How tight is sphere-packed formation flying?

Da-Wei Gu, Yoonsoo Kim, Ian Postlethwaite

    Research output: Contribution to journalArticlepeer-review


    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.
    Original languageEnglish
    Pages (from-to)427-435
    JournalThe Journal of Aerospace Engineering
    Issue number4
    Publication statusPublished - 1 Apr 2010


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