Tight formation flying and sphere packing

Kim, Yoonsoo, Gu, Da-Wei and Postlethwaite, Ian (2007) Tight formation flying and sphere packing. In: Proceedings of the 2007 American Control Conference. IEEE, Piscataway, NJ, pp. 1085-1090. ISBN 978-1424409884

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Abstract

In this paper, we introduce a method for finding a tight formation of unmanned air vehicles (UAVs) via the classical sphere packing scheme. We first translate the tight formation finding problem to the problem of maximizing the second smallest eigenvalue lambda2(G) of the graph Laplacian LG. We then show how close the formation Gs obtained from the sphere packing scheme is to the optimal formation G* that maximizes lambda2(G). We show that lambda2(G*)/lambda2(Gs) is relatively small when the communication strength between two UAVs decays slowly with the distance between the two UAVs. This result implies 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:	Book Section
Additional Information:	Proceedings of the 2007 ACC '07: American Control Conference, held in New York, USA from 9-13 July 2007.
Subjects:	H600 Electronic and Electrical Engineering
Department:	Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User:	Sarah Howells
Date Deposited:	05 Dec 2012 12:35
Last Modified:	12 Oct 2019 22:29
URI:	http://nrl.northumbria.ac.uk/id/eprint/10462

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