How tight is sphere-packed formation flying?

Gu, Da-Wei, Kim, Yoonsoo and Postlethwaite, Ian (2010) How tight is sphere-packed formation flying? Journal of Aerospace Engineering, 224 (4). pp. 427-435. ISSN 0954-4100

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Official URL: http://dx.doi.org/10.1243/09544100JAERO577

Abstract

In this article, a method for finding a tight formation of unmanned air vehicles (UAVs) via the classical sphere packing scheme is introduced. First, the tight formation finding problem is translated to the problem of maximizing the second smallest eigenvalue ?2(G) of the graph Laplacian LG. It is then shown how close the formation Gs, obtained from the sphere packing scheme, is to the optimal formation G? that maximizes ?2(G). ?2(G?)/?2(Gs) is shown to be relatively small (close to 1) when the communication strength between two UAVs decays slowly with the distance between the two UAVs. This result is also useful in that Gs can serve as a certificate that allows every graph to be quantitatively compared to G?. In the light of this tight formation result, a modelling technique is given for the optimal airborne refuelling of multiple UAVs.

Item Type: Article
Uncontrolled Keywords: tight formation, sphere packing, algebraic connectivity, optimal refuelling, multiple unmanned, air vehicles
Subjects: H400 Aerospace Engineering
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: EPrint Services
Date Deposited: 20 Dec 2010 16:10
Last Modified: 10 Aug 2015 11:22
URI: http://nrl.northumbria.ac.uk/id/eprint/2526

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