We consider the positioning problem of aerial drone systems for efficient three-dimensional (3-D) coverage. Our solution draws from molecular geometry, where forces among electron pairs surrounding a central atom arrange their positions. In this paper, we propose a 3-D clustering algorithm for autonomous positioning (VBCA) of aerial drone networks based on virtual forces. These virtual forces induce interactions among drones and structure the system topology. The advantages of our approach are that (1) virtual forces enable drones to self-organize the positioning process and (2) VBCA can be implemented entirely localized. Extensive simulations show that our virtual forces clustering approach produces scalable 3-D topologies exhibiting near-optimal volume coverage. VBCA triggers efficient topology rearrangement for an altering number of nodes, while providing network connectivity to the central drone. We also draw a comparison of volume coverage achieved by VBCA against existing approaches and find VBCA up to 40% more efficient.
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