2013 Covering Points of Interest With Mobile Sensors

8/11/2019 2013 Covering Points of Interest With Mobile Sensors

1/12

Covering Points of Interest with Mobile SensorsMilan Erdelj, Tahiry Razafindralambo, and David Simplot-Ryl

AbstractThe coverage of Points of Interest (PoI) is a classical requirement in mobile wireless sensor applications. Optimizing the

sensors self-deployment over a PoI while maintaining the connectivity between the sensors and the base station is thus a fundamental

issue. This paper addresses the problem of autonomous deployment of mobile sensors that need to cover a predefined PoI with a

connectivity constraint. In our algorithm, each sensor moves toward a PoI but has also to maintain the connectivity with a subset of its

neighboring sensors that are part of the Relative Neighborhood Graph (RNG). The Relative Neighborhood Graph reduction is chosen

so that global connectivity can be provided locally. Our deployment scheme minimizes the number of sensors used for connectivity

thus increasing the number of monitoring sensors. Analytical results, simulation results and practical implementation are provided to

show the efficiency of our algorithm.

Index TermsMobile robots, mobile sensors, deployment, coverage, point of interest

1 INTRODUCTION

WIRELESS sensor networks have received a lot ofattention in recent years due to their potential

applications in various areas such as environmentalmonitoring [2], [11]. Covering and monitoring events fromthe environment in a given area are difficult tasks. Indeed,sensors have to be correctly placed to monitor the eventsand a connection between the monitoring sensors and abase station have to be kept to report data.

In this context, sensor placement can be divided intooffline and online schemes. Although offline deploymentscan provide optimal placement of sensors, they requireprecise knowledge of the events locations. Online deploy-

ments can cope with this drawback but are only feasiblewhen sensors have motion capabilities. However, the mainadvantage of online deployments is the possibility to obtainparticular topologies which can provide properties such asconnectivity, especially in unknown environments.

In classical wireless sensor deployment, communicationsfollow a N to 1 paradigm, that is, all the sensors have toreport the sensed data to a base station (data sink). Unlikead hoc networks, communication between two sensors isnot considered. However, a sensor can play a forwardingrole for other sensors but all the data packets have only onedestination (the base station). While considering thiscommunication paradigm, most of the sensor deployment

schemes proposed in the literature can be optimized.Indeed, in these deployments, network connectivity isevaluated based on a N to N communication paradigm.

Mobile sensor deployment allows to control the resultingconnectivity graph of the network and thus can stronglyincrease the quality of such deployment.

The placement of sensors related to coverage issues isintensively studied in the literature, and can be divided intothree categories. The full coverage problem aims at coveringthe whole area. Sensors are deployed to maximize thecovered area [4]. The barrier coverage problem aims atdetecting intrusion on a given area. Sensors have to forma dense barrier in order to detect each event that crosses thebarrier [6]. Point of Interest coverage aims at monitoringspecific points in the field of interest [7]. Different examples

and results related to the deployment of sensors can befound in [28]. These coverage requirements can be eitherprovided using offline or online deployment.

Previous works on Points of Interest (PoI) coverage usingmobile sensors, such as [7], do not consider the use of a basestation where sensors have to report data and to which asensor have to be permanently connected either directly orin a multihop fashion. The use of a base station in PoIcoverage increases the deployment complexity since aconnectivity constraint is added.

In this paper, we report a solution that solves the PoIcoverage problem. We consider a network composed bymobile sensors and a base station. We also assume that at the

beginning of the deployment the sensors are connected tothe base station. In our deployment solution, connectivityis the main constraint and, therefore, is maintained all alongthe deployment procedure by a local control of the topology.

In the proposed solution, each sensor moves toward aPoI but has also to maintain the connectivity with a subsetof its neighboring sensors. Depending on the chosen subsetof neighbors, keeping these local connections can provide aglobal connectivity of the network. Such a subset is chosenbased on results from the literature of graph theory.Relative Neighborhood Graphs (RNG) or Gabriel Graphs(GG) are examples of such graphs. Once global connectivity

can be provided locally, we want the sensors to deploy insuch a way that the number of sensors used for connectivityis minimized and the number of sensors that covers the PoIis maximized.

32 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 24, NO. 1, JANUARY 2013

. M. Erdelj and T. Razafindralambo are with the IRCICA/LIFL, CNRSUMR 8022, INRIA LNE/FUN, Univ. Lille 1, Parc scientifique de la hauteborne, 50, avenue Halley, 59650 VilleneuvedAscq, France.E-mail: {milan.erdelj, tahiry.razafindralambo}@inria.fr.

. D. Simplot-Ryl is with the LIFL, CNRS UMR 8022, INRIA Lille - NordEurope research centre, Univ. Lille1, Parc scientifique Haute Borne - Ba t.IRCICA, 50, avenue Halley - BP 70478, 59658 Villeneuve dAscq, France.E-mail: [email protected].

Manuscript received 25 Aug. 2011; revised 12 Dec. 2011; accepted 18 Jan.

2012; published online 27 Jan. 2012.Recommended for acceptance by V. Misic.For information on obtaining reprints of this article, please send e-mail to:[email protected], and reference IEEECS Log Number TPDS-2011-08-0566.Digital Object Identifier no. 10.1109/TPDS.2012.46.

1045-9219/13/$31.00 2013 IEEE Published by the IEEE Computer Society


2/12

The main contribution of this paper is a deploymentalgorithm that has the following properties:

. Our algorithm achieves PoI coverage. Examples ofstatic, moving, and multiple PoI coverage areprovided.

. Connectivity between each sensor and the basestation is kept all along the deployment procedure.

. Our algorithm is local, i.e., every decision taken isbased on local neighborhood information only anddoes not require synchronization.

. It is efficient, since it minimizes the number ofconnectivity sensors and maximizes the number ofcovering sensors.

The rest of this paper is organized as follows: Section 2provides some backgrounds which include state of the art,assumptions, definitions, and a problem statement. Section 3describes our deployment algorithm with its properties.Simulation results are given in Sections 4, 5, and 6 in whichwe consider static PoI, moving PoI and multiple PoIs,

respectively. Real implementation of our algorithm usingWifibots [22] is presented in Section 7 and conclusions aredrawn in Section 8.

2 BACKGROUND AND ASSUMPTIONS

2.1 State of the Art

In this section, papers about deployment and self-deploy-ment of wireless sensor networks are reviewed and weshortly extend this state of the art to mobile robotsdeployment. As our main focus is Point of Interest coveragewith connectivity constraint, we only cite papers that

consider these two properties. Moreover, we consider thedeployment of mobile sensors but more interested readerscan refer to [4], [16] for static random deploymentstrategies, to [1], [8], [14] for offline computation of sensorplacement and to [10], [20], [26], [28] for complete surveys.The evaluation of the impact of number and placement ofheterogeneous resources on performance in networks ofdifferent sizes and densities is presented in [27]. Regardingthe deployment or placement of mobile sensors, there aremainly three ways of optimization that were previouslydescribed in [20].

