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research-article

Optimal Paths for Polygonal Robots in SE(2)

[+] Author and Article Information
Monroe Kennedy

GRASP Laboratory, MEAM Department, University of Pennsylvania, Philadelphia, Pennsylvania 19104
kmonroe@seas.upenn.edu

Dinesh Thakur

GRASP Laboratory, MEAM Department, University of Pennsylvania, Philadelphia, Pennsylvania 19104
tdinesh@seas.upenn.edu

M. Ani Hsieh

GRASP Laboratory, MEAM Department, University of Pennsylvania, Philadelphia, Pennsylvania 19104
m.hsieh@seas.upenn.edu

Subhrajit Bhattacharya

CSE Department, Lehigh University, Bethlehem, Pennsylvania 18015
sub216@lehigh.edu

Vijay Kumar

GRASP Laboratory, MEAM Department, University of Pennsylvania, Philadelphia, Pennsylvania 19104
kumar@seas.upenn.edu

1Corresponding author.

ASME doi:10.1115/1.4038980 History: Received September 22, 2017; Revised December 14, 2017

Abstract

We consider navigation for a polygonal, holonomic robot in an obstacle-filled environment in SE(2). To determine the free space, we first represent obstacles as point clouds in the robot configuration space (C). A point-wise Minkowski sum of the robot and obstacle points is then calculated in C using obstacle points and robot convex hull points for varying robot configurations. Using graph search, we obtain a seed path which is used in our novel method to compute overlapping convex regions for consecutive seed path chords. The resulting regions provide collision-free space useful for finding feasible trajectories that optimize a specified cost functional. The key contribution is the proposed methods' ability to easily generate a set of convex, overlapping polytopes that effectively represent the traversable free space. This, in turn, lends itself to (a) efficient computation of optimal paths, and (b) extending these basic ideas to non-Euclidean spaces such as SE(2). We provide simulated examples and implement this algorithm on a KUKA youBot omnidirectional base.

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