 | | 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: | | 12788 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8028
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| In English (Mech. Solids): | | 4760 |
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| M.V. Levskii, "Quaternion Solution of the Problem on Optimum Control of the Orientation of a Solid (Spacecraft) with a Combined Quality Criteria," Mech. Solids. 59 (1), 167-182 (2024) |
| Year |
2024 |
Volume |
59 |
Number |
1 |
Pages |
167-182 |
| DOI |
10.1134/S0025654423601283 |
| Title |
Quaternion Solution of the Problem on Optimum Control of the Orientation of a Solid (Spacecraft) with a Combined Quality Criteria |
| 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 problem on optimal rotation of a solid (spacecraft) from an arbitrary initial to a prescribed final angular position in the presence of restrictions on the control variables is studied.
The turnaround time is set. To optimize the rotation control program, a combined quality criterion
that reflects energy costs is used. The minimized functional combines in a given proportion the integral of the rotational energy and the contribution of control forces to the maneuver. Based on the Pontryagin’s maximum principle and quaternion models of controlled motion of a solid, an analytical
solution of the problem has been obtained. The properties of optimal movement are revealed in analytical form. To construct an optimal rotation program, formalized equations and calculation formulas
are written. Analytical equations and relations for finding optimal control are given. The key relations
that determine the optimal values of the parameters of the rotation control algorithm are given.
In addition, 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 described. For a dynamically symmetric solid, a closed-form solution for the reorientation problem is
obtained. A numerical example and mathematical modeling results that confirm the practical feasibility of the developed method for controlling the orientation of a spacecraft are presented. |
| Keywords |
quaternions, orientation control, maximum principle, combined quality criterion, control functions, control algorithm, boundary value problem |
| Received |
16 May 2023 | Revised |
22 June 2023 | Accepted |
01 July 2023 |
| Link to Fulltext |
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