Many nonholonomic mechanical systems, such as common wheeled mobile robots, are controllable but cannot be stabilized to given positions and orientations bv using smooth pure-state feedback control. However, as shown in Samson (1990), such systems may still be stabilized by using smooth time-varying feedbacks,—i.e., feedbacks that explicitly depend on the time variable. This possibility is here applied to the stabilization of a class of nonlinear systems whose equations encompass simple car models. A set of stabilizing smooth time-varying feedbacks is derived, and simulation results are given.
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