978-1-4577-0101-6/11/$26.00 c©2011 IEEE

Flocking Based Distributed Deployment for Target

Monitoring in Mobile Sensor Networks: Algorithm

and Implementation

Yibo Wang, Zhiliang Tu, Qiang Wang, Member, IEEE, Yi Shen, Member, IEEE, Jiayi Li

Department of Control Science and Engineering, Harbin Institute of Technology, 150001, P. R. China

wybhit@gmail.com, wangqiang@hit.edu.cn

Abstract—Improved algorithms based on our previous work ondistributed deployment for monitoring over a region of interestcentered at a target which could be stationary and mobile are firstprovided. Then a developed platform consisting of ComBots isintroduced detailedly. Implementation of the proposed algorithmson the developed experimental platform is discussed. Simulationsdemonstrate the high effectiveness of the algorithms and exper-imental results further show the effectiveness of our platformconsisting of 7 ComBots and the flocking based deploymentalgorithms.

Index Terms—Flocking, mobile sensor network, sensor deploy-ment, triangle tessellation.

I. INTRODUCTION

Distributed sensor deployment of mobile sensor networks

(MSNs) has attracted significant attention [1]–[4]. Owing

to the locomotion ability, an MSN can self-deploy flexibly

and adaptively to monitor unknown and hostile environments

such as harsh fields, disaster areas, battlefields, toxic regions

or target tracking, while conventional static sensor networks

are not qualified since the deployment cannot be performed

manually and is not adaptive to the environmental dynamics.

In contrast to centralized deployment strategies which prob-

ably suffer from communication delay and bandwidth lim-

itation [5], distributed sensor deployment methods control

each mobile sensor based on only local and neighborhood

information. Therefore, distributed ways are more scalable and

more suitable for dynamic environments monitoring.

Most previous research efforts on deployment optimization

focus on how to deploy sensors over a given region of interest

(ROI), i.e., within a boundary. However, there is a kind of

applications that mobile sensors are required to be deployed

around a Target of Interest (TOI) which could be stationary or

moving. For example, the target could be any enemy target in

the battlefield surveillance, or the leak source in the leakage

detection and the pollution source in the pollution monitoring

[6]. In [7], Liu et al. proposed a simple control algorithm

based on Hooke’s law and Coulomb’s law to construct a bi-

connected network around a central point that can produce a

hexagonal tessellation. In [8], Li et al. considered the problem

of constructing focused coverage around a Point of Interest

(POI) and proposed two localized protocols GA and GRG

for deployment around the POI. They drive sensors to move

along a locally-computable equilateral triangle tessellation to

surround the POI. However, above works have drawbacks in

common that every sensor is required to be aware of the

position of its own as well as the central point, i.e., support

from GPS-like devices is required, and moreover, the situations

of mobile POI as well as nonuniform deployment are not

considered. In [9], Garetto et al. studied the problem of self-

deployment in MSNs for environmental monitoring purpose.

They proposed a distributed virtual force based algorithm,

which obtains a regular tessellation based on detectable event

density. Only 1-hop neighborhood information and direction of

the event is needed, but the dynamic environment case is still

not considered, neither is stability being provided. Moreover,

full coverage cannot be guaranteed, i.e., coverage holes cannot

be avoided.

Flocking including schooling of fish, birds and swarming

of ants is a group behavior that a large number of agents

regulate into a coordinated motion by only limited interaction

and simple rules. Flocking has attracted a lot of attention

from researchers in biology, physics and computer science for

decades [10]–[12].

In our previous work [13], we presented two categories

of distributed algorithms, i.e., algorithms based on single

integrator and double integrator dynamics which are also

called first-order and second-order algorithms for short, in

both isotropic and anisotropic mobile sensor networks. The

two algorithms both aim to relocate sensors to around a TOI

uniformly and drive the network to approach an equilateral

triangle tessellation centered at the TOI, which maximizes the

effective coverage area without coverage hole. All information

required in the first-order deployment algorithm is:(1) relative

positions of 1-hop neighbors which can be easily obtained

by IR or acoustic sensors; (2) relative direction to the TOI

which can be implemented by analyzing images taken from

a camera equipped on top of the mobile sensor or inferred

from the local sensory data providing the steepest variation

[9]. Compared to the first-order algorithm, the second-order

algorithm makes an extra assumption that relative velocities

of neighbors and the TOI can be detected. It not only drives

the network to an equilateral triangle tessellation but also

results in a flocking behavior, i.e., all sensors reach a common

velocity with the TOI while keeping a constant distance from

neighbors. Hence the network configuration obtained by the

second-order algorithm is more stable which is good for

U.S. Government work not protected by U.S. copyright

wireless communicating.

