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In this paper, the problem of guidance of a swarm of Unmanned Aerial Vehicles (UAVs) to track the spatio-temporal evolution of a contaminant in 3-dimensional space is addressed. The contaminant and the UAV swarm are both modelled using Partial Differential Equations (PDEs). The spread of the contaminant is modelled using an advection PDE, while the PDE governing the UAV swarm is based on a nonlinear gas dynamic-like model. A dynamic inversion-based approach, combined with an optimisation formulation, is used to design optimal guidance laws that enable the UAV swarm to track the evolution of the contaminant, so that the swarm takes a configuration such that its spatial density distribution is proportional to the contaminant density. The robustness of the guidance laws to the unknown interaction effects among the UAVs within the swarm is assessed. The efficacy of the guidance laws is illustrated using simulations.

Macroscopic model-based swarm guidance for a class of contaminant tracking applications