Locally Computable Navigation Functions for Sphere Worlds

In this paper we present a new navigation function for a sphere world that can be computed locally with limited knowledge of the environment. By requiring smooth and not analytic NF, the effect of each obstacle is exactly nullified outside a sensing zone around the obstacle (the only required parameter is the width of the sensing zone). This allows the computation of the navigation function using information from a single obstacle each time. We present simulations to verify the validity of this approach.