Trajectory tracking of an uncertain wheeled mobile robotic manipulator with a hybrid control approach

Abstract

In this paper, a novel hybrid control approach is used for trajectory-tracking control of wheeled mobile robotic manipulators (WMRMs) in the presence of model uncertainties and external disturbances. Due to the existence of nonholonomic constrains in wheeled mobile robots, the proposed controller should be able to tackle the challenge of underactuation in such systems. To attain this objective, the dynamic equations of motion for a WMRM are derived in closed form using the Gibbs–Appell (G-A) formulation, which is an efficient method for obtaining the dynamic motion equations of nonholonomic systems. Then, a novel control scheme is developed which is both optimal and robust and which enjoys updated gains under an adaptive law. In this regard, to benefit from the advantages of two distinct methods, a high-order sliding mode control (HOSMC) is employed as a robust controller with the aim of handling system uncertainties and a state-dependent Riccati equation (SDRE) is used as a nonlinear optimal controller. In order to systematically deal with system uncertainties and to avoid the manual calculation of the upper bound of uncertainties, the gain of HOSMC is updated via an adaptive law. The most important advantage of this novel approach over the existing methods is that not only is it robustly stable against external disturbances when controlling an uncertain nonlinear system but also optimal for a predefined quadratic cost function. Lyapunov stability theory is employed to verify the stability of the proposed controller. Finally, to demonstrate the superiority of this novel controller, computer simulation results for a WMRM are compared with those of an adaptive sliding mode controller. It can be observed that the proposed hybrid control approach is capable of optimizing control inputs while achieving stability for a WMRM in the presence of model uncertainties.