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

Oren Salzman and Dan Halperin
IEEE Trans. Robotics, Vol. 32, No. 3, pp. 473-483, June, 2016

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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 + ε 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 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.

BibTeX Reference
title = {Asymptotically Near-Optimal RRT for Fast, High-Quality Motion Planning},
author = {Oren Salzman and Dan Halperin},
booktitle = {IEEE Trans. Robotics},
notes = {http://ieeexplore.ieee.org/document/7452671/},
month = {June},
year = {2016},
volume = {32},
number = {3},
pages = {473-483},