The coverage pattern-based movement [21]. In thiscategory, target locations of the sensors are computed based

on a predefined regular pattern such as hexagons. The finalpositions of the sensors can be given at the beginning of thedeployment (global coverage). Or, a particular sensor playsa specific role and helps the other neighboring sensors tofind their final positions based on the seeds position. Withthis strategy, connectivity is not provided all along thedeployment procedure. Moreover, the coverage pattern-based movement is not suitable for PoI coverage.

Grid quorum based movement [5]. In this category, thesensors field is partitioned into many small grid cells, andthe number of sensors in each cell is considered as the loadof the cell. Coverage and connectivity requirements depend

on the grid size. The sensors mobility is viewed as aclassical load balancing problem of each cell. As in coveragepattern-based movement, this deployment strategy cannotguarantee connectivity and cannot provide PoI coverage.

Virtual force based movement [3]. In this category,sensors are repelled or attracted each other by using virtualforces like electromagnetic particles. The sensors move stepby step. The virtual forces are computed based on the set ora subset of neighboring sensors and allow the computationof the sensors next movement. The sensor can undergoattractive forces, for preferential coverage areas, repulsiveforces for obstacle avoidance, and forces exerted by anothersensor. With this deployment strategy connectivity and PoIcoverage can be provided. The work proposed in this paperbelongs to this category.

The coverage requirement is the primary aim thatdescribes how the sensors have to be deployed over thefield. Even if some ways of moving are strongly related tothe coverage requirements, it is important to notice thatmovement and coverage are independent. From our pointof view, these two aspects must be decorrelated in order tohave simple deployment algorithms. Coverage require-ments can be divided into three categories:

. In the full coverage problem, sensors have tomaximize the covered area. The work proposed in[18] and [12] uses virtual force-based movement toincrease the covered area. The main difference ofthese two works is the connectivity consideration. In[18], a connectivity checking procedure is imple-mented. That is, a specific sensor regularly floodsthe network, and a sensor that does not receive theflooding message considers itself as disconnectedfrom the rest of the network. Thus, the disconnectedsensor moves back to its previous position. In [12],authors use local geometry and potential field

theory to maximize the area covered by mobilerobots. They use a Neighbor-Every-Theta (NET)graph to compute the robots movements. Theauthors apply the forces described in [13]. By usinga combination of mutually opposing forces, eachsensor maximizes its coverage and maintains theNET condition of having at least one neighbor inevery sector.

. In barrier coverage problem, sensors must form abarrier that detects any event crossing the barrier. Abarrier is defined as a segment between two points ofthe sensor field between which the sensors have to beevenly distributed. In the work proposed in [15],

authors use virtual forces to relocate the sensors. Therepulsive forces are used to have a uniform distribu-tion of thesensors. On theother hand, attractive forcesare used to gather sensors into the same horizon. It isimportant to notice here that, when the number ofsensors is sufficiently large, connectivity can beprovided at the end of the deployment. In [17] theauthors analyze the detectability of crossing events.However in both cases, it is hard to guaranteeconnectivity all along the deployment procedure.

. In the PoI coverage, only some specific points of thesensor field need to be monitored. Surprisingly, very

few works consider the problem of PoI coverage. Tothe best of our knowledge, works that considers PoIcoverage are [7] and [25]. In [7], authors propose analgorithm to periodically monitor some specific

ERDELJ ET AL.: COVERING POINTS OF INTEREST WITH MOBILE SENSORS 33


3/12

points (instead of all along). Unlike the workpresented in this paper, results from [7] do notconsider connectivity issue. In [25], authors firstanalyze the relationship among information accessdelay, information access probability, and thenumber of required mobile nodes for PoI coverage.Then, they design a distributed algorithm based on avirtual 3D map of local gradient information toguide the movement of mobile nodes to achievesweep coverage of dynamic PoIs. In [9], authorsdeveloped an algorithm to deploy the sensorsaround a PoI following a triangle tesselation. Inthis work, the PoI is not covered by all the sensorsand is only used as a focus point.

In this paper, we consider single and multiple PoIcoverage where connectivity has to be kept between thesensors that cover the PoIs and a base station. Moreover, weincrease the connectivity constraint and provide an algo-rithm in which connectivity is kept all along the deploy-ment procedure.

2.2 Motivating Application

A typical application of wireless sensor networks is theenvironment monitoring. Furthermore, military applica-tions are demanding in terms of efficient monitoring ofenemy troups and bases. The efficient solutions should beprovided in order to solve the problem of deployment ofmobile sensors capable of capturing the real-time video ofpossibly mobile enemy targets (Points of Interest in thisapplication). In all these application, sensors have to bedeployed and placed on strategic locations to monitor thearea of interest. In many cases, monitoring the whole area

might be unnecessary. Therefore, monitoring some PoIsincreases the sensing performance and reduces thedeployment cost since the number of sensors that monitorthe area can be increased by a given fixed number ofsensors. When sensors have motion capabilities, monitor-ing only some PoIs instead of the whole area also allowstime dependent coverage.

In this paper, we consider an environment and enemytarget monitoring applications. We assume that a fixed basestation is placed somewhere inside the field of interest. Atthe beginning of the deployment, the base station alreadypossesses all the information about PoI locations. Its tasksare to:

. spread out the information about PoI locationsamong the sensors,

. collect the information reported from the sensorsabout the events happening at the PoI.

Mobile sensors communicate to the base station in amultihop fashion.

We assume that it is possible to have several simulta-neous PoIs in the field and that the PoI can also be mobile.Hence, the deployment algorithm has to adapt its behaviordepending on evolving requirements. In order to dynami-cally adapt to the changing requirements, the deployment

algorithm must guarantee the connectivity all throughoutthe deployment procedure. This enables the base station totrack the position of the existing PoIs and/or to consider anew PoI even during the deployment procedure.

2.3 Preliminaries

We use the following definitions and notations for thenetwork model.

Definition 1. Let GV ; E be the graph representing the sensornetwork.Vis the set of vertices each one representing a sensor.EV2 is the set of edges; E fu; v 2V2 ju6vdu; v Rg, where du; v is the euclidean distance betweensensorsuandvandRis the communication range.G

V ; E

is

our model of the sensor network.

Definition 2.Nu fv2Ejdu; v Rg.Nuis the set of1-hop neighbors of sensor u.

