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

• Published in: IEEE transactions on robotics Vol. 32; no. 3; pp. 473 - 483
• Main Authors: Salzman, Oren, Halperin, Dan
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.06.2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithm design and analysis; Algorithms; Approximation; Approximation algorithms; Asymptotic methods; Asymptotic properties; Convergence; Data structures; Graphs; Heuristic algorithms; Interpolation; Mathematical analysis; Motion control; Motion planning; nonholonomic motion planning; Optimization; Planning; Robots; nonholonomic motion planning; Motion control
• ISSN: 1552-3098; 1941-0468
• DOI: 10.1109/TRO.2016.2539377

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.