Abstract
The problem of increasing the maneuverability of a spacecraft (SC) by minimizing the duration of rotations around the center of mass is solved. The case is studied when the orientation is controlled using inertial actuators (power gyroscopes, gyrodynamics). The problem of the fastest possible turn of an SC using gyrodynes from an arbitrary initial angular position to the desired final angular position is considered in detail. Using the maximum principle of L.S. Pontryagin, as well as quaternion models and methods for solving the problems of controlling the motion of an SC, a solution to the problem is obtained. The conditions of the optimality of the reorientation mode without unloading the gyrosystem are written in an analytical form and the properties of the optimal motion are studied. Formalized equations and calculation expressions are presented for constructing an optimal control program taking into account the possible perturbations. The key relationships that determine the optimal values of the parameters of the rotation control law are given. The results of mathematical modeling of the motion of an SC with the optimal control are presented, demonstrating the practical feasibility of the developed algorithm for controlling the spatial orientation of an SC. A condition is formulated for determining the moment of the start of braking from measurements of the current motion parameters, which significantly increases the accuracy of bringing an SC into a predetermined resting position in the presence of restrictions on the control moment.
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REFERENCES
K. B. Alekseev, A. A. Malyavin, and A. V. Shadyan, “Spacecraft extensive attitude control based on fuzzy logic,” Polet, No. 1, 47 (2009).
M. A. Velishchanskii, A. P. Krishchenko, and S. B. Tkachev, “Synthesis of spacecraft reorientation algorithms using the concept of the inverse dynamic problem,” J. Comput. Syst. Sci. Int. 42, 811 (2003).
M. V. Levskii, “About method for solving the optimal control problems of spacecraft spatial orientation,” Probl. Nonlin. Anal. Eng. Syst. 21 (2) (2015).
V. N. Branets and I. P. Shmyglevskii, Application of Quaternions in Problems of Orientation of a Rigid Body (Nauka, Moscow, 1973) [in Russian].
. Scrivener and R. Thompson, “Survey of time-optimal attitude maneuvers,” J. Guidance, Control Dyn. 17 (2) (1994)
H. Shen and P. Tsiotras, “Time-optimal control of axi-symmetric rigid spacecraft with two controls,” AIAA J. Guidance, Control Dyn. 22 (5) (1999).
S. A. Reshmin, “Threshold absolute value of a relay control when time-optimally bringing a satellite to a gravitationally stable position,” J. Comput. Syst. Sci. Int. 57, 713 (2018).
A. V. Molodenkov and Ya. G. Sapunkov, “Analytical solution of the minimum time slew maneuver problem for an axially symmetric spacecraft in the class of conical motions,” J. Comput. Syst. Sci. Int. 57, 302 (2018).
A. V. Molodenkov and Ya. G. Sapunkov, “Special control regime in optimal turn problem of spherically symmetric spacecraft,” J. Comput. Syst. Sci. Int. 48, 891 (2009).
A. V. Molodenkov and Ya. G. Sapunkov, “A solution of the optimal turn problem of an axially symmetric spacecraft with bounded and pulse control under arbitrary boundary conditions,” J. Comput. Syst. Sci. Int. 46, 310 (2007).
B. V. Raushenbakh and E. N. Tokar’, Spacecraft Orientation Control (Nauka, Moscow, 1974) [in Russian].
V. N. Platonov and V. S. Kovtun, “A method of controlling a spacecraft using reactive executive bodies when performing a software turn,” RF Patent No. 2098325, Byull. Izobret., No. 34 (1997).
V. A. Sarychev, M. Yu. Belyaev, S. G. Zykov, V. V. Sazonov, and V. P. Teslenko, “Mathematical models of the processes of maintaining the orientation of the Mir orbital station using gyrodines,” KIAM Preprint No. 10 (Keldysh Inst. Appl. Math., Moscow, 1989).
V. S. Kovtun, V. V. Mitrikas, V. N. Platonov, S. G. Revnivykh, and N. A. Sukhanov, “Mathematical support for conducting experiments in controlling the orientation of the Gamma astrophysical space module,” Izv. Akad. Nauk SSSR, Tekh. Kibernet., No. 3 (1990).
M. V. Levskii, “The use of universal variables in problems of optimal control of the orientation of spacecraft,” Mekhatron., Avtomatiz., Upravl., No. 1 (2014).
M. V. Levskii, “Optimal spacecraft terminal attitude control synthesis by the quaternion method,” Mech. Solids 44, 169 (2009).
M. V. Levskii, “The method of controlling the rotation of the spacecraft,” RF Patent No. 2093433, Byull. Izobret., No. 29 (1997).
M. V. Levskii, “On optimal spacecraft damping,” J. Comput. Syst. Sci. Int. 50, 144 (2011).
S. A. Reshmin, “Threshold absolute value of relay control during the fastest bringing the satellite into a gravitationally stable position,” Dokl. Akad. Nauk 480 (6) (2018).
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes (Nauka, Moscow, 1983; Wiley, New York, 1962).
L. C. Young, Lectures on the Calculus of Variations and Optimal Control Theory (Am. Math. Soc., Philadelphia, 2000; Mir, Moscow, 1974).
M. V. Levskii, “The system for determining the parameters of regular solid state precession,” RF Patent No. 2103736, Byull. Izobret., No. 3 (1998).
F. P. Vasil’ev, Lectures on Methods for Solving Extreme Problems (Mosk. Gos. Univ., Moscow, 1974) [in Russian].
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Levskii, M.V. On Improving the Maneuverability of a Space Vehicle Managed by Inertial Executive Bodies. J. Comput. Syst. Sci. Int. 59, 796–815 (2020). https://doi.org/10.1134/S1064230720020094
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DOI: https://doi.org/10.1134/S1064230720020094