Convex hull asymptotic shape evolution

Maxim Arnold, Yuliy Baryshnikov, Steven M. Lavalle

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)


The asymptotic properties of Rapidly exploring Random Tree (RRT) growth in large spaces is studied both in simulation and analysis. The main phenomenon is that the convex hull of the RRT reliably evolves into an equilateral triangle when grown in a symmetric planar region (a disk). To characterize this and related phenomena from flocking and swarming, a family of dynamical systems based on incremental evolution in the space of shapes is introduced. Basins of attraction over the shape space explain why the number of hull vertices tends to reduce and the shape stabilizes to a regular polygon with no more than four vertices.

Original languageEnglish
Title of host publicationSpringer Tracts in Advanced Robotics
EditorsEmilio Frazzoli, Nicholas Roy, Tomas Lozano-Perez, Daniela Rus
PublisherSpringer Verlag
Number of pages16
ISBN (Print)9783642362781
Publication statusPublished - Jan 1 2013
Externally publishedYes
Event10th International Workshop on the Algorithmic Foundations of Robotics, WAFR 2012 - Cambridge, United States
Duration: Jun 13 2012Jun 15 2012

Publication series

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


Conference10th International Workshop on the Algorithmic Foundations of Robotics, WAFR 2012
Country/TerritoryUnited States

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering
  • Artificial Intelligence


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