Abstract
The paper summarizes the results of the research on angular motion dynamics carried out by the team of the authors and some problems of attitude control of nanosatellites (NS). The features of CubeSat NS passive motion dynamics are described. Conditions for the possible emergence of resonance modes are studied and discussed. Recommendations are given allowing the requirements for mass-inertia characteristics and initial conditions of NS motion to be formulated at the design stage, aimed at the NS stable motion with regard to the required equilibrium position for a wide range of orbital altitudes. Algorithms for reorientation and stabilization of NS motion are proposed based on the solution of the inverse problem of dynamics and selection of optimal nominal attitude control programs. The results of this work are implemented in practice and may be useful to the developers of small spacecraft.
REFERENCES
Puig-Suari, J., Turner, C., and Twiggs, R.J., CubeSat: The development and launch support infrastructure for eighteen different satellite customers on one launch, 15 th AIAA/USU Conference on Small Satellites, 2001.
Bouwmeester, J. and Guo, J., Survey of worldwide pico- and nanosatellite missions, distributions and subsystem technology, Acta Astronautica, 2010, vol. 67, pp. 854–862. https://doi.org/10.1016/j.actaastro.2010.06.004
Puig-Suari, J., Coelho, R., and Williams, S., CubeSat design specification Rev. 12 The CubeSat program, Cal Poly SLO, 2009.
Hevner, R., Holemans, W., Puig-Suari, J., and Twiggs, R., An advanced standard for CubeSats, 25th AIAA/USU Conference on Small Satellites, 2011.
Selva, D. and Krejci, D., A survey and assessment of the capabilities of Cubesats for Earth observation, Acta Astronautica, 2012, vol. 74, pp. 50–68. https://doi.org/10.1016/j.actaastro.2011.12.014
Poghosyan, A. and Golkar, A., CubeSat evolution: Analyzing CubeSat capabilities for conducting science missions, Progress in Aerospace Sciences, 2017, vol. 88, pp. 59–83. https://doi.org/10.1016/j.paerosci.2016.11.002
Nanosats Database. URL: https://www.nanosats.eu/ (Accessed February 11, 2023).
ScienceDirect. URL:https://www.sciencedirect.com/search?qs=nanosatellite&lastSelectedFacet=publicationTitles (Accessed February 11, 2023).
URL: https://www.elibrary.ru/query_results.asp (Accessed February 11, 2023).
IntechOpen. URL: https://www.intechopen. com/chapters/69962 (Accessed February 11, 2023).
Belokonov, I.V., Timbai, I.A., and Orazbaeva, U.M., Special features of low-altitude aerodynamically stabilized nanosatellite movement, Izv. vuzov. Priborostroenie, 2016, vol. 59, no. 6, pp. 507–512. https://doi.org/10.17586/0021-3454-2016-59-6-507-512
Barinova, E.V., Belokonov, I.V., and Timbai, I.A., Motion features of aerodynamically stabilized Cubesat 6U nanosatellites, 29th Saint Petersburg International Conference on Integrated Navigation Systems, ICINS 2022, Proceedings, St. Petersburg, Concern CSRI Elektropribor, 2022. https://doi.org/10.23919/ICINS51784.2022.9815390
Elisov, N.A., Kramlikh, A.V., Lomaka, I.A., et al., An attitude control by the functional series in the problem of nanosatellite reorientation, Aerospace Science and Technology, 2023, vol. 132. https://doi.org/10.1016/j.ast.2022.108038
