A Distrlbuted Sensor Relocatlon Scheme for ... - CiteSeerX

A Distrlbuted Sensor Relocatlon Scheme for Environmental Control Michele Garetto, Marco Gribaudo Dipartimento di Informatica Universita di Torino, Italy {garetto,marcog} @di.unito.it

Carla-Fabiana Chiasserini, Emilio Leonardi Dipartimento di Elettronica Politecnico di Torino, Italy {chiasserini,leonardi} @polito.it

Abstract We consider the problem of self-deployment and relocation in mobile wireless networks, where nodes are both sensors and actuators. We propose a unified, distributed algorithm that has the following features. During deployment, our algorithm yields a regular tessellation of the geographical area with a given node density, called monitoring configuration. Upon the occurrence of a physical phenomenon, network nodes relocate themselves so as to properly sample and control the event, while maintaining the network connectivity. Then, as soon as the event ends, all nodes return to the monitoring configuration. To achieve these goals, we use a virtual force-based strategy, which proves to be very effective even when compared to an optimal centralized solution.

1. Introduction We consider mobile wireless networks composed of wireless devices that, besides featuring sensing, computing and communication capabilities, also integrate actuators [1]. They are well suited for applications like habitat and environment monitoring, exploration of hostile areas, object tracking, and disaster relief. A flurry of robot systems with sensing capabilities are being designed with scopes such as underwater monitoring [2], asteroids exploration [3], human movement detection [4], and detection/relief of chemical plumes or fires. For the sake of concreteness, we consider the case of a sensor-actuator network whose task is to detect fires in a forestal area and counteract them by sprinkling water or other fire retardants [1]. In this case, exact deployment of the sensor-actuators may not be possible due to the characteristics of the environment. Also, localization techniques based on GPS may not be available due to the high cost (see for example [5] for the requirements that GPS receivers must meet to properly work in a forest environment). Upon occurrence of a fire outbreak, sensoractuators should be able to surround the event area and track the movement of the fire front, while keeping them-

selves at a safe distance, from which they can control the fire without being damaged. Finally, the node density should be increased in proximity of the fire front so as to contain its expansion. In this work, we present a distributed solution that is able to meet all of the above requirements. Our network system is composed of numerous mobile sensor-actuator nodes that autonomously organize and react to triggers from the environment. The specific problem we address here is how to enable these nodes to both self-deploy and relocate in a distributedfashion. Traditionally, network deployment [6] is performed at the initial stage of the network functioning, to obtain the desired geographical coverage or spatial sensor density. For the particular applications that we consider, selfdeployment of mobile sensor-actuators is necessary since node placement cannot be performed manually and accurately, due to possible hostile environmental conditions and/or to the large number of nodes to deploy. The goal in our case is to form a connected network with roughly the same node density and continuous coverage, starting from an initial random topology or from a configuration in which nodes are progressively released in the environment from a single point in the area. Relocation, instead, is needed when the network has to react to a physical phenomenon [7], which in our application may be an environmental disaster (event-based relocation). Here, we do not deal with fine-grained relocation aimed at stopping a coverage hole created for example by a node failure [8,9], but focus on event-based relocation, where the node positions and density have to be adapted to properly sample and control a large-scale event. When developing solutions for deployment and relocation of sensor-actuator networks, it is clear that one must obey to the system constraints imposed by the application and the employed technology. In the case of mobile nodes, the current trends in robotics push towards small, light, low-cost devices to be used in teams or swarms; it follows that mobile sensor-actuator networks are subject to limitations in computation, memory and energy capabilities and that distributed solutions are required. Several papers have addressed the problem

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of mobility-assisted deployment and relocation in sensor networks. However, we are the first to propose a unified, distributed algorithm that enables the network nodes to self-deploy for environmental monitoring, relocate upon an event occurrence, and return to the monitoring configuration as the event ends. Also, the solution we define has the following features: (i) it does not require the use of absolute node localization; (ii) it meets the constraints on the devices' computation, memory and energy capabilities; (iii) it provides real-time response to events as well as coordination among nodes as emergent behavior (swarm intelligence [10]).

