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Space-filling trees: A new perspective on incremental search for motion planning

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2 Author(s)
James J. Kuffner ; The Robotics Institute, Carnegie Mellon University, Pittsburgh, PA, 15213 USA ; Steven M. LaValle

This paper introduces space-filling trees and analyzes them in the context of sampling-based motion planning. Space-filling trees are analogous to space-filling curves, but have a branching, tree-like structure, and are defined by an incremental process that results in a tree for which every point in the space has a finite-length path that converges to it. In contrast to space-filling curves, individual paths in the tree are short, allowing any part of the space to be quickly reached from the root. We compare some basic constructions of space-filling trees to Rapidly-exploring Random Trees (RRTs), which underlie a number of popular algorithms used for sampling-based motion planning. We characterize several key tree properties related to path quality and the overall efficiency of exploration and conclude with a number of open mathematical questions.

Published in:

2011 IEEE/RSJ International Conference on Intelligent Robots and Systems

Date of Conference:

25-30 Sept. 2011