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:: 2018-08-20

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.

Copy to clipboard


                    Boardman, Beth, Harden, Troy, & Martínez, Sonia. Improved Performance of Asymptotically Optimal Rapidly Exploring Random Trees.  United States.  https://doi.org/10.1115/1.4040970

Copy to clipboard


                    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.

Copy to clipboard


                    
@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}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1115/1.4040970

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 1 work

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

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

Kavraki, L. E.; Svestka, P.; Latombe, J. -C.
IEEE Transactions on Robotics and Automation, Vol. 12, Issue 4
DOI: 10.1109/70.508439

Motion planning using adaptive random walks
journal, February 2005

Carpin, S.; Pillonetto, G.
IEEE Transactions on Robotics, Vol. 21, Issue 1
DOI: 10.1109/TRO.2004.833790

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

Karaman, Sertac; Frazzoli, Emilio
The International Journal of Robotics Research, Vol. 30, Issue 7
DOI: 10.1177/0278364911406761

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

Bruce, J. W.; Giblin, P. J.
Proceedings of the American Mathematical Society, Vol. 90, Issue 3
DOI: 10.1090/S0002-9939-1984-0728368-8

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

Dubins, L. E.
American Journal of Mathematics, Vol. 79, Issue 3
DOI: 10.2307/2372560

Anytime Motion Planning using the RRT*
conference, May 2011

Karaman, Sertac; Walter, Matthew R.; Perez, Alejandro
2011 IEEE International Conference on Robotics and Automation (ICRA)
DOI: 10.1109/ICRA.2011.5980479

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

Arslan, Oktay; Tsiotras, Panagiotis
2013 IEEE International Conference on Robotics and Automation (ICRA)
DOI: 10.1109/ICRA.2013.6630906

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

Akgun, Baris; Stilman, Mike
2011 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2011)
DOI: 10.1109/IROS.2011.6095077

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

Islam, Fahad; Nasir, Jauwairia; Malik, Usman
2012 IEEE International Conference on Mechatronics and Automation (ICMA)
DOI: 10.1109/ICMA.2012.6284384

Replanning with RRTs
conference, January 2006

Ferguson, D.; Kalra, N.; Stentz, A.
Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006.
DOI: 10.1109/ROBOT.2006.1641879

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

Zucker, Matt; Kuffner, James; Branicky, Michael
Proceedings 2007 IEEE International Conference on Robotics and Automation
DOI: 10.1109/ROBOT.2007.363553

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

Bruce, J.; Veloso, M.
IROS 2002: IEEE/RSJ International Conference on Intelligent Robots and Systems
DOI: 10.1109/IRDS.2002.1041624

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

Gayle, Russell; Klingler, Kristopher R.; Xavier, Patrick G.
Proceedings 2007 IEEE International Conference on Robotics and Automation
DOI: 10.1109/ROBOT.2007.363167

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

Kuffner, J. J.; LaValle, S. M.
2000 ICRA. IEEE International Conference on Robotics and Automation, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065)
DOI: 10.1109/ROBOT.2000.844730

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

Boardman, Beth; Harden, Troy; Martinez, Sonia
2014 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton)
DOI: 10.1109/ALLERTON.2014.7028567

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

Karaman, Sertac; Frazzoli, Emilio
2010 49th IEEE Conference on Decision and Control (CDC)
DOI: 10.1109/CDC.2010.5717430

Similar Records in DOE PAGES and OSTI.GOV collections:

Sampling-Based Motion Planning Algorithms for Replanning and Spatial Load Balancing

Technical Report Boardman, Beth Leigh

The common theme of this dissertation is sampling-based motion planning with the two key contributions being in the area of replanning and spatial load balancing for robotic systems. Here, we begin by recalling two sampling-based motion planners: the asymptotically optimal rapidly-exploring random tree (RRT*), and the asymptotically optimal probabilistic roadmap (PRM*). We also provide a brief background on collision cones and the Distributed Reactive Collision Avoidance (DRCA) algorithm. The next four chapters detail novel contributions for motion replanning in environments with unexpected static obstacles, for multi-agent collision avoidance, and spatial load balancing. First, we show improved performance of the RRT*more »« less
https://doi.org/10.2172/1400115

Full Text Available
Multi-agent motion planning with sporadic communications for collision avoidance

Journal Article Boardman, Beth Leigh ; Harden, Troy Anthony ; Martinez, Sonia - IFAC Journal of Systems and Control

Here, a novel multi-vehicle motion planning and collision avoidance algorithm is proposed and analyzed. The algorithm aims to reduce the amount of onboard calculations and inter-agent communications needed for each vehicle to successfully navigate through an environment with static obstacles and reach their goals. To this end, each agent first calculates a path to the goal by means of an asymptotically optimal rapidly-exploring random tree (RRT*) with respect to the static obstacles. Then, other agents are treated as dynamic obstacles and potential collisions are determined by means of collision cones. Collision cones depend on the position and velocity from othermore »« less
https://doi.org/10.1016/j.ifacsc.2020.100126

Full Text Available
Adversarial Sampling-Based Motion Planning

Journal Article Nichols, Hayden ; Jimenez, Mark ; Goddard, Zachary ; ... - IEEE Robotics and Automation Letters

In this report there are many scenarios in which a mobile agent may not want its path to be predictable. Examples include preserving privacy or confusing an adversary. However, this desire for deception can conflict with the need for a low path cost. Optimal plans such as those produced by RRT* may have low path cost, but their optimality makes them predictable. Similarly, a deceptive path that features numerous zig-zags may take too long to reach the goal. We address this trade-off by drawing inspiration from adversarial machine learning. We propose a new planning algorithm, which we title Adversarial RRT*.more »« less
https://doi.org/10.1109/LRA.2022.3148464
The Frobenius metric in image registration: Technical report

Technical Report Zikan, K ; Silberberg, T M

Image registration involves estimating how one set of n-dimensional points is rotated, scaled, and translated into a second set of n-dimensional points. In practice, n is usually 2 or 3. We consider a Frobenius norm approach in which a point-to-point matching between the sets (if they are of the same cardinalities) and the corresponding transformation are determined. Two strategies are investigated: the pruned tree approach and the parametric linear programming approach. Various versions of tree pruning approach have been investigated by other authors, whereas the parametric programming method is believed to be new. It addresses several inherent problems of themore »« less
Hybrid Parallel Contour Trees, Version 1.0

Software Sewell, Christopher ; Fasel, Patricia ; Carr, Hamish ; ...

A common operation in scientific visualization is to compute and render a contour of a data set. Given a function of the form f : R^d -> R, a level set is defined as an inverse image f^-1(h) for an isovalue h, and a contour is a single connected component of a level set. The Reeb graph can then be defined to be the result of contracting each contour to a single point, and is well defined for Euclidean spaces or for general manifolds. For simple domains, the graph is guaranteed to be a tree, and is called the contourmore »« less
View Software

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