2012, vol. 114, no. 1, pp. 77–106.
8. Zeng, H., Zhang, J., Modelin g low-thrust transfers between periodic orbits about five libration points: Manifolds and hierarchical design, Acta Astronautica, 2018, 145, pp. 408–423.
9. Du, C., Starinova, O.L., Liu, Y., Transfer between the planar Lyapunov orbits around the Earth–Moon L2 point using low-thrust engine, Acta Astronautica, 2022, 201, pp. 513–525.
10. Xiangyu, L., Dong, Q., Yu, C., Progress of three-body orbital dynamics study, Chinese Journal of Theoretical and Applied Mechanics, 2021, 53, no. 5, pp. 1223–1245.
11. Петухов В.Г. Метод продолжения для оптимизации межпланетных траекторий с малой тягой // Космические исследования. 2012. Т. 50. № 3. С. 258–258.
12. Pérez-Palau, D., Epenoy, R., Fuel optimization for low-thrust Earth–Moon transfer via indirect optimal control, Celestial Mechanics and Dynamical Astronomy, 2018, 130, № 2, pp. 1–29.
13. Ranieri, C.L., Ocampo, C.A., Indirect optimization of spiral trajectories, Journal of Guidance, Control, and Dynamics, 2006, 29, № 6, pp. 1360–1366.
14. 14. Russell, R.P., Primer vector theory applied to global low-thrust trade studies, Journal of Guidance, Control, and Dynamics, 2007, 30, № 2, pp. 460–472.
15. Pan, B., Pan, X., Ma, Y., A quadratic homotopy method for fuel-optimal low-thrust trajectory design, Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2019, 233, no. 5, pp. 1741–1757.
16. Singh, S.K. et al., Low-Thrust Earth-Moon Transfers via manifolds of a halo orbit in the cis-lunar space, 43rd Annual AAS Guidance, Navigation and Control Conference, Breckenridge, Colorado, 2020.
17. Широбоков М.Г., Трофимов С.П. Перелеты с малой тягой на окололунные орбиты с гало-орбит вокруг лунных точек либрации L1 и L2 // Космические исследования. 2020. 58. № 3. С. 223–234.
18. Hargraves, C.R., Paris, S.W., Direct trajectory optimization using nonlinear programming and collocation, Journal of Guidance, Control, and Dynamics, 1987, 10, no. 4. pp. 338–342.
19. Trélat, E., Optimal control and applications to aerospace: some results and challenges // Journal of Optimization Theory and Applications, 2012, 154, no. 3, pp. 713–758.
20. Racca, G.D., Whitcomb, G.P., Foing, B.H., The SMART-1 mission, ESA bulletin, 1998, 95, pp. 72–81.
21. Foing, B.H. et al., SMART-1 mission to the Moon: status, first results and goals, Advances in Space Research, 2006, 37, no. 1, pp. 6–13.
22. Sarli, B.V. et al., Destiny trajectory design to (3200) Phaethon, The Journal of the Astronautical Sciences, 2018, 65, no. 1, pp. 82–110.
23. Pritchett, R., Howell, K., Grebow, D. Low-thrust transfer design based on collocation techniques: applications in the restricted three-body problem, Astrodynamics Specialist Conference, Stevenson, Washington, August 21–24, 2017, pp. 1–92.
24. Старинова О.Л. Расчет межпланетных перелетов космических аппаратов с малой тягой / изд. 2-е. М.: ЛЕНАНД, 2020. 200 c.
25. Shampine, L.F. et al., Solving boundary value problems for ordinary differential equations in MATLAB with bvp4c, Tutorial notes, 2000, pp. 1–27.
26. Howell, C.K., Three-dimensional, periodic,‘halo’orbits, Celestial mechanics, 1984, 32, no. 1, pp. 53–71.
27. Ким В.П. Стационарные плазменные двигатели в России: проблемы и перспективы // Труды МАИ. 2013. Т. 60. C. 1–12.
Review
For citations:
Du C., Starinova O.L., Demina A.Yu. Methodology of Optimal Control of Low-Thrust Spacecraft Transfer Between Halo Orbits around the Earth-Moon L2 Libration Point. Gyroscopy and Navigation. 2023;31(3):36-47. (In Russ.) EDN: KPQRCG
Views:
46
Email this article 