Assumption 1.We assume that the positions of sensor uand PoIpare denoted byux; y andpx; y, respectively. This positioncan be provided by any internal mechanisms or externalsystems such as GPS.

Assumption 2. We assume that at the beginning of thedeployment the sensors are randomly spread out aroundthe base station at a maximum distance ofd < R=4 from thebase station. This condition ensures that the network isinitially connected and that it remains connected during thedeployment (detailed explanation can be found in Section 3.3,proof of Theorem 4).

Assumption 3.We assume that the locations of PoIs are knownand provided to the sensors before the deployment. Theselocations consist of the geographical coordinates that will beused in the deployment algorithm to calculate the travellingdirections and distances.

2.4 Relative Neighborhood Graph

The RNG [19] is a graph reduction method. Given an initialgraph G, the RNG graph extracted from G is a graph with areduced number of edges but the same number of vertices.Let the sensors be the vertices of the initial graph and thatan edge between two vertices exists if the two sensors cancommunicate directly. We assume that the communicationbetween two sensors is possible only if the distancebetween them is shorter than a given communicationrange. To build a RNG from an initial graph G, an edgethat connects two sensors is removed if there exists anothersensor that is at a lower distance from both sensors. Fig. 1shows an example of edge removal, where edge betweensensorsuandvis removed since there exists a sensor wthat

is closer to bothu

andv

.The formal definition of the RNG graph is as follows:

Definition 3. Let RNGG be the relative neighborhood graphextracted fromGV ; E. RN GG V ; Erng), where


Fig. 1. Example of RNG edge removal.


4/12

Erng fu; v 2Ej 69w2 Nu \ Nv ^ du; w< du; v ^ dv; w< du; vg:

Definition 4. NRNGu is the set ofus RNG neighbors,NRNGu fv; w2Nu ^ v2Nw jdu; v< dv; w

^d

u; w

< d

v; w

g:

We denote byjNRNGuj the number of sensors in NRNGu.Definition 5. NRNGu (resp. NRNGu) is the farthest sensor

that is part ofNRNGu, the distance betweenu and NRNGu(resp. NRNGu) is denoted by du (resp. du).

The RNG reduction has two main advantageousproperties. First, the RNG reduction can be computedlocally by each sensor, with the knowledge of its 2-hopneighborhood [19]. Second, given that the initial graph isconnected, the RNG reduction is also connected. These twoproperties are important for scalability and connectivity

preservation. Indeed, to preserve the connectivity of thewhole network, each sensor has to preserve the connectiv-ity with its RNG neighbors. In our algorithm, we use theseproperties to preserve connectivity and to ease the move-ment computation.

3 DEPLOYMENTALGORITHM FOR POI COVERAGE

3.1 Basic Idea

At the beginning of the deployment, all the sensors arewithin both the communication range of the base stationand the communication range of each other. Each sensormoves independently from the other sensors. All the sensors

run the same algorithm, but their motion decisions are takenindividually and the algorithm steps are not synchronizedbetween the sensors. It is important to notice that the basestation could compute an optimal placement for each sensorand provide them with this information, so that they wouldbe able to move toward the optimal positions. However, bydoing so, it is hard to ensure that the network would remainconnected all throughout the deployment procedure. There-fore, also the tracking of a moving PoI would resultinaccurate because sensors may not have up-to-dateinformation about position and placement.

In order to cover the PoI, sensors move toward one

predefined point that could be the PoI itself or the barycenterof PoIs. These movements are constrained by the connectiv-ity requirements. While sensors are moving, they mustmaintain connectivity with their RNG neighbors of the

dynamic graph. Indeed, even if a sensor does not cover the

PoI, it must stop moving in order to maintain the connection

with its RNG neighbors. It is worth noting that, when a

sensor covers the PoI, it also stops its movement. The

direction of a sensor is given by the following unit vector:

! dp!=kdp!k, where dp! is the vector connecting the currentposition of the sensor with the PoI (Fig. 2). When a sensor has

computed !

, it will move in this direction. However, the

distance traveled by the mobile sensor is constrained by

maintaining connectivity with its RNG neighbors. Thus, themovement vector of a sensor is m! d !, where d is themaximum distance that the sensor can travel while main-

taining connectivity with its RNG neighbors.Fig. 3 shows an example of movements. We can see how

sensors move toward the PoI and how connectivity is

preserved by maintaining the connectivity with the RNG

neighbors. It is worth noting that xis a neighbor, but not an

RNG neighbor, of sensorv. We can also notice in this figure

that sensorvdoes not move at distanceRof sensoru. This is

due to the upper bound on the distance d R du=2(detailed explanation about this constraint on dcan be found

in Section 3.3, the proof of Theorem 1). The fact that sensorvis not at distance R from sensor u also helps to have a straight

line deployment between the base station and the PoI since

after each iteration the sensor v moves toward the PoI andtoward the segment between the PoI and the base station.

We set the following conditions for the maximum

distanced:

1. d R du=2,2. ifd < 1, then d 0,3. ifd < 2, then d 0,

whereR is the communication range, du is the distancefrom sensoruto its farthest RNG neighbor,1and2are twothreshold values.

Condition 1 ensures that sensoru and RN Guremainconnected to each other, even in the case of movements in


Fig. 2. PoI coverage algorithm illustration.

Fig. 3. Example of sensor movement.


5/12

opposite directions, as we will formally prove it bymathematical demonstration in the following section.

Condition 2 will be used to avoid an infinite sequence ofsensor movements by introducing the minimal distance (1)that a sensor can travel.

Condition 3 will be used to stop sensor movement whentheir distance to the PoI is below the treshold 2.

3.2 Algorithm Sketch

Algorithm 1 (PoI Deployment Algorithm, PDA) formallydescribes our deployment process.

Algorithm 1. Single PoI deployment algorithm (PDA) thatruns on all the sensors.Require:The PoI location px; y.Ensure:The coverage of the PoI px; y.

1: repeat2: //Part 1: Direction computation

3: !

dp!

kdp!k4: //Part 2: Distance computation and movement:5: d R du=26: Sensor movement using the direction

!and

distanced.7: until the PoI is reached

In an asynchronous environment, sensors can run PDA atany time. In the first part of the PDA, the sensor ucomputesits direction based on its own position and the coordinates ofthe PoI, thus the sensor can compute the movement direction!

. In the second part, the sensor ucalculates the distance to

travel, and it performs the actual movement. The calculateddistance must take into account the connectivity constraintby considering the worst case movement of the RNGneighbors of the sensor. Since the connectivity with thefarthest RNG neighbor (du) must be preserved, themoving distance should always satisfy Condition 1. Recallthat all the sensors run the same algorithm. Therefore, if asensor vRN Gu, then du; v dv. This inequalityensures that if sensor v is the farthest RNG neighbor ofsensoru, and sensoruis not the farthest RNG neighbor of asensor v, connectivity is still preserved between these twosensors. Note that the usage of virtual force-based move-

ment implies a step by step computation of sensor move-ments. At the end of the Part 2 in the algorithm, the sensorknows the distance it has to travel and it proceeds with thereal movement. After the movement is done, the steps arerepeated until the PoI is reached.

