Connectivity Tracking Methods for a Network of Unmanned Aerial Vehicles

The communication links shared among a team of Unmanned Aerial Vehicles (UAVs) can be represented as a Laplacian matrix. The second smallest eigenvalue of the matrix, known as algebraic connectivity, is a metric typically used to measure the connectivity of UAVs. Algebraic connectivity represents the robustness of the communication network. For an increasing number of UAV applications, varying levels of connectivity at different points throughout the duration of a mission are needed to meet operational requirements. Thus, the ability to track and obtain a desired connectivity profile over the course of a mission is critical. This work compares four different methods for increasing or decreasing the connectivity for a team of UAVs by adding or removing communication links between UAVs. A connectivity tracking algorithm was developed using these methods to track a profile of varying connectivity over time and an analysis of the results is provided.

[1]  Fred W. Glover,et al.  Tabu Search - Part I , 1989, INFORMS J. Comput..

[2]  Dengfeng Sun,et al.  Algebraic connectivity maximization of an air transportation network: The flight routes' addition/deletion problem , 2012 .

[3]  Stephen P. Boyd,et al.  Growing Well-connected Graphs , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[4]  A. Jamakovic,et al.  On the relationship between the algebraic connectivity and graph's robustness to node and link failures , 2007, 2007 Next Generation Internet Networks.

[5]  Gang Li,et al.  Maximizing Algebraic Connectivity via Minimum Degree and Maximum Distance , 2018, IEEE Access.

[6]  Xin Wang,et al.  A New Performance Metric for Construction of Robust and Efficient Wireless Backbone Network , 2012, IEEE Transactions on Computers.

[7]  Damon Mosk-Aoyama,et al.  Maximum algebraic connectivity augmentation is NP-hard , 2008, Operations Research Letters.

[8]  Piet Van Mieghem,et al.  Algebraic connectivity optimization via link addition , 2008, BIONETICS.

[9]  Dragoš Cvetković,et al.  Applications of Graph Spectra: an Introduction to the Literature , 2009 .

[10]  Jorge Cortés,et al.  Distributed motion constraints for algebraic connectivity of robotic networks , 2008, CDC.

[11]  Fred Glover,et al.  Tabu Search - Part II , 1989, INFORMS J. Comput..

[12]  M. Fiedler Algebraic connectivity of graphs , 1973 .

[13]  Peng Wei,et al.  Weighted Algebraic Connectivity: An Application to Airport Transportation Network , 2011 .

[14]  Kyung Sup Kwak,et al.  Energy-Connectivity Tradeoff through Topology Control in Wireless Ad Hoc Networks , 2017 .

[15]  Yongsun Kim Bisection algorithm of increasing algebraic connectivity by adding an edge , 2009 .

[16]  Stephen P. Boyd,et al.  Graph Implementations for Nonsmooth Convex Programs , 2008, Recent Advances in Learning and Control.

[17]  Magnus Egerstedt,et al.  Graph-theoretic connectivity control of mobile robot networks , 2011, Proceedings of the IEEE.

[18]  G. P. Barker Theory of cones , 1981 .