2. Related Work Movement-assisted deployment, driving mobile sensor-actuators from an initial random configuration sme dsirale network etwok state, as been een addressed ddresed stte, has to some todesirable in [6, 11-15]. In particular, [1] presents a centralized algorithm to be executed by a cluster head, which has perfect knowledge of sensor positions and is able to orchestrate the movement of all sensors toward the desired locations. A distributed approach is proposed in [6],' where three iterative protocols for sensor deployment

are presented. Sensors move from high- to low-density

zones so as to increase coverage; at each protocol iteration, coverage holes are detected by sensors using Voronoi diagrams. The scheme in [6], however, requires sensors to have knowledge of their absolute position. More related to our work are [12-14] in which distributed algorithms based on virtual repulsive forces exchanged by sensors are considered for the sake of network deployment only (i.e, no event-based movement), However, the solutions in [12,13] require sensors to have knowledge of their absolute position, while the scheme in [14] is applicable only to deploy sensors over a limited area with well defined boundaries. Finally, in [15] the focus is on a sensor deployment scheme that provides

workload balancing, besides coverage; global informa-

tion about the sensor positions, however, is still required. With regards to self-deployment, we emphasize that our solution, in contrast to previous work, does require neither a network-wide knowledge of the node location nor the use of GPS. Moreover, we aim at obtaining a network featuring a desired node density (not maximum coverage). By achieving a regular tessellation of the network area with assigned inter-nodal distance, we attain our goal, while providing also load balance. In the context of event-based relocation, a pioneer work is [7], where the aim is to relocate sensors so as to approximate the spatial distribution of events taking place within the network area. Our objective is different: we do not want to approximate the event distribution, rather we want to relocate nodes in response to an occurred event so as to provide the necessary sampling,

tracking and control functionalities, and then restore the network configuration used for normal monitoring after the event ends. In [8] sensor relocation mainly aims at filling coverage holes created by a single node that fails or moves away. The proposed scheme assumes an initial grid structure for the network and the presence of grid-head nodes. Our goal and assumptions are different from the one proposed in that work. We do not address the problem of filling a hole created by a single sensor that becomes unavailable; rather we deal with event-based relocation, that typically requires the simultaneous movement of several nodes. Also, our algorithm starts from any initial deployment of the nodes and no sensor has to be selected for playing special logical roles. To conclude, we empDhasize that our solution differs fo previus wo semnodes atrnot utiro lear from previous work since nodes are not required to learn thiabouelcinwtinhera,orheoain their nor the location o absolute location within the

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are needed. Furthermore, we provide a unifled, distributed algorithm which enables sensors to self-

ing nodes

deploy, as well as move upon an event occurrence and return to the monitoring configuration once the event ends. 3. Goals and Assumptions In this section we state more precisely the goals and assumptions of our work, and introduce some notation and definitions.

3.1. Goals Our objective is to design a distributed solution that allows nodes to automatically relocate themselves so that the following functionalities are provided: (i) Self-deployment. Starting from any (connected) initial deployment of the nodes, the network achieves a target structure at the equilibrium, called

monitoring configuration. As monitoring network

topology, ideally we would like a connected tessellation of the network area, with continuous coverage and a desired node density Pm. In particular, we have selected a regular triangular tessellation for the following two reasons: (i) among the regular tesselations is the one providing the highest connectivity degree; (ii) results in [16] show that, when the node communication range is not smaller than 3 times the sensing range (which is typically the case), a triangular tessellation maximizes the network area covered by a given number of nodes (conversely, it requires the minimum number of nodes to cover a gvnntokae) gvnntokae) (ii) Reaction to physical phenomena and environmental disasters. When an event occurs, the nodes

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detecting the event move toward its location. We require nodes to relocate around the area where the event takes place, yielding a desired sensor density in its proximity. Network connectivity is maintained throughout the nodes relocation. As the event is no longer detected, nodes move back to the network monitoring configuration (although they are not required to return to their exact initial positions).

