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Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2021, Volume 21, Issue 2, Pages 213–226
DOI: https://doi.org/10.18500/1816-9791-2021-21-2-213-226
(Mi isu887)
 

Scientific Part
Mechanics

Analytical algorithm of energy and time quasioptimal turn of a spacecraft under arbitrary boundary conditions

Ya. G. Sapunkov, A. V. Molodenkov

Institute of Precision Mechanics and Control, Russian Academy of Sciences, 24 Rabochaya St., Saratov 410028, Russia
References:
Abstract: The optimal attitude maneuver control problem without control constraints is studied in the quaternion statement for an axially symmetric spacecraft as a rigid body under arbitrary boundary conditions on angular position and angular velocity of a spacecraft. The performance criterion is given by a functional combining the time and energy used for the attitude maneuver. Using substitutions of variables, the original problem is simplified (in terms of dynamic Euler equations) to the optimal slew problem for a rigid body with a spherical mass distribution. The simplified problem contains one additional scalar differential equation. In the class of generalized conical motions, the traditional optimal slew problem is modified to obtain analytical solutions for motion equations. The solutions contain arbitrary constants and two arbitrary scalar functions (generalized conical motion parameters). The proposed approach fits well with the Poinsot concept that any arbitrary angular motion of a rigid body around a fixed point can be considered as some generalized conical motion of a rigid body. Moreover, for the cases of analytic solvability of the classical problem of optimal reversal spherically symmetric spacecraft, when restrictions are imposed on the edge conditions of the problem (plane Euler turn, conical motion) solutions of the classical and modified tasks are completely the same. An optimization problem is formulated and solved with respect to these functions, the second derivatives of which serve as controls in the optimization problem. The resulting analytical solution of the modified problem can be treated as an approximate (quasioptimal) solution of the traditional optimal slew problem under arbitrary boundary conditions. The quasioptimal algorithm of the optimal turn of a spacecraft is given. Numerical example showing the closeness of the solutions of the traditional and modified optimal slew problems for an axially symmetric spacecraft is given.
Key words: quasioptimal control, attitude maneuver, spacecraft, axially symmetric rigid body, arbitrary boundary conditions.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00205
This work was supported by the Russian Foundation for Basic Research (project No. 19-01-00205).
Received: 05.07.2020
Revised: 14.08.2020
Bibliographic databases:
Document Type: Article
UDC: 629.78
Language: Russian
Citation: Ya. G. Sapunkov, A. V. Molodenkov, “Analytical algorithm of energy and time quasioptimal turn of a spacecraft under arbitrary boundary conditions”, Izv. Saratov Univ. Math. Mech. Inform., 21:2 (2021), 213–226
Citation in format AMSBIB
\Bibitem{SapMol21}
\by Ya.~G.~Sapunkov, A.~V.~Molodenkov
\paper Analytical algorithm of energy and time quasioptimal turn of~a~spacecraft under arbitrary boundary conditions
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2021
\vol 21
\issue 2
\pages 213--226
\mathnet{http://mi.mathnet.ru/isu887}
\crossref{https://doi.org/10.18500/1816-9791-2021-21-2-213-226}
\elib{https://elibrary.ru/item.asp?id=45797875}
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