 | | 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: | | 12882 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8071
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| In English (Mech. Solids): | | 4811 |
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| G. P. Sachkov, S. V. Feshchenko, and A. I. Chernomorskii, "Stability and Stabilization of Motion of a Uniaxial Wheel Transport Platform," Mech. Solids. 44 (4), 514-525 (2009) |
| Year |
2009 |
Volume |
44 |
Number |
4 |
Pages |
514-525 |
| DOI |
10.3103/S0025654409040037 |
| Title |
Stability and Stabilization of Motion of a Uniaxial Wheel Transport Platform |
| Author(s) |
G. P. Sachkov (Moscow Aviation Institute (State University of Aerospace Technologies), Volokolamskoe sh. 4, GSP-3, A-80, Moscow, 125993 Russia)
S. V. Feshchenko (Moscow Aviation Institute (State University of Aerospace Technologies), Volokolamskoe sh. 4, GSP-3, A-80, Moscow, 125993 Russia, av38545@comtv.ru)
A. I. Chernomorskii (Moscow Aviation Institute (State University of Aerospace Technologies), Volokolamskoe sh. 4, GSP-3, A-80, Moscow, 125993 Russia, kaf305-mai@nm.ru) |
| Abstract |
We consider a uniaxial wheel transport platform with a
single-degree-of-freedom gyroscope moving without slipping either on a plane nonrotating horizontal surface or on the spherical rotating Earth surface. We obtain a general mathematical model which, in a special case, coincides with the model in the form of Chaplygin equations, which permits obtaining a physical interpretation of the Chaplygin equations. In the case of stationary motion where only the balance weight is controlled, we find the minimum value of the gyro angular momentum that ensures the system stability. An example with parameters of the breadboard model is used to consider the problem of the stationary motion stability and stabilization without gyro; the control matrix minimizing the quadratic performance functional is obtained. The characteristic curves of the transient process in the system are given. |
| Keywords |
uniaxial wheel platform, gyroscope, translation-rotational motion, nonholonomic model, stability |
| References |
| 1. | D. E. Okhotsimskii and Yu. G. Martynenko,
"New Problems of Dynamics and Motion Control of Mobile Wheeled Robots,"
Uspekhi Mekh.
2 (1), 3-46 (2003). |
| 2. | Mechanotronics, Automatization, and Control.
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(Novye Tekhnologii, Moscow, 2004)
[in Russian]. |
| 3. | Ya. N. Roitenberg,
Gyroscopes
(Nauka, Moscow, 1966)
[in Russian]. |
| 4. | A. Yu. Ishlinskii,
Orientation, Gyros, and Inertial Navigation
(Nauka, Moscow, 1976)
[in Russian]. |
| 5. | A. Yu. Ishlinskii,
Mechanics of Gyroscopic Systems
(Izd-vo AN SSSR, Moscow, 1963)
[in Russian]. |
| 6. | N. B. Sudzilovskii (Editor),
Foundations of Theory of Automatic Control
(Mashinostroenie, Moscow, 1986)
[in Russian]. |
| 7. | B. V. Bulgakov,
Applied Theory of Gyroscopes
(Gostekhizdat, Moscow, 1955; Israel Program for Scientific Translations, Jerusalem, 1960). |
| 8. | Yu. I. Neimark and N. A. Fufaev,
Dynamics of Nonholonomic Systems
(Nauka, Moscow, 1967; Amer. Math. Soc., Rhode Island, 1972). |
| 9. | F. R. Gantmakher,
Lectures on Analytical Mechanics
(Nauka, Moscow, 1966; Chelsea, New York, 1970). |
| 10. | Physical Encyclopedia, Vol. 5
(Bol'shaya Ross. Entsiklopediya, Moscow, 1998)
[in Russian]. |
| 11. | L. D. Landau and E. M. Lifshitz,
Course of Theoretical Physics, Vol. 1: Mechanics
(Nauka, Moscow, 1965; Pergamon Press, Oxford, 1976). |
| 12. | A. G. Aleksandrov,
Synthesis of Regulators for Multidimensional Systems
(Mashinostroenie, Moscow, 1986)
[in Russian]. |
|
| Received |
18 June 2008 |
| Link to Fulltext |
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