Research Papers

Improved Performance of Asymptotically Optimal Rapidly Exploring Random Trees

[+] Author and Article Information
Beth Boardman

Applied Engineering and Technology,
Los Alamos National Laboratory,
Los Alamos, NM 87545
e-mail: bboardman@lanl.gov

Troy Harden

Applied Engineering and Technology,
Los Alamos National Laboratory,
Los Alamos, NM 87545
e-mail: harden@lanl.gov

Sonia Martínez

Department of Mechanical Engineering,
University of California,
San Diego, CA 92093-0411
e-mail: soniamd@ucsd.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received May 18, 2017; final manuscript received July 19, 2018; published online August 20, 2018. Assoc. Editor: Suman Chakravorty.

J. Dyn. Sys., Meas., Control 141(1), 011002 (Aug 20, 2018) (10 pages) Paper No: DS-17-1259; doi: 10.1115/1.4040970 History: Received May 18, 2017; Revised July 19, 2018

Three algorithms that improve the performance of the asymptotically optimal Rapidly exploring Random Tree (RRT*) are presented in this paper. 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.

Copyright © 2019 by ASME
Topics: Algorithms , Vehicles
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Grahic Jump Location
Fig. 1

An illustrative example on choosing xnew when refining a single path. The rectangle is an obstacle in the environment. The dots are the set of vertices, VΠ, used to determine the region from which xnew is sampled. The k-component of xnew is a uniform random sample between the maximum and minimum (plus and minus ε, respectively) k-component values from VΠ. Next, with respect to xnewk, determine the nearest k-component from VΠ and label its corresponding j-component as xnearestj. Finally, xnewj is a random value from between xnearestj−ε and xnearestj+ε, ε>0. Sample xnew is represented as the green dot.

Grahic Jump Location
Fig. 2

The sampling region for a Dubins' vehicle as described in Definition 4

Grahic Jump Location
Fig. 3

Typical Dubins' vehicle trees in the 25 obstacle environment found by the (a) RRT*, (b) Grandparent-Connection, (c) Grandparent Connection with Focused-Refinement, (d) Focused Refinement, (e) RRT*-Smart, and (f) RRT with path smoothing algorithms

Grahic Jump Location
Fig. 4

Typical Dubins' vehicle trees after replanning in the 26 obstacle environment using the RRT* and GT algorithms: (a) RRT* and (b) Goal Tree

Grahic Jump Location
Fig. 5

The box is added to the environment so that it is in conflict with the manipulator's path

Grahic Jump Location
Fig. 6

The Goal Tree algorithm successfully replans to find a collision-free path



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