 | | 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: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4760 |
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| M.V. Levskii, "Control of the Rotation of a Solid (Spacecraft) with a Combined Optimality Criterion Based on Quaternions," Mech. Solids. 58 (5), 1483-1499 (2023) |
| Year |
2023 |
Volume |
58 |
Number |
5 |
Pages |
1483-1499 |
| DOI |
10.3103/S002565442360040X |
| Title |
Control of the Rotation of a Solid (Spacecraft) with a Combined Optimality Criterion Based on Quaternions |
| Author(s) |
M.V. Levskii (Maksimov Space System Research and Development Institute, Khrunichev State Research and Production Space Center, Korolev, Moscow oblast, 141091 Russia, levskii1966@mail.ru) |
| Abstract |
The dynamic problem of the optimal rotation of a rigid body (for example, a spacecraft) from an arbitrary initial to a designated final angular position in the presence of restrictions on the control variables is studied. Rotation time is not fixed. To optimize the rotation control program, a combined quality criterion is used, the minimized functional combines the energy costs and the duration of the maneuver in a given proportion. Based on the L. S. Pontryagin maximum principle and quaternion models of controlled motion of a solid, a solution to the problem was obtained. The reorientation optimality conditions are written in analytical form, and the properties of optimal rotation are shown. To construct an optimal rotation program, formalized equations and calculation formulas are written. Optimal control is presented in the form of a synthesis. The control law is formulated as an explicit dependence of the control variables on the phase coordinates. Analytical equations and relations for finding the optimal motion are given. Key relationships are given that determine the optimal values of the parameters of the rotation control algorithm. A constructive scheme for solving the boundary value problem of the maximum principle for arbitrary rotation conditions (initial and final positions and moments of inertia of a rigid body) is also described. For a dynamically symmetric rigid body, a closed-form solution of the reorientation problem is obtained. A numerical example and the results of mathematical modeling are presented, demonstrating the practical feasibility of the developed method for controlling the attitude of a spacecraft. |
| Keywords |
reorientation, quaternion, control function, maximum principle, combined optimality criterion, boundary value problem, control law |
| Received |
22 May 2022 | Revised |
30 August 2022 | Accepted |
19 October 2022 |
| Link to Fulltext |
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