3D path planning based on nonlinear geodesic equation

A lot of methods have been proposed for 2D path planning of mobile robot, which could be a mobile platform or a wheelchair, in planar maps. This paper addresses a concept of the shortest path planning for a mobile robot to traverse a 3D surface, which is a parametrized regular surface that models the non-flat terrain on which the mobile robot traverses. Geodesic curve linking a given start to a given target that is locally shortest on non-flat terrain is used as path. Nonlinear geodesic equations are computed by a gradient descent method with energy function of geodesic, which is shown to converge to the geodesic path in a neighborhood of target position in which a certain Lipschitz condition holds.We present numerical simulations to illustrate the geodesic path planning on non-flat terrains.