A preliminary study of the problem of the feedback control of mobile robots is presented. The robot considered is a two-wheel-driven nonholonomic cart. Despite the controllability of the system, pure state feedback stabilization of the cart's configuration around a given terminal configuration is not possible. However, feedback stabilization of the position of any point of the cart is possible. Extension to the problem of trajectory tracking in Cartesian space is then considered, and it is shown that stabilization of the cart's configuration around the configuration of a virtual reference cart becomes possible as long as the reference cart keeps moving. Several simple control laws are proposed, and simulation results are given. Connections with the path planning problem are pointed out.>

When a nonlinear system is not stabilizable by a smooth state feedback, it is common to think of the discontinuous feedback as being the alternative. However, another possibility is to consider a smooth time-varying feedback in which the independent time index plays the role of an extra variable. This possibility is illustrated in the case of two degrees-of-freedom nonholonomic wheeled mobile robot for which the globally stabilizing smooth feedback is derived.>