Distributed Actor Deployment

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A Distributed Actor Deployment Algorithm for Maximum Connected

Coverage in WSAN

Ren Xiao-ping, Cai Zi-xing

School of Information Science & Engineering, Central South University,

Changsha ,410083,ChinaEmail:[email protected]; [email protected]

Abstract

Wireless sensor and actor networks receive more

interests with the appearance of wireless sensor

networks weakness and the development of robotics.

In this new autonomous network, actors are deployed

to cover the monitored area, receiving sense data from

sensors and taking proper actions. In this paper, we

presented a distributed actor deployment algorithm for

maximum coverage. We prove that regular six-polygon

can achieve maximum coverage with the least waste,

and our approach is based on it. This distributed

algorithm moves actor nodes to extend their coverage

while maintaining sensor-actor connectivity and with

less blind-areas. Finally all actors can reach

equilibrium by this self-excitation mechanism. The

performance of our algorithm is validated analytically

and experimentally.

0B1. Introduction

A Wireless Sensor Network (WSN) is a self-

organizing network with potential applications in

autonomous monitoring, urban search and rescue[1]. It

consists of a group of static nodes, which are deployed

in large quantities to form an autonomous network.

However, they can only perform one task. Recently the

development of robotics enables Wireless Sensor and

Actor Networks (WSANs) receive more and more

attentions, because WSAN is integrated by a large

quantity of sensor nodes and a few number of special

nodes called as actuators or actors[2]. Coordination andcooperation between sensor and actor are required to

provide the best response, so reliable communication

and maximum coverage of sensors and actors is

required in WSANs applications.

Sensor nodes are small, inexpensive, usually with

limited power, computation resources, and

communication capabilities, and these devices behave

like passive elements which monitor the environment.

Sensors may not only stop by fault but also suffer from

arbitrary faults. Furthermore, wireless communication

is less reliable due to noise and shortage of power of

sensors. Actor nodes are resource-rich and usually

mobile, and these characteristics enable an actor that

can make independent decisions to execute appropriate

actions in accordance to the collected information. Inpractical application, one case is that WSANs often

operate unattended in harsh environments where actors

can easily fail or get damaged; another case is that

sensors may stop work because of the power

limitations or failure. Such failures can partition the

sensor-actor network, form a hole in the monitoring

fields and thus eventually make the whole network

useless[3]. Mobile actors can move around to cover the

sensing field and interact with static sensors, this

mobility and decision making ability brings WSANs

some extents of fault-tolerance. If failures happen to

WSANs, actors decision making process should check

the fault rapidly, and form a connected network amongsensors and actors in order to make WSANs can

continue to work for some time.

This paper is organized as follows: the next section

describes the related work. Section 3 discusses the

system model, assumptions. Details of our approach

are discussed in section 4 and the experiment of the

approach is in section 5. Section 6 concludes the paper

with a summary and our planned future extensions.

1B2. Related Work

Node deployment is an essential and important

issue in WSANs, because it not only determines theenergy cost and communication delays for sensors

network, but also affects how efficient and maximum a

region is covered and monitored by sensors and actors.

Many researches on nodes deployment have been

done in WSANs regarding fault tolerance and coverage

respectively. For example, the work in [4] presents a

distributed Partition Detection and Recovery

Algorithm(PADRA) which can determine possible

partitioning in advance and recover the connectivity in

2009 Fifth International Conference on Natural Computation

978-0-7695-3736-8/09 $25.00 2009 IEEE

DOI 10.1109/ICNC.2009.247

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978-0-7695-3736-8/09 $25.00 2009 IEEE

