Revisiting the Asymptotic Optimality of RRT
Kiril Solovey, Lucas Janson, Edward Schmerling, Emilio Frazzoli, Marco Pavone
Abstract
RRT* is one of the most widely used sampling-based algorithms for asymptotically-optimal motion planning. RRT* laid the foundations for optimality in motion planning as a whole, and inspired the development of numerous new algorithms in the field, many of which build upon RRT* itself. In this paper, we first identify a logical gap in the optimality proof of RRT*, which was developed by Karaman and Frazzoli (2011). Then, we present an alternative and mathematically-rigorous proof for asymptotic optimality. Our proof suggests that the connection radius used by RRT* should be increased from γ (log n/n)1/d to γ' (log n/n)1/(d+1) in order to account n n for the additional dimension of time that dictates the samples' ordering. Here γ, γ' are constants, and n, d are the number of samples and the dimension of the problem, respectively.
BibTeX
@inproceedings{icra2020_revisitingtheasy,
title = {Revisiting the Asymptotic Optimality of RRT},
author = {Kiril Solovey and Lucas Janson and Edward Schmerling and Emilio Frazzoli and Marco Pavone},
booktitle = {ICRA 2020},
year = {2020}
}