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

[+] Author and Article Information
Nafiseh Masoudi

136 Fluor Daniel Engineering and Innovation Building Clemson University Clemson, SC 29634 nmasoud@g.clemson.edu

202 Fluor Daniel EIB Department of Mechanical Engineering Clemson, SC 29634-0921 fgeorge@clemson.edu

Margaret M. Wiecek

Martin Hall O-208 Clemson University Clemson, SC 29631 wmalgor@CLEMSON.EDU

1Corresponding author.

Manuscript received October 6, 2018; final manuscript received April 16, 2019; published online xx xx, xxxx. Assoc. Editor: NABIL ANWER.

ASME doi:10.1115/1.4043566 History: Received October 06, 2018; Accepted April 16, 2019

## Abstract

Planar path planning is the problem of finding a collision-free and shortest path in a 2D environment scattered with polygonal obstacles. The problem is oftentimes tackled by modeling the environment as a collision-free graph. Search algorithms such as Dijkstra's can later on be applied to find an optimal path on the 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 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 problem based on the notion of convex hulls is introduced. We start by geometrically modeling the 2D workspace of the problem; we then explain the developed algorithm capable of constructing the collision-free graph using a series of convex hulls. The proposed algorithm focuses only on a portion of the workspace interacting with the straight line connecting the start and goal points, hence reducing the size of the roadmap while generating the exact globally optimal solution. Considering the worst case that all the obstacles are intersecting, the algorithm yields a time complexity of O(nlog(n/f)), with n number of total vertices and f obstacles. Finally, Dijkstra's algorithm explores the graph and finds the shortest path between the two points.

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