Sampling-diagram automata: A tool for analyzing path quality in tree planners

Oren Nechushtan*, Barak Raveh, Dan Halperin

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Sampling-based motion planners are a central tool for solving motion-planning problems in a variety of domains, but the theoretical understanding of their behavior remains limited, in particular with respect to the quality of the paths they generate (in terms of path length, clearance, etc.). In this paper we prove, for a simple family of obstacle settings, that the popular dual-tree planner Bi-RRT may produce low-quality paths that are arbitrarily worse than optimal with modest but significant probability, and overlook higher-quality paths even when such paths are easy to produce. At the core of our analysis are probabilistic automata designed to reach an accepting state when a path of significantly low quality has been generated. Complementary experiments suggest that our theoretical bounds are conservative and could be further improved. To the best of our knowledge, this is the first work to study the attainability of high-quality paths that occupy a significant (non-negligible) portion of the space of all paths. The formalism presented in this work can be generalized to other algorithms and other motion-planning problems by defining appropriate predicates, and pave the way to deeper understanding of hallmark planning algorithms.

Original languageEnglish
Title of host publicationAlgorithmic Foundations of Robotics IX - Selected Contributions of the Ninth International Workshop on the Algorithmic Foundations of Robotics
Pages285-301
Number of pages17
EditionSTAR
DOIs
StatePublished - 2010
Event9th International Workshop on the Algorithmic Foundations of Robotics, WAFR 2010 - Singapore, Singapore
Duration: 13 Dec 201015 Dec 2010

Publication series

NameSpringer Tracts in Advanced Robotics
NumberSTAR
Volume68
ISSN (Print)1610-7438
ISSN (Electronic)1610-742X

Conference

Conference9th International Workshop on the Algorithmic Foundations of Robotics, WAFR 2010
Country/TerritorySingapore
CitySingapore
Period13/12/1015/12/10

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