STABILIZATION OF TRAJECTORIES FOR SYSTEMS WITH NONHOLONOMIC CONSTRAINTS

A new technique for stabilizing nonholonomic systems to trajectories i s presented. It is well known (see [2]) that such systems cannot be st abilized to a point using smooth static-state feedback. In this note, we suggest the use of control laws for stabilizing a system about a tr ajectory, instead of a point. Given a nonlinear system and a desired ( nominal) feasible trajectory, the note gives an explicit control law w hich will locally exponentially stabilize the system to the desired tr ajectory. The theory is applied to several examples, including a car-l ike robot.