Analysis of Motion Planning by Sampling in Subspaces of Progressively Increasing Dimension

Despite the performance advantages of modern sampling-based motion planners, solving high dimensional planning problems in near real-time remains a challenge. Applications include hyper-redundant manipulators, snake-like and humanoid robots. Based on the intuition that many of these problem instances do not require the robots to exercise every degree of freedom independently, we introduce an enhancement to popular sampling-based planning algorithms aimed at circumventing the exponential dependence on dimensionality. We propose beginning the search in a lower dimensional subspace of the configuration space in the hopes that a simple solution will be found quickly. After a certain number of samples are generated, if no solution is found, we increase the dimension of the search subspace by one and continue sampling in the higher dimensional subspace. In the worst case, the search subspace expands to include the full configuration space - making the completeness properties identical to the underlying sampling-based planer. Our experiments comparing the enhanced and traditional version of RRT, RRT-Connect, and BidirectionalT-RRT on both a planar hyper-redundant manipulator and the Baxter humanoid robot indicate that a solution is typically found much faster using this approach and the run time appears to be less sensitive to the dimension of the full configuration space. We explore important implementation issues in the sampling process and discuss its limitations.