Elisov, N.A., Kramlikh, A.V., and Lomaka, I.A., An approach to the control of the nanosatellite’s longitudinal axis reorientation, 29th Saint Petersburg International Conference on Integrated Navigation Systems, ICINS 2022, Proceedings, St. Petersburg, Concern CSRI Elektropribor, 2022. https://doi.org/10.23919/ICINS51784.2022.9815362
Sinitsin, L.I. and Kramlikh, A.V., Synthesis of the optimal control law for the reorientation of a nanosatellite using the procedure of analytical construction of optimal regulators, J. Physics: Conference Series, 2021, vol. 1745, Is. 1. https://doi.org/10.1088/1742-6596/1745/1/012053
Chekashov, A.S. and Kramlikh, A.V., Research of optimality of the nanosatellite nominal reorientation trajectory, Journal of Physics: Conference Series, 2021, vol. 1745, Is. 1. https://doi.org/10.1088/1742-6596/1745/1/012071
Belokonov, I.V., Kramlikh, A.V., and Melnik, M.E., Analysis of the influence of the error of the nanosatellite design and dynamic performances on the quality of angular motion control processes, IOP Conference Series: Materials Science and Engineering, 2020, vol. 984, Issue 1. https://doi.org/10.1088/1757-899X/984/1/012016
Kramlikh, A.V. and Melnik, M.E., Algorithm for reorientation of the CubeSat nanosatellites, 24th Saint Petersburg International Conference on Integrated Navigation Systems, ICINS 2017, Proceedings, St. Petersburg, Concern CSRI Elektropribor, 2017. https://doi.org/10.23919/ICINS.2017.7995671
Belokonov, I.V., Timbai, I.A., and Nikolaev P.N., Analysis and synthesis of motion of aerodynamically stabilized nanosatellites of the CubeSat design, Gyroscopy and Navigation, 2018, vol. 9, no. 4, pp. 287–300. https://doi.org/10.1134/S2075108718040028
QB-50. URL: https://www.qb50.eu/ (Accessed November 13, 2020).
Belokonov, I., Kramlikh, A., Timbai, I., and Lagno, O., Problems of satellite navigation and communications for nanosatellites launched as piggyback payload from the orbital stage of carrier rockets, 21st Saint Petersburg International Conference on Integrated Navigation Systems, ICINS 2014, Proceedings, St. Petersburg, Concern CSRI Elektropribor, 2014, pp. 407–415.
Beletskii, V.V., Dvizhenie iskusstvennogo sputnika otnositel’no tsentra mass (Motion of an Artificial Satellite Relative to the Center of Mass), Moscow: Nauka, 1965.
He, L., Chen, X., Kumar, K.D., Sheng, T., and Yue, C., A novel three-axis attitude stabilization method using in-plane internal mass-shifting, Aerospace Science and Technology, 2019, vol. 92, pp. 489–500. https://doi.org/10.1016/j.ast.2019.06.019
Chesi, S., Gong, Q., and Romano, M., Aerodynamic three-axis attitude stabilization of a spacecraft by center-of-mass shifting, Journal of Guidance, Control, and Dynamics, 2017, vol. 40, no. 7, pp. 1613–1626. https://doi.org/10.2514/1.G002460
Belokonov, I. and Timbai, I., The selection of the design parameters of the aerodynamically stabilized nanosatellite of the CubeSat standard, Procedia Engineering, 2015, vol. 104, pp. 88–96. https://doi.org/10.1016/j.proeng.2015.04.100
Belokonov, I.V., Timbai, I.A., and Barinova, E.V., Design parameters selection for CubeSat nanosatellite with a passive stabilization system, Gyroscopy and Navigation, 2020, vol. 11, no. 2, pp. 149–161. https://doi.org/10.1134/S2075108720020029
Sarychev, V.A. and Ovchinnikov, M.Y., Dynamics of a satellite with a passive aerodynamic attitude control system, Cosmic Research, 1994, vol. 32, no. 6, pp. 561–575.
