PDE-based Swarm Control for Contaminant Tracking Applications

In this paper, the problem of guiding a swarm of UAVs to monitor the spatio-temporal evolution of a contaminant moving on a plane is addressed. The contaminant and the UAV swarm are both modeled using Partial Differential Equations (PDEs). The spread of the contaminant is modeled using an advection PDE, while the PDE model of the UAV swarm has its foundations in gas dynamics, and these PDEs govern the density, average velocity and speed variance of the swarm. A Lyapunov-based approach, combined with an optimization formulation, is used to design suitable control laws that enable the UAV swarm to track the contaminant as it moves in 2-dimensional space. The robustness of the control laws to interaction effects among the UAVs within the swarm are evaluated. The efficacy of the designed control laws are demonstrated through simulations.