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Title: Improved Performance of Asymptotically Optimal Rapidly Exploring Random Trees

Abstract

Three algorithms that improve the performance of the asymptotically optimal Rapidly exploring Random Tree (RRT*) are presented here. First, we introduce the Goal Tree (GT) algorithm for motion planning in dynamic environments where unexpected obstacles appear sporadically. The GT reuses the previous RRT* by pruning the affected area and then extending the tree by drawing samples from a shadow set. The shadow is the subset of the free configuration space containing all configurations that have geodesics ending at the goal and are in conflict with the new obstacle. Smaller, well defined, sampling regions are considered for Euclidean metric spaces and Dubins' vehicles. Next, the Focused-Refinement (FR) algorithm, which samples with some probability around the first path found by an RRT*, is defined. The third improvement is the Grandparent-Connection (GP) algorithm, which attempts to connect an added vertex directly to its grandparent vertex instead of parent. The GT and GP algorithms are both proven to be asymptotically optimal. Finally, the three algorithms are simulated and compared for a Euclidean metric robot, a Dubins' vehicle, and a seven degrees-of-freedom manipulator.

Authors:
ORCiD logo [1]; ORCiD logo [1];  [2]
+ Show Author Affiliations
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Univ. of California, San Diego, CA (United States). Dept. of Mechanical Engineering
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1467259
Report Number(s):
LA-UR-17-24020
Journal ID: ISSN 0022-0434
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Dynamic Systems, Measurement, and Control
Additional Journal Information:
Journal Volume: 141; Journal Issue: 1; Journal ID: ISSN 0022-0434
Publisher:
ASME
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 42 ENGINEERING; Motion Planning, Robotics

Citation Formats

Boardman, Beth, Harden, Troy, and Martínez, Sonia. Improved Performance of Asymptotically Optimal Rapidly Exploring Random Trees. United States: N. p., 2018. Web. doi:10.1115/1.4040970.
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Boardman, Beth, Harden, Troy, & Martínez, Sonia. Improved Performance of Asymptotically Optimal Rapidly Exploring Random Trees. United States. doi:https://doi.org/10.1115/1.4040970
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Boardman, Beth, Harden, Troy, and Martínez, Sonia. Mon . "Improved Performance of Asymptotically Optimal Rapidly Exploring Random Trees". United States. doi:https://doi.org/10.1115/1.4040970. https://www.osti.gov/servlets/purl/1467259.
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@article{osti_1467259,
title = {Improved Performance of Asymptotically Optimal Rapidly Exploring Random Trees},
author = {Boardman, Beth and Harden, Troy and Martínez, Sonia},
abstractNote = {Three algorithms that improve the performance of the asymptotically optimal Rapidly exploring Random Tree (RRT*) are presented here. First, we introduce the Goal Tree (GT) algorithm for motion planning in dynamic environments where unexpected obstacles appear sporadically. The GT reuses the previous RRT* by pruning the affected area and then extending the tree by drawing samples from a shadow set. The shadow is the subset of the free configuration space containing all configurations that have geodesics ending at the goal and are in conflict with the new obstacle. Smaller, well defined, sampling regions are considered for Euclidean metric spaces and Dubins' vehicles. Next, the Focused-Refinement (FR) algorithm, which samples with some probability around the first path found by an RRT*, is defined. The third improvement is the Grandparent-Connection (GP) algorithm, which attempts to connect an added vertex directly to its grandparent vertex instead of parent. The GT and GP algorithms are both proven to be asymptotically optimal. Finally, the three algorithms are simulated and compared for a Euclidean metric robot, a Dubins' vehicle, and a seven degrees-of-freedom manipulator.},
doi = {10.1115/1.4040970},
journal = {Journal of Dynamic Systems, Measurement, and Control},
number = 1,
volume = 141,
place = {United States},
year = {2018},
month = {8}
}
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DOI:  https://doi.org/10.1115/1.4040970
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