The problem of finding a stabilizing control for a wheeled robot with constrained control resource is studied. The goal of the control is to bring the robot to an assigned path and to stabilize its motion along it. A new change of variable is suggested that reduces the problem of stabilizing robot's motion to that of stabilizing the zero solution in the form that admits feedback linearization. A control law stabilizing robot's motion along an arbitrary feasible curvilinear target path is synthesized. For a straight target path, the closed-loop system is shown to be asymptotically stable for any initial conditions except for the case where the initial direction of motion is perpendicular to the target path.