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Nonuniform Coverage With Time-Varying Diffusive Density

[+] Author Affiliations
Suruz Miah, Bao Nguyen, Alex Bourque

DRDC–CORA, Ottawa, ON, Canada

Davide Spinello

University of Ottawa, Ottawa, ON, Canada

Paper No. DSCC2014-6249, pp. V003T40A004; 8 pages
doi:10.1115/DSCC2014-6249
From:
  • ASME 2014 Dynamic Systems and Control Conference
  • Volume 3: Industrial Applications; Modeling for Oil and Gas, Control and Validation, Estimation, and Control of Automotive Systems; Multi-Agent and Networked Systems; Control System Design; Physical Human-Robot Interaction; Rehabilitation Robotics; Sensing and Actuation for Control; Biomedical Systems; Time Delay Systems and Stability; Unmanned Ground and Surface Robotics; Vehicle Motion Controls; Vibration Analysis and Isolation; Vibration and Control for Energy Harvesting; Wind Energy
  • San Antonio, Texas, USA, October 22–24, 2014
  • Conference Sponsors: Dynamic Systems and Control Division
  • ISBN: 978-0-7918-4620-9
  • Copyright © 2014 by ASME and Her Majesty the Queen in Right of Canada

abstract

We address nonuniform coverage with networked multi-agent systems and a nonuniform, time varying risk density function throughout the spatial workspace. The proposed solution for the nonuniform coverage problem is different from existing ones in that the evolution of the density is described by a conservation law with time-varying boundary conditions. By adopting a first gradient constitutive relation between the flux and the density we obtain a simple diffusion equation. The diffused density is then employed by a platoon of autonomous agents for spatially configuring themselves in optimum locations so that the coverage metric is maximized or minimized. We exploit the generalized centroidal Voronoi tessellation technique for generating the motion control of autonomous agents. By assuming that the risk density evolves much faster than the boundary conditions, we prove that the generalized Voronoi centroids are equilibrium points for the coverage metric. A set of numerical simulations illustrate the theoretical results.

Copyright © 2014 by ASME and Her Majesty the Queen in Right of Canada
Topics: Density

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