Multi-resolution path planning: Theoretical analysis, efficient implementation, and extensions to dynamic environments

A multi-resolution path planning algorithm based on the wavelet transform of the environment has been reported previously in the literature. In this paper, we provide a proof of completeness of this algorithm. In addition, we present an implementation of this algorithm that reuses information obtained in previous iterations to perform subsequent iterations more efficiently. Finally, we extend this path planning algorithm to dynamic environments by presenting a simple scheme for updating the wavelet transform coefficients to reflect changes in the environment.