Robust path-following control with exponential stability for mobile robots

Abstract

We present a new method for determining a path following controller for a nonholonomic mobile robot, which is robust with respect to position and orientation errors. We consider the kinematic model of a unicycle and dynamic extension. The control design is based on a change of variables allowing to define a set of n decoupled auxiliary variables. The exponential convergence of the state variables is deduced from the convergence of the auxiliary variables. We prove the control robustness by showing that, when the state variables measurement is noisy, the representative point of the system converges towards a compact attractive domain centred at the equilibrium point. As the auxiliary variables are decoupled, the computation of this attractive domain is done in a very simple and accurate way. The determination of such a domain can be used to determine a security margin to avoid obstacles during the path following process.