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.
This paper addresses the deployment problem for a swarm of autonomous mobile robots initially randomly distributed in 3 dimensional space. A fully decentralized geometric self-configuration approach is proposed to deploy individual robots at a given spatial density. Specifically, each robot interacts with three neighboring robots in a selective and dynamic fashion without using any explicit communication so that four robots eventually form a regular tetrahedron. Using such local interactions, the proposed algorithms enable a swarm of robots to span a network of regular tetrahedrons in a designated space. The convergence of the algorithms is theoretically proved using Lyapunov theory. Through extensive simulations, we validate the effectiveness and scalability of the proposed algorithms. A new decentralized control method, named Regular Tetrahedron Formation (RTF) strategy, is presented for a swarm of simple robots operating in three dimensional space. This strategy is based on virtual spring mechanism and basically, allows four neighboring robots to autonomously form a Regular Tetrahedron (RT) regardless of their initial positions. RTF strategy is made scalable and applied for various sizes of swarms through a dynamic neighbor selection procedure. Thus, each robot's behavior in each time step is only dependent on the local position information of three dynamically selected neighbors. In addition, an obstacle avoidance model suitable for swarm maneuvering is also introduced. Algorithm is studied with computational experiments which demonstrated that it is effective and practical.