 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10522 |
| In Russian (ĎĚĚ): | | 9723
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| In English (J. Appl. Math. Mech.): | | 799 |
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| M.V. Levskii, "The problem of the time-optimal control of spacecraft reorientation," J. Appl. Math. Mech. 73 (1), 16-25 (2009) |
| Year |
2009 |
Volume |
73 |
Issue |
1 |
Pages |
16-25 |
| Title |
The problem of the time-optimal control of spacecraft reorientation |
| Author(s) |
M.V. Levskii (Yubileinyi, Russia, niiks@khrunichev.com) |
| Abstract |
The use of Pontryagin's maximum principle to solve spacecraft motion control problems is demonstrated. The problem of the optimal control of the spatial reorientation of a spacecraft (as a rigid body) from an arbitrary initial angular position to an assigned final angular position in the minimum rotation time is investigated in detail. The case in which velocity parameters of the motion are constrained is considered. An analytical solution of the problem is obtained in closed form using the method of quaternions, and mathematical expressions for synthesizing the optimal control programme are given. The kinematic problem of spacecraft reorientation is solved completely. A design scheme for solving the maximum principle boundary-value problem for arbitrary turning conditions and inertial characteristics of the spacecraft is given. A solution of the problem of the optimal control of spatial reorientation for a dynamically symmetrical spacecraft is presented in analytical form (to expressions in elementary functions). The results of mathematical modelling of the motion of a spacecraft under optimal control, which confirm the practical feasibility of the control algorithm developed, are given. Estimates have shown that the turn time of modern spacecraft with a constrained magnitude of the angular momentum can be reduced by 15–25% compared with conventional reorientation methods. The greatest effect is achieved for turns through large angles (90° or more) when the final rotation vector is equidistant from the longitudinal axis and the transverse plane of the spacecraft. |
| References |
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| 2. | K.B. Alekseyev and G.G. Bebenin, Spacecraft Control, Mashinostroyeniye, Moscow (1974). |
| 3. | N.Ye. Zubov, Optimal control of terminal spacecraft reorientation based on an algorithm with a predicting model, Kosm Issled 29 (3) (1991), pp. 340–351. |
| 4. | A.A. Krasovskii, Automatic Flight Control Systems and Their Analytical Design, Nauka, Moscow (1973). |
| 5. | Yu.N. Chelnokov, Spacecraft attitude control using quaternions, Kosm Issled 32 (3) (1994), pp. 21–32. |
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| 10. | A.P. Markeyev, Theoretical Mechanics, Nauka, Moscow (1990). |
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| 12. | Platonov V.N., Kovtun V.S. A method for spacecraft control using thrusters when making a programmed turn. Russian Federation Patent No. 2098325. Byull Izobret. Zayavki Patenty 1997; (34) Published 10 December, 1997. |
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| 14. | The Gamma astrophysical space observatory. Determination of the feasibility of orientation regimes using available angular momentum. P25869-118. Kaliningrad: NPO Energiya im S.P. Koroleva; 1991; 11–4. |
| 15. | M.Yu. Belyayer, S.G. Zykov, V.V. Sazonov, V.M. Stazhkov and V.P. Teslenko, The use of mathematical models for the flight control of an orbital station, Proceedings of the 21–22nd K E Tsiolkovskii Readings. Problems of Rocket and Space Technology Section Moscow (1988), pp. 132–138. |
| 16. | Sarychev V.A., Belyayev M.Yu., Zykov S.G., Teslenko V.P. Mathematical models of the attitude control process of the Mir orbital space station using gyrodynes. In: Abstracts of Papers read at the Sixth All-Union Conference on Control in Mechanical Systems. L’vov: 1988; 138–9. |
| 17. | Sarychev V.A., Belyayev M.Yu., Zykov S.G., Zuyeva Ye.Yu., Sazonov V.V., Saigirayev Kh.U. Several problems of the attitude control of the Mir–Kvant-1–Kvant-2 orbital system. In: Proceedings of the 25th Readings Dedicated to the Development of the Scientific Legacy and Ideas of K E Tsiolkovskii. Problems of Rocket and Space Technology Section. Moscow: 1991; 25–32. |
| 18. | Levskii M.V. A system for determining the parameters of the regular precession of a rigid body. Russian Federation Patent No. 2103736. Byull Izobret. Zayavki i Patenty 1998; (3) Published 27 January, 1998. |
| 19. | Levskii M.V. A method of controlling the turn of a spacecraft. Russian Federation Patent No. 2093433. Byull Izobret. Zayavki i Patenty 1997; (29) Published 20 October, 1997. |
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| 21. | Levskii M.V. A System for determining the parameters of regular precession (versions). Russian Federation Patent No. 2153446. Byull Izobret. Zayavki i Patenty 2000; (21) Published 27 July, 2000. |
|
| Received |
06 May 2008 |
| Link to Fulltext |
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