The two parts of the PDA are related to two importantaspects of deploying a fleet of mobile sensors. The first part isrelated to the deployment scheme while the second partguarantees connectivity preservation and sensor movement.Since this algorithm is divided into two separate parts, weare able to modify the parts independently from one another,and thus use different direction calculation techniques.

3.3 Algorithm Properties

Theorem 1.Connectivity. If at time tT1the graph is connected,8tT2, withT2 > T1 the resulting graph is connected.

Proof.Let u and vbe two sensors and u and v areconnected attime tT1. Let u2RN Gv, v2RN Gu and du; v du. Let us assume that two sensors run PDA at thesame time and that they are moving in oppositedirections. The maximum distance traveled by sensor vdepends on du; v. Since du; v dv the maximumdistance traveled by sensor v is dv R dv=2

R

d

u

=2. Therefore, the maximum distance betweensensor u and v after their movements are du; v R du=2 R dv=2R. Thus, after theirmovements, sensors u and v are still connected. If theconnection to the farthest RNG neighbor is maintained,then the connection to closer RNG neighbors is main-tained as well. Therefore, if the connectivity with RNGneighbors is preserved, network connectivity is alsopreserved [19]. tu

Theorem 2.Termination. There exists a timet > T3when all thesensors stop moving.

Proof. Let us observe a case where sensor deployment is

composed of the base station bxb; yb, the PoI pxp; ypand the mobile sensor uxu; yu. At the beginning of thedeployment (t0), du0; b< R. After the first itera-tion du1; b du0; b R du0; b=2 after the ithiteration,

d

ui; b 1

2i

2i 1R du0; b; 1thus, we have

limi!1

R dui; b 0: 2

Therefore, there exists a t > T3 such that condition Rdui; b< 1 is satisfied, and sensor ustops moving. The

same proof also holds for an arbitrary number of sensors.Moreover, if we have a number of sensors large enoughto reach and cover the PoI while maintaining connectiv-ity, then the value of T3 can be further reduced bysatisfying Condition 3, du; p< 2. tu

Theorem 3. Straight line deployment. Let bxb; yb be the basestation,pxp; yp be the position of the PoI and let us assumethat sensoruxu; yu is not on the segment b; p. The distancehbetween sensoru and the segmentb; p is strictly decreasing.

Proof.At each step of the deployment algorithm, sensor umoves toward the PoI. Since the direction of the sensormovement is up!, whereu is the sensor position and thetraveled distance isd0, the distance between a sensorand the PoI is strictly decreasing. As a consequence, thedistance between the sensor and the segmentb; pis alsodecreasing. It is worth noting that when the sensoru2 b; p, it remains on the segment during the move-ment andh0. tu

Theorem 3 shows that the deployment is more likely toplace sensors along the straight line between the base

station and the point of interest.Theorem 4. Minimization of number of connectivity sensors. If

the PoI pxp; yp is at distance d 1, at the end of thedeployment each sensor has two RNG neighbors at the most.



6/12

Proof.Without loss of generality, we consider that the PoI isat distanced 1for two reasons. First, this assumptionimplies that sensors are moving parallel to the segmentb; p. Second, ensures that no sensor can reach the PoI,therefore all sensors are connectivity sensors.

If the deployment terminates, then the distancebetween the generic sensor u and one of its neighbors visdu; v> R 1. To better understand the proof, let usconsider the configuration depicted in Fig. 4.

In this configuration, the sensorsuandvcannot moveanymore since they are at distanceR 1 from bandu,respectively. It is also important to notice that due toTheorem 3, sensors stay at a distance of R=4 from thesegment b; p at the most. Let us assume that sensor uhasmore than two RNG neighbors when the deployment iscomplete. In this case, a sensorw2RN Gu exists. In theconfiguration depicted in Fig. 4, w must fall into one ofthe surfaces indicated by A, B,B0, orC.

Case A or C. If w falls into surface A (or C),w2RNGu, but b62RN Gu (or v62RN Gu). There-fore, db; w R 1 (or dv; w R 1) and w canmove. Which is contrary to our assumption that the

deployment terminated.CaseB0.Sensorw cannot fall into surfaceB0, since we

assume that sensors are at the maximum distance dR=4 of the base station at the beginning of thedeployment, and Theorem 3 ensures that this distanceis decreasing.

Case B. If sensor w falls into surface B, w2RN Guand Theorem 3 is verified. However, ifw2B, du; w R 1 and thus w can move, which is contrary to ourassumption that the deployment is complete. This proofcan be extended to any configuration since the max-imum distance between u and the set of intersection

points 1, 2, 3, and 4 is max

du; i R ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 ffiffiffi3pp , fori fa;b;c;dg. This is the case, if we observe intersectiondwhen b and u are located on the bottom dashed line.Therefore, ifw2B, then

du; w Rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

2 ffiffiffi

3pq < R 1; 81 < R 1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2

ffiffiffi3

pq :

utThe theorems above show that our algorithm preserves

connectivity all along the deployment procedure. Further-more, we bring proofs that the deployment will eventuallyterminate and that, at the end of the deployment, sensors

used for connectivity are more likely to form a straight lineand to be at distance R 1 from their neighbors. We alsoshow that, at the end of the deployment, each sensor usedfor connectivity has two RNG neighbors at the most,

which proves that the number of connectivity sensors isminimized.

4 STATICPOI

This section shows the performance evaluation results ofour algorithm. Simulations were performed using WSNet[24]. In the simulations, we set the communication range tobe equal to the sensing range but this assumption can beeasily modified without affecting the behavior of thedeployment. In this paper, we mainly focus on connectivityfor PoI coverage. Therefore, comparisons with other worksare hard to provide since literature lacks similar algorithms.Simulation parameters are given in Table 1.

4.1 Deployment Example

Fig. 5 shows an example of the deployments evolutionwhere the PoI is located at position p70; 100. After 180 s,the deployment is finished. In the simulation setup, thesensors move during 5 seconds and compute a newdirection after their movements. This figure shows thatthe sensors form a straight line between the base station andthe PoI which reduces the number of sensors used forconnectivity preservation and therefore increases the

number of sensors involved in coverage.