Sarychev, V.A., Mirer, S.A., Degtyarev, A.A., and Duarte, E., Investigation of equilibria of a satellite subjected to gravitational and aerodynamic s, Celestial Mechanics and Dynamical Astronomy, 2007, vol. 97, no. 4, pp. 267–287. https://doi.org/10.1007/s10569-006-9064-3
Sarychev, V. A. and Gutnik, S.A., Satellite dynamics under the influence of gravitational and aerodynamic s. A study of stability of equilibrium positions, Cosmic Research, 2016, vol. 54, no. 5, pp. 388–398. https://doi.org/10.1134/S0010952516050063
Barinova, E.V. and Timbai, I.A., Study of relative equilibrium positions of a dynamically symmetric Cubesat nanosatellite under aerodynamic and gravitational moments, 26th Saint Petersburg International Conference on Integrated Navigation Systems, ICINS 2019, Proceedings, St. Petersburg, Concern CSRI Elektropribor, 2019. https://doi.org/10.23919/ICINS.2019.8769356
Barinova, E.V. and Timbai, I.A., Relative equilibria of dynamically symmetric CubeSat nanosatellite under the action of aerodynamic and gravitational s, Vestnik of Samara University. Aerospace and Mechanical Engineering, 2019, vol. 18, no. 2, p. 21-32. https://doi.org/10.18287/2541-7533-2019-18-2-21-32
Barinova, E.V. and Timbai, I.A., Determining of equilibrium positions of CubeSat nanosatellite under the influence of aerodynamic and gravitational moments, 27th Saint Petersburg International Conference on Integrated Navigation Systems, ICINS 2020 – Proceedings, St. Petersburg, Concern CSRI Elektropribor, 2020. https://doi.org/10.23919/ICINS43215.2020.9133842
GOST 4401-81 Atmosfera standartnaya. Parametry. Vvedenie (Standard atmosphere. Parameters. Introduction) 1981-02-27. Moscow: Izvatel’stvo standartov, 1981.
Rawashdeh, S.A. and Lumpp, J.E., Aerodynamic stability for CubeSats at ISS orbit, Journal of Small Satellites, 2013, vol. 2, no. 1, pp. 85–104.
Rawashdeh, S., Jones, D., Erb, D., Karam, A., Lumpp, J.E. Jr, Aerodynamic attitude stabilization for a ram-facing CubeSat, Advances in the Astronautical Sciences, 2009, vol. 133, pp. 583–595.
Rawashdeh, S.A., Attitude analysis of small satellites using model-based simulation, International Journal of Aerospace Engineering, 2019, vol. 2019, pp. 1–11. https://doi.org/10.1155/2019/3020581
Ovchinnikov, M.Yu. and Roldugin, D.S., A survey on active magnetic attitude control algorithms for small satellites, Progress in Aerospace Sciences, 2019, vol. 109. https://doi.org/10.1016/j.paerosci.2019.05.006
Armstrong, J., Casey, C., Creamer, G., and Dutchover, G., Pointing control for low altitude triple CubeSat space darts, 23rd Annual AIAA/USU Conference on Small Satellites, 2009, no. 202, pp. 1–8.
Psiaki, M.L., Nanosatellite attitude stabilization using passive aerodynamics and active magnetic torquing, Journal of Guidance, Control, and Dynamics, 2004, vol. 27, no. 3, pp. 347–355. https://doi.org/10.2514/1.1993
Chesi, S., Gong, Q., and Romano, M., Satellite attitude control by center-of-mass shifting, Advances in the Astronautical Sciences, 2014, vol. 150, pp. 2575–2594.
Grassi M., Attitude determination and control for a small remote sensing satellite, Acta Astronautica, 1997, vol. 40, no. 9, pp. 675–681. https://doi.org/10.1016/S0094-5765(97)00023-4
Lovera M. and Astolfi A., Global magnetic attitude control of spacecraft in the presence of gravity gradient, IEEE Transactions on Aerospace and Electronic Systems, 2006, vol. 42, no. 3. pp. 796–805. https://doi.org/10.1109/TAES.2006.248214
Belokonov, I.V., Timbai, I.A. and Kurmanbekov, M.S., Passive gravitational aerodynamic stabilization of nanosatellite, 24th Saint Petersburg International Conference on Integrated Navigation Systems, ICINS 2017, Proceedingsm, St. Petersburg, Concern CSRI Elektropribor, 2017, pp. 543–546. https://doi.org/10.23919/ICINS.2017.7995675
Belokonov, I.V., Timbai, I.A. and Davydov, D.D., Passive three-axis stabilization of a nanosatellite in low-altitude orbits: Feasibility study, 25th Saint Petersburg International Conference on Integrated Navigation Systems, ICINS 2018—Proceedings, St. Petersburg, Concern CSRI Elektropribor, 2018, pp. 1–4. https://doi.org/10.23919/ICINS.2018.8405939.
