Wireless Pers CommunDOI 10.1007/s11277-013-1516-y

Connectivity-Preserved and Force-Based DeploymentScheme for Mobile Sensor Network

Chun Zhang · Shumin Fei

© Springer Science+Business Media New York 2013

Abstract This paper considers the self-deployment of wireless sensor networks. Conven-tional deployment problem usually focuses on enhancing the coverage, while the conditionsfor network connectivity are largely simplified. We present a deployment scheme to enhancethe coverage while keeping the network connected at each step of the deployment. Ourscheme contains two parts. The coverage improvement part proposes an improved force-based mechanism. A limit is provided to determine the sensors which should attractive eachother, so the wasted overlap and communication resource can be reduced. The connectivitypreservation part provides constrains for the movement distance of each sensor, in order totake account of both connectivity and coverage enhancement. Some simulation results arepresented to show the connectivity preservation and coverage maximization properties of ourmechanism.

Keywords Wireless sensor networks · Deployment · Coverage · Connectivity

1 Introduction

Wireless sensor networks (WSNs) have been extensively used in many application areas.Due to the dynamics of environment, sensors are usually scattered in a monitored regionby aircrafts. However, the random deployment does not always lead to effective coverage.Uncovered holes could appear in the monitored region, and sensors may be partitioned intodisconnected groups. Hence, the effectiveness of a WSN is determined primarily by sensordeployment [1–3]. By introducing mobility to a WSN, sensors can self-deployment and move

C. Zhang (B)School of Computer Science and Technology, Nanjing University of Posts and Telecommunications,Jiangsu, Chinae-mail: zhc1088@outlook.com

S. FeiKey Laboratory of Measurement and Control of Complex Systems of Engineering,Ministry of Education, Southeast University, Nanjing 210096, People’s Republic of China

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to particular locations to achieve particular missions for many application scenarios [4–6].The self-deployment of sensors can enhance the coverage and connectivity of a WSN.

Force-based deployment is a commonly used self-deployment approach. Based on thisapproach, when two sensors are too close to each other, a repulsive force will push them apart.This mechanism can minimize sensing overlaps, and avoid poor coverage in other parts ofthe monitored region. On the other hand, when two sensors are far from each other, theyexert an attractive force on each other. This mechanism ensures a globally uniform sensordeployment and enhances the coverage. Although the approach can improve the coverage,it has a problem in practice. According to the mechanism they proposed, two sensors movetowards each other when the Euclidean distance between them is larger than the threshold.However, when there is not any uncovered hole between these two sensors, this mechanismwill result in “wasted overlap”.

Another problem with existing studies is that they assume that the network remains con-nected during the process of deployment. However, the network topology can be changed bythe movement of sensors. The partition of the network can occur even if the sensor densityis high.

In this study, the problem needs to be solved is: Given a monitored region with an initialsensor deployment, how should these sensors self-organize into a network that has the max-imum coverage, while preserving connectivity at each step of the deployment? Our schemeis localized, i.e. the WSN is connected at the beginning of deployment. Sensors make eachdecision based on the local neighborhood information only. Moreover, during the first phaseof coverage improvement, sensors do not physically move but a series of new positions isdetermined. A one-time movement will be performed to deploy sensors after the executionof connectivity preservation.

Our contribution in this research is to provide a connectivity preservation and force-baseddeployment scheme for a mobile sensor network. Our scheme is split into two major parts:the coverage improvement part and the connectivity preservation part. In order to expandingthe coverage, an enhanced form of the force-based mechanism is proposed. We provideconstraints to determine the sensors which exert repulsive (attractive) forces on each other.Compared with the traditional force-based method, the enhanced form can minimize “wastedoverlaps” and converge more easily. In the connectivity preservation part, the definition ofRelative Neighborhood Graph (RNG) is introduced. Each sensor judges whether its RNGneighbors are within its communication range. If not, they will exert attractive force oneach other. Meanwhile, it exerts attractive forces on other neighbors in order to maintain thedistances between them obtained in the first part.

The rest of this paper is organized as follows. Section 2 discusses related work. Sec-tion 3 provides the proposed connectivity-preserved and force-based deployment scheme.Simulation results and concluding remarks are given in Sects. 4 and 5, respectively.

2 Related Work

Sensor deployment is an important issue since it determines detection ability of WSNs. Itis widely recognized that a good deployment should satisfy both coverage and connectivity.There have been many solutions to solve this problem. Papers about self-deployment of WSNsare reviewed in this section. Moreover, interested readers can refer to [7–10] for completesurveys.