4.2 Coverage Quality

Fig. 6a presents the number of covering sensors w.r.t. thedistance between the PoI and the base station. In thesimulation, the base station is considered as a sensor whichis not mobile. That is, we consider 20 sensors including thebase station. This figure shows that the number of sensorsused for connectivity is minimized and that the number ofcovering sensors is maximized. For example, when the PoIis at distance 40, we need three sensors for connectivity atdistances 10, 20, 30 and the base station at distance 0, whichmeans that four sensors are needed for connectivity and16 sensors can cover the PoI for a total of 20 sensors.

4.3 Deployment Speed

Fig. 6b plots the number of covering sensors depending ontime. In this simulation, PoI is at distance 100 and 20 mobilesensors are considered. A movement decision is takenevery5 s. This figure shows that the first PoI is covered


Fig. 4. Minimization of number of connectivity sensors.

TABLE 1Summary of the Simulation Parameters

Fig. 5. Evolution of sensors positions depending on time. In thissimulation there are 20 sensors with a range of 10 on a square of100 100. The PoI is located at p70; 100.


7/12

by at least one sensor after 120 s. Note here that we checkthe coverage every 1 s. This means that the first coveringsensor has a mean speed of0:75 m=s(90 mcovered distanceafter 120 s).

Note that in an ideal case, the distance a sensor can cover

at each step is R meters (the communication range) andeach step lasts for5 s(motion decision). This means thatthe maximum (in the best case) speed of a sensor is :10=52 m=s. Note here that since we want to ensureconnectivity, a sensor must consider the worst case move-ment of its neighbors since we assume that the sensors arenot synchronized. Therefore, the maximum speed isreduced to 2=21 m=s to take the connectivity con-straint into account. These results are very close to theresults obtained above. One way to increase deploymentspeed is to reduce the motion decision period or to increasethe communication range.

4.4 Energy Consumption

In order to evaluate the deplyoment algorithm energyconsumption, we compare it with the perfect deployment,the deployment where all the sensors are provided withtheir final positions and where they move toward themwithout any movement or connectivity constraint. Forboth case, we consider a simple energy model where theenergy consumed by a sensor u is: Eu d , wheredis the covered distance and and are constants (here,1, 1). This simple energy model considersthe distance covered by a sensor but also penalizesmultiple small movements.

Fig. 6c shows the energy consumption of each sensor fora deployment of 20 sensors and a PoI at p100; 100. Thisfigure shows that the energy consumption is lineardepending on the covered distance. Moreover, our schemeconsumes small amount of energy since (for example) for acovered distance of105 m, 130 energy units are needed. Wecan notice that a sensor can cover R=25 m in everymovement decision period since it has to maintain con-nectivity with its neighbors. Therefore, the sensor needs atleast 105=521 iterations to cover 105 m. The energyconsumed by the sensor is at least Eu 105 1 1 21126 which is very close to 130.

Fig. 6c shows that the energy consumed by each sensor isrelated to the covered distance and that the energyoverhead is mainly due to the periodic motion decision.In order to reduce energy consumption by removing this

periodicity, each sensor can be given its final destination atthe beginning of the deployment. However, this deploy-ment cannot guarantee connectivity during the deployment,is not robust against obstacles, and is not suitable for thecoverage of moving PoI.

5 MOVINGPOI

In this section, we consider a single moving PoI. Indeed,when the sensors are deployed over a given PoI, the sensingapplication may require the sensor to move to anotherlocation. This scenario is possible with our algorithm sinceit maintains connectivity all along the deployment proce-dure. Note here that we consider only one PoI.

5.1 Tracking Strategies

There are three different strategies for covering a new PoI

when the sensors are already deployed. In the first strategy(Algorithm 2), hereafter referred to as STR1, the sensorsfirst move back to the base station before deploying towardthe new location of the PoI. This first strategy provides ahigh coverage quality but increases the deployment dura-tion and the amount of energy consumed.

Algorithm 2.First tracking strategy (STR1).Require:The PoI location pxp; yp.Ensure:The coverage of the PoI pxp; yp.

1: Run the PDA to reach the base stationb0; 02: Run the PDA to cover the PoIpxp; yp

In the second strategy (Algorithm 3), hereafter referredto as STR2, the sensors try to move directly toward thelocation of the PoI without going back to the base station.This second strategy reduces the time needed to cover thenew PoI but also reduces the coverage quality since anincreasing number of sensor is needed to preserveconnectivity.

Algorithm 3.Second tracking strategy (STR2).Require:The PoI location pxp; yp.Ensure:The coverage of the PoI pxp; yp.

1: Run the PDA to cover the PoIpxp; yp

The third strategy (Algorithm 4) is a mix of STR1 andSTR2 and is referred to as STR3. In this strategy, sensorsmove toward the segment b; p and when the distancebetween the particular sensor and the segment is lower than


Fig. 6. Coverage quality, deployment speed, and energy consumption.


8/12

R=4, the sensor moves toward the PoI. This strategycombines the advantages ofSTR1and STR2.

Algorithm 4.Third tracking strategy (STR3).Require:The PoI location pxp; yp.Ensure:The coverage of the PoI pxp; yp.

1: Run PDA in order to reach the segmentb; p2: Run the PDA to cover the PoIpxp; yp

5.2 Example of Deployment for Moving PoI

Fig. 7 shows the example of deployment for different

tracking strategies. Figs. 7a, 7b, 7c, 7d, and 7e show thedeployment usingSTR1. We can see from this set of figuresthat after 450 sthe deployment reaches its end and that thefirst covering sensor reaches the PoI between350-450 s.Figs. 7f, 7g, 7h, 7i, and 7j show the deployment using STR2.This set of figures shows that the deployment terminatesafter 7 hours but that the PoI is reached after 300 s. The longtermination time is mainly due to the fact that sensors canonly make small movements since they are at a distanceclose to R of each other. Figs. 7k, 7l, 7m, 7n, and 7o showthat the deployment using STR3terminates after 900 s andthat the PoI is first reached between350-900 s , which is aconsequence of this deployment strategy being a tradeoffbetween STR1and STR2.

5.3 Coverage Quality and Deployment Speed

In this section, we evaluate the coverage quality and thedeployment speed of each strategy. We run a simulation of3;000 s with 20 sensors and move the PoI at a randomlocation every 500 s. Fig. 8 plots the number of coveringsensors depending on time, coverage quality and (re)de-ployment speed for these three strategies.

