Stabilization of trajectories for systems with nonholonomic constraints

Abstract

A new 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. In this note, we 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, the note gives an explicit control law which will locally exponentially stabilize the system to the desired trajectory. The theory is applied to several examples, including a car-like robot.

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