 | | 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 |
|
| << Previous article | Volume 52, Issue 2 / 2017 | Next article >> |
| V.G. Biryukov and Yu.N. Chelnokov, "Kinematic Problem of Optimal Nonlinear Stabilization of Angular Motion of a Rigid Body," Mech. Solids. 52 (2), 119-127 (2017) |
| Year |
2017 |
Volume |
52 |
Number |
2 |
Pages |
119-127 |
| DOI |
10.3103/S0025654417020017 |
| Title |
Kinematic Problem of Optimal Nonlinear Stabilization of Angular Motion of a Rigid Body |
| Author(s) |
V.G. Biryukov (Institute for Precision Mechanics and Control Problems of the Russian Academy of Sciences, ul. Rabochaya 24, Saratov, 410028 Russia)
Yu.N. Chelnokov (Institute for Precision Mechanics and Control Problems of the Russian Academy of Sciences, ul. Rabochaya 24, Saratov, 410028 Russia; Chernyshevskii Saratov State University, ul. Astrakhanskaya 83, Saratov, 410012 Russia, chelnokovyun@gmail.com) |
| Abstract |
The problem of optimal transfer of a rigid body to a prescribed trajectory of preset angular motion is considered in the nonlinear statement. (The control is the vector of absolute angular velocity of the rigid body.) The functional to be minimized is a mixed integral quadratic performance criterion characterizing the general energy expenditure on the control and deviations in the state coordinates.
Pontryagin's maximum principle is used to construct the general analytic solution of the problem in question which satisfies the necessary optimality condition and ensures the asymptotically stable transfer of the rigid body to any chosen trajectory of preset angular motion. It is shown that the obtained solution also satisfies Krasovskii's optimal stabilization theorem. |
| Keywords |
optimal control, rigid body, angular motion, quaternion, stabilization |
| References |
| 1. | V. N. Branets and I. P. Shmyglevskii, "Kinematical Problems of
Attitude Control in a Rotating Coordinate Systems," Izv. Akad.
Nauk SSSR. Mekh. Tverd. Tela, No. 6, 36-43 (1972) [Mech. Solids
(Engl. Transl.)]. |
| 2. | V. N. Branets and I. P. Shmyglevskii,
"Application of Quaternions in Rigid Body Control by the Angular Position,"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela,
No. 4, 24-31 (1972)
[Mech. Solids (Engl. Transl.)]. |
| 3. | B. Wie and P. M. Barda,
"Quaternion Feedback for Spacecraft Large Angle Maneuvers,"
J. Guid. Contr. and Dynam.
8 (3), 360-365 (1985). |
| 4. | B. Wie, H. Weiss, and A. Arapostathis,
"Quaternion Feedback Regulator for Spacecraft Eigenaxis Rotations,"
J. Guid. Contr. and Dynam.
12 (3), 375-380 (1989). |
| 5. | P. K. Plotnikov, A. N. Sergeev, Yu. N. Chelnokov, "Kinematic
Problem of Attitude Control of a Rigid Body," Izv. Akad. Nauk
SSSR. Mekh. Tverd. Tela, No. 5, 9-18 (1991) [Mech. Solids (Engl.
Transl.)]. |
| 6. | Yu. N. Chelnokov, "Quaternion Solution of Kinematic Problems in
Rigid Body Attitude Control - Equations of Motion, Problem
Statement, Preset Motion, and Control," Izv. Ross. Akad. Nauk.
Mekh. Tverd. Tela, No. 4, 7-14 (1993) [Mech. Solids (Engl.
Transl.)]. |
| 7. | Yu. N. Chelnokov, "Quaternion Solution of Kinematic Problems of
Solid Attitude Control: Equations of Errors, Correction Laws and
Algorithms," Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 4,
3-12 (1994) [Mech. Solids (Engl.
Transl.)]. |
| 8. | Yu. N. Chelnokov,
"Construction of Attitude Control Laws for a Rigid Body Using Quaternions
and Standard Forms of Equations Governing Transient Processes. Part 2,"
Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela,
No. 2, 3-17 (2002)
[Mech. Solids (Engl. Transl.)
37 (2), 1-12 (2002)]. |
| 9. | Yu. N. Chelnokov,
"Construction of Attitude Control Laws for a Rigid Body Using Quaternions
and Standard Forms of Equations Governing Transient Processes. Part 1,"
Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela,
No. 1, 3-17 (2002)
[Mech. Solids (Engl. Transl.)
37 (1), 1-12 (2002)]. |
| 10. | V. G. Biryukov and Yu. N. Chelnokov,
"Kinematic Problem of Optimal Nonlinear Stabilization of a Rigid Body Angular Motion,"
in Mathematics, Mechanics, Collection of Scientific Papers, No. 4
(Izdat. Saratov Univ., Saratov, 2002),
pp. 172-174
[in Russian]. |
| 11. | Yu. N. Chelnokov,
Quaternion and Biquaternion Models and Methods of Mechanics of Solids and Their Applications. Geometry and Kinematics of Motion
(Fizmatlit, Moscow, 2006)
[in Russian]. |
| 12. | Yu. N. Chelnokov,
"Biquaternion Solution of the Kinematic Control Problem for the Motion
of a Rigid Body and Its Application to the Solution of Inverse Problems of Robot-Manipulator Kinematics,'
Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela,
No. 1, 38-58 (2013)
[Mech. Solids (Engl. Transl.)
48 (1), 31-46 (2013)]. |
| 13. | V. N. Branets and I. P. Shmyglevskii, Application of Quaternions in Problems of Attitude Control of a Rigid Body
(Nauka, Moscow, 1973) [in Russian]. |
| 14. | Ya. N. Roitenberg,
Automatic Control
(Nauka, Moscow, 1978)
[in Russian]. |
| 15. | I. G. Malkin,
Theory of Stability of Motion
(Nauka, Moscow, 1966)
[in Russian]. |
|
| Received |
30 March 2015 |
| Link to Fulltext |
|
| << Previous article | Volume 52, Issue 2 / 2017 | Next article >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English