Open Access
2012 Adaptive Sliding Mode Control of Mobile Manipulators with Markovian Switching Joints
Liang Ding, Haibo Gao, Kerui Xia, Zhen Liu, Jianguo Tao, Yiqun Liu
J. Appl. Math. 2012(SI08): 1-24 (2012). DOI: 10.1155/2012/414315


The hybrid joints of manipulators can be switched to either active (actuated) or passive (underactuated) mode as needed. Consider the property of hybrid joints, the system switches stochastically between active and passive systems, and the dynamics of the jump system cannot stay on each trajectory errors region of subsystems forever; therefore, it is difficult to determine whether the closed-loop system is stochastically stable. In this paper, we consider stochastic stability and sliding mode control for mobile manipulators using stochastic jumps switching joints. Adaptive parameter techniques are adopted to cope with the effect of Markovian switching and nonlinear dynamics uncertainty and follow the desired trajectory for wheeled mobile manipulators. The resulting closed-loop system is bounded in probability and the effect due to the external disturbance on the tracking errors can be attenuated to any preassigned level. It has been shown that the adaptive control problem for the Markovian jump nonlinear systems is solvable if a set of coupled linear matrix inequalities (LMIs) have solutions. Finally, a numerical example is given to show the potential of the proposed techniques.


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Liang Ding. Haibo Gao. Kerui Xia. Zhen Liu. Jianguo Tao. Yiqun Liu. "Adaptive Sliding Mode Control of Mobile Manipulators with Markovian Switching Joints." J. Appl. Math. 2012 (SI08) 1 - 24, 2012.


Published: 2012
First available in Project Euclid: 3 January 2013

zbMATH: 1251.93089
MathSciNet: MR2948107
Digital Object Identifier: 10.1155/2012/414315

Rights: Copyright © 2012 Hindawi

Vol.2012 • No. SI08 • 2012
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