Feedback stabilization of nonlinear affine systems

A class of iterative methods have been proposed for the path planning of nonholonomic systems. These methods warp an initial path iteratively to an acceptable final path by using Newton-Raphson algorithms. In this paper we modify the iterative off-line method to render it a feedback controller. The main idea is to couple the iteration variable to the actual time, thus the control is executed during the path iteration, before convergence. We show that this scheme guarantees the closed loop asymptotic stability for systems with drift