On a Wheeledmobile Robot Trajectory Tracking Control: 1st and 2nd Order Sliding Modes Applied to a Compensated Inverse Dynamics
Résumé
In this paper, a trajectory tracking control for a nonholonomic wheeled mobile robot based on the compensated inverse dynamics approach combined with sliding mode control strategies is investigated. The main advantages of using sliding mode control are robustness to parameter uncertainty, insensitivity to load disturbance, and fast dynamics response. But the major drawback of sliding mode control is the so called chattering phenomenon. As an initial procedure a first order sliding mode control law in connection with inverse dynamics is described. In this case the chattering effects appears directly in the control signal, because it acts in first order derivative of the sliding surface. To overcome this situation higher order sliding modes were proposed in literature, in which the control acts on a high order derivative of the surface $\sigma(x)$. So next, a second order sliding mode technique is presented. It consists of forcing a second order sliding mode on a surface $\sigma(x)$, in the system state space, with $\dot{s}(x)$ identically equal to zero, by using a control signal depending on $\sigma(x)$, but directly acting only on $\ddot{\sigma}(x)$. The advantage of this latter approach is mainly related to its chattering reduction capability. Analysis and numerical simulations are provided to show the effectiveness of the investigated control strategy