519.6 Modeling and optimization of low–mass satellite control when flying from Earth orbit to Mars orbit under a solar sail

Mozzhorina T. Y. (Bauman Moscow State Technical University), Rakhmankulov D. A. (Bauman Moscow State Technical University)

SOLAR SAIL, THE FALSE POSITION METHOD, BOUNDARY VALUE PROBLEMS OF ORDINARY DIFFERENTIAL EQUATIONS, OPTIMAL CONTROL, PONTRYAGIN'S MAXIMUM PRINCIPLE, FLIGHT BETWEEN THE ORBITS OF THE EARTH AND MARS


doi: 10.18698/2309-3684-2021-3-7487


In this paper, the optimization of the transfer of a low–mass satellite from the Earth's orbit to the Mars orbit under a solar sail is considered. Optimization of the control of the pitch angle of the solar sail is carried out using the Pontryagin maximum principle while minimizing the flight time. In contrast to previous works on this topic, the solution of the boundary value problem, to the solution of which the maximum principle is reduced, was obtained by the false position method. The calculation program is written in the C++ programming language. Despite the computational difficulties arising when using the false position method, it was possible to achieve good convergence of the Newton method underlying the algorithm. The analysis of the accuracy of the results obtained is carried out and the possibility of using the false position method in solving such problems is shown. A comparison is made with the data of previously published works. Despite some assumptions used in the development of the calculation algorithm, the work has its value in terms of assessing the possibility of using the false position method, which gives the most accurate numerical optimization results.


Andreev A.A. Regata pod solnechnym parusom [Regatta under a solar sail]. STImul. Zhurnal ob innovaciyah v Rossii [Stymul. Journal of Innovations in Russia] [Electronic resource], 2019. URL: https://stimul.online/articles/science-and-technology/regata-pod-solnechnym-parusom / (accessed: 06.14.2021)
Grigoriev I.S., Zapletin M.P., Samokhin A.S., Samokhina M.A. Ocenka vozmozhnogo vyigrysha po masse pri ispol'zovanii dvigatelej maloj tyagi v ekspedicii k Marsu [Estimation of the possible gain in mass when using low-thrust engines in an expedition to Mars]. Sbornik dokladov ХI Vserossijskogo s"ezda po fundamental'nym problemam teoreticheskoj i prikladnoj mekhaniki [Collection of reports of the XI All-Russian Congress on Fundamental problems of Theoretical and Applied Mechanics], Kazan, 2015, pp.1063–1065.
Ishkov S.A., Starinova O.L. Optimization and modelling of movement with the solar sail. Izvestia of Samara Scientific Center of the Russian Academy of Sciences, 2005, vol.7, no.1, pp.99–106.
Lietmann G. Optimization techniques: with applications to aerospace systems. Academic Press, 1962, 453 p.
Fedorenko R.P. Priblizhennoe reshenie zadach optimal'nogo upravleniya [Approximate solution of optimal control problems]. Moscow, Nauka Publ., 1978, 486 p.
Mozzhorina T.Yu. Numerical solution to problems of optimal control with switching by means of the shooting method. Mathematical modeling and Computational Methods, 2017, no.2 (14), pp.94–106.
Mozzhorina T.Yu., Osipov V.V. Numerical solution of the problem of a soft landing by false position method. Innovative development, 2018, no.8 (25), pp.11–15.
Fedorenko A.N. Matematicheskoe modelirovanie pereorientacii orbital'nogo kosmicheskogo apparata so sfericheskim solnechnym parusom [Mathematical modeling of the reorientation of an orbiting spacecraft with a spherical solar sail]. Diss. Cand. (Eng.) Sc. Moscow, 2014, 126 p.
Chernyakina I.V. Programmy lokal'no-optimal'nogo upravleniya i traektorii geliocentricheskih pereletov kosmicheskogo apparata s solnechnym parusom s uchetom vozmushchenij [Programs of locally optimal control and trajectories of heliocentric flights of a spacecraft with a solar sail, taking into account disturbances]. Cand. (Eng.) Sc. Samara, 2020, 138 p.
Starinova O.L., Gorbunova I.V. Optimizaciya geliocentricheskogo dvizheniya kosmicheskogo apparata s solnechnym parusom [Optimization of the heliocentric motion of a spacecraft with a solar sail]. Sbornik trudov XVII Vserossijskogo seminara po upravleniyu dvizheniem i navigacii letatel'nyh apparatov [Proceedings of the XVII All-Russian Seminar on Motion Control and Navigation of aircraft], Samara, 2015, pp.168–171.
Starinova O.L., Kurochkin D.V., Materova I.L. Optimal control choice of non-keplerian orbits with low-thrust propulsion. AIP Conference Proceedings, 2012, no.1493 (1), pp.964–971.
Somov E.I., Butyrin S.A., Starinova O.L. Reguliruemyj solnechnyj parus v sisteme upravleniya dvizheniem minisputnika zemleobzora: modeli i ocenki effektivnosti [Adjustable solar sail in the motion control system of a mini-satellite Earth survey: models and efficiency estimates]. Sbornik trudov 7-oj Rossijskoj mul'tikonferencii po problemam upravleniya «Upravlenie v morskih i aerokosmicheskih sistemah (UMAS–2014)» [Proceedings of the 7th Russian Multi-conference on Management Problems "Management in Marine and Aerospace Systems (UMAS–2014)"], St. Petersburg, 2014, pp.545–556.


Мозжорина Т.Ю., Рахманкулов Д.А. Моделирование и оптимизация управлением спутника малой массы при перелете с орбиты Земли на орбиту Марса под солнечным парусом. Математическое моделирование и численные методы, 2021, № 3, с. 74–87.



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