0
Research Papers

Synthesizing Robust Communication Networks for Unmanned Aerial Vehicles With Resource Constraints

[+] Author and Article Information
Harsha Nagarajan, Sivakumar Rathinam

Mechanical Engineering,
Texas A & M University,
College station, TX 77843

Swaroop Darbha

Mechanical Engineering,
Texas A & M University,
College Station, TX 77843

A spanning tree is a graph in which there is a unique path connecting any pair of nodes.

If A, B are two sets, we refer to A − B = {x: x ∈ A, x ∉ B}

Pmax is determined by the application at hand; it also depends on the resource constraints placed on the UAVs (i.e., size of the UAVs). Specifically, it will depend on whether the application is using micro UAVs or fixed wing UAVs or much larger aerial vehicles.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received November 26, 2013; final manuscript received October 21, 2014; published online January 27, 2015. Assoc. Editor: Yongchun Fang.

J. Dyn. Sys., Meas., Control 137(6), 061001 (Jun 01, 2015) (12 pages) Paper No: DS-13-1472; doi: 10.1115/1.4028955 History: Received November 26, 2013; Revised October 21, 2014; Online January 27, 2015

In this article, we address the problem of synthesizing communication networks for unmanned aerial vehicles (UAVs) in the presence of resource constraints. UAVs can be deployed as backbone nodes in ad hoc networks that can be central to civilian and military applications. The cost of operation of the network depends on the resources that are used such as the total power consumption associated with the network and the number of communication links in the network. The objective of the problem is to synthesize a communication network that maximizes connectivity subject to the cost of operation being within the specified budget for the resources. It is known that algebraic connectivity is a measure of robust connectivity and hence, it is chosen as an objective for optimization. We pose the network synthesis problem as a mixed-integer semidefinite program (MISDP): (1) provide an algorithm for computing optimal solutions using cutting plane methods; (2) develop lower bounds by posing the problem as a binary semidefinite program; and (3) construct feasible solutions using heuristics and estimate their quality. The network synthesis problem is a nondeterministic polynomial--time (NP)-hard problem. We provide some computational results to corroborate the performance of the proposed algorithms.

FIGURES IN THIS ARTICLE
<>
Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.

