Corrections planning for a spacecraft Low-Thrust Geo-Transfer

Аuthors

Agishev A. R.^1*, Kasatkin V. G.^2**

1. Moscow Institute of Physics and Technology (National Research University), 9, Institutskiy per., Dolgoprudny, Moscow region, 141701, Russia
2. Company “Space special-purpose systems corporation “Kometa”, 5, Velozavodskaya str., Moscow, 115280, Russia

*e-mail: artur.agishev@phystech.edu
**e-mail: vg_kasatkin@mail.ru

Abstract

After the spacecraft (SC) is put into geostationary orbit (GEO), its longitude may differ from the longitude of the stand point. The initial deviation of longitude may be of several tens of degrees, while the period deviation corresponds to the larger speeds of a SC drift along the orbit. The plan of deployment correction, including information on the initial time, corrective action duration and direction, that change the orbit period and eccentricity, is required to set the SC into stand point.

The purpose of the work consists in developing a high-speed algorithm for GEO transfer plan computing.

The existing methods of transfer employ complex control optimization methods, requiring extra memory and computational resources. Their application onboard the SC is not always possible due to the limited computing resources. Another group of methods uses analytical calculations of the correction plan, but their application is impossible in practice due to the actual space systems’ limitations.

In the proposed method, the correction plan is computed while simulation process. Computing is performed in a cycle by control intervals. One iteration contains testing of the simplest logical conditions and flight simulation at the current control interval. The control interval duration is equal or greater than 24 hours by the correction value by the current 24 hours.

A distinctive feature of the proposed method is the optimal dependence between longitude and orbital period. If the spacecraft deviations match this dependence, the spacecraft would be set into nominal GEO longitude by these daily period corrections.

The algorithm workability was verified for 1000 GEO transfer computations from different initial orbits. The final deviations of the longitude after the maneuver are acceptable for spacecraft station-keeping.

The efficiency of the method was being checked by comparing deviations of longitude and period, as well as maneuver duration and the characteristic speed with the calculation by a well-known method using difficult, resource-intensive algorithm of GEO transfer. The comparison results revealed the proposed algorithm effectiveness, and the relative simplicity of calculations by the method and characteristics of the maneuver give it an advantage in the computations onboard of the spacecraft.

Keywords:

Geostationary orbit (GEO), many-revolution maneuvers, low-thrust maneuvers, Geo-transfer

References

1. Salmin V.V., Chetverikov A.S. Vestnik Samarskogo gosudarstvennogo aerokosmicheskogo universiteta, 2015, vol. 14, no. 4. pp. 92 – 101.

2. Filippov G.A. Vestnik Samarskogo universiteta, 2017, vol. 16, no. 3, pp. 125 – 137.

3. Sukhoi Yu.G. Korrektsii orbit geostatsionarnykh sputnikov (GEO satellites orbits corrections), Moscow, Sputnik+, 2011, part. 1, 120 p.

4. Chernyavskii G.M., Bartenev V.A., Malyshev V.A. Upravlenie orbitoi statsionarnogo sputnik (Geostationary satellite orbit control), Moscow, Mashinostroenie, 1984, 144 p.

5. Kruzhkov D.M. Trudy MAI, 2012, no. 57, available at: http://trudymai.ru/eng/published.php?ID=30953

6. Betanov V.V., Makhnenko Yu.Yu. Vestnik MGTU im. N.E. Baumana. Ser. Mashinostroenie, 2009, no. 3, pp. 83  – 95.

7. Reshetnev M.F., Lebedev A.A., Bartenev V.A., Krasil’shchikov M.N., Malyshev V.A., Malyshev V.V. Upravlenie i navigatsiya iskusstvennykh sputnikov Zemli na okolokrugovykh orbitakh (Control and navigation of satellites in circular orbits), Moscow, Mashinostroenie, 1988, 336 p.

8. J. Liu. Spacecraft TT&C and Information Transmission Theory and Technology, National Defense Industry Press, Beijing, 2015, 531 p.

9. Krasilshikov M.N., Fedorov A.V., Kozorez D.A., Sypalo K.I. Low-Thrust Geo Transfer Off-Line Navigation and Control, 25^thInternational Symposium on Space Flight Dynamics, 2015, Münich, available at: http://issfd.org/ 2015/files/ downloads/papers/010_Krasilshchikov.pdf

10. Jonathan D. Aziz, Jeffrey S. Parkery, Daniel J. Scheeresz, Jacob A. Englander Low-thrust many-revolution trajectory optimization via differential dynamic programming and a Sundman Transformation, The Journal of the Astronautical Sciences, 2018, vol. 65, issue 2, pp. 205 – 228.

11. Darin Koblick, Shujing Xu, Joshua Fogel. Praveen Shankar Low Thrust Minimum Time Orbit Transfer Nonlinear Optimization Using Impulse Discretization via the Modified Picard–Chebyshev Method, Computer Modeling in Engineering & Sciences, 2016, vol.111, no.1, pp.1 – 27.

12. Haberkorn T., Martinon P., Gergaud J. Low-thrust minimum-fuel orbital transfer: a homotopic approach, Journal of Guidance, Control and Dinamics, 2004, vol. 27, no. 6, pp.1046 – 1060.

13. James K Whiting. Orbital Transfer Trajectory Optimization, Massachusetts Institute of Technology (MIT), 2004, 87 p.

14. Sokolov A.V., Ulybyshev Yu.P. Izvestiya Akademii nauk. Teoriya i sistemy upravleniya, 1999, no. 2, pp. 95 – 100.

15. Ganzburg M.F., Kropotin S.A., Murashko V.M. et al. Kosmicheskaya tekhnika i tekhnologii, 2015, no. 4 (11), pp. 25 – 39.

16. Malyshev V.V., Starkov A.V., Fedorov A.V. Trudy MAI, 2012, no. 57, available at: http://trudymai.ru/eng/published.php?ID=30798

17. Law A.M., Kelton W.D. Simulation modeling and analysis, The McGraw-Hill Companies, 2000, 784 p.

18. Chao C. Applied orbit perturbation and maintenance, The Aerospace Press, 2005, 297 p.

19. Howard D Curtis. Orbital Mechanics for Engineering Students (Aerospace Engineering), Butterworth-Heinemann, 2013, 768 p.

20. Reklaitis G.V., Ravindran A., Ragsdell K.M. Engineering Optimization Methods and Applications, New York, 2006, 688 p.

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