Improved Performance of Asymptotically Optimal Rapidly Exploring Random Trees

Boardman, Beth; Harden, Troy; Martínez, Sonia

doi:10.1115/1.4040970

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:

^[1];

^[1]; Martínez, Sonia ^[2]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Univ. of California, San Diego, CA (United States). Dept. of Mechanical Engineering

Publication Date:: Mon Aug 20 00:00:00 EDT 2018

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.  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.  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         = {Mon Aug 20 00:00:00 EDT 2018},

  month        = {Mon Aug 20 00:00:00 EDT 2018}

}

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Works referenced in this record:

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Similar Records

Title: Improved Performance of Asymptotically Optimal Rapidly Exploring Random Trees

Abstract

Citation Formats

Probabilistic roadmaps for path planning in high-dimensional configuration spaces journal, January 1996

Motion planning using adaptive random walks journal, February 2005

Sampling-based algorithms for optimal motion planning journal, June 2011

An elementary approach to generic properties of plane curves journal, March 1984

On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents journal, July 1957

Anytime Motion Planning using the RRT* conference, May 2011

Use of relaxation methods in sampling-based algorithms for optimal motion planning conference, May 2013

Sampling heuristics for optimal motion planning in high dimensions conference, September 2011

RRT∗-Smart: Rapid convergence implementation of RRT∗ towards optimal solution conference, August 2012

Replanning with RRTs conference, January 2006

Multipartite RRTs for Rapid Replanning in Dynamic Environments conference, April 2007

Real-time randomized path planning for robot navigation conference, January 2002

Lazy Reconfiguration Forest (LRF) - An Approach for Motion Planning with Multiple Tasks in Dynamic Environments conference, April 2007

RRT-connect: An efficient approach to single-query path planning conference, January 2000

Optimal kinodynamic motion planning in environments with unexpected obstacles conference, September 2014

Optimal kinodynamic motion planning using incremental sampling-based methods conference, December 2010

Probabilistic roadmaps for path planning in high-dimensional configuration spaces
journal, January 1996

Motion planning using adaptive random walks
journal, February 2005

Sampling-based algorithms for optimal motion planning
journal, June 2011

An elementary approach to generic properties of plane curves
journal, March 1984

On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents
journal, July 1957

Anytime Motion Planning using the RRT*
conference, May 2011

Use of relaxation methods in sampling-based algorithms for optimal motion planning
conference, May 2013

Sampling heuristics for optimal motion planning in high dimensions
conference, September 2011

RRT^∗-Smart: Rapid convergence implementation of RRT^∗ towards optimal solution
conference, August 2012

Replanning with RRTs
conference, January 2006

Multipartite RRTs for Rapid Replanning in Dynamic Environments
conference, April 2007

Real-time randomized path planning for robot navigation
conference, January 2002

Lazy Reconfiguration Forest (LRF) - An Approach for Motion Planning with Multiple Tasks in Dynamic Environments
conference, April 2007

RRT-connect: An efficient approach to single-query path planning
conference, January 2000

Optimal kinodynamic motion planning in environments with unexpected obstacles
conference, September 2014

Optimal kinodynamic motion planning using incremental sampling-based methods
conference, December 2010