DOI 10.1109/ICNC.2009.247

283


978-0-7695-3736-8/09 $25.00 2009 IEEE

DOI 10.1109/ICNC.2009.247

283


978-0-7695-3736-8/09 $25.00 2009 IEEE

DOI 10.1109/ICNC.2009.247

283


978-0-7695-3736-8/09 $25.00 2009 IEEE

DOI 10.1109/ICNC.2009.247

283


978-0-7695-3736-8/09 $25.00 2009 IEEE

DOI 10.1109/ICNC.2009.247

283


978-0-7695-3736-8/09 $25.00 2009 IEEE

DOI 10.1109/ICNC.2009.247

283


978-0-7695-3736-8/09 $25.00 2009 IEEE

DOI 10.1109/ICNC.2009.247

283


978-0-7695-3736-8/09 $25.00 2009 IEEE

DOI 10.1109/ICNC.2009.247

283


978-0-7695-3736-8/09 $25.00 2009 IEEE

DOI 10.1109/ICNC.2009.247

283


978-0-7695-3736-8/09 $25.00 2009 IEEE

DOI 10.1109/ICNC.2009.247

283


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case of such failures. If a partitioning is to occur,

PADRA designates one of the neighboring nodes to

initiate the connectivity restoration process. This

process involves repositioning of a set of actors in

order to restore the connectivity. However it only

considered inter-actor network, handling the failure of

actor nodes locally. Holes formed by the failure of

sensor nodes are not concerned here. Similarly, a fault-

tolerant model called multi-actor/multi-sensor

(MAMS) was discussed in [5]. In this model, each

sensor sends information to multiple actors and an

actor receives sensed information on a same event

from multiple sensors. Even if some sensors are faulty

and messages are lost in the wireless link, each actor

can receive proper sensed information from the other

proper sensors. This fault-tolerant strategy depends on

the redundancy of information, once some fields

sensors is useless and cannot sense the environment,

this method cant help to guarantee this fields are still

be under control.

Akkaya and Janapala proposed a distributed actordeployment algorithm that strived to maximize the

coverage and maintain the inter-actor connectivity

[6].They were inspired by the principle of repulsion in

physics when the molecules start diffusing in order to

reach equilibrium. As is shown in fig.1, their

deployment algorithm was based on triangular grid,

and still there are uncovered areas (shadow areas).

Once sensors deploy in this areas, actors can not sense

the existence of these nodes. In this paper, we present a

Distributed Actor Deployment Algorithm for

Maximum Coverage, namely DA2MC, which is

inspired by [6] and [8]. The main concern of this paper

is achieving maximum actor coverage under somelimitations, solving the problem that how to deploy

actor nodes in order to maximize the coverage of actor

nodes without blind-monitor-area.

ijdcr

sr

Figure 1.Actor deployment based on triangular grid

2B3. Problem description and system

modeling

We assume a WSAN operate randomly throughout

a Field of Interest (FoI). The number of actors is

limited since the robot is expensive. All the sensor

nodes are homogeneous, that means the same abilities

(communication distance cr and sensor distance sr , thedifference is shown in fig.1), and so do actor nodes.

Actors can discover each other and collaborate with

other actors in the filed through wireless

communication, and they can also collect and transmit

sensors data. One efficient actor deployment

algorithm should meet the following requirement: the

actor nodes can coverage all the FoI without less

uncovered areas; for the limitation of the actors

number, the covered area should maximize; maintain

the inter-actor connectivity.

For the actors communication range is a circle, first

consider a simple scenario of deployment, which is

covering a regular square fields with a circle. We can

substitute circle with inscribed regular polygon to

cover the FoI

[7]

. We assume that there are m angles ofregularNpolygon around a vertex, the equation of theangels is:

( 2)2

2(1 ) 2

Nm

Nm

N

= = (1)

Then we can list the following restriction

equations (2):

*

2

2

, , 2, 2 Z

2(1 ) 2

m

N

m n m N

m

N

>

>

=

(2)From (2) we can get three answers:

2 4, 2 1 6, 3

2 2, 2 2 4, 4

2 1, 2 4 3, 6

N m N m

N m N m

N m N m

= = = =

= = = =

= = = =

(3)

This results show that there are three ways to cover

a plane area using inscribed regular polygon: (a) using

six equilateral triangles; (b) using four squares; (c)using three regular hexagons.

