Study of an adaptive algorithm for motion control of small spacecraft in a group

V.V. Perliuk; M.A. Eprincev

doi:10.18127/j20700814-202605-06

Study of an adaptive algorithm for motion control of small spacecraft in a group

research article UDC 629.7 Pages: 35-41 doi.org/10.18127/j20700814-202605-06

^1,2 Saint Petersburg State University of Aerospace Instrumentation (St.-Petersburg, Russia)

Keywords: Small spacecraft low-orbit constellation terminal control adaptive filtering Kalman filter spectral analysis residual signal

Abstract

This paper examines the pressing issue of accurately determining the relative positions of small satellites in group flights. An adaptive filtering algorithm based on spectral analysis of the residual signal in a Kalman filter is proposed. The algorithm compensates for the uncertainty and variability of the statistical characteristics of measurement noise, thereby improving the accuracy of estimating the relative distances between satellites.

Objective – this paper examines algorithms for controlling the relative motion of small satellites (S/C) in a low-orbit constellation, focusing on practical implementation in onboard control systems. The problem of terminal control, which involves transferring a spacecraft to a specified point while ensuring acceptable system behavior throughout the entire process, is considered. A decomposition of the rendezvous problem into three sequential stages is proposed: transfer to the final approach line, orientation and stabilization of the relative position, and the rendezvous itself.

Mathematical models of spacecraft relative motion based on optimal control problems with quadratic performance functionals are presented, and analytical solutions for synthesizing control laws are proposed. The algorithm's effectiveness is confirmed by mathematical modeling results.

The adaptive motion control algorithm is computationally simple and can be implemented onboard nanosatellites.

Received: 14.07.2026
Approved after review: 24.07.2026
Accepted: 01.09.2026

How to cite

Перлюк В.В., Епринцев М.А. Исследование адаптивного алгоритма для управления движением малых космических аппаратов в группе // Информационно-измерительные и управляющие системы. 2026. Т. 24. № 5. С. 35−41. DOI: https://doi.org/10.18127/j20700814-202605-06

References

Brown R.G., Hwang P.Y.C. Introduction to Random Signals and Applied Kalman Filtering. John Wiley & Sons. 2012. P. 341–362.
Schilling K. Distributed Space Missions for Earth System Monitoring. New York: Springer Heidelberg Dordrecht London. 2016. P. 224–227.
Panferov A.I., Nebylov A.V., Brodskij S.A. Sistema upravleniya otnositel'nym dvizheniem malyh kosmicheskih apparatov (KA). Materialy konferencii «Upravlenie v morskih i aerokosmicheskih sistemah» (UMAS-2016). Rossiya. 2016. S. 355–364 (In Russian).
Perliuk V.V. Research of an optical method for determining the mutual positioning of microsatellites to ensure the safety of a low-orbital constellation. Acta Astronautica. 2026. V. 240. P. 24–31. DOI: 10.1016/j.actaastro.2025.11.045.
Perliuk V.V., Panferov A.I. Control Systems for Spacecraft Rendezvous and Docking. Journal of Aerospace Engineering. 2020. V. 33, № 1. P. 04019050.
Fedorinov A.Yu. Issledovanie algoritma ustanovleniya svyazi mezhdu malymi kosmicheskimi apparatami s ispol'zovaniem mashinnogo zreniya dlya obespecheniya gruppovogo poleta s podderzhaniem chetkoj formacii stroya. Informacionno-izmeritel'nye i upravlyayushchie sistemy. 2024. T. 22. № 6. S. 23–31. DOI: 10.18127/j20700814-202406-03 (In Russian).
Alpatov A.P. i dr. Sistemy upravleniya poletom kosmicheskih apparatov. M.: Mashinostroenie. 2018. S. 64–87 (In Russian).
Zaharov Yu.V., Peshekhonov V.G. Navigacionnye sistemy kosmicheskih apparatov. M.: Fizmatlit. 2019. S. 122–158 (In Russian).
Stepanov O.A. Primenenie fil'trov Kalmana v navigacionnyh sistemah. M.: Fizmatlit. 2018. S. 55–68 (In Russian).
Sutyagin Yu.G., Ivanov N.M. Perspektivy ispol'zovaniya nanosputnikov v gruppovyh poletah. Kosmicheskie issledovaniya. 2021. T. 59. № 4. S. 345–356 (In Russian).
Kramlih A.V. Adaptivnaya sistema upravleniya uglovym dvizheniem malorazmernogo kosmicheskogo apparata. Giroskopiya i navigaciya. 2025. T. 33. № 1 (128). S. 106–124 (In Russian).
Yang Y. Spacecraft modeling, attitude determination, and control: quaternion-based approach. CRC Press. 2019. P. 211–243.
Mikrin E.A., Zvyagin F.V. Vvedenie v mekhaniku poleta i upravlenie kosmicheskimi apparatami. M.: Izd-vo MGTU im. N. E. Baumana. 2020. S. 89–112 (In Russian).