The force-based method is based on the concept of virtual forces. This method imitates thebehavior of magnetic particles: when two magnetic particles are far from each other, they will

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be attracted by each other. Contrarily, they will be push apart by a repulsive force. The goal ofthis method is to extend sensing coverage of WSNs. Interested readers can refer to [11–13].Reference [11] proposed that each sensor is moved by a compound force, including attractiveforces and repulsive forces. In [12], the forces exerted on each sensor are only repulsive forcesgenerated from one-hop neighbors. Better network coverage may be obtained if multi-hopneighbors are used. The work [13] considered sensors with probability sensing model. Theobjective was to main a high detection probability with a minimum number of sensors. Toachieve this, sufficient sensors were first deployed. Then, sensors were repulsed by othersensors, so the number of sensors may be reduced since some sensors may be pushed outsidethe monitored field. However, the works [11–13] mainly focus on enhancing the networkcoverage. They have not considered connectivity as essential during the deployment. Thisconnectivity allows a sensor to communicate with other sensors or the base station.

The work in [14] used a grid-based network structure to detect low density areas, and thenmoved sensors from high-density grids to low-density ones to balance the sensor distribution.The work in [15] also used the same structure to construct a uniform topology. However,the grid structure is feasible only for networks with high densities or sensors with largecommunication ranges. In addition, the grid structure is only suitable for an obstacle-freefield.

Dietrich and Dressler [16] introduced connected coverage as a combination of coverageand connectivity and showed that this is a different requirement than connectivity and cover-age on their own. Wang et al. [17] used a centralized and a distributed scheme to place the leastnumber of sensors for coverage and connectivity properties. The first scheme aimed to findan optimal solution for the maximum-matching problem. The second scheme used a greedystrategy to select the most suitable locations for sensors as their destinations. However, asensor placement algorithm should be executed before the two schemes are performed. Notethat the implement of the two schemes were based on the former placement results, and con-nectivity can not be guaranteed all along the two schemes. The authors of [18] took advantageof a Neighbor-Every-Theta (NET) to construct efficient topologies. In controlled deploymentof a static sensor network, an autonomous agent was used to make decisions about the bestlocations for new nodes. For self-deploying mobile sensors, this local condition was used todecide their motion strategy. However, the deployment algorithm can not preserve connec-tivity since a sensor in a sector that guarantee connectivity may not be selected as a NETneighbor. The closest works to NET are proposed in [19] and [20]. Since proximity graphssuch as the RNG, Gabriel Graph (GG) have several properties such as connectivity, efficientnetwork routes, etc., they can be used to obtain desirable network topologies.

3 The Connectivity-Preserved and Force-Based Deployment Scheme (CPFB)

Our scheme is split into two major parts: the coverage maximization part and the connectivitypreservation part.

3.1 Preliminaries

Our first assumption is: the topology of a WSN is connected at the beginning of the deploy-ment. From this initial conformation, the conception of RNG is introduced. Each sensorneed to preserve its connection with its relative neighbors during each step of movement. Weassume that all sensors have the same sensing range rs and communication range rc. Bothranges are modeled as circles. Sensors within rc of a sensor are called the sensor’s neighbors.

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(a) (b) (c)

Fig. 1 Illustration for, a Improved force-based mechanism, , b Illuminantes, and c Barrier

Each sensor is aware of its own location and the locations of its neighbors. In each step, asensor moves at a uniform speed in a straight line for a fixed amount of time, which is termeda period. Sensors move in steps of variable sizes, and at the end of each period, the directionand size of the next step is determined.

The coverage is denoted as the detection probability of a target at a point being detectedby a sensor. Assume a sensor Sk is deployed at point (xk, yk). For any point gi at (x, y),the distance between Sk and gi is denoted as dk

i , i.e. dki = √

(xk − x)2 + (yk − y)2. For asimplified binary sensor model, the coverage Pk

i of a point by Sk is expressed as Eq. (1).

Pki =

{1, if dk

i ≤ rs0, otherwise

(1)

3.2 Maximizing Sensing Coverage

The traditional force-based method offers a number of important advantages. These includelocal communication, negligible computation, coverage maximization and a one-time repo-sitioning of the sensors. However, the force-based method can be made more efficient if itis provided with reasonable constraints to determine which sensors exert repulsive (attrac-tive) forces on each other. Figure 1 is given for illustration. As shown in Fig. 1a, the circlesrepresent the sensing range of sensors. Sn is defined as the sensor whose identification (ID)is n. According to the traditional force-based mechanism, S j will be attracted by S3 andSi , and Si will be attracted by S3, S4 and S j . However, without the attractive force fromS j , S3 and S4 can also pull Si towards them to eliminate the coverage hole. Likewise, thecoverage hole between S3 and S j can be eliminated without the attractive force between Si

and S j . Hence, the attractive force between Si and S j will result in “wasted overlap andcommunication resource”. Under this circumstance, the traditional force-based mechanismcan’t enhance the coverage efficiently. Due to the demerit of the traditional mechanism, animproved force-based mechanism is proposed in this section.

