Multiresolution path-planning with traversal costs based on time-varying spatial fields

We address the problem of finding an optimal path for a vehicle in a planar environment where traversal costs are based on a time-varying spatial field defined over the environment. We assume that the accuracy with which the values of the spatial field are known gradually decreases with increasing distance from the vehicle´s current location. To extend previous results in the literature, we present a wavelet transform-based multiresolution motion-planning approach that incorporates traversal costs based on a time-varying spatial field. To enable fast online computations, we use 2D wavelet transforms with time-varying coefficients, instead of computing wavelet transforms with three independent variables. We discuss methods to compute time-varying traversal costs and an optimal path with a multiresolution approximation of the spatial field, we illustrate the proposed approach with a simulation example.