The main contribution of this paper is to demonstrate

the experimental results of improved algorithm based on the

previously proposed flocking based deployment algorithm with

our developed platform. In particular, details of the architec-

ture, characteristics and implementation technologies are first

provided. And then experiments with seven robots are depicted

and analyzed.

The rest of the paper is organized as follows: Section II

presents some preliminaries and the two proposed deploy-

ment algorithm. Section III introduces the platform. Section

IV evaluates the performance of the proposed algorithm by

simulations and experiments. Section V concludes this paper.

II. PRELIMINARIES AND DEPLOYMENT ALGORITHMS

A. Graph Theory Notations

We consider a mobile sensor network with N mobile nodes

in an n-dimensional space, where xi ∈ Rn denotes the position

of node i, i = 1, · · · , N . Suppose the whole network can be

modeled by an undirected graph G = (V, E), with V denoting

the set of sensors and E ⊆ {(i, j)|i, j ∈ V, i 6= j, ‖xi − xj‖ ≤R} the set of information links. Node i can obtain information

like relative position and velocity of node j if (i, j) ∈ E .

R = Rc when a GPS-like device is available, where Rc is the

communication radius. While in some applications like indoor

environments where GPS is not available, sensor i can measure

the relative position and velocity by equipped devices, then

R = Rd, where Rd is the detection range. Usually, Rc ≥ Rd.

Neighbors of node i is defined as a set Ni , {j| (i, j) ∈ E}.

The adjacency matrix A = (aij)N×N is a weighted matrix,

where aij 6= 0 iff j 6= i, (i, j) ∈ E , aij ∈ [0, 1]. For homoge-

nous undirected sensor networks, matrix A is symmetric, i.e.,

A = AT. aij represents the weight between nodes i and j,

which reflects the strength of the interaction between them.

The larger aij is, the closer the node i and node j are. Let xi

be the location of node i and X = (xT

1, · · · , xT

N )T denotes the

position configuration of the network. There are many ways to

define A, for simplicity and performance evaluation purpose,

we adopt the definition in [14]:

aij(X) = ρh(‖xi − xj‖σ/‖R‖σ), j 6= i and aii = 0 (1)

where

ρh(z) =

1, z ∈ [0, h),1

2

[

1 + cos(

πz − h

1− h

)]

, z ∈ [h, 1],

0, otherwise.

(2)

where the σ-norm ‖ · ‖σ is a differentiable function defined as

‖z‖σ = 1

ǫ(√

1 + ǫ‖z‖2 − 1) with a parameter ǫ > 0, h serves

as a threshold that adjusts the interaction strength between

neighbors. A larger h contributes more to velocity consensus.

B. Problem Formulation

Consider the binary sensor model, i.e., the probability

P (i,E) that an event E occurs at location XE is detected by

sensor i located at xi is:

P (i,E) =

{

1, if ‖xi − xE‖ ≤ Rs

0, otherwise.(3)

where Rs is the sensing radius of sensor.

For given three homogenous sensors, it has been shown that

coverage is maximized when they constitute an equilateral

triangle under the constraint that there is no coverage gap

between them [15], [16].

Fig. 1. The deployment to surround a TOI: from an initial random distributionto an equilateral triangle tessellation.

Therefore, to monitor an ROI centered at the TOI, effective

coverage area is maximized without coverage hole inside the

network when sensors form an equilateral triangle tessellation

as shown in Fig. 1. In the ideal case, the coverage area is

maximized with the network connectivity guaranteed when the

inter-node distance d =√3Rs iff R ≥

√3Rs. Otherwise, d =

R to guarantee connectivity if R <√3Rs.

