Non-Autonomous Coverage Control With Diffusive Evolving Density

Abstract

We consider nonuniform coverage optimization with respect to a non-autonomous coverage metric by spatially deploying a platoon of mobile agents in a planar region. Conventional coverage metrics usually encode a density field that weights points in the workspace. We consider a time-varying diffusive density that evolves according to a conservation law, and the induced time-varying coverage. Boundary conditions can model a time-varying flux across the boundary, and/or a time varying boundary density. We propose a decentralized state-feedback control law that maximizes the generalized non-autonomous coverage metric. The current approach of nonuniform deployment of autonomous agents applies to environmental monitoring and intervention, with deployment of mobile sensors in areas affected by penetration of substances governed by diffusion mechanisms, as for example oil in a marine environment, that pose immediate or long-term threats. We establish asymptotic convergence results illustrated by simulations.