[1] Brown R.G., Hwang P.Y.C. Introduction to Random Signals and Applied Kalman Filtering. John Wiley & Sons. 2012. P. 341–362.

[2] Schilling K. Distributed Space Missions for Earth System Monitoring. New York: Springer Heidelberg Dordrecht London. 2016. P. 224–227.

[3] Panferov A.I., Nebylov A.V., Brodskij S.A. Sistema upravleniya otnositel'nym dvizheniem malyh kosmicheskih apparatov (KA). Materialy konferencii «Upravlenie v morskih i aerokosmicheskih sistemah» (UMAS-2016). Rossiya. 2016. S. 355–364 (In Russian).

[4] Perliuk V.V. Research of an optical method for determining the mutual positioning of microsatellites to ensure the safety of a low-orbital constellation. Acta Astronautica. 2026. V. 240. P. 24–31. DOI: 10.1016/j.actaastro.2025.11.045.

[5] Perliuk V.V., Panferov A.I. Control Systems for Spacecraft Rendezvous and Docking. Journal of Aerospace Engineering. 2020. V. 33, № 1. P. 04019050.

[6] Fedorinov A.Yu. Issledovanie algoritma ustanovleniya svyazi mezhdu malymi kosmicheskimi apparatami s ispol'zovaniem mashinnogo zreniya dlya obespecheniya gruppovogo poleta s podderzhaniem chetkoj formacii stroya. Informacionno-izmeritel'nye i upravlyayushchie sistemy. 2024. T. 22. № 6. S. 23–31. DOI: 10.18127/j20700814-202406-03 (In Russian).

[7] Alpatov A.P. i dr. Sistemy upravleniya poletom kosmicheskih apparatov. M.: Mashinostroenie. 2018. S. 64–87 (In Russian).

[8] Zaharov Yu.V., Peshekhonov V.G. Navigacionnye sistemy kosmicheskih apparatov. M.: Fizmatlit. 2019. S. 122–158 (In Russian).

[9] Stepanov O.A. Primenenie fil'trov Kalmana v navigacionnyh sistemah. M.: Fizmatlit. 2018. S. 55–68 (In Russian).

[10] Sutyagin Yu.G., Ivanov N.M. Perspektivy ispol'zovaniya nanosputnikov v gruppovyh poletah. Kosmicheskie issledovaniya. 2021. T. 59. № 4. S. 345–356 (In Russian).

[11] Kramlih A.V. Adaptivnaya sistema upravleniya uglovym dvizheniem malorazmernogo kosmicheskogo apparata. Giroskopiya i navigaciya. 2025. T. 33. № 1 (128). S. 106–124 (In Russian).

[12] Yang Y. Spacecraft modeling, attitude determination, and control: quaternion-based approach. CRC Press. 2019. P. 211–243.

[13] Mikrin E.A., Zvyagin F.V. Vvedenie v mekhaniku poleta i upravlenie kosmicheskimi apparatami. M.: Izd-vo MGTU im. N. E. Baumana. 2020. S. 89–112 (In Russian).

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