Therefore, to maximize coverage area and ensure no cov-

erage hole inside the network, our goal is to deploy sensors

around the TOI uniformly to approximate an equilateral tri-

angle tessellation while reducing sensor movements as much

as possible. Moreover, to reach a steady monitoring configu-

ration, when the TOI is moving, movements of sensors should

coincide with TOI.

C. First-order Deployment Algorithm

Ignoring the low-level control, the first-order dynamics of

sensors can be described as:

xi = ui, i = 1, 2, · · · , N. (4)

Then control law of node i is:

ui = vmaxtanh(k1‖uαi ‖)

uαi

‖uαi ‖

, (5)

where vmax is the maximum allowed velocity, k1 > 0, and

uαi = −ω1∇xi

∑

j∈Ni

Vji(X, d) + c1(xi, xT ) · ~xiT , i /∈ NT ,

uαi = −ω1∇xi

∑

j∈Ni

Vji(X, d)− ωT∇xiViT (xi, xT , d

∗T )

+c1(xi, xT ) · ~xiT , i ∈ NT , (6)

where ~xiT = xT−xi

‖xT−xi‖. The neighbor set Ni is a set satisfying

j ∈ Ni ⇔ i ∈ Nj . NT is the node set which can detect relative

position and velocity to the TOI. d∗T is the appropriate distance

between NT and the TOI. ω1, ωT and c1(xi, xT ) are positive

parameters, ωT > ω1 and c1(xi, xT ) is defined as:

c1(xi, xT ) =

{

C0 , xi ∈ ROI;

C′

0, otherwise .

(7)

where C′

0> C0 > 0. In practice, we don’t have to know

where the ROI exactly is to choose among C′

0and C0, the

sensory data can be used to estimate it, (e.g., C′

0is chosen

if a sensed item is beyond a threshold), or in visual sensor

networks, the pixel size of TOI also can be used to reach the

decision. When a smaller c1 is chosen, a better approximation

of inter-node distance to the optimal d∗ can be obtained, while

splitting happens when too small c1 is adopted. To get a more

uniform and compact deployment, we adjust C0(i) adaptively:

C0(i) = f

(

‖∇xi

∑

j∈Ni

Vji(X, d)‖)

, (8)

where f is a monotonically increasing function. In this paper,

we adopt

f = C0

1

(

‖∇xi

∑

j∈NiVji(X, d)‖

fmax

)

+ Cmin (9)

C0

1is the maximum value and fmax is the estimated maximum

potential force. Cmin is a lower bound to ensure network

cohesion. The potential function is defined as:

Vij(X) = ϕα(‖xi − xj‖σ), (10)

ϕα(z) =

∫ z

‖d∗‖σ

ωα(s, ‖d∗‖σ)φα(s)ds (11)

where

ωα(s, ‖d∗‖σ) =

−M1 − 1

‖d∗‖σ(s− ‖d∗‖σ) + 1, s ≤ ‖d∗‖σ;

M2 − 1

‖R‖σ − ‖d∗‖σ(s− ‖d∗‖σ) + 1, otherwise.

(12)

φα(z) =1

2ρh(z/‖R‖σ)[(a+b)σ1(z+c−‖d‖σ)+a−b] (13)

where σ1(z) = z/√1 + z2, 0 < a ≤ b, c = |a − b|/

√4ab,

M1, M2 > 1 are the amplification coefficients.

The first gradient based term is used to guide sensors to

move toward the direction of potential gradient descent, and

the second term is used to guide sensors toward TOI . Hence

the final equilibrium should be in the way that mobile sensors

distribute around TOI and have a unified space from each other

and keep cohesion.

D. Second-order Deployment Algorithm

Consider N mobile sensor nodes moving in an n-

dimensional plane, with second-order dynamics:

{

xi = vi,vi = ui, i = 1, 2, · · · , N.

(14)

where vi, ui ∈ Rn are the corresponding velocity and the input

control law which acts as acceleration, respectively.

