Corrections to "Probabilistic Completeness of RRT for Geometric and Kinodynamic Planning With Forward Propagation"
Michal Kleinbort, Kiril Solovey, Zakary Littlefield, Kostas E. Bekris, Dan Halperin
Abstract
Our original publication Kleinbort et al. (2019) contains an error in the analysis of the case of the kinodynamic RRT. Here, we rectify the problem by modifying the proof of Theorem <xref ref-type="theorem" rid="theorem2" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</xref> , which, in particular, necessitated a revision of Lemma <xref ref-type="lemma" rid="lemma1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</xref> . Briefly, the original (and erroneous) proof of Theorem <xref ref-type="theorem" rid="theorem2" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</xref> used a sequence of equal-size balls. The correction uses a sequence of balls of increasing radii. We emphasize that the correction is in Lemma <xref ref-type="lemma" rid="lemma1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</xref> and the proof of Theorem <xref ref-type="theorem" rid="theorem2" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</xref> only. The main results remain unchanged.
BibTeX
@inproceedings{ral2023_correctionstopro,
title = {Corrections to "Probabilistic Completeness of RRT for Geometric and Kinodynamic Planning With Forward Propagation"},
author = {Michal Kleinbort and Kiril Solovey and Zakary Littlefield and Kostas E. Bekris and Dan Halperin},
booktitle = {RA-L 2023},
year = {2023}
}