Belokonov, I.V., Timbai, I.A. and Davydov, D.D., Passive stabilization systems for CubeSat nanosatellites: general principles and features, 26th Saint Petersburg International Conference on Integrated Navigation Systems, ICINS 2019, Proceedings, St. Petersburg, Concern CSRI Elektropribor, 2019, pp. 1–4. https://doi.org/10.23919/ICINS.2019.8769434
Belokonov, I.V., Timbai, I.A. and Ustyugov, E.V., Eurasian patent for invention (21) 201400132 (13) A1, Method for aerodynamic stabilization of a CubeSat and the device for its implementation, July, 2015.
Yaroshevskii, V.A. Dvizhenie neupravlyaemogo tela v atmosphere (Uncontrolled Body Motion in the Atmosphere), Moscow: Mashinostroenie, 1978.
Aslanov, V.S. and Boiko V.V., Nonlinear resonant motion of an asymmetrical spacecraft in the atmosphere, Cosmic Research, 1985, vol. 23, no. 3, pp. 341–347.
Zabolotnov, Y.M. and Lyubimov, V.V., Application of the method of integral manifolds for construction of resonant curves for the problem of spacecraft entry into the atmosphere, Cosmic Research, 2003, vol. 41, no. 5, pp. 453–459. https://doi.org/10.1023/A:1026046232640
García-Pérez, Á., Sanz-Andrés, A., Alonso, G., and Chimeno Manguán, M., Dynamic coupling on the design of space structures, Aerospace Science and Technology, 2019, vol. 84, pp. 1035–1048. https://doi.org/10.1016/j.ast.2018.11.045
Fakoor, M., Mohammad Zadeh, P., and Momeni Eskandari, H., Developing an optimal layout design of a satellite system by considering natural frequency and attitude control constraints, Aerospace Science and Technology, 2017, vol. 71, pp. 172–188. https://doi.org/10.1016/j.ast.2017.09.012
Liaño, G., Castillo, J.L., and García-Ybarra, P.L., Nonlinear model of the free-flight motion of finned bodies, Aerospace Science and Technology, 2014, vol. 39, pp. 315–324.
Xu, Y., Yue, B., Yang, Z., Zhao, L., and Yang, S., Study on the chaotic dynamics in yaw–pitch–roll coupling of asymmetric rolling projectiles with nonlinear aerodynamics, Nonlinear Dynamics, 2019, vol. 97, no. 4, pp. 2739–2756. https://doi.org/10.1007/s11071-019-05159-3
Bardin, B.S. and Chekina, E.A., On the stability of resonant rotation of a symmetric satellite in an elliptical orbit, Regular and Chaotic Dynamics, 2016, vol. 21, no. 4, pp. 377–389. https://doi.org/10.1134/S1560354716040018
Bardin, B.S. and Chekina, E.A., On the constructive algorithm for stability analysis of an equilibrium point of a periodic Hamiltonian system with two degrees of freedom in the case of combinational resonance, Regular and Chaotic Dynamics, 2019, vol. 24, no. 2, pp. 127–144. https://doi.org/10.1134/S1560354719020011
Cheng, Y., Gómez, G., Masdemont, J.J., and Yuan, J., Analysis of the relative dynamics of a charged spacecraft moving under the influence of a magnetic field, Communications in Nonlinear Science and Numerical Simulation, 2018, vol. 62, pp. 307–338. https://doi.org/10.1016/j.cnsns.2018.02.023
Aleksandrov, A.Y. and Tikhonov A.A., Averaging technique in the problem of Lorentz attitude stabilization of an Earth-pointing satellite, Aerospace Science and Technology, 2020, vol. 104. https://doi.org/10.1016/j.ast.2020.105963
Kurkina, E.V. and Lyubimov, V.V., Estimation of the probability of capture into resonance and parametric analysis in the descent of an asymmetric spacecraft in an atmosphere, Journal of Applied and Industrial Mathematics, 2018, vol. 12, no. 3, pp. 492–500. https://doi.org/10.1134/S1990478918030092
Lyubimov, V.V. and Lashin, V.S., External stability of a resonance during the descent of a spacecraft with a small variable asymmetry in the Martian atmosphere, Advances in Space Research, 2017, vol. 59, no. 6, pp. 1607–1613.
