Abstract
The process of formation of a rotating tethered constellation of microsatellites in the form of a regular triangle is considered. A combined control method for deploying the system using tether tension control and thrusters is proposed. Two models are used to substantiate the proposed control method. The first model is obtained by the Lagrange method and is intended for constructing a nominal group formation program. In this model, microsatellites are considered as mass points and tethers are inextensible mechanical bonds. The second model is developed to assess the possibility of implementing a nominal control program, since it takes into account the extensibility of tethers, simulates the operation of cable release mechanisms, and takes into account the motion of microsatellites relative to their centers of mass on which the direction of low thrust forces depends. The equations of the spatial motion of the constellation, corresponding to the second model, are written in a fixed geocentric coordinate system and make it possible to estimate the effect of the static and inertial asymmetry of microsatellites on their motion relative to the center of mass. The results of numerical calculations are presented, confirming the possibility of using the proposed control method for the formation of a tethered constellation in the form of a regular triangle, rotating at the constant given angular velocity in its final state.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
P. M. Bainum, R. E. Harkness, and W. Stuive, “Attitude stability and damping of a tethered orbiting interferometer satellite system,” J. Astronaut. Sci. 19 (5), 364–389 (1972).
J. V. Breakwell and G. B. Andeen, “Dynamics of a flexible passive space array,” J. Spacecraft Rockets 14 (9), 556–561 (1977).
V. A. Chobotov, “Gravitationally stabilized solar power station in orbit,” J. Spacecraft Rockets 14 (4), 249–251 (1977).
A. K. Misra and G. S. Diamond, “Dynamics of a subsatellite system support by two tether,” J. Guid. Control Dyn. 9 (1), 12–16 (1986).
A. V. Luk’yanov, Film Reflectors in Space (MGU, Moscow, 1977) [in Russian].
Ch. Wang and Yu. M. Zabolotnov, “Analysis of the dynamics of the formation of a tether group of three nanosatellites taking into account their motion around the centers of mass,” Mech. Solids 56 (7), 1181–1198 (2021).
I. Bekey, “Tethers open new space options,” J. Astronaut. Aeronaut. 21, 32–40 (1983).
V. V. Beletskii and E. M. Levin, Dynamics of Space Tether Systems (Nauka, Moscow, 1990) [in Russian].
A. K. Misra and A. Pizzaro-Chong, “Dynamics of tethered satellites in a hub-spoke formation,” Adv. Astronaut. Sci. 117, 219–229 (2004).
A. Pizzaro-Chong and A. K. Misra, “Dynamics of multi-tethered satellite formations containing a parent body,” Acta Astronaut. 63, 1188–1202 (2008).
K. D. Kumar and T. Yasaka, “Rotating formation flying of three satellites using tethers,” J. Spacecraft Rockets 41 (6), 973–985 (2004).
M. Kim and C. D. Hall, “Control of a rotating variable-length tethered system,” J. Guid. Control Dyn. 27 (5), 849–858 (2004).
P. Williams, “Optimal deployment/retrieval of a tethered formation spinning in the orbital plane,” J. Spacecraft Rockets 43 (3), 638–650 (2006).
Z. Cai, X. Li, and Z. Wu, “Deployment and retrieval of a rotating triangular tethered satellite formation near libration points,” Acta Astronaut. 98, 37–49 (2014).
Z. Cai, X. Li, and H. Zhou, “Nonlinear dynamics of a rotating triangular tethered satellite formation near libration points,” Aerosp. Sci. Technol. 42, 384–391 (2015).
B. Su, F. Zhang, and P. Huang, “Robust control of triangular tethered satellite formation with unmeasured velocities,” Acta Astronaut. 186, 190–202 (2021).
S. Chen, A. Li, and C. Wang, “Analysis of the deployment of a three-mass tethered satellite formation,” in International Workshop on Navigation and Motion Control (NMC 2020), IOP Conf. Series: Materials Science and Engineering (Samara, 2020), vol. 984, pp. 012–028.
Yu. M. Zabolotnov, “Control of the deployment of an orbital tether system that consists of two small spacecraft,” Cosmic Res. 55 (3), 224–233 (2017).
A. A. Shilov, “Optimal correction of the matrix of directional cosines in calculations of the rotation of a solid body,” Uch. Zap. TsAGI 8 (5), 137–139. (1977).
Funding
This work was supported by the Russian Science Foundation, grant no. 21-51-53002.
Author information
Authors and Affiliations
Corresponding authors
Ethics declarations
The authors declare that they have no conflicts of interest.
Additional information
Publisher’s Note.
Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Chen, S., Zabolotnov, Y.M. Method of Forming a Regular Triangular Tethered Constellation of Microsatellites with Considering Their Motion Relative to the Centers of Mass. J. Comput. Syst. Sci. Int. 62, 27–42 (2023). https://doi.org/10.1134/S1064230723010112
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1064230723010112