3.2. Assumptions and definitions We consider a network composed of N mobile sensoractuator nodes, which are deployed over a bidimensional geographical region. Let us denote with xi(t) the position of node i at time t, and with dik (t) the Euclidean distance between nodes i and k at time t. Network nodes can move at a maximum speed of Vmax, and have common sensing range Rs and communication range Rc. A node is able to communicate with the nodes within its communication range, and to detect any event having effect on at least one spatial point within its sensing range. We consider the triangular tessellation to be our network monitoring configuration, and we assume RC > 3R, [16]. One of the goals achieved by our selfdeployment procedure is to yield a triangular tessellation featuring the desired monitoring node density Pm. With this goal in mind, each node (not on the border) should be surrounded at the equilibrium by six nodes placed at the vertices of a regular hexagon of radius Di,m with:

DmP2 =Pm sin 600

3Pm

(1)

Indeed by geometric considerations, one can see that a triangular tessellation with inter-nodal distance equal to Dm corresponds to a node density: Pm = 1/Am, where Am is twice the area of an equilateral triangle of side Dmi. Note that Pm should be such that Dm < Rc. Given (1), hereinafter we use interchangeably inter-nodal distance and node density. After deployment, we want the network to be able to react to physical phenomena or environmental disasters (event-based relocation). Note that nodes may become aware of such events either because they detect a varnation in the standard values measured by their sensing device (e.g., temperature variation in case of fire), or because they are alerted by other nodes through the transmission of notification messages. For simplicity, in the following we only consider the first case. In the presence of an event, sensors have to relocate themselves so as to provide a new desired node density. Similarly to the case of self-deployment, the new density is achieved by specifying a target inter-node distance d7jk (t) (i, k=1, ... ., N). We assume that the target internode distance is a function of the event intensity sensed

by each pair of nodes. By denoting with si (t) the intensity of the event sensed by node i at time t, we have: dTj(t) f (si (t), Sk (t)) . In general, f (.) should be chosen such that the higher the event intensity detected by a node, the higher the target node density (i.e., the smaller the target inter-node distance to be used). We model the event intensity as follows. In order to simplify the presentation, let each event have an epicenter (the case of events occurring over an extended area will be considered later). The signal sensed by the generic node i at time t is given by: s(t)

a(t)

(2)

die (t)

where die (t) is the Euclidean distance between the node position xi(t) and the epicenter location at time t, a(t) is the energy emitted by the event at the epicenter at time t, and Q is the decaying exponent of the event energy. We chose to use this sensing model because, in spite of its simplicity, it is able to represent various types of signals (e.g., radio, acoustic, etc.) and physical phenomena (e.g., heat, temperature); for this reason, it has also been largely used in the literature (see [17] and the references therein). Note that a high value of si (t) corresponds either to an event of moderate intensity happening close to node i, or to a very catastrophic one occurring far away from the node position. In both cases, some action is required by the nodes detecting the event. Let us denote with Smin the minimum intensity for detecting an event, and with Smax the maximum intensity a node can measure without damage for the device. We model the detectiona function by the generic node i at time t by defining of an event ab (t), which can take three values: {-1, 0, 1}. If no event is detected at time t, then Smax, 0) is also necessary to bring the system to a complete stop within finite time. Note that, using a minimum force threshold that prevents a node from starting to move in response to arbitrarily small forces is a reasonable design choice to save energy. ____________________ 1An animated picture of the transient behavior is available at [2 1]

5.1.1

Coverage

Since the algorithm does not achieve a perfect triangular tessellation, it is important to quantify how the equilibrium configurations reached by the algorithm differ from the ideal triangular tessellation (which provides the optimal coverage). triangular lattice network area

