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Stabilizing the second-order nonholonomic systems with chained form by finite-time stabilizing controllers

Published online by Cambridge University Press:  10 February 2015

Guangping He ,
Chenghao Zhang ,
Wei Sun  and
Zhiyong Geng
Guangping He*
Affiliation:
Department of Mechanical and Electrical Engineering, North China University of Technology, Beijing, 100041, P. R. China
Chenghao Zhang
Affiliation:
Department of Mechanical and Electrical Engineering, North China University of Technology, Beijing, 100041, P. R. China
Wei Sun
Affiliation:
Department of Mechanical and Electrical Engineering, North China University of Technology, Beijing, 100041, P. R. China
Zhiyong Geng
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, Peking University, Beijing, 100871, P. R. China
*
*Corresponding author. E-mail: [email protected]
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Summary

An underactuated mechanical system is generally a good test bed for advanced nonlinear controllers and can be applied to design a novel mechanical system with better energy efficiency and good controllability. It has been shown that the dynamics of many underactuated mechanical systems could be transformed into the chained canonical form. To improve the performance of the controllers presented in the literature, a novel controller design method is proposed in this paper. It is shown that the set-point stabilization problem of the second-order chained form systems can be changed into a trajectory-tracking problem based on the nonsmooth Hölder continuous feedback. By designing the tracked trajectory, the presented controller permits the achievement of exponential stability. Some numerical simulations demonstrate the stability of the proposed controller for an underactuated Hovercraft system.

Keywords

UnderactuationNonholonomic constraintsGlobal stabilityFinite-timeControl
Type
Articles
Information
Robotica , Volume 34 , Issue 10 , October 2016 , pp. 2344 - 2367
Copyright
Copyright © Cambridge University Press 2015 

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