Zabolotnov, M.Y., A study of oscillations near a resonance during the descent of a spacecraft in the atmosphere, Cosmic Research, 2003, vol. 41, no. 2, pp. 171–177. https://doi.org/10.1023/A:1023339215214
Barinova, E.V., Belokonov, I.V., and Timbai, I.A., Study of resonant modes of CubeSat nanosatellite motion under the influence of the aerodynamic moment, 27th Saint Petersburg International Conference on Integrated Navigation Systems, ICINS 2020, Proceedings, St. Petersburg, Concern CSRI Elektropribor, 2020, pp. 1–4.
Barinova, E.V., Belokonov, I.V., and Timbai, I.A., Study of resonant modes of motion of a CubeSat nanosatellite with small inertia-mass asymmetry under the aerodynamic moment, 28th Saint Petersburg International Conference on Integrated Navigation Systems, ICINS 2021 - Proceedings, St. Petersburg, Concern CSRI Elektropribor, 2021, pp. 1–5. https://doi.org/10.23919/ICINS43216.2021.9470875.
Barinova, E.V., Belokonov, I.V., and Timbai, I.A., Preventing resonant motion modes for low-altitude CubeSat nanosatellites, Gyroscopy and Navigation, 2021, vol. 12, no. 4, pp. 350–362. https://doi.org/10.1134/S2075108721040027
Platus, D.H., Dispersion of spinning missiles due to lift nonaveraging, AIAA Journal, 1977, vol. 15, no. 7, pp. 909–915. https://doi.org/10.2514/3.60733
ROSCOSMOS. News. URL: https://www.roscosmos.ru/22198/ (Accessed May 20, 2023).
NORAD GP Element Sets Current Data. URL: https://celestrak.com/NORAD/elements/ (Accessed May 11, 2022).
Belokonov I.V., Timbai I.A., and Nikolaev P.N. Reconstruction of motion relative to the center of mass of a low-altitude nanosatellite from trajectory measurements, Proceedings of 72nd International Astronautical Congress, IAC-21, 2021, vol. B4.
Lomaka, I.A., Elisov, N.A., Boltov, E.A., et al., A novel design of CubeSat deployment system for transformable structures, Acta Astronautica, 2022, vol. 197., p. 179–190. https://doi.org/10.1016/j.actaastro.2022.05.027
Xing, L., Zhang, J., Liu, C., and Zhang, X., Fuzzy-logic-based adaptive event-triggered sliding mode control for spacecraft attitude tracking, Aerospace Science and Technology, 2021, vol. 108. https://doi.org/10.1016/j.ast.2020.106394
Bello, Á., del Castañedo, Á., Olfe, K.S., Rodríguez, J., and Lapuerta, V., Parameterized fuzzy-logic controllers for the attitude control of nanosatellites in low earth orbits. A comparative studio with PID controllers, Expert Systems with Applications, 2021, vol. 174. https://doi.org/10.1016/j.eswa.2021.114679
Song, C., Islas, G., and Schilling, K., Inverse dynamics based model predictive control for spacecraft rapid attitude maneuver, IFAC-PapersOnLine, 2019, vol. 52, pp. 111–116. https://doi.org/10.1016/j.ifacol.2019.11.078
Boyarko, G.A., Romano, M., and Yakimenko, O.A., Time-optimal reorientation of a spacecraft using an inverse dynamics optimization method, Journal of Guidance, Control, and Dynamics, 2011, vol. 34, pp. 1197–1208. https://doi.org/10.2514/1.49449
Yang, J. and Stoll, E., Time-optimal spacecraft reorientation with attitude constraints based on a two-stage strategy, Advances in the Astronautical Sciences, 2018, vol. 167, pp. 2967–2983.
