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Asymptotically near-optimal RRT for fast, high-quality, motion planning

Oren Salzman and Dan Halperin
Conference Paper, Carnegie Mellon University, IEEE International Conference on Robotics and Automation (ICRA), pp. 4680-4685, May, 2014

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We present Lower Bound Tree-RRT (LBT-RRT), a single-query sampling-based 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 approximation factor is 1 (i.e., no approximation is allowed), LBT-RRT behaves like the RRT* algorithm. When the approximation factor is unbounded, LBT-RRT behaves like the RRT algorithm. 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 which is a sub-graph of the RRG roadmap and a second, auxiliary tree, which we call the lower-bound tree. The combination of the two trees, which is faster to maintain than the tree maintained by RRT*, efficiently guarantee 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 to RRT*) with little runtime overhead when compared to RRT.

BibTeX Reference
title = {Asymptotically near-optimal RRT for fast, high-quality, motion planning},
author = {Oren Salzman and Dan Halperin},
booktitle = {IEEE International Conference on Robotics and Automation (ICRA)},
school = {Robotics Institute , Carnegie Mellon University},
month = {May},
year = {2014},
pages = {4680-4685},
address = {Pittsburgh, PA},