Optimal Paths in a Constrained Image Plane for Purely Image-Based Parking

This paper presents a correct solution to the optimal feedback control for a nonholonomic vehicle with limited field-of-view. Previous work on this subject has shown that the search for a shortest path can be limited to simple families of trajectories. We preliminarily provide an extension of the alphabet of optimal control words, to cover some regions of the vehicle plane where the synthesis of turns out to be suboptimal. The main contribution of this paper is an algorithm to translate the optimal synthesis to the image plane, thus enabling a purely image-based optimal control scheme. This allows better performance and increases the robustness of the overall process, avoiding the need of slowly-converging and error-prone parameter estimation algorithms. Simulations and experiments are reported which demonstrate the effectiveness of the proposed technique.