— We present an anytime algorithm for planning paths through high-dimensional, non-uniform cost search spaces. Our approach works by generating a series of Rapidly-exploring Random Trees (RRTs), where each tree reuses information from previous trees to improve its growth and the quality of its resulting path. We also present a number of modifications to the RRT algorithm that we use to bias the search in favor of less costly solutions. The resulting approach is able to produce an initial solution very quickly, then improve the quality of this solution while deliberation time allows. It is also able to guarantee that subsequent solutions will be better than all previous ones by a user-defined improvement bound. We demonstrate the effectiveness of the algorithm on both single robot and multirobot planning domains.