Nonholonomic path-planning with obstacle avoidance: a path-space approach

For the problem of nonholonomic motion planning in the presence of obstacles, a path-iteration algorithm with an "exterior penalty" function has recently been proposed. The convergence of the iterative algorithm requires the avoidance of singular controls. With the inclusion of a penalty function, the set of singular control may increase substantially. In this paper, we propose a specific guideline for choosing the penalty function which does not introduce additional singular controls. In the case of the N-trailer system, this result can be used to guarantee the convergence of the path planning algorithm. To demonstrate the effectiveness of the proposed algorithm, simulation results are included.