Some definitions used are given as follows.

(1) Cn : the sensing range of Sn (a circle with Sn at the center);(2) Illuminant: We assume that Si and S j are two random sensors and the distance between

them is large than 2rs . When we discuss whether Si and S j will attract each other, Si

and S j are considered as two illuminants.

Take Fig. 1b for illustration, L1 and L2 are two straight lines which are tangent to Ci andC j . They are two parallel lines. The shaded section is considered as the transformation routeof luminous ray when Si and S j shine on each other.

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(3) Barrier: The sensing range which overlaps with the transformation route is considered as abarrier. The barriers on the transformation route will shade the luminous ray. Take Fig. 1afor example. When Si and S j are considered as illuminants, C3 and C4 are considered asbarriers. Due to the existence of C3 and C4, the luminous ray is shaded entirely and thetwo illuminants can’t shine on each other. In Fig. 1c, the ray from Si and S j can comethrough the interstice between C5 and C6, so Si and S j can shine on each other.

In order to enhance the coverage efficiently, we now provide the limit to find the sensorswhich should attractive each other. First, find the sensors, the distance between which islarger than 2rs , and consider each pair of sensors as a pair of illuminants. Then, if one pairof illuminants can’t shine on each other, they don’t need to exert an attractive force on eachother. The reason is that, under this circumstance, the coverage holes can be eliminated bythe gravitation between the illuminants and barriers, and the gravitation between illuminantswill result in wasted overlap. Otherwise, if one pair of illuminants can shine on each other,they should attract each other.

Next we describe the mechanism to judge whether two illuminants can shine on eachother. Take Fig. 1b for illustration. Si and S j are considered as illuminants. The points A andB are the intersection points of L1, L2 and Y-axis respectively. The coordinates of A and Bare (0, yi j1) and (0, yi j2) respectively. We can obtain (2).

⎧⎪⎨

⎪⎩

yi j1 = −r√

(x j −xi )2+(y j −yi )

2

x j −xi

yi j2 = r√

(x j −xi )2+(y j −yi )

2

x j −xi

(2)

where (xi , yi ) and (x j , y j ) are the coordinates of Si and S j respectively. The set of barrierson the transformation route between Ci and C j is called Ii j . Elements belonging to Ii j arecalled Ck , where k represents a series of integers. Then we have: Ck ∈ Ii j . The straight lineswhich are tangent to Ck and parallel to L1 are called Lk . The coordinates of intersectionpoints of Lk and Y-axis are (0, yk1) and (0, yk2) respectively. We can obtain (3) by simplegeometric calculation.

⎧⎪⎨

⎪⎩

yk1 = −r√

(x j −xi )2+(y j −yi )

2−xk (y j −yi )+yk (x j −xi )

x j −xi

yk2 = r√

(x j −xi )2+(y j −yi )

2−xk (y j −yi )+yk (x j −xi )

x j −xi

(3)

where (xk, yk) is the coordinate of Sk . Then, when (4) is satisfied, the two illuminants don’tneed to attract each other.

[yi j1, yi j2

] ⊂ ∪Sk∈Ii j

[yk1, yk2] (4)

To sum up, the force �fab between random sensors Sa and Sb can be expressed as (5). Notethat �fab = (r, θ) implies a magnitude r and orientation θ for vector �fab.

�fab =

⎧⎪⎨

⎪⎩

(α(d(a, b) − 2rs), θab) if d(a, b) > 2rs and [yab1, yab2] �⊂ ∪Sk∈Iab [yk1, yk2](β(dmin − d(a, b)), θab + π) if d(a, b) < dmin

0 otherwise

(5)

where d(a, b) is the Euclidean distance between Sa and Sb, θab is the angle of a line segmentfrom Sa to Sb, d min is the threshold on the distance between Sa and Sb, and α(β) is a measureof the attractive (repulsive) force.