G 0.001 - no errors G 0.01 - no errors G 0.001 - errors G 0.01 - errors

random deployment

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Figxure 2. the traction of area covered (left y axes) and the network size (right y axes) as functions of he monitoring distance Dn f dff n d In Figure 2 we show the percentage of the area covered by at least one node as a function of the monitoring distance Dm (the sensing range is fixed to 1), for several deployment strategies and N 400. The thick solid line corresponds to the regular triangular tessellation, for which the coverage percentage is 100% up to 3 1.732; after this point the coverage deDm creases for increasing values of Di, and can be computed using elementary geometry. The lower dotted line with error bars corresponds to the coverage achieved if nodes are just randomly deployed over the area and do not move from their initial location. The coverage percentage is computed using a Monte-Carlo technique and averaging the results over 30 experiments (error bars refer to 95%-level confidence intervals). In between the ~~~~~above two extreme cases there are results related to four variants of our algorithm: we consider two values of G

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0.6 0.4

(namely, 0.01 and 0.001), as well as the presence or not of measurement errors. Measurement errors are modelled as follows: distance errors follow a uniform distribution with zero mean and maximum value equal to 5% of Dm [22], while angle measurements are independently introduced according to a uniform distribution in the range ±100 [20]. In presence of errors, the static friction coefficient ko has to be chosen so that the worst possible error in the location of neighbors does not make a sensor resume moving.

coverage cannot be always guaranteed, moreover this strategy has the important drawback of reducing the size of the network area: in Figure 2 the curve labeled 'network area' (right y axes) actually serves as a reminder that the network area (normalized to 1 at Dm = 3) is proportional to the square of Di,m thus a trade-off exists between coverage percentage and network size.

5.1.2 Transient behavior

To evaluate the performance of the algorithm during the transient phase, we consider both the amount of time rno errors taken to reach the equilibrium, and the energy spent by c) 5 nodes to move from their initial location to their final po~) 4 sition. The first metric is meaningful if one wants to minimize the duration of the deployment phase; the second o 3 metric is probably more relevant, since sensors usually >2 t 0have severe energy limitations. By assuming that the eni.~/ // ergy required to move a node is proportional to the traveled distance [8], we can focus on the total movement 11 11.2 1.4 1 1 2 performed by the nodes to reach the final configuration. 2 1.4 1.6 1.8 2.2 2.4 We compare our distributed algorithm with an optiDm mal centralized one, i.e., the algorithm that instructs each Figure 3. Difference between the fraction of sensor-actuator to move in such a way that the aggrearea covered through a perfect triangular gate movement performed by all nodes to reach the final our algorifhm. Results are tessellation and and mouraorithm. is minimized. The optimal solution reduces to plottessellativersus Resultsare Dtopology Dfinding the minimum weighted matching (mWM) of a biplotted istc withe mondithouterori partite N x N graph, where N vertices correspond to the initial locations of the nodes, and N vertices correspond In Figure 3 we present the difference (in percentage) to their location in the final configuration. We draw an between the fraction of area covered by the triangular tessellation and our algorithm. We set G = 0.001, and edge between any vertex in the first set to any vertex in the second set, with associated weight equal to the we consider the two cases with and without measurement Euclidean distance between the corresponding locations. errors. Again, error bars refer to 95%-level confidence intervals. Then, the mWM computes which node goes where, i.e., the identity of the location where each node has to go so Looking at Figures 2 and 3, we observe that the differas to minimize the aggregate movement. Finally, each ence in performance of our solution with respect to a pernode moves at the maximum speed Vmax till it reaches fect triangular tessellation is very small, i.e., about 5% in its final position. the worst case as shown in Figure 3. Also, the algorithm We consider the example scenario with N = 400 and performs slightly better (i.e., it is closer to the perfect triinitial topology as shown in the left plot of Figure 1. To angular tessellation) when errors are present and when G is small (see Figure 2). Note that the difference in perobtain a fair comparison, the final configuration for the formance with and without errors is not caused by the mWM solution is assumed to be the one achieved by our algorithm at the equilibrium (e.g., for G = 0.01, the one inaccuracy affecting the simulation results, as confirmed in shown in the right plot of Figure 1). In Figure 4, we by the confidence interval reported Figure 3. Intuthe of errors can be considercompare our algorithm with the centralized, optimal one itively, impact explained for two different values of G, namely 0.001 and 0.01. ing the equivalent effect played by temperature in simulated annealing: local vibrations increase the probability When G = 0.01, our algorithm produces about twice the of avoiding spurious equilibrium points thus resulting in total movement and takes about twice the time to reach a more regular monitoring configuration. A small G also the final configuration, with respect to the optimal solureduces the responsiveness of the system away from the tion. When G =0.00 1, the total movement produced equilibrium point, helping to explore more patiently the by our algorithm is reduced (still 75% more of the total solution space. Note that, to obtain a coverage percentmovement obtained with mWM), but the duration of the age closer to 100%, one could just reduce the monitoring transient is significantly increased (note the different x distance Dm (e.g., use Dm = 1.4). However, a perfect scale). 6

