2D Voronoi Coverage Control with Gaussian Density Functions by Line Integration. Issue 2 (1st March 2017)

• Record Type: Journal Article
• Authors: Hayashi, Naoki; Segawa, Kohei; Takai, Shigemasa
• Is Part Of: SICE journal of control, measurement, and system integration. Volume 10:Issue 2(2017)
• Page Start: 110
• Page End: 116
• Publication Date: 2017-03-01
• Subjects: multi-agent systems -- coverage control -- centroidal Voronoi partitions
• DOI: 10.9746/jcmsi.10.110
• Languages: English
• ISSNs: 1882-4889

Abstract

Abstract : This paper considers Voronoi coverage control for two-dimensional space with a non-uniform density function. In general, the computation of a mass and a centroid of a Voronoi cell for a non-uniform density function requires spatial discretization since they cannot be represented by a closed form. However the spatial discretization approach may result in exhaustive computation. In this paper, we consider a transformation of a surface integral over a Voronoi cell into a line integral around its boundary by Green's theorem to alleviate such a computational issue. We show that the proposed method can be implemented only by coordinates of vertices of a Voronoi cell and parameters of a density function when the density function is represented by a sum of Gaussian functions.