As a model that has a higher similarity to real physical

system, second-order dynamic model is extensively used. As-

suming every sensor has a unit mass, when TOI is stationary,

the control input for are formulated as following:

uβ1i = −ω1∇xi

∑

j∈Ni

Vji(X)− ωT∇xiViT (xi, xT , d

∗T )

+ω2

∑

j∈Ni

aji(x)(vj − vi)

+c1(xi, xT ) · ~xiT − c2vi, (15)

while TOI is moving, the control law is:

uβ2i = −γsgn

{

1NT(i)(viT − vT ) +

∑

j∈Ni

(viT − vjT )}

−ω1∇xi

∑

j∈Ni

Vji(X)− ωT∇xiViT (xi, xT , d

∗T )

+ω2

∑

j∈Ni

aji(x)(vj − vi)

+c1(xi, xT ) · ~xiT − c21NT(i)(vi − vT ), (16)

where

˙viT = −γsgn{

1NT(i)(viT−vT )+

∑

j∈Ni

(viT−vjT )}

, i = 1, · · · , N.

(17)

viT is the estimate of vT by node i. All parameters here which

have been involved in Eq. (6) have the same meanings. ω2, c2are positive constants, γ > ‖aT ‖∞. And also the control

law and velocity are shrunk in the same way as Eq. (5) . In

Eq. (15), the second line is a velocity consensus term which

regulates all sensors’ velocities converge to a common one.

It displays the collaborative behavior of sensors and decreases

oscillation effectively. The last line, which acts as a navigation

feedback term in flocking behavior, includes a cohesion term

which enhances compactedness of network and a velocity

damping term which effectively decreases oscillation.

III. EXPERIMENT PLATFORM

The experiment platform consists of seven ComBots, each

of which is a mobile robot developed by the Detection and

Control Center (DCC) at Harbin Institute of Technology (HIT).

Fig. 2 shows the physical configuration of a specific combot.

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Fig. 2. The physical configuration of a ComBot.

A. ComBot: A composable robot

The ComBot is equipped with PXA270 processor as the

central processing controller for embedded operating system.

All the ComBots have the ability of communication, calcu-

lation and evaluation. After ComBot i gets its distributed

information, such as relative location between target and itself,

and relative locations between neighbor ComBots and itself,

it will utilize the potential function to calculate the desired

direction angle and velocity, and then send these control

signals to CDS5500, the steering engine, to command the

subsystem to its desired confituration.

Each Combot has three degrees of feedom actuated by six

steering motors. The two of the six steering motors in the

lower-level are used to control the forward and backward

speed through the open loop model. The rest four of them

use servo engines to control the moving directions ranging

between [−90, 90]. The illustrative configurations are shown

in Fig. 4.

B. Network model

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Fig. 3. Architecture of experimental platform.

The experimental platform is setting to test the proposed

flocking-based mobile sensor deployment algorithms. The

platform consists of a PC running MATLAB software suit, the

ComBot physical subsystem and the wireless communication

modules. The function of the MATLAB based host machine is

to collect and process global image of the working area to get

the location and orientation of each ComBot. The information

is transmitted to the ComBot subsystem through the wireless

communication modules. The ComBot subsystem acts as the

decision maker and final executer of the generated commands.

1) Positioning system: Mixed programming in host com-

puter is realized using OpenCV, C++ and MATLAB to process

data collected by the overhead cameras. A red identification

digit-plate paper is attached on the top of each ComBot with

white numbers. Those white numbers equally represent the

number of each ComBot. The center and direction of the

red digit-plate are considered as the center and direction of

ComBot.

The collected information include the identification number

on the top of each ComBot and the position messages.

The global information P = {(Xi, θi) |i ∈ V } , where Xi

denotes global position and θi is the global angle. We

can transform global coordinates into local coordinates, so

the local information of ComBot i is P (i) = {(Xi −Xj)A(θi) |i, j ∈ V, i 6= j , i ∈ Ni}, where A(θi) is rotational

coordinates transformation matrix.

2) Communication system: In ComBot, the PXA270 based

controller connects WLAN card VT6656 through USB port. It

also implements TCP by C++ to communicate with client and

server in embedded operating system. In Instrument Control,

one toolbox of MATLAB software suit, TCP objects are

provided to achieve TCP transmission, which acts as a pas-

sageway in the communication system. It delivers information

P (i) to ComBot i from host computer. During the communi-

cation, following the rules of message packing and information

analysis, the data sending and receiving are separated from the

transmission process to significantly improves the accuracy of

data transmission.