Then two circles public area was shown in Fig.

2. AB was one border of the inscribed regularNpolygon, arc ADB s central angle is 2 /n . 1O A is

actors communication radius, cr ; area of 1AO B is21/ 2sin(2 / ) cn r and area of sector 1AO B is

21/ 2(2 / ) cn r ,so the shadows area sA in the figure

is:2 21/ 2(2 / ) 1/ 2sin(2 / )s c cA n r n r = (4)

284284284284284284284284284284284


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cr

Figure 2.Two circles public area

Then we can calculate two circles public area

is n scale of one circle:2 2

2 2

2 1/ 2(2 / ) 1/ 2sin(2 / )2s c cn

c c

A n r n r

r r

= =

/ sin(2 / ) / 22

n n

= (5)

Let 3, 4, 6n n n= = = , and we can get the results

that3

39.10% = ,4

18.17% = ,6

5.77% = .

Now we prove that using regular six polygons canreach maximum coverage and maintain all the areas

are covered by actors .We define the system models as

follows: Given n actors and m sensors placedrandomly in FoI. Assuming that actor and sensors

know their locations and neighbors. We are interested

in redeploy nodes in order to form a connected network

that maximizes area coverage.

3B4. Distributed Actor Deployment

Algorithm for Maximum Coverage

In section 3, we prove that regular six polygon canbe used to achieve maximum coverage with least

waste, and deploy nodes can be carried out through aglobal manner. We presents Distributed Actor

Deployment Algorithm for Maximum Coverage(DA

2MC), which can stimulate actors can reach

equilibrium by self-excitation. DA2MC moves actor

nodes to extend their coverage while maintaining

sensor-actor connectivity and without blind-monitor-area. This distributed manner was inspired by [6] and

[8].Each node has repelling forces to move the actors

for better area coverage and pulling forces to ensure

actor-sensor connectivity.

As is shown in Fig.3, assuming that there are onlythree nodes 1 2 3, ,O O O , which are deployed in FoI

randomly, 12f

is the repelling force on 2O from 1O ,

and 32f

is repelling force on 2O from 3O . ijf

can be

confirmed by(6):

( ) 2

0, 2

ij i j c

ij

ij c

f d if d rf

if d r


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' '

2 2 2 2 2 2k x y k x= + (11)

Actor nodes movement must satisfy inter-actor

connectivity, as shown in equation (12), 3 / 2cr is

distance of 3O C ,computing method is in fig.3(b).' 2 ' 2 2

1 2( ) 2 1 2 1

' 2 ' 2 2

3 2( ) 2 3 2 3

( ) ( ) ( 3 )

( ) ( ) ( 3 )

= + = = + =

new c

new c

O O y y x x r

O O y y x x r (12)

Some symbols explanations:

A : Area in which actor nodes and sensors nodes

operate.

G : Aggregate of all the actor nodes in WSAN.

i : ID number of an actor node in WSAN, each

nodes has a different number.

N: Number of actor nodes in WSAN.

( )d i : Node degree of node i .

( , )i iy : Coordinate of node i .

iL : Neighbor list of node i .i

r: Maximum communication distance of node i ,

here is a constant cr .

: Interval of broadcast an Ackmessage, is a

random value between[0, ]AckInterval .

DA2MC Procedure:

i. Initially each node in A broadcasts an Ack

message with its ID and coordinate ( , )i iy every

other time.

ii. When i receives Ack from j , it updates iL

unceasingly.

iii. Compute ( )d i according to iL , adds it toAck

message and broadcasts this updatedAckmessage.

iv. i compares its ( )d i with its neighbors in iL ,if it

has the maximum value in its neighborhood, begin to

compute new location by using equation (10)-(12),

then go to procedure v; if ( )d i = ( )d j , then go to

vii, else go to vi.

v. i updates its new location inAckmessage and

send Leaving message to inform its neighbors.

vi. i listens toAckmessage until it hears Leavingmessage from neighbors, then go to iv.

vii.Compare ID number, if


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Table 1. Destination of original nodes

n d Original k Unopti. Dest. Dest. d(un) d(opt.)

