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.