Adaptive Sliding Mode Control of Mobile Manipulators with Markovian Switching Joints

Abstract

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.

Quantised control of delayed Markovian jump systems with partly known transition probabilities

“…} and other elements are defined in (12) and (44). Here, the controller gain of the state feedback controller (7) can be characterised by (45) in Theorem 2.…”

“…Then, the major contributions and advantages of this paper can be generalised as follows: (1) the state feedback quantised control problem is addressed for a more general class of continuous-time uncertain Markovian jump systems with mixed time delays and partly known transition probabilities; and (2) according to the known and unknown cases of the diagonal elements of the transition rate matrix, the corresponding stability criterion is given by introducing several new matrix inequality conditions. Moreover, a numerical example and a practical example (the dynamic model of the wheeled mobile manipulator in [14,45]) are presented to verify the feasibility and availability of the designed state feedback controller.…”

Stochastic stability analysis of Markovian jump linear systems with incomplete transition descriptions

“…4, it can be seen that the obtained controller by Theorem 4 effectively retains the stochastic stability of the considered system (2) with partly known transition probabilities. Example 3 (practical example) Consider the following dynamic model of the wheeled mobile manipulator where q denotes the generalised coordinates for the mobile platform and the robotic manipulator joints, and , are the symmetric positive definite inertia matrix, the Centripetal and Coriolis torque, the gravitational torque vector, the input transformation matrix, and the control input, respectively. By applying the design method in [15], the continuous‐time Markovian jump linear system (1) with the following matrices: …”

Dynamic balance and motion control for wheeled inverted pendulum vehicle via hierarchical sliding mode approach

“…However, designing a conventional sliding mode control method for the underactuated subsystem is not enough to manipulate the subsystem that has 2 DOFs. [16][17][18] Plenty of control strategies have been presented by some researchers to analyze the stability or the motion control for the WIP vehicles, but the control algorithm with concise and high generality is relatively rare to the best of our knowledge.…”