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3.3 Connectivity Preservation Mechanism

Let G = (V, E) be the graph representing the topology of the initial sensor network. Vis the set of vertices, each element representing a sensor. E is the set of edges, defined byE = {

(a, f ) ∈ V 2 |a �= f ∧ d(a, f ) ≤ rc}

, where d(·) is the Euclidean distance betweenSa and S f . Note that, during the execution of the improved force-based mechanism, sensorsdon’t physically move but a sequence of new locations is determined for them. Thus, the newlocations of sensors form a new network topology, which is expressed as G f b = (V, E f b).E f b is defined by E f b = {

(a, h) ∈ V 2 |a �= h ∧ d(a, h) ≤ rc}

. The distance between twosensors determined by their new locations is expressed by d f b(·). The set of 1-hop neighborsof each sensor determined by E f b is expressed by N f b(a) = {

h ∈ V∣∣(a, h) ∈ E f b

}. Since

the G f b may not be connected, a connectivity preservation mechanism is proposed in thissection.

The RNG is a graph reduction method, which is expressed as Grng = (V, Erng). Erng isdefined by (6), where N (a) is defined by (7).

Erng ={ (a, f ) ∈ E |/∃m ∈ (N (a) ∩ N ( f ) ∧ d(a, m) < d(a, f ) ∧ d( f, m) < d(a, f )) }(6)

N (a) = { f ∈ V |(a, f ) ∈ E } (7)

Hence, given that the initial graph G is connected, the RNG is also connected. Nrng(a) isdefined by Nrng(a) = {

k ∈ V∣∣(a, k) ∈ Erng

}. Since the RNG can be computed locally by

each sensor, it is introduced in this paper.The main idea of the connectivity preservation mechanism contains two sides:

(1) In order to preserve the connectivity of the sensor network, each sensor a should preservethe connectivity with Nrng(a). When (8) is satisfied, Sa and Sk will exert an attractiveforce on each other. The force between them is expressed as (9).

d

(

aa∈V

, kk∈Nrng(a)

)

> rc (8)

{ �fak = ( 12 (d(a, k) − rc), θak

)

�fka = ( 12 (d(a, k) − rc), θka

) (9)

(2) The G f b is a coverage enhanced graph derived from G. In order to take account of con-nectivity preservation and coverage enhancement, during the connectivity preservationprocess, each sensor a

a∈Vshould preserve its distance from sensor j

j∈N f b(a) and j /∈Nrng(a)

equal to d f b(a, j). When Sa and Sk exert a force on each other, the distance betweenSa and S j will change.

In order to maintain the distance equal to d f b(a, j), Sa should exert an attractive force�f ja on S j . �f ja is expressed as �f ja = �fak .

3.4 Procedural description

Figure 2 shows the implementation details in pseudo code form. Since the coverage of theinterested region is evaluated by the number of grid points that have been covered. Theconvergence of the improved force-based mechanism is controlled by the threshold value

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Connectivity-Preserved and Force-Based Deployment Scheme

Fig. 2 Pseudo code of the CPFB

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Fig. 3 Initial sensor locationsafter random deployment

�P . The current grid coverage of the number loops iteration is denoted by P(loops). Ourscheme continues to iterate until | P(loops) − Pth | ≤ �P , and �P is set to 0.001.

4 Simulation Results

In this section, we carry out a comprehensive performance evaluation of the proposed scheme.Besides the area coverage, the moving distance of sensors is also considered. For all sim-ulation results presented in this section, distances are measured in units of grid points.In our simulations, sensors are randomly distributed in an area which is 500 by 500 indimension. As mentioned in Sect. 3.1, at the beginning of the deployment, all sensorsare within communication range of each other, which implies that the initial topology ofthe WSN is connected. The simulation is done using Matlab. The parameters are set asα = 0.5, β = 0.5, �p = 0.1, loopsmax = 100. We compare our proposed CPFB with theconnectivity preservation and coverage maximization scheme (CPCM) proposed in literature[21]. The CPCM use a repelling force between RNG neighbors to maximize area coverage.The resulting vector of each sensor is computed using a weighted sum. The impact of closerRNG neighbors is increased. Each sensor computes the maximum distance it can travel giventhat in its new location, it still remains connected to its RNG neighbors. Figures 3, 4, 5 presentsimulation results based on the binary sensor model. Figure 3 shows the initial locations ofthe sensors. The final sensor locations determined by the CPFB are shown in Fig. 5. Thedark points represent sensors. The lines which connect sensors represent edges of the RNG.Figure 4 depicts the execution of the CPFB on a connected initial topology. We can see theseveral steps of the algorithm in action. We can observe from Fig. 4 that, at different stages,the area coverage is expanding, and the topology of the network remains connected. Fig-ure 6 shows the coverage of CPFB and CPCM for varying number of sensors. We can notefrom this figure that CPFB outperforms CPCM in all cases. The reason is that, accordingto CPFB, we can deem that the coverage holes pull sensors moving towards them, so themovement of sensors can minimize the coverage holes efficiently. However, according toCPCM, each sensor exerts a repelling force on its RNG neighbors to expand the coverage