We can see from Fig. 8 that each new PoI location iscovered by at least one sensor for each strategy. We can alsosee that from the coverage quality point of view, STR1 shows

very good performances compared to other strategies.Actually, if we consider the coverage of the last PoI (between2;500-3;000 s), STR1 has more than 15 covering sensors,STR2 has less than five covering sensors and STR3 has

around seven covering sensors. More generally, when usingSTR1 the coverage quality depends only on the distancebetween the base station and the PoI which is not the case forSTR2 and STR3. From the redeployment speed point ofview,STR2shows very good performances. We can see, forexample, that between1;000-1;500 s the PoI is covered atmost after 10 s (we sample the number of covering sensorsevery 10 s). For STR1, 200 s are needed and for STR3, 30 s areneeded. We can notice here that at time between500-1;000the PoI is located atp93; 27 and between 1;000-1;500 s it isatp

75; 1

.

This section shows that when the PoI is moving or whensensor redeployment is needed, our three proposedstrategies have their advantages and drawbacks but theykeep the properties described in Section 3.3 such asconnectivity and termination. Note that the tradeoffproposed with STR3 can be optimized depending on theapplication requirements. Moreover, it could be of interestto use STR1 or STR2 depending on the distance betweenthe old and the new location of the PoI or any other metric,such as angle. This study is left for future works.

6 MULTIPLEPOIS

In this section, we give some results regarding the coverageof multiple PoIs. We limit our assessment to two static PoIs.However, our algorithms can be applied to more PoIswithout modifications.

6.1 Multiple PoI Coverage Strategy

Starting from the single PoI case (PDA, Algorithm 1), weextend the initial algorithm and design two approaches formultiple PoI coverage, Random PoI Deployment Algo-rithm (R-PDA), and Barycenter PoI Deployment Algorithm(B-PDA). The management of the multiple PoI case is doneby downgrading the problem complexity to single PoI

problem, followed by the utilization of PDA.The first approach in multiple PoI coverage is the

application of PDA to a multiple PoI coverage scenario,where each sensor in the deployment randomly chooses one


Fig. 7. Evolutionof sensors positiondependingon time. In this simulationthere is 20sensors witha range of 10on a square of 100 100. The PoI isfirst located atp0

70; 0

and then at p00

70; 70

after 200 s.

Fig. 8. Number of covering sensors w.r.t time. Simulation parameters:R

10, Sensing

10, 20 sensors including the base station. The

simulation lasts3;000 s. A new location of the PoI is chosen every 500 s.


9/12

of the PoIs and runs the PDA. Coverage of all the targets willbe achieved if we assume that a large enough number ofsensors is used for the deployment. The deployment processis named R-PDA and is formally described in Algorithm 5.

Algorithm 5. R-PDA, multiple PoI coverage algorithmwhere sensor u randomly chooses one of the PoIs andmoves to cover it by using PDA.

Require:Positions of all the PoIs.Ensure:Multiple PoI coverage.

1: Randomly choose one of the PoIs, prandx; y2: Run the PDA to cover the chosen PoI

Second approach relies on covering the barycenter of allthe PoIs and the base station location, before the applicationof R-PDA. In this approach, every sensor calculates thelocation of the barycenter (Bx; y) for all the PoIs andthe base station and runs the PDA to cover it. After coveringthe calculated barycenter, the sensors run theR-PDA in orderto cover given set of PoIs. This deployment process isformally described in Algorithm 6 and named B-PDA. Note

that we can also consider the Steiner tree [23] in order tochoose intermediate points instead of barycenter.

Algorithm 6. B-PDA, multiple PoI coverage algorithm thatuses the barycenter of PoIs and base station as theintermediate point.Require:Positions of all the PoIs.Ensure:Multiple PoI coverage.

1: Calculate the barycenter (Bx; y) for all the PoIs andthe base station

2: Run the PDA to coverBx; y3: Run the R-PDA to cover all the PoIs

Since both R-PDA and B-PDA directly use the PDA, theproofs of network connectivity and deployment terminationare trivial and, therefore, will be omitted. The properties ofPDA assure that the final deployment comprises straight linesegments, that the number of connectivity sensors is mini-mized andthat thenumber of covering sensors is maximized.

6.2 Example of Deployment for Multiple PoIs

Fig. 9 shows the example of deployment for R-PDA and B-PDA, respectively. In these simulations, we consider twoPoIs (p190; 50 and p250; 90) and 30 sensors. For R-PDA,we consider that the set of sensors is divided into twosubsets and each subset is assigned to one PoI. Fig. 9 shows

that for R-PDA the deployment terminates after 180 s andthat the PoIs are considered independently. For B-PDA, wechoose the gravity center of the two PoIs and the basestation as an intermediate point. In B-PDA (as in R-PDA),

each sensor is also assigned to a given PoI by the basestation. However, before effectively moving toward its PoI,the sensors need to reach the intermediate point. Fig. 9shows the two steps of the deployment for B-PDA.

6.3 Coverage Quality and Deployment SpeedFig. 10 plots the number of covering sensors depending ontime for the two families of deployment strategies. Thisfigure shows the tradeoff performance between deploymentspeed and coverage quality. Indeed, R-PDA outperforms B-PDA regarding deployment speed since the two PoIs arecovered by at least one sensor at 140 s for R-PDA and thisvalue is 160 s for B-PDA. However, the coverage qualityprovided by B-PDA is better than the coverage provided byR-PDA since the maximum number of covering sensors is 6for R-PDA and 8 for B-PDA. Note that for R-PDA, thenumber of covering sensors is not equal for the two PoIs

since in our simulation setup 30 sensors are considered,including the base station. Therefore, 14 sensors arededicated to one PoI and 15 sensors are dedicated to theother. This is not the case for B-PDA since a subset ofsensors is used in common for connectivity.

7 IMPLEMENTATION

7.1 Wifibots

Wifibots (Fig. 11) are differentially driven, battery powered,mobile development platforms with integrated on-boardcomputer. Designed and programmed to reach the targetwith manual guidance, they are equipped with VGA videocamera and user control software, communicating via WiFidevice. Since robot operator has the actual real-time video


Fig. 9. Sensors positions with multiple PoIs depending on time.

Fig. 10. Number of covering sensors w.r.t. time for R-PDA and B-PDA.

Fig. 11. Wifibot robots.


10/12

information of the robots surroundings, there is no need forcomplex set of other types of sensors, and therefore, Wifibotmobile robots are additionally equipped with only two IRproximity sensors on the front side of the chassis. Theirrobust construction allows them to be used in wide range ofapplications including otherwise unreachable or harshenvironments. The on-board computer serves us as theplatform for the deployment algorithm implementation,while the motor driver provides us with the real-timeinformation on power drawn from the battery (detaileddescription can be found on Wifibot website [22]).

