Trajectory tracking of a mobile robot with frictions and uncertainties using hierarchical sliding-mode under-actuated control

At beginning, the kinematic model and dynamic model of a differential mobile robot (DMR), and the dynamic model of left- and right-wheel DC motors are combined to be the controlled system. The control inputs of the proposed controlled system are the input voltages for the left- and right-wheel motors. The (indirect) outputs are the two-dimensional (2D) position and orientation of a DMR. Owing to the under-actuated characteristic, the direct reference input (i.e. two desired motor currents) using the first sliding surface is designed, so that the 2D position and orientation of the DMR are simultaneously controlled by two motor currents (i.e. the direct output). On the other hand, the second sliding surface is designed as the linear dynamics of tracking error of motor currents. Under completely (or partially) known frictions and uncertainties, the hierarchical sliding-mode under-actuated control with suitable conditions is designed, such that two motor currents asymptotically track two desired motor currents, respectively. Then the asymptotic tracking for the 2D position and orientation of a DMR is achieved. The simulations for various trajectories, completely and partially known frictions and uncertainties, and control parameters are presented to evaluate the effectiveness and robustness of the proposed method.