Wang, Z. and Li, Y., Rigid spacecraft robust adaptive attitude stabilization using state-dependent indirect Chebyshev pseudospectral method, Acta Astronautica, 2020, vol. 174, pp. 94–102. https://doi.org/10.1016/j.actaastro.2020.03.042
Banerjee, A., Amrr, S.M., and Nabi, M.A., A pseudospectral method based robust-optimal attitude control strategy for spacecraft, Advances in Space Research, 2019, vol. 64, pp. 1688–1700. https://doi.org/10.1016/j.asr.2019.08.008
Li, J. and Xi, X.N., Time-optimal reorientation of the rigid spacecraft using a pseudospectral method integrated homotopic approach, Optimal Control Applications and Methods, 2015, vol. 36, pp. 889–918. https://doi.org/10.1002/oca.2145
Zhuang, Y. and Huang, H., Time-optimal trajectory planning for underactuated spacecraft using a hybrid particle swarm optimization algorithm, Acta Astronautica, 2014, vol. 94, pp. 690–698. https://doi.org/10.1016/j.actaastro.2013.06.023
Fakoor, M., Nikpay, S., and Kalhor, A., On the ability of sliding mode and LQR controllers optimized with PSO in attitude control of a flexible 4-DOF satellite with time-varying payload, Advances in Space Research, 2021 vol. 67, pp. 334–349. https://doi.org/10.1016/j.asr.2020.07.010
Molodenkov, A.V. and Sapunkov, Y.G., Analytical quasi-optimal solution of the slew problem for an axially symmetric rigid body with a combined performance index, J. Computer and Systems Sciences International, 2020, vol. 59, pp. 347–357. https://doi.org/10.1134/S1064230720030107
Molodenkov, A.V. and Sapunkov, Y.G., Analytical solution of the minimum time slew maneuver problem for an axially symmetric spacecraft in the class of conical motions, J. Computer and Systems Sciences International, 2018, vol. 57, pp. 302–318. https://doi.org/10.1134/S1064230718020120
Molodenkov, A.V. and Sapunkov, Y.G., Analytical quasi-optimal solution for the problem on turn maneuver of an arbitrary solid with arbitrary boundary conditions, Mechanics of Solids, 2019, vol. 54, pp. 474–485. https://doi.org/10.3103/S0025654419020110
Levskii, M.V., An analytical solution to the problem of optimal control of the reorientation of a rigid body (spacecraft) using quaternions, Mechanics of Solids, 2019, vol. 54, pp. 997–1015. https://doi.org/10.3103/S002565441907001X
Lee, U. and Mesbahi, M., Spacecraft reorientation in presence of attitude constraints via logarithmic barrier potentials, Proceedings of American Control Conference, 2011, pp. 450–455. https://doi.org/10.1109/ACC.2011.5991284
Ermoshina, O.V. and Krishchenko, A.P., Synthesis of programmed controls of spacecraft orientation by the method of inverse dynamics problem, Izv. Ross. Akad. Nauk. Teoriya i sistemy upravleniya, 2000, vol. 39, no. 2, pp. 155–162.
Storn, R. and Price, K., Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces, J. Global Optimization, 1997, vol. 11, pp. 341–359. https://doi.org/10.1023/A:1008202821328
Belokonov I.V. and Lomaka, I.A., Towards in-flight identification of design parameters of a nanosatellite, Kosmicheskaya tekhnika i tekhnologii, 2022, no. 3 (38), pp. 37–52.
Abrashkin, V.I., Puzin, Y.Y., Filippov, A.S., Voronov, K.E., Piyakov, A.V., Semkin, N.D., Sazonov, V.V., and Chebukov, S.Y., Uncontrolled rotational motion of the AIST small spacecraft prototype, Cosmic Research, 2017, vol. 55, no 2, p. 128–141.
Belokonov I.V. and Lomaka, I.A., Methodology of parametric identification of nanosatellite angular motion model, Kosmonavtika i raketostroenie, 2020, no. 6 (117), pp. 134–145.
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The work was carried out within the framework of project 0777-2020-0018 financed from the state assignment to the winners of the competition of scientific laboratories of educational institutions of higher education subordinate to the Ministry of Education and Science of Russia.
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Barinova, E.V., Belokonov, I.V., Elisov, N.A. et al. Some Features of Dynamics and Attitude Control of Nanosatellites in Low Orbits. Gyroscopy Navig. 14, 183–204 (2023). https://doi.org/10.1134/S2075108723030021
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DOI: https://doi.org/10.1134/S2075108723030021