References

Lehpamer, H., 2012, RFID Design Principles, Artech House Publishers, Norwood, MA.
Jakes, W. C., and Cox, D. C., eds., 1994, Microwave Mobile Communications, Wiley-IEEE, Hoboken, NJ.
Wang, H., 2009, “Robustness of Networks,” Ph.D. thesis, Delft University of Technology, Delft, The Netherlands.
Ibrahim, A. S., Seddik, K. G., and Liu, K. J. R., 2007, “Improving Connectivity Via Relays Deployment in Wireless Sensor Networks,” GLOBECOM, Washington, DC, Nov. 26–30, pp. 1159–1163.
Frew, E. W., and Brown, T. X., 2009. “Networking Issues for Small Unmanned Aircraft Systems,” J. Intell. Rob. Syst., 54(1–3), pp. 21–37. [CrossRef]
Han, Z., Swindlehurst, A. L., and Liu, K. J. R., 2009, “Optimization of Manet Connectivity Via Smart Deployment/Movement of Unmanned Air Vehicles,” IEEE Trans. Veh. Technol., 58(7), pp. 3533–3546. [CrossRef]
Burdakov, O., Doherty, P., Holmberg, K., Kvarnström, J., and Olsson, P.-R., 2010, “Relay Positioning for Unmanned Aerial Vehicle Surveillance,” International Journal of Robotics Research, 29(8), pp. 1069–1087.
Zhan, P., Yu, K., and Swindlehurst, A. L., 2010, “Wireless Relay Communications With Unmannned Aerial Vehicles: Performance and Optimization,” IEEE Trans. Aerosp. Electron. Syst., 47(3), pp. 2068–2085. [CrossRef]
Asher, M. S., Stafford, S. J., Bamberger, R. J., Rogers, A. Q., Scheidt, D., and Chalmers, R., 2011, “Radionavigation Alternatives for U.S. Army Ground Forces in GPS Denied Environments,” International Technical Meeting of The Institute of Navigation, San Diego, CA, Jan. 24–26, pp. 508–532.
Gu, D. L., Pei, G., Ly, H., Gerla, M., Zhang, B., and Hong, X., 2000, “UAV Aided Intelligent Routing for Ad-Hoc Wireless Network in Single-Area Theater,” IEEE Wireless Communications and Networking Conference, Chicago, IL, Sept. 23–28, pp. 1220–1225.
Srinivas, A., Zussman, G., and Modiano, E., 2009, “Construction and Maintenance of Wireless Mobile Backbone Networks,” IEEE/ACM Trans. Networking, 17(1), pp. 239–252. [CrossRef]
Craparo, E. M., How, J. P., and Modiano, E., 2011, “Throughput Optimization in Mobile Backbone Networks,” IEEE Trans. Mobile Comput., 10(4), pp. 560–572. [CrossRef]
Seshu, S., and Reed, M. B., 1961, Linear Graphs and Electrical Networks, Addison-Wesley Pub. Co, Boston, MA.
Nagarajan, H., Rathinam, S., Darbha, S., and Rajagopal, K., 2012, “Algorithms for Synthesizing Mechanical Systems With Maximal Natural Frequencies,” Nonlinear Anal.: R. World Appl., 13(5), pp. 2154–2162. [CrossRef]
Nagarajan, H., 2014, “Synthesizing Robust Networks for Engineering Applications With Resource Constraints,” Ph.D. thesis, Texas A & M University, College Station, TX.
Mosk-Aoyama, D., 2008, “Maximum Algebraic Connectivity Augmentation is NP-Hard,” Oper. Res. Lett., 36(6), pp. 677–679. [CrossRef]
Varshney, L., 2010, “Distributed Inference Networks With Costly Wires,” IEEE American Control Conference (ACC), Baltimore, MD, June 30–July 2, pp. 1053–1058.
Maas, C., 1987, “Transportation in Graphs and the Admittance Spectrum,” Discrete Appl. Math., 16(1), pp. 31–49. [CrossRef]
Kim, Y., and Mesbahi, M., 2006, “On Maximizing the Second Smallest Eigenvalue of a State-Dependent Graph Laplacian,” IEEE Trans.Autom. Control, 51(1), pp. 116–120. [CrossRef]
Martinez, S., Cortes, J., and Bullo, F., 2007, “Motion Coordination With Distributed Information,” IEEE Control Syst. Mag., 27(4), pp. 75–88. [CrossRef]
Zavlanos, M. M., and Pappas, G. J., 2007, “Potential Fields for Maintaining Connectivity of Mobile Networks,” IEEE Trans. Rob., 23(4), pp. 812–816. [CrossRef]
Yadlapalli, S. K., Darbha, S., and Rajagopal, K. R., 2006, “Information Flow and its Relation to Stability of the Motion of Vehicles in a Rigid Formation,” IEEE Trans. Autom. Control, 51(8), pp. 1315–1319. [CrossRef]
Malik, W. A., Rajagopal, S., Darbha, S., and Rajagopal, K. R., 2009, “Maximizing the Algebraic Connectivity of a Graph Subject to a Constraint on the Maximum Number of Edges,” Advances in Dynamics and Control: Theory, Methods and Applications, Cambridge Scientific Publishers Ltd, Cottenham, UK, pp. 135–148.
Ghosh, A., and Boyd, S., 2006, “Upper Bounds on Algebraic Connectivity Via Convex Optimization,” Linear Algebra Appl., 418(2–3), pp. 693–707. [CrossRef]
Wei, P., and Sun, D., 2011, “Weighted Algebraic Connectivity: An Application to Airport Transportation Network,” 18th IFAC World Congress, IFAC, Milan, Italy, Aug. 28–Sept. 2, pp. 13864–13869.
Nagarajan, H., Rathinam, S., and Darbha, S., 2012, “Synthesizing Robust Communication Networks for Unmanned Aerial Vehicles With Resource Constraints,” ASME Paper No. DSCC2012-MOVIC2012-8837, pp. 393–402. [CrossRef]
Nagarajan, H., Rathinam, S., Darbha, S., and Rajagopal, K., 2012, “Synthesizing Robust Communication Networks for UAVs,” IEEE American Control Conference, Montreal, QC, June 27–29, pp. 3730–3735.
Magnanti, T. L., and Wolsey, L. A., 1995, “Optimal Trees,” Handbooks in Operations Research and Management Science, Vol. 7, pp. 503–615.
Nagarajan, H., Rathinam, S., Darbha, S., and Rajagopal, K., 2012, “Algorithms for Finding Diameter-Constrained Graphs With Maximum Algebraic Connectivity,” Dynamics of Information Systems: Mathematical Foundations, Springer Proceedings in Mathematics & Statistics, Vol. 20, Springer, Heidelberg, Germany, pp. 121–135.
Croes, G. A., 1958, “A Method for Solving Traveling-Salesman Problems,” Oper. Res., 6(6), pp. 791–812. [CrossRef]
Gabow, H., Galil, Z., Spencer, T., and Tarjan, R., 1986, “Efficient Algorithms for Finding Minimum Spanning Trees in Undirected and Directed Graphs,” Combinatorica, 6(2), pp. 109–122. [CrossRef]

