Design of smooth dynamic feedback for stabilization of nonholonomic systems

In this paper, a new technique for stabilization of nonlinear (nonholonomic) systems by smooth dynamic feedback is proposed. This technique is based on the authors´ design of the smooth (time-invariant) feedback for asymptotic stabilization of a nonholonomic system on the equilibrium manifold. The authors use this feedback, in conjunction with the averaging solution to the nonholonomic motion planning problem, in order to design an explicitly time-dependent dynamic feedback that ensures convergence of the state vector to the state space origin. The authors discuss the advantages of the proposed technique with respect to other comparable approaches. Furthermore, the authors consider a class of chained canonical systems, and demonstrate an interesting and surprising result: a chained system controlled by the time-invariant dynamic feedback formulated in this paper converges to an arbitrary small ball centered at the origin under certain circumstances. Examples and simulations are provided for illustration