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Research Papers

Centroidal Area-Constrained Partitioning for Robotic Networks

[+] Author and Article Information
Rushabh Patel

Department of Mechanical Engineering,
University of California,
Santa Barbara, CA 93106
e-mail: r_patel@engineering.ucsb.edu

Paolo Frasca

Department of Applied Mathematics,
University of Twente,
7500 AE Enschede, The Netherlands
e-mail: p.frasca@utwente.nl

Francesco Bullo

Department of Mechanical Engineering,
University of California,
Santa Barbara, CA 93106
e-mail: bullo@engineering.ucsb.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received April 1, 2013; final manuscript received November 28, 2013; published online March 10, 2014. Assoc. Editor: Jongeun Choi.

J. Dyn. Sys., Meas., Control 136(3), 031024 (Mar 10, 2014) (8 pages) Paper No: DS-13-1142; doi: 10.1115/1.4026344 History: Received April 01, 2013; Revised November 28, 2013

We consider the problem of optimal coverage with area-constraints in a mobile multi-agent system. For a planar environment with an associated density function, this problem is equivalent to dividing the environment into optimal subregions such that each agent is responsible for the coverage of its own region. In this paper, we design a continuous-time distributed policy which allows a team of agents to achieve a convex area-constrained partition of a convex workspace. Our work is related to the classic Lloyd algorithm, and makes use of generalized Voronoi diagrams. We also discuss practical implementation for real mobile networks. Simulation methods are presented and discussed.

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Figures

Grahic Jump Location
Fig. 1

The image on the left is the standard Voronoi partition generated by nodes A–E. The image on the right shows the dual graph for this partition

Grahic Jump Location
Fig. 2

Simulation of 9 agents partitioning a square environment with uniform density using the iterative gradient algorithm

Grahic Jump Location
Fig. 3

Simulation of 9 agents partitioning a square environment with uniform density using the simultaneous gradient algorithm

Grahic Jump Location
Fig. 4

Area (left) and position (right) trajectories for 9 agents partitioning a square environment with uniform density using the simultaneous gradient algorithm

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