Stabilization of trajectories for systems with nonholonomic constraints

A technique for stabilizing nonholonomic systems to trajectories is presented. It is well known that such systems cannot be stabilized to a point using smooth static-state feedback. The authors suggest the use of control laws for stabilizing a system about a trajectory, instead of a point. Given a nonlinear system and a desired nominal feasible trajectory, an explicit control law which will locally exponentially stabilize the system to the desired trajectory is given. The theory is applied to several examples, including a car-like robot.