errors

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We start by considering the case of a single event, occurring after the network deployment, and evaluate the performance of our algorithm both at the equilibrium and during the transient phase. We assume that the event epicenter is located outside the initial area in which nodes -------------------------------------------- are deployed (for a single event whose epicenter is located inside the initial area, even better results than those presented here are obtained). The case of multiple events ar algorithm G m0.001I overlapping in time is considered at the end of the sec-

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tion.

5.2.1 At the equilibrium

Figure 4. Comparison of the proposed algorithm with the centralized, optimal one

Figure 5 shows the topology obtained through selfdeployment and the final topology achieved by our relocation algorithm, for the same parameters of the scenario

that minimizes the total movement performed by the nodes

in Figure 1 (N = 400 nodes). The event occurs at position and is characterized by a(t) = 1 and (se th-30], We conclude that, when the deployment durationWd is2s [-30, 'vn oen().TeprmtrWi theet en t tod2, il Sma) i suchmtha the not crucial, it is convenient to slow down the system dy' iS set to 2, while Sma, iS such that the target density ~~~~~~~~~~~~the namics using a small G: by doing so, the total movement minimum distance De from the epicenter at which the (and thus the node energy expenditure) is reduced, and nodes can be located is equal to 6. Note that, assuming also the achieved percentage of covered area is higher an event with circular symmetry, the event frontier turns (see Figure 2). out to be a circle of radius De, centered at the epicenter. Furthermore, here we assume that all nodes are able to 5.2. Event-based relocation detect the event since it starts, i.e., si(t) > Smin Vi, t. We now evaluate the performance of our algorithm in relocating the nodes when one or more physical events 20 initial are detected. We consider the event intensity to have a 10 40 circular symmetry around the epicenter, although this is 0 . *30 not a requirement for our algorithm, and we set the para10 meter P of the potential force to 0.01. Recall that our goal is to make sensor-actuators -20 move toward an event, and possibly surround it, while a node inter-nodal distance 30 achieving target density (i.e., d7 (t)) and preserving network connectivity. In the fol.0 lowing, we take the target density to be proportional to final -50 the local intensity of the event (2). More specifically, 40 30 20 10 0 10 20 x we assume that the desired density on the frontier of the event (i.e., where s(t) Smax) iS W times larger than 5. and Figure Initial final configuration obthe monitoring density Pm, and it decays as the event inby algorithm in case of event the tained tensity. Thus, the target density computed by node i at epicenter at [-30, 30], W =2, 2 and 2 time t is: De = 6 -----

-

Pm pT(t) PiL

+

i(t) (W-1) Smax]

(6)

