Exponential stabilization of mobile robots with nonholonomic constraints

The authors present an exponentially stable controller for a two degree of freedom robot with nonholonomic constraints. They propose a piecewise smooth controller to make the origin exponentially stable for any initial condition in the state space. The main difference with respect to other approaches can be summarized as follow. The proposed scheme does not seek to render the discontinuous surface invariant, as opposed to the principles of sliding control, but rather to make this surface non-attractive. Infinite switching in the control law and the undesirable chattering phenomenon, can thus be avoided. Furthermore, this control law yields exponential stability so that the convergence can be chosen arbitrarily fast