Journal of Applied Mathematics
Volume 2012 (2012), Article ID 414315, 24 pages
Research Article

Adaptive Sliding Mode Control of Mobile Manipulators with Markovian Switching Joints

State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin 150080, China

Received 22 February 2012; Accepted 6 April 2012

Academic Editor: Xianxia Zhang

Copyright © 2012 Liang Ding et al. 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 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.