7.2 Algorithm ImplementationIn order to cope with deployments in unknown environ-ments, we integrated simple obstacle avoidance techniqueinto the initial PDA. If a robot detects an obstacle duringthe deployment, it tries to cover the auxiliary PoI(pAxA; yA) based on the gathered local information aboutthe obstacle. After the auxiliary PoI is reached, it continueswith initial PoI coverage steps. Note that in case of obstacledetection during the auxiliary PoI coverage, obstacleavoidance steps are run iteratively until all the auxiliaryPoIs are covered or the boundary of the communicationrange is reached. This deployment process is formallydescribed in Algorithm 7 and named Implemented PoIDeployment Algorithm (I-PDA).

Algorithm 7.Implemented PoI deployment algorithm(I-PDA) that runs on all the robots.

Require:The PoI location px; y.Ensure:The coverage of the PoI px; y.

1: repeat

2: ! dp

!

kdp!k3: d R du=24: Movement using the direction

!and distance d.

5: if obstacle detected then6: Run I-PDA for auxiliary PoI pAxA; yA7: end if8: until the PoI is reached

The I-PDA is implemented by using the softwarearchitecture shown in Fig. 12. The I-PDA core steps run indirection and connectivity blocks which need theRNG information, calculated based on the Hello messagesreceived from the neighbors. Hello messages from otherrobots and commands from base station are processed in udpinblock, while robot Hello messages are broadcast throughthe udp out block. Robots are using simple odometry toobtain the localization information, represented by the blocklocalization. The output ofposition and rngblocks isusedastheinputoftheI-PDAthatprovidesthe movingblockwith the movement decisions.

7.3 Testing Results

In first deployment example, we observe the coverage ofp40; 60while the communication range of all robots is set


Fig. 12. Robot main application structure.

Fig. 13. Coverage of p40; 60 with communication range of 15 m (sixrobots).

Fig. 14. Coverage of p70; 100 with communication ranges of 20 and15 m, respectively, (nine robots).

Fig. 16. Implementation of R-PDA and B-PDA for two PoI coverage,p125; 45 and p245; 25.

Fig. 15. Coverage of p50; 40 with changing the communication rangefrom 8 to 15 m (five robots).


11/12

to 15 m. The PoI is covered after approximately 160 s anddeployment frames are shown in Fig. 13. It can be clearly

seen in these examples how deployment actually works: allthe robots are moving to a known target with constraintsregarding movement forward and constantly preservingconnection with the base station. As the group of robotsadvances toward the target, after reaching the boundary ofthe communication range, the robot closest to the basestation stops with its movement, thus creating a commu-nication path back to the base station.

Fig. 14 present our deployment examples withp70;100,communication ranges are set to 20 and 15 m, respectively. Inboth examples the PoI is covered after approximately 260 swhich shows that the deployment time is not related to thenumber of robots or communication range, but just to robots

maximal speed (if there are enough robots to reach the PoI).The situation where group of robots cannot reach the

target is shown in Fig. 15. Five robots are trying to reach thetarget with their communication range set to 8 m, but afterapproximately 90 s they all reach the end of their commu-nication range and therefore complete deployments stops.

Fig. 16 shows deployment results after the implementa-tion of R-PDA and B-PDA (as presented in Section 6). In thisexperimentation we used eigt Wifibots with a range of15 mand two PoIs, p125; 45 and p245; 25.

Fig. 17 shows the example of deployment for a single PoIas presented in Section 4 with an obstacle. In this experi-mentation, we have three Wifibots and a base station b

0; 0

.

In order to cover the PoIp0; 11, the communication range isset to 4:5 m while all other parameters are the same as insimulations. This example illustrates the behavior of theimplemented obstacle avoidance technique in an indoorenvironment. Fig. 17 provides several photos of the environ-ment and the robots during the deployment, as well.

All the presented simulation and implementation results,together with simulation source codes for WSNet, sourcecode for the implementation, deployment photos and videoscan be found on the authors webpage.1

8 CONCLUSION

We present an algorithm for Point of Interest coverage withmobile wireless sensors. In our algorithm, the sensors must

cover the PoI while maintaining the connectivity with a fixedbase station. The algorithm is distributed, needs only local

information at each sensor, does not require synchronizationand is divided into three parts. In the first part, the sensorcomputes its direction. In the second part, the distance thathas to be covered by the sensor and its speed is computed.The third part is devoted to sensors motion. Unlike otheralgorithms described in the literature, our algorithm main-tains the connectivity all along the deployment procedureand therefore allows the tracking of mobile PoI. Theconnectivity maintenance of our algorithm is done by usingthe properties of the RNG. Indeed, if a graph G is connected,the Relative Neighborhood Graph extracted from G is alsoconnected. Hence, during their movements, the sensors haveonly to keep the connection with their RNG neighbors to

keep the whole graph connected. Moreover, the computa-tion of the RNG uses only local information.

We evaluate the performances of our algorithm regardingthe number of sensors that covers the PoI, the deploymentspeed, and the energy consumption. We also provide someproofs about the connectivity preservation, the algorithmstermination and the shape of the resulting graph (straightline). We provide some results regarding the coverage ofmoving PoI and multiple PoIs. Moreover, we implement ouralgorithm on Wifibots and show that our algorithm can beeasily implemented and can work in real conditions by usinga simple collision avoidance scheme rule and by alleviatingmessage losses. The next step of this work is to consider the

coverage of multiple moving PoIs and to consider the effectof having more than one base station.

ACKNOWLEDGMENTS

This work is partially funded by the French NationalResearch Agency (ANR) under the project ANR VERSORESCUE (ANR-10-VERS-003).

REFERENCES[1] X. Bai, S. Kumar, D. Xuan, Z. Yun, and T.H. Lai, Deploying

Wireless Sensors to Achieve Both Coverage and Connectivity,

Proc. MobiHoc 06, pp. 131-142, 2006.[2] G. Barrenetxea, F. Ingelrest, G. Schaefer, M. Vetterli, O. Couach,and M. Parlange, Sensorscope: Out-of-the-Box EnvironmentalMonitoring, Proc. Intl Conf. Information Processing in SensorNetworks (IPSN), pp. 332-343, 2008.


Fig. 17. Wifibot deployment with an obstacle.

1. http://researchers.lille.inria.fr/~erdelj.


12/12

[3] M.A. Batalin and G.S. Sukhatme, Spreading Out: A LocalApproach to Multi-Robot Coverage, Proc. Sixth Intl Symp.Distributed Autonomous Robotic Systems, pp. 373-382, 2002.

[4] J. Carle and D. Simplot-Ryl, Energy-Efficient Area Monitoring forSensor Networks,Computer, vol. 37, no. 2, pp. 40-46, Feb. 2004.

[5] S. Chellappan, W. Gu, X. Bai, D. Xuan, B. Ma, and K. Zhang,Deploying Wireless Sensor Networks under Limited MobilityConstraints, IEEE Trans. Mobile Computing, vol. 6, no. 10,pp. 1142-1157, Oct. 2007.

