Path Planning with Forests of Random Trees: Parallelization with Super Linear Speedup ; CU-CS-1079-11

We propose a new parallelized high-dimensional single-query path planning technique that uses a coupled forest of random trees (i.e., instead of a single tree). We present both theoretical and experimental results that show using forests of random trees can lead to expected super linear speedup, with respect to the number of trees in the forest. In other words, with T trees running in parallel, we expect to get a particular quality result in less than 1/T the time required by a single tree (this is also known as having efficiency greater than 1). Our algorithm works by linking the random sampling and pruning mechanisms of all trees in the forest to the length of the current best path found by any tree. This enables all trees to avoid sampling from large portions of the configuration space that cannot possibly lead to better solutions, and increases speed by enabling trees to prune obsolete nodes. The current best solution is also passed between trees, so that it may be improved by any tree in the forest. Given the potential of super linear speedup, we additionally propose a sequential version of the forest algorithm that works by dividing computation time between each of T trees. We perform a series of experiments and find that both the parallel and sequential versions of the forest algorithm perform well in practice (e.g., vs. a single tree or smaller forests). To demonstrate that our algorithm is generally applicable, experiments are performed using two different state-of-the-art random tree algorithms for the underlying random trees. Theoretical analysis suggest that these results can be duplicated for any random tree path planning algorithm that meets a few requirements stated in the paper.