2D Voronoi Coverage Control with Gaussian Density Functions by Line Integration

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.