To compute the target inter-nodal distance d7T(t), each sensor-actuator i first collects the event intensity S(t) sensed by its neighbor k. Then, assuming a perfect triangular tessellation (1) and using the target density defined in (6), it derives d7jk (t) as: T 1 / 1

0 + T(t)) dik(t)= t 1T(t)

Looking at Figure 5, we observe that the relocation takes place successfully, and nodes surround the event getting denser as the distance from the epicenter decreases. To verify that the target density is indeed achieved, we compute the theoretical number of nodes, NT(d), that are expected to fall within distance d from the epicenter. NT(d) can be obtained by integrating the target density defined above, over a ring with inner radius De and outer radius d. Figure 6 shows the good match the number of nodes counted on a single exper~~~~~betweenwithin ~iment disks of increasing radius d, and the cor-

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responding theoretical value NT (d), for different combinations of W and Q. We observe that potential forces tend to greatly compress the nodes in proximity of the event; it follows that the local adaptation of the parameter Gik (t) in the expression of the exchange forces (4) is indeed necessary to obtain the desired density. =1 - W 3-algonithm 1 -W 3 - target 3=2-W=2-algorithm 32-W =2- -target

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Figure 6. Number of nodes within distance d from the epicenter (in the final configuration), for different values of W and S. Comparison between algorithm performance and theoretical target values 5.2.2 Transient behavior The performance of our relocation algorithm during the transient phase is compared against the results provided te otima, cntraize mW soltio ec. by theby optimal, solution (asin (as in Sec. centralized mWM 5.1l.2). We consider the same scenario as for Figure 5. To get a fair comparison, the initial and final network configurations are assumed to be the same for both our algorithm and the mWM solution. Also, by setting De = 6, the mWM trajectories are constrained to pass at a distance not smaller than 6 from the event epicenter; this implies that the optimal trajectory to reach a position behind the event consists of two segments connected by a piec of

rc bloning

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th cirula evet frntie of

radius 6. In Figure 7 we present the number of nodes within a distance d smaller than 9, 12, 18 from the event epicenter as a function of time, for both our algorithm and mWM. We observe that the temporal dynamics of the two solutions are very similar. Our algorithm takes a longer time to make all nodes arrive within distance 18 from the epicenter, however it brings nodes close to the event more quickly, as can be seen looking at the curves labeled by 'd < 9' and 'd < 12'. This is due to the fact that in our I--- +],-A algorithm nodes are attracted by the potential force and tend to move toward the epicenter, while in the mWM solution sensor-actuators follow the optimal trajectory,

hence move directly towards their final position. Also,

the hump presented by the mWM curves for d < 9 and

d < 12 can be explained by the fact that many trajectories pass along the circular frontier of the event, which, as previously mentioned, correspond to the shortest path toward a final position located behind the event. So far we have assumed that all nodes can detect the event since it begins. However, our algorithm is able to correctly relocate the network, even when only a subset of the nodes (in the extreme case, just a single node) initially detect the event. Let R be the maximum distance from the epicenter at which the event is detected. We consider three values of R, namely 30, 40, 80, as shown in Figure 5. When R =80, all nodes sense the event in When R the sinceitit s. starts. When R = 40, about halso half of the nodes nodes 40, about detect the event at the beginning, whereas just a few of them initially detect it for R =30. We highlight that them inialltopologiestachieved by thenetwork ht theeqi librium as we vary R are all very similar (they are not reported for the sake of brevity). Instead, it is interesting for thate otaininterms toste of network responsiveness, i.e., how long it takes tothe network to reach the final configuration, as R changes. n Figre8wp the tempora tion o thennumIn Figure 8 we plot the temporal evolution of the number of nodes arrived within distance 9, 12, 18 from the epicenter, for each considered value of R. We observe that the performance of the algorithm are essentially the same as long as at least half of the nodes are aware of the event (R 40, 80). When only a few nodes initially detect the event (R 30), it takes much longer to the nodes to arrive within distance 18 from the epicenter, however the number of nodes in the close proximity of the event (d < 9) is almost unchanged with respect to the case 2 relationof som s e o-ttorsin e c poim~relocation of some sensor-actuators in the close proxim-

ityofthres eetitha.atr msnmnycsso inest 2Animlatedl picture: showing what really happens in this case are available at [21]

