Nonuniform Coverage With Time-Varying Diffusive Density Available to Purchase

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.