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Connectivity-Preserved and Force-Based Deployment Scheme

Fig. 4 Execution of the CPFB. aAfter iteration 3. b After iteration6

(a)

(b)

area of network. Applying this mechanism, the moving direction of each sensor is not basedon the locations of coverage holes, so the probability of the wasted overlaps’ occurrence isincreased, and the coverage is impaired. We can also make an observation from this figure:as the communication range increases, the CPFB can get a better coverage performance.Figure 7 highlights the impact of rc/rs ratio in the coverage performance. This figure showsthe coverage of CPFB for n = 30, rs = 70 and rc/rs ∈ [0.6, 1], where n represents thenumber of sensors. The result indicates the overall ascending tendency in the coverage ofCPFB with increasing rc/rs ratio. When the value of rc is small, the movement of sensorsfor coverage maximization is constrained. The reason is that each sensor should preservethe connectivity with its RNG neighbors, hence the freedom of sensors is limited. Figure 8shows the average moving distance of the two schemes. The simulation results of CPFB

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Fig. 5 Sensor locations after theexecution of the CPFB

10 20 30 40 50 60 70 80 900.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

number of sensors

% c

over

age

CPCM,rs=70,rc=60

CPFB,rs=70,rc=70

CPFB,rs=70,rc=60

Fig. 6 coverage of CPFB and CPCM versus number of sensors

and CPCM both rely on a good initial sensor distribution. We can find that CPFB performsbetter by comparing CPFB with CPCM. That is, when the CPFB is used, each sensor movestowards the coverage holes adjacent to it. Hence, the movement of sensors is “in purpose”,and the redundant motion is avoided. Due to the limited battery resources of sensors, energyefficiency is very important. The decrease in the moving distances of sensors implies that thereduction of energy consumption.

5 Conclusions

Connectivity is an important property in wireless sensor networks. In this paper we havepresented a deployment scheme for mobile sensor networks with connectivity guarantee. Our

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Connectivity-Preserved and Force-Based Deployment Scheme

0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 10.3

0.32

0.34

0.36

0.38

0.4

0.42

0.44

0.46

0.48

rc/rs ratio

% c

over

age

CPFB,rs=70,n=30

Fig. 7 coverage of CPFB versus rc/rs ratio

30 35 40 45 50 55 60 65 70200

250

300

350

400

450

500

550

600

number of sensors

aver

age

mov

ing

dist

ance

CPFB,rs=70,rc=70CPCM,rs=70,rc=70

Fig. 8 average moving distance versus number of sensors

scheme is split into two major parts. (1) Coverage maximization part. In this part, we provideconstrains for the sensors which should exert an attractive force on each other. Compared tothe traditional force-based algorithm, our algorithm reduces the motion oscillation of sensors.(2) Connectivity preservation part. In this part, each sensor should maintain the connectivitywith its RNG neighbors. Meanwhile, our algorithm will constrain the distance between eachsensor and its other neighboring sensors, in order to guarantee the coverage enhancement.

The next steps of our work will focus on a higher degree of connectivity, such as k-connectivity. We will also try to investigate obstacle avoidance scheme and message lossesproblem.

Acknowledgments This project was supported in part by National Nature Science Foundation of China(61273119).

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Author Biographies

Chun Zhang was born in 1985. She received her M.S. degree in Con-trol Theory and Control Engineering from Anhui University of Tech-nology, Maanshan, PR China, 2008. She is currently pursuing the Ph.D.degree at College of Automation, Southeast University, Nanjing, PRChina. The main research interests include wireless sensor networksand RFID, etc.

Shumin Fei was born in 1961. He received the Ph.D. degree from Bei-hang University, Beijing, PR China, 1995. From 1995 to 1997, he didpostdoctoral research in the Research Institute of Automation at South-east University, Nanjing, PR China. He is now a professor, doctoraltutor and the president of the School of Automation, Southeast Univer-sity, Nanjing, PR China. His research interests include robust control,wireless sensor networks, adaptive control and analysis and synthesisof time-delay systems, non-line control system design and integration,hybrid systems analysis, neural network, etc.

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