Dynamic Plume Tracking by Cooperative Robots

Abstract

This paper presents cooperative control of autonomous mobile robots to monitor and track dynamic pollutant plume propagation in $m$ -dimensional space. The dynamics of the pollutant plume is modeled by an advection-diffusion partial differential equation (PDE), and the plume front is described by a level set with a prespecified threshold value. We solve the problem of cooperative plume tracking using two cooperating robots under formation control, one is assigned as the sensing robot and the other is assigned as the tracking robot, where the sensing robot estimates the gradient and divergence information of the entire field based on its current concentration measurement, and the tracking robot tracks the plume front and patrols on it. Rigorous convergence analysis is provided using the set stability concept. Numerical simulations of pollutant plume tracking in both two- and three-dimensional spaces demonstrate the effectiveness of the proposed control scheme. This paper extends existing literature from static-level curve tracking to dynamic plume front tracking and presents a PDE-observer-based plume front tracking control design. The results are applicable to emerging environmental monitoring tasks by cooperative robots.