Stabilization of Trajectories for Systems with Nonholonomic Constraints

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G. Walsh, D. Tilbury, S. Sastry, R. Murray, and J-P. Laumond
IEEE T. Automatic Control, 39: (1) 216-222

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 paper 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 paper 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.