Autonomous Unmanned Aerial Vehicles (UAVs) have gained popularity due to their many potential application fields. Alongside sophisticated sensors, UAVs can be equipped with communication adaptors aimed for inter-UAV communication. Inter-communication of UAVs to form a UAV swarm raises questions on how to manage its communication structure and mobility. In this paper, we consider therefore the problem of establishing an efficient swarm movement model and a network topology between a collection of UAVs, which are specifically deployed for the scenario of high-quality forest-mapping.
When considering three dimensions, the question for optimal node positioning is called the @cite_14 . A related problem in geometry is the @cite_1 , which is the number of non-overlapping unit spheres arranged such that each sphere touches another.
@cite_14 @cite_1
1993644547 2169164634
Abstract The sphere packing problem asks whether any packing of spheres of equal radius in three dimensions has density exceeding that of the face-centered-cubic lattice packing (of density φ 18 ). This paper sketches a solution to this problem. The kissing number k(3) is the maximal number of equal size nonoverlapping spheres in three dimensions that can touch another sphere of the same size. This number was the subject of a famous discussion between Isaac Newton and David Gregory in 1694. The first proof that k(3) = 12 was given by Schutte and van der Waerden only in 1953. In this paper we present a new solution of the Newton--Gregory problem that uses our extension of the Delsarte method. This proof relies on basic calculus and simple spherical geometry.