Double Sliding Surfaces based on a Sliding Mode Control for a Tracking Control of Mobile Robots

This paper proposes a double sliding surfaces based on a sliding mode control for a tracking control of nonholonomic mobile robots in the Cartesian coordinates. In order to remove sliding surface constraints, we design the additional sliding surface for the heading angle with respect to the newly defined coordinates. Then, we define the switching law based on the posture error to combine the designed sliding surface with the previous one. By using the double sliding surfaces and the switching law, we obtain the control law for arbitrary trajectories. It is proved that the position tracking error and the heading direction error asymptotically converge to zero, respectively, with the Lyapunov stability theory. Finally, through computer simulations, we demonstrate the effectiveness of the proposed control system.