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6. Conclusions

....d...We proposed a unified, distributed algorithm for self-

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deployment and event-based relocation in mobile networks where nodes have both sensor and actuator capabilities. Our approach is based on virtual forces, which allow nodes to coordinate their movements without the need of any central controller. Starting from an initial

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random topology, the algorithm enables the network to ,self-organize so as to form a triangular tessellation with the desired inter-node distance. Upon occurrence of an event, such as a physical phenomenon or an environmental disaster, nodes relocate themselves around the target location, achieving a desired density which can depend on the local intensity of the event. We showed that,

, 4000

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Figure 8. Temporal evolution of the number of nodes arrived within distance 9,12,18 from the epicenter, according to our algoo rithm, for different values oftinhe maximu m detection distance R

compared with a centralized, optimal approach, our algo-

rithm provides satisfactory performance in terms of both nodes' total movement and system responsiveness.

events

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[i] I.F. Akyildiz, I.H. Kasimoglu, "Wireless sensor and actor networks: Re-

[2] V. Bokser, C. Oberg, G.S. Sukhatme, A.A. Requicha, "A small submarine robot for experiments in underwater sensor networks," IFAC, 2004. [3] Sub-Kilogram Tele-robots (SKIT), http:// Intelligent -wwwrobotics.usc.edu/behar/SKIT.html, visited in June

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search challenges," Ad Hoc Networks Journal, vol. 2, no. 4, pp. 351-367, 500 600 700 800 50607080Oct. 2004.

De

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[4] Sandia National Laboratories, http://www.sandia.gov/media/ NewsRe1/NR2001/minirobot .htm, visited in June 2006. [5] GPS Receiver for Outdoor Use, http://forestry.about.com/ od/mappinggis/p/GPS-essentials.htm, visited in December 2006.

[6] G. Wang, G. Cao, T.F. La Porta, "Movement-assisted sensor deployment," IEEE Trans. on Mobile Computing, vol. 5, no. 6, pp. 640-652, June 2006.

x

Figure 9. Final configuration achieved at the equilibrium by 1000 nodes in response to the multiple events described on the

right of the plot

5.2.3

~~~~~~~~~References

[7] Z. Butler, D. Rus, "Event-based motion control for mobile sensor networks," IEEE Pervasive Computing, vol. 2, no. 4, pp. 10-18, 2003. [8] G. Wang, G. Cao, T.F. La Porta, W. Zhang, "Sensor relocation in mobile

Mar. 2005. Miami, [9] X. Li, N. Santoro, and I. Stojmenovic, "Mesh-based Sensor Relocation for Coverage Maintenance in Mobile Sensor Networks," In Proc. UIC '07, Hong Kong, China, July 2007. [10] E. Bonabeau, M. Dorigo and G. Theraulaz, "Swarm intelligence: From natural to artificial systems," Oxford University Press, 1999 sensor networks," INFOCOM '05,

FL, pp. 2302-12,

[11]

Multiple events

To conclude, we show an example of the behavior of our algorithm in the case of multiple events (e.g.; fires) overlapping in time. Figure 9 depicts the final configuration achieved by N = 1000 nodes, in response to the events described on the right of the figure. Sensor-actuators are initially deployed over a disk of radius 30 centered at (0, 0). The epicenter of three events is inside the de-

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We observe that the nodes relocate around the events, satisfying the target density around them and preserving network connectivity. Notice however that there are not

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ployment region, whereas event 3

occurs

enough nodes to surround event 3, jointly with the other '

events. This complex example allows us to emphasize the robustness of our distributed solution i.e., the ability of our algorithm to handle multiple events without re-

quiring global coordination.

[17]

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