A 6 (710.8,744.8) 0.23 (781.3,761.2) (759.3,756.1) 72.4 49.8

B 5 (732.0,746.8) 4.34 (764.5,888.0) (764.5,888.0) 144.9 144.9

C 5 (764.9,922.4) 0.49 (778.2,929.0) (870.2,974.4) 14.8 117.4

D 5 (719.1,847.5) 1.96 (778.5,964.0) (784.5,975.9) 130.8 144.1

E 4 (627.2,732.7) -4.23 (629.0,725.3) (643.4,664.3) 7.6 70.3

F 4 (698.7,841.3) 0.58 (821.5,912.2 ) (670.1,824.7) 141.8 33.1

G 3 (679.2,978.3) 0.19 (847.4,1010.3) (649.1,972.6) 171.2 30.6

H 3 (723.8,664.1) -0.12 (810.0,651.8) (896.4,645.7) 87.0 173.6

I 2 (604.4,765.1) -0.86 (593.5,774.5) (580.5,785.7) 14.4 31.6

J 2 (822.0,850.3) -1.62 (846.8,810.2) (885.6,747.3) 47.1 121.1

K 2 (743.5,977.1) -1.35 (704.4,1030.1) (840.3,846.6) 65.9 162.5

L 1 (846.4,647.2) -0.03 (772.2,649.4) (772.2,649.4) 74.2 74.2

M 1 (609.4,944.9) 0.48 (569.3,925.7) (569.3,925.7) 510.7 44.5

N 1 (895.6,645.9) -0.03 (1020.6,642.0) (1020.6,642.0)

125.1 125.1

O 0 (978.6,796.6) -3.82 (991.5,747.3) 51.0

In the experiment of DA2MC, we evaluate the

performance of DA2MC. When all the nodes reach a

equilibrium, average distance actors traveled is

91.6 m , whereas this value is 114.9 m when they

move to a unoptimizable destination, which means

iterative application of DA2MC can get a better

configuration result at the cost of time. The

connectivity-rate of inter-nodes is22.0% and coverage

area is 147245.1

2

m , before we applied DA2

MCcoverage area is 108693.6

2m .Coverage area expands

about 35.47%.

5B6. Conclusions

WSANs are more and more popular in recent years,

and receive an increased interest of researchers. In

WSAN, a set of mobile actor nodes are deployed inaddition to sensors in order to collect sensors data and

perform specific tasks. The main goal of DA2MC is

maximizing the coverage of actor nodes with the

limitations of inter-actor communications. This idea is

inspired by combination of virtual repelling forces inorder to estimate the directions and locations of nodes

movement.Since this scheme may not connect all actors, in our

experiment of DA2MC, the connectivity rate is 22.0%,

but the coverage area extends obviously, by 35.47%.

DA2MC is completely distributed, in the future, we

plan to apply this approach to a real WSANs scenario.

BAcknowledgements

This work was supported in part by the National

Natural Science Foundation of China under Grant90820302 and 60805027, Research Fund for the

Doctoral Program of Higher Education under Grant200805330005, Academician Foundation of Hunan

Province under Grant 2009FJ4030, and also in part by

Quality and Supervision Commonweal Profession

Research Project under Grant 200810002.

7BReferences

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[2] C.J. Rozell, D.H. Johnson, Power Scheduling forWireless Power Scheduling for Wireless Sensor and Actuator

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Networking Conf., Las Vegas ,2008,pp.2480-2485.[5] K. Ozaki, K. Watanabe, S. Itaya, H. Naohiro, T.Enokido and M. Takizawa, A Fault-Tolerant Model forWireless Sensor-Actor System, 20th Int. Conf. on Advanced

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[6]

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