@inproceedings{135bcb99a5ab4820bb0cc2b64f716bef,
title = "Convex hull asymptotic shape evolution",
abstract = "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.",
author = "Maxim Arnold and Yuliy Baryshnikov and Lavalle, {Steven M.}",
note = "Funding Information: Supported by grants from AFOSR (FA9550-10-1-0567) and ONR (N00014-11-1-0178). Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 2013.; 10th International Workshop on the Algorithmic Foundations of Robotics, WAFR 2012 ; Conference date: 13-06-2012 Through 15-06-2012",
year = "2013",
doi = "10.1007/978-3-642-36279-8_21",
language = "English (US)",
isbn = "9783642362781",
series = "Springer Tracts in Advanced Robotics",
publisher = "Springer",
pages = "349--364",
editor = "Emilio Frazzoli and Nicholas Roy and Tomas Lozano-Perez and Daniela Rus",
booktitle = "Springer Tracts in Advanced Robotics",
address = "Germany",
}