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IssuesArchive of Issues2009-4pp.514-525

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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. Proceedings of the First All-Russia Scientific-Technical Conference with International Participation (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
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