Pareto-optimal parametric programs for spacecraft relative motion control at near circular orbits

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

Abstract

The problem of designing a set of nominal Pareto optimal control programs for the relative motion of a spacecraft maneuvering in circular orbits relative to a passive target is considered. Motion is considered in an orbital cylindrical reference frame in variables characterizing secular and periodic motion in a dimensionless form, invariant with respect to the magnitude of acceleration from the thrust of a maneuvering spacecraft and the height of the reference orbit. On the basis of analytical studies, areas of boundary conditions have been constructed that allow the use of simpler relative motion control programs with two active areas oriented in the transversal direction. The solution of a two-criterion parametric problem for the criteria is obtained: the motor operating time of the engine, and the total duration of the maneuver. The application of the Pareto optimality principle made it possible to simplify the numerical procedure for constructing the desired set of non-improved solutions to the problem from the available sample satisfying the boundary conditions of the transfer.

Full Text

Restricted Access

About the authors

S. A. Ishkov

Samara University

Email: filippov.ga@ssau.ru
Russian Federation, Samara

G. A. Filippov

Samara University

Author for correspondence.
Email: filippov.ga@ssau.ru
Russian Federation, Samara

References

  1. Sabatini M., Palmerini G.B. Mixed-integer GA optimization for the tracking control of a formation of small satellites equipped with multi-constrained electric thrusters // Acta Astronautica. 2023. V. 202. P. 1–8. https://doi.org/10.1016/j.actaastro.2022.10.009
  2. Song Y., Park S.-Y., Lee S. et al. Spacecraft formation flying system design and controls for four nanosats mission // Acta Astronautica. 2021. V. 186. P. 148–163. https://doi.org/10.1016/j.actaastro.2021.05.013
  3. Li S., Liu Ch., Sun Zh. Finite-time distributed hierarchical control for satellite cluster with collision avoidance // Aerospace Science and Technology. 2021. V. 114. https://doi.org/10.1016/j.ast.2021.106750
  4. Li L., Zhang J., Li. Y. et al. Geostationary station-keeping with electric propulsion in full and failure modes // Acta Astronautica. 2019. V. 163. Pt B. P. 130–144. https://doi.org/10.1016/j.actaastro.2019.03.021
  5. Corpino S., Stesina F. Inspection of the cis-lunar station using multi-purpose autonomous Cubesats // Acta Astronautica. 2020. V. 175. P. 591–605. https://doi.org/10.1016/j.actaastro.2020.05.053
  6. Zhao X., Zhang Sh. Adaptive saturated control for spacecraft rendezvous and docking under motion constraints // Aerospace Science and Technology. 2021. V. 114. Art. ID. 106739. https://doi.org/10.1016/j.ast.2021.106739
  7. Guo Y., Zhang D., Li Ai-jun et al. Finite-time control for autonomous rendezvous and docking under safe constraint // Aerospace Science and Technology. 2021. V. 109. Art. ID. 106380. https://doi.org/10.1016/j.ast.2020.106380
  8. Zhang Y., Zhu B., Cheng M. et al. Trajectory optimization for spacecraft autonomous rendezvous and docking with compound state-triggered constraints // Aerospace Science and Technology. 2022. V. 127. Art. ID. 107733. https://doi.org/10.1016/j.ast.2022.107733
  9. Ишков С.А., Филиппов Г.А. Исследование оптимальных программ управления относительным движением космического аппарата с ограниченной тягой // Косм. исслед. 2023. Т. 61. № 3. С. 248–257. https://doi.org/10.31857/S0023420622600155
  10. Красильщиков М.Н., Малышев В.В., Федотов А.В. Автономная реализация динамических операций на геостационарной орбите. I. Формализация задачи управления // Известия РАН. Теория и системы управления. 2015. № 6. С. 82–96.
  11. Войсковский А.П., Красильщиков М.Н., Малышев В.В. и др. Автономная реализация динамических операций на геостационарной орбите. II. Синтез алгоритмов управления // Известия РАН. Теория и системы управления. 2016. № 6. С. 107–128.
  12. Аппазов Р.Ф., Сытин О.Г. Методы проектирования траекторий носителей и спутников Земли. М.: Наука, Гл. ред. физ.-мат. лит., 1987. 440 с.
  13. Константинов М.С. Механика космического полета. М.: Наука, 1989.
  14. Эльясберг П.Е. Введение в теорию полета искусственных спутников Земли. М.: Наука, 1969.
  15. Ишков С.А. Сближение космических аппаратов с малой тягой на околокруговых орбитах // Косм. исслед. 1992. Т. 30. № 2. С. 165–179.
  16. Понтрягин Л.С., Болтянский В.Г., Гамкрелидзе Р.В. и др. Математическая теория оптимальных процессов. М.: Наука, 1969. 384 с.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download
2. Fig. 1. Analysis of secular motion trajectories

Download (97KB)
Indexing metadata
3. Fig. 2. Pareto set of optimal solutions to the problem for the boundary conditions small deviation and large deviation

Download (122KB)
Indexing metadata
4. Fig. 3. An example of a secular motion trajectory (top) and the dependence of the minor semi-axis of the relative motion ellipse on time (bottom), program control with two thrust activations of different signs

Download (40KB)
Indexing metadata
5. Fig. 4. An example of a secular motion trajectory (top) and the dependence of the minor semi-axis of the relative motion ellipse on time (bottom), program control with two thrust activations of the same sign

Download (151KB)
Indexing metadata

Copyright (c) 2025 Russian Academy of Sciences