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IssuesArchive of Issues2001-4pp.40-46

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V. I. Kalenova, V. M. Morozov, and E. N. Sheveleva, "Stability and stabilization of motion of a monocycle," Mech. Solids. 36 (4), 40-46 (2001)
Year 2001 Volume 36 Number 4 Pages 40-46
Title Stability and stabilization of motion of a monocycle
Author(s) V. I. Kalenova (Moscow)
V. M. Morozov (Moscow)
E. N. Sheveleva (Moscow)
Abstract Recently, together with numerous publications on the dynamics of multi-link and multi-wheeled robots, publications have appeared dealing with the dynamics of single-wheel robots that can move rectilinearly and make turns [1-3]. This makes topical the study of stability and controllability of a nonholonomic mechanical system that can describe the motion of a single-wheel controlled vehicle.

Steady state motions are given for a nonholonomic mechanical system representing a model of a monocycle moving along a horizontal plane. Necessary conditions for stability of these motions are obtained, and the possibilities for their stabilization by means of appropriate control actions are analyzed.
References
1.  H. B. Brown Jr and Y. Xu, "A single-wheel, gyroscopically stabilized robot," in Proc. of 1966 IEEE Intern. Conf. on Robotics and Automation. Minneapolis, 1996, pp. 3558-3661, IEEE, New York, 1966.
2.  Z. Sheng, K. Yamafuji, and S. Ulanov, "Study on the stability and motion control of a unicycle 4th reports: Fuzzy gain schedule PD controller for managing nonlinearity of system," JSME Intern. Journal, Ser. C, Vol. 39, No. 3, pp. 569-576, 1996.
3.  S. Takemori and Y. Okuyama, "Stabilization control of a mono-cycle based on H control theory," in Proc. Asian Control Conf., pp. 591-594, Tokio, 1994.
4.  Yu. I. Neimark and N. A. Fufaev, Dynamics of Nonholonomic Systems [in Russian], Nauka, Moscow, 1967.
5.  A. V. Karapetyan and V. V. Rumyantsev, "Stability of conservative and dissipative systems," in Achievements in Science and Technology. Ser. General Mechanics. Volume 6 [in Russian], VINITI, Moscow, 1983.
6.  N. G. Chetaev, Stability of Motion [in Russian], Gostekhizdat, Moscow, 1955.
7.  A. P. Markeev, Dynamics of a Body Having Contact with a Rigid Surface [in Russian], Nauka, Moscow, 1992.
8.  A. J. Laub and W. F. Arnold, "Controllability and observability criteria for multivariable linear second-order models," IEEE Trans. Automat. Control, Vol. AC-29, No. 2, pp. 163-165, 1984.
9.  V. I. Kalenova, V. M. Morozov, and M. I. Salmina, "Controllability and observability in the problem of stabilization of mechanical systems with cyclic coordinates," PMM [Applied Mathematics and Mechanics], Vol. 56, No. 6, pp. 959-967, 1992.
Received 24 April 1999
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