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Mathematical Problems in Engineering
Volume 2012, Article ID 870498, 17 pages
Research Article

Stochastic Stabilization of Nonholonomic Mobile Robot with Heading-Angle-Dependent Disturbance

1Institute of Automation, Qufu Normal University, Shandong 273165, China
2School of Mathematics and Informational Science, Yantai University, Shandong 264005, China

Received 28 April 2011; Accepted 18 July 2011

Academic Editor: Weihai Zhang

Copyright © 2012 Zhao Jing Wu and Yong Hui Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The problem of exponential stabilization for nonholonomic mobile robot with dependent stochastic disturbance of heading angle is considered in this paper. An integrator backstepping controller based on state-scaling method is designed such that the state of the closed-loop system, starting from a nonzero initial heading angle, is regulated to the origin with exponential rate in almost surely sense. For zero initial heading angle, a controller is designed such that the heading angle is driven away from zero while the position variables are bounded in a neighborhood of the origin. Combing the above two cases results in a switching controller such that for any initial condition the configuration of the robot can be regulated to the origin with exponential rate. The efficiency of the proposed method is demonstrated by a detailed simulation.