Figures

Grahic Jump Location
Fig. 2

A typical representation of the UAV backbone network where backbone UAVs/nodes provide communication support to the regular nodes and each regular node is assigned to one backbone node as shown

Grahic Jump Location
Fig. 1

In this figure, part (a) represents an initial configuration of backbone UAVs communicating with ground robots in disparate regions. As shown with the coloring of robots, not all robots are able to maintain a ground-to-air communication link with the UAVs. But in part (b), after a rigid body rotation of the backbone network about the centroid, the remaining ground robots are able to maintain a ground-to-air communication link with the UAVs. (a) Initial configuration and (b) configuration after rigid body rotation.

Grahic Jump Location
Fig. 4

This figure represents the positioning of UAVs for various objective values subject to power consumption constraint. Maximizing λ2(L) indicates that the UAV locations are more uniformly distributed with well connected topologies: (a) Eight nodes and (b) 20 nodes.

Grahic Jump Location
Fig. 3

Convex hull of the projections of five UAVs' locations on the horizontal plane with the centroid of the area at the origin

Grahic Jump Location
Fig. 5

This figure represents the trajectories of the UAVs when the backbone UAV network (eight nodes) is subject to a rigid body rotation by 360 deg about their respective centroids. Radius of communication of 0.1 was chosen for all the UAVs. Note that the network corresponding to largest λ2 value has the maximum coverage unlike the networks with lower λ2. (a) λ2 = 9.76, (b) λ2 = 4.11, and (c) λ2 = 0.52.

Grahic Jump Location
Fig. 6

This figure illustrates the 2-opt heuristic on an initial feasible solution, T0. After removing a selected pair of edges {(1, 4)(4, 3)} from T0, the three connected components are shown in (a). Part (b) shows the 2-opt exchange on the connected components to obtain new feasible solutions (spanning trees). (a) Left: Remove chosen edges; right: Corresponding connected components and (b) all 2-opt feasible solutions without power constraint.

Grahic Jump Location
Fig. 7

In this figure, part (a) represents a complete graph of seven nodes with random edge weights between every pair of nodes. Part (b) represents an optimal network with maximum algebraic connectivity (λ2*=7.1278) and satisfying the power consumption constraint (λ2*+λ3*≤15) synthesized from the above complete graph by solving MISDP using Algorithm 1. Note that the locations of the nodes in (b) are along the second and third eigenvector directions. (a) Complete graph for n = 7 and (b) optimal network for n = 7.

Grahic Jump Location
Fig. 8

Enumeration of all spanning trees for a random instance with six nodes. It can be observed that spanning trees with lesser sum of edge weights incur lesser power consumption.

Grahic Jump Location
Fig. 9

Two-opt solution for a problem with 25 nodes with random edge weights whose λ22opt = 49.9379 (% gap = 0.12) and satisfying the power constraint, λ22-opt+λ32-opt≤100. This figure is just a representation of the connectivity of the network and does not necessarily represent the location of nodes.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In