Asymptotically Near-Optimal RRT for Fast, High-Quality Motion Planning

Abstract

We present lower bound tree-RRT (LBT-RRT), a single-query sampling-based motion-planning algorithm that is asymptotically near-optimal . Namely, the solution extracted from LBT-RRT converges to a solution that is within an approximation factor of $1+\boldsymbol{\varepsilon}$ of the optimal solution. Our algorithm allows for a continuous interpolation between the fast RRT algorithm and the asymptotically optimal RRT* and RRG algorithms when the cost function is the path length. When the approximation factor is $\text{1}$ (i.e., no approximation is allowed), LBT-RRT behaves like RRG. When the approximation factor is unbounded, LBT-RRT behaves like RRT. In between, LBT-RRT is shown to produce paths that have higher quality than RRT would produce and run faster than RRT* would run. This is done by maintaining a tree that is a subgraph of the RRG roadmap and a second, auxiliary graph, which we call the lower-bound graph. The combination of the two roadmaps, which is faster to maintain than the roadmap maintained by RRT*, efficiently guarantees asymptotic near-optimality. We suggest to use LBT-RRT for high-quality anytime motion planning. We demonstrate the performance of the algorithm for scenarios ranging from 3 to 12 degrees of freedom and show that even for small approximation factors, the algorithm produces high-quality solutions (comparable with RRG and RRT*) with little running-time overhead when compared with RRT.