On the power of manifold samples in exploring configuration spaces and the dimensionality of narrow passages

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

Abstract

We extend our study of Motion Planning via Manifold Samples (MMS), a general algorithmic framework that combines geometric methods for the exact and complete analysis of low-dimensional configuration spaces with sampling-based approaches that are appropriate for higher dimensions. The framework explores the configuration space by taking samples that are low-dimensional manifolds of the configuration space capturing its connectivity much better than isolated point samples. The contributions of this paper are as follows: (i) We present a recursive application of MMS in a sixdimensional configuration space, enabling the coordination of two polygonal robots translating and rotating amidst polygonal obstacles. In the adduced experiments for the more demanding test cases MMS clearly outperforms PRM, with over 20-fold speedup in a coordination-tight setting. (ii) A probabilistic completeness proof for the most prevalent case, namely MMS with samples that are affine subspaces. (iii) A closer examination of the test cases reveals that MMS has, in comparison to standard sampling-based algorithms, a significant advantage in scenarios containing high-dimensional narrow passages. This provokes a novel characterization of narrow passages which attempts to capture their dimensionality, an attribute that had been (to a large extent) unattended in previous definitions.

Original languageEnglish
Title of host publicationSpringer Tracts in Advanced Robotics
EditorsEmilio Frazzoli, Nicholas Roy, Tomas Lozano-Perez, Daniela Rus
Pages313-329
Number of pages17
DOIs
StatePublished - 2013
Event10th International Workshop on the Algorithmic Foundations of Robotics, WAFR 2012 - Cambridge, United States
Duration: 13 Jun 201215 Jun 2012

Publication series

NameSpringer Tracts in Advanced Robotics
Volume86

Conference

Conference10th International Workshop on the Algorithmic Foundations of Robotics, WAFR 2012
Country/TerritoryUnited States
CityCambridge
Period13/06/1215/06/12

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering
  • Artificial Intelligence

Fingerprint

Dive into the research topics of 'On the power of manifold samples in exploring configuration spaces and the dimensionality of narrow passages'. Together they form a unique fingerprint.

Cite this