Feedback Stabilization of Nonholonomic Systems in Presence of Obstacles

A class of iterative methods have recently 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 or gradient type of algorithms. Once a path is found off-line, a feedback controller is then used to follow the path. In this paper, we propose a modification of these off-line methods to transform them directly into 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 the convergence. We show that this scheme guarantees the closed loop asymptotic stability when the system model is known, and possesses certain robustness when the model information is imperfect. By using interior penalty functions, inequality constraints can also be handled by the algorithm. Simulation results are included, showing promise of the approach.