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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.

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Figures

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. 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

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Fig. 3

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

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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.

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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.

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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.

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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.

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.

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