 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 13088 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8125
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| In English (Mech. Solids): | | 4963 |
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| M.V. Levskii, "Analytical Solution of the Problem of Optimal Control of Reorientation of Solid Body (Spacecraft), in Sense of a Combined Criteria of Quality, Based on the Quaternions," Mech. Solids. 60 (1), 31-47 (2025) |
| Year |
2025 |
Volume |
60 |
Number |
1 |
Pages |
31-47 |
| DOI |
10.1134/S0025654424604506 |
| Title |
Analytical Solution of the Problem of Optimal Control of Reorientation of Solid Body (Spacecraft), in Sense of a Combined Criteria of Quality, Based on the Quaternions |
| Author(s) |
M.V. Levskii (Maksimov Space System Research and Development Institute, a Branch of Khrunichev State Research and Production Space Center, Korolev, Moscow Region, 141091 Russia, levskii1966@mail.ru) |
| Abstract |
The problem on optimal reorientation of a solid (spacecraft) from an initial position into a
prescribed final angular position on the basis of quaternions is solved. A combined criteria of quality
is used, combining in a given proportion the contribution of control forces and the duration of maneuver, as well as the integral of the rotational energy. The synthesis of optimal control is based on a differential equation relating the attitude quaternion and angular momentum of a spacecraft. Analytical
solution of optimal control problem is obtained using the necessary conditions of optimality in the
form of the Pontryagin’s maximum principle. The properties of optimal rotation are studied in detail.
Formalized equations and computational formulas are written to construct the optimal rotation program. Analytical equations and relations for finding the optimal control are presented. Key relations
that determine the optimal values of the parameters of rotation control algorithm are given. A constructive scheme for solving the boundary-value problem of the maximum principle for arbitrary turning conditions (initial and final positions and moments of inertia of a solid) is given also. The made
numerical experiments confirm the analytical conclusions. In the case of a dynamically symmetric
solid body, the problem of spatial reorientation with minimum energy and time consumption is completely solved (in closed form). An example and results of mathematical modeling that confirm the
practical feasibility of the developed method for orientation control are given. |
| Keywords |
control of reorientation, the combined criterion of optimality, maximum principle, control function, control algorithm, quaternion, the boundary-value problem |
| Received |
26 December 2023 | Revised |
02 July 2024 | Accepted |
05 July 2024 |
| Link to Fulltext |
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