Asymptotic feedback stabilization of a nonholonomic mobile robot using a nonlinear oscillator

Abstract

This paper addresses the problem of point-to-point stabilization of a two-wheeled mobile robot. It is well known that there does not exist a smooth static state feedback controller for the stabilization of the mobile robot to arbitrary fixed postures. Researchers in the past have therefore used smooth time-varying control, piecewise smooth control and hybrid control for stabilization. In this paper we present a piecewise smooth dynamic controller for the global asymptotic stabilization of the mobile robot. As different from other piecewise smooth controllers, our controller has at most one switching, otherwise it is smooth. Our controller is also dynamic in the sense that the control inputs are obtained as a solution to a first order differential equation and convergence to the desired posture is guaranteed for any nonzero initial condition. The controller, inherently simple in its formulation, uses the dynamics of a nonlinear oscillator that plays a key role in preventing the mobile robot from getting stuck at any point other than the desired posture. The controller guarantees the simultaneous asymptotic stabilization of the states of the mobile robot to their desired values and the states of the oscillator to zero. Simulation results presented aptly demonstrate the efficacy of the stabilizing control.