[6] A. Chen, S. Kumar, and T.H. Lai, Designing LocalizedAlgorithms for Barrier Coverage, Proc. ACM MobiCom 07,pp. 63-74, 2007.

[7] W. Cheng, M. Li, K. Liu, Y. Liu, X. Li, and X. Liao, SweepCoverage with Mobile Sensors,Proc. IEEE Intl Symp. Parallel andDistributed Processing (IPDPS), pp. 1-9, 2008.

[8] A. Krause, C. Guestrin, A. Gupta, and J. Kleinberg, Near-OptimalSensor Placements: Maximizing Information while MinimizingCommunication Cost,Proc. Fifth Intl Conf. Information Processingin Sensor Networks (IPSN 06), pp. 2-10, 2006.

[9] X. Li, H. Frey, N. Santoro, and I. Stojmenovic, Strictly LocalizedSensor Self-Deployment for Optimal Focused Coverage, IEEETrans. Mobile Computing, vol. 10, no. 11, pp. 1520-1533, Dec. 2010.

[10] X. Li, A. Nayak, D. Simplot-Ryl, and I. Stojmenovic, SensorPlacement in Sensor and Actuator Networks, pp. 263-294. Wiley, 2010.

[11] K. Martinez, R. Ong, and J. Hart, Glacsweb: A Sensor Network

for Hostile Environments,Proc. IEEE Comm. Soc. Conf. Sensor andAd Hoc Comm. and Networks. (IEEE SECON 04), pp. 81-87, Oct.2004.

[12] S. Poduri, S. Pattem, B. Krishnamachari, and G.S. Sukhatme,Using Local Geometry for Tunable Topology Control in SensorNetworks, IEEE Trans. Mobile Computing, vol. 8, no. 2, pp. 218-230, Feb. 2009.

[13] S. Poduri and G. Sukhatme, Constrained Coverage for MobileSensor Networks, Proc. IEEE Intl Conf. Robotics and Automation(ICRA 04), vol. 1, pp. 165-171, May 2004.

[14] D. Pompili, T. Melodia, and I.F. Akyildiz, Deployment Analysisin Underwater Acoustic Wireless Sensor Networks, Proc. First

ACM Intl Workshop Underwater Networks (WUWNet 06),pp. 48-55,2006.

[15] C. Shen, W. Cheng, X. Liao, and S. Peng, Barrier Coverage withMobile Sensors,Proc. Intl Symp. Parallel Architectures, Algorithms,and Networks (ISPAN 08), pp. 99-104, 2008.

[16] D. Simplot-Ryl, I. Stojmenovic, and J. Wu, Energy-EfficientBackbone Construction, Broadcasting, and Area Coverage inSensor Networks, Handbook of Sensor Networks, pp. 43-380343-380, John Wiley & Sons, 2005.

[17] Z. Tafa and V. Milutinovic, Detectability of Static and MovingTargets in Randomly Deployed Military Surveillance Networks,

Ad Hoc and Sensor Wireless Networks, vol. 13, nos. 3/4, pp. 291-312,2011.

[18] G. Tan, S.A. Jarvis, and A.-M. Kermarrec, Connectivity-Guaran-teed and Obstacle-Adaptive Deployment Schemes for MobileSensor Networks, IEEE Trans. Mobile Computing, vol. 8, no. 6,pp. 836-848, June 2009.

[19] G.T. Toussaint, The Relative Neighbourhood Graph of a FinitePlanar Set,Pattern Recognition, vol. 12, no. 4, pp. 261-268, 1980.

[20] B. Wang, H.B. Lim, and D. Ma, A Survey of Movement Strategiesfor Improving Network Coverage in Wireless Sensor Networks,Computer Comm.,vol. 32, nos. 13/14, pp. 1427-1436, 2009.

[21] Y.-C. Wang and C.-C. Hu, Efficient Placement and Dispatch ofSensors in a Wireless Sensor Network, IEEE Trans. MobileComputing,vol. 7, no. 2, pp. 262-274, Feb. 2008.

[22] Wifibot. Mobile robots, www.wifibot.com, 2012.[23] P. Winter, Steiner Problem in Networks: A Survey,Networking,

vol. 17, no. 2, pp. 129-167, 1987.[24] WSNet., An Event-Driven Simulator for Large Scale Wireless

Sensor Networks, wsnet.gforge.inria.fr, 2012.[25] M. Xi, Y. Qi, K. Wu, J. Zhao, and M. Li, Using Potential to Guide

Mobile Nodes in Wireless Sensor Networks, Ad Hoc and SensorWireless Networks, vol. 12, nos. 3/4, pp. 229-251, 2011.

[26] G. Xing and V.B. Mii, Wireless Ad Hoc and Sensor Networks,

Intl J. Parallel, Emergent and Distributed Systems, vol. 25, no. 6,pp. 437-438, 2010.[27] M. Yarvis, A. Kushalnagar, H. Singh, Y. Liu, and S. Singh,

Exploiting Heterogeneity in Sensor Networks, Proc. IEEEINFOCOM,2005.

[28] M. Younis and K. Akkaya, Strategies and Techniques for NodePlacement in Wireless Sensor Networks: A Survey, Ad HocNetworks,vol. 6, no. 4, pp. 621-655, 2008.

Milan Erdelj received the Msc degree incomputer engineering at the University of NoviSad, Serbia in 2009 and is currently workingtoward the PhD degree at the University of Lille1, funded by INRIA. His research interests aredistributed algorithms and mobile robotics.

Tahiry Razafindralambo received the MScdegree in applied statistics and computerscience from the university of Antananarivo in2001 and the PhD degree in computer sciencefrom the INSA de Lyon in 2007. He is currentlyan INRIA full researcher. His research interestsare mainly focused on distributed algorithms andprotocols design for wireless networks andperformance evaluation. He is involved in manyorganization and program committees of na-

tional and international conferences such as MASS, PE-WASUN,MSWIM, PIMRC, ICC.

David Simplot-Ryl received the PhD (1997)degree in theoretical computer science. Afterthe PhD degree in theoretical computer science,he joined the Universit Lille1Sciences etTechnologies where he is a full professor since2004. He is a member of the Institut Universi-taire de France (2009 campaign), and is ascientific head of the POPS project-team (jointproject of INRIA, Universit Lille1 and CNRS)which is focused on small computing devices

like smartcard or electronic tags. His research interests include sensorand mobile ad hoc networks, mobile and distributed computing,embedded operating systems, smart objects and RFID technologies.He is involved in numerous international conferences and workshopsand in editorial activities.

. For more information on this or any other computing topic,please visit our Digital Library at www.computer.org/publications/dlib.


Documents

2013 Covering Points of Interest With Mobile Sensors