A covering projection for robot navigation under strong anisotropy

Path planning can be subject to different types of optimization. Some years ago a German researcher, U. Leuthausser, proposed a new variational method for reducing most types of optimization criteria to one and the same: minimization of path length. This can be done by altering the Riemannian metric of the domain, so that optimal paths (with respect to whatever criterion) are simply seen as shortest. This method offers an extra feature, which has not been exploited so far: it admits direction-dependent criteria. In this paper we make this feature explicit, and apply it to two different anisotropic settings. One is that of different costs for different directions: E.g. the situation of a countryside scene with ploughed fields. The second is dependence on oriented directions, which is called here "strong" anisotropy: the typical scene is that of a hill side. A covering projection solves the additional difficulty. We also provide some experimental results on synthetic data.