Dynamic pollutant plume front tracking and monitoring by a single mobile robot

Abstract

This paper presents an observer-based motion control scheme for a single mobile robot to track and monitor a dynamic pollutant plume propagation in m-dimensional space. The spatiotemporal 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. In the suggested control scheme, a Luenberger-type PDE observer using the local area concentration measurement taken from the onboard concentration sensor is first constructed to derive the concentration field knowledge over the entire spatial domain. Then, a motion control law is constructed based on the observer equation to drive the robot to track and patrol on the plume front. Rigorous convergence analysis of the suggested control algorithm is provided by the set stability concept and Lyapunov's direct method. Numerical simulations of planar pollutant plume front tracking and monitoring are demonstrated for the effectiveness of the proposed control scheme.