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Research Papers

Planning the Shortest Path in Cluttered Environments: A Review and a Planar Convex Hull-Based Approach

[+] Author and Article Information
Nafiseh Masoudi

Department of Mechanical Engineering,
Clemson University,
Clemson, SC 29634
e-mail: nmasoud@clemson.edu

Georges M. Fadel

Fellow ASME
Department of Mechanical Engineering,
Clemson University,
Clemson, SC 29634
e-mail: fgeorge@clemson.edu

Margaret M. Wiecek

Department of Mathematical Sciences,
Clemson University,
Clemson, SC 29634
e-mail: wmalgor@clemson.edu

Manuscript received October 6, 2018; final manuscript received April 16, 2019; published online June 7, 2019. Assoc. Editor: Nabil Anwer.

J. Comput. Inf. Sci. Eng 19(4), 041011 (Jun 07, 2019) (11 pages) Paper No: JCISE-18-1274; doi: 10.1115/1.4043566 History: Received October 06, 2018; Accepted April 16, 2019

Routing or path-planning is the problem of finding a collision-free and preferably shortest path in an environment usually scattered with polygonal or polyhedral obstacles. The geometric algorithms oftentimes tackle the problem by modeling the environment as a collision-free graph. Search algorithms such as Dijkstra’s can then be applied to find an optimal path on the created graph. Previously developed methods to construct the collision-free graph, without loss of generality, explore the entire workspace of the problem. For the single-source single-destination planning problems, this results in generating some unnecessary information that has little value and could increase the time complexity of the algorithm. In this paper, first a comprehensive review of the previous studies on the path-planning subject is presented. Next, an approach to address the planar problem based on the notion of convex hulls is introduced and its efficiency is tested on sample planar problems. The proposed algorithm focuses only on a portion of the workspace interacting with the straight line connecting the start and goal points. Hence, we are able to reduce the size of the roadmap while generating the exact globally optimal solution. Considering the worst case that all the obstacles in a planar workspace are intersecting, the algorithm yields a time complexity of O(n log(n/f)), with n being the total number of vertices and f being the number of obstacles. The computational complexity of the algorithm outperforms the previous attempts in reducing the size of the graph yet generates the exact solution.

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Figures

Grahic Jump Location
Fig. 1

Convex hull of the end-points and intersecting obstacle

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Fig. 2

Process of generating the convex hulls

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Fig. 3

Sample collision-free graph from C-hull based roadmap algorithm

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Fig. 4

Start point lying inside the convex hull of an object

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Fig. 5

Intersecting triangles of the (a) object and (b) final graph

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Fig. 6

Shortest path determined using Dijkstra’s search

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Fig. 8

C-hull based roadmap versus visibility

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Fig. 9

Shortest path on the visibility graph

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Fig. 10

Comparison of C-hull based and Delaunay triangulation solutions

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Fig. 11

Number of edges created by C-hull based versus visibility

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Fig. 12

A non-convex enclosure (left) and its conversion to a hollow obstacle with surface normals (right)

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Fig. 13

Convex hull generation per intersecting object

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Fig. 14

The path’s location with respect to the convex hull: (a) inside and (b) outside of the hull

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