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Fig. 4. The schematic of ComBot.

As shown in Fig. 4, each ComBot operating in global

coordinate frame A follows the kinematics:

x = u cos θ + θ

y = u sin θ + θ

θ = ω

(18)

where u is the speed of body-fixed reference frame B, which is

attached to the centroid of the robot. The position of the frame

B in the global coordinate frame A is given by(x, y). The

orientation of the frame B is given by the angle θ with respect

to Y -axis. The angel θ denotes the wheel orientation with

respect to Y-axis, so that (θ+θ) denotes the moving direction of

ComBot. ω and ω is the angular speed of θ and θ respectively.

The dynamic equations for the motion of the ComBot are

governed by,{

mu = −ηx+ (FR + FL)Jω = −ϕω + l · △F

(19)

where m is the mass of the ComBot, J is its moment of inertia,

FL and FR are the forces generated by the left and right

wheels respectively, η and ϕ are the coefficients of rotational

and viscous frictions respectively. △F, can be considered as

an error between the difference of FL and FR which leads

the ComBot body to rotate. l denotes the moment arm of the

forces where the geometry center and center of mass in the

ComBot are assumed to coincide. Since the force inputs are

immeasurable, we would like to transform the model into a

form, in which the voltages applied on both left and right

wheels can be considered as control inputs. The force, F is

generated by a CDS5500 steering engine, which is the actuator

of ComBot. The steering engine has two patterns. One is

position servo control mode and the other one is open-loop

speed adjustment mode. The force generated by FLand FR is

under the open loop mode. It keeps wheels rotating precisely

as VL and VR. Thus, the last formula can be simplified as:{

u = 1

2(VR + VL)

ω = (VR − VL)l(20)

Therefore, the motion mode is significantly simplified. In

ComBot, the diversion of robot depends on ω , not ω, so

we can set VL and VR equal. Since the steering engine works

under open-loop mode, it is hard to keep VL and VR equal

which may lead to the rotation of body-fixed frame B .

In this experiment, ω will be treated as an error and can

be reconstructed directly from overhead cameras. Then we

calculate θ and rectify θ, the direction of steering machine.

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Fig. 5. Direction control of ComBot.

IV. SIMULATIONS AND EXPERIMENTS

A. Simulations

We first conduct two sets of simulations to verify the

effectiveness of proposed algorithms. Limited to the space

here, we provide only results obtained by algorithm (15) and

(16) and it’s not hard to predict the effectiveness of algorithm

(5) based on the demonstrated results.

The first simulation is to deploy 100 sensors that initially

distribute as Fig. 6(a). The TOI located at (−30m,−30m) is

far outside the network. By algorithm (15), mobile sensors

surround TOI uniformly without coverage hole, as shown in

Fig 6(b), and the distance of center of mass (CoM) of the

network from the TOI is just 0.7864m.

The second simulation is to regulate 36 sensors to monitor

a TOI with time-varying velocity. xT (0) = (0, 0), vT (0) =(0.05m/s, 0.08m/s), and aT (t) = (0,−0.0016 sin(0.02t)), γ =0.0017, therefore TOI moves along a sine curve with varying

acceleration. The snapshots at 0s, 300s, and 600s are depicted

in Fig. 6(c), respectively. Combine Fig. 6(d) which shows the

normalized velocity deviation defined as:

NVD(V ) =1

N

( N∑

i=1

‖vi − vT ‖2)

1

2

, (21)

we can see that a steady and uniform deployment around the

mobile TOI is obtained. Hence the second-order algorithms is

effective.

B. Experiments

Here we present detailed results from the two proposed

algorithms, respectively. The maximum speed is 0.19m/s. The

update frequency from ComBots is 5 Hz. The first experiment

is to deploy six followers to one stationary TOI. Snapshots of

the deployment process at t = 0, 15, 150s are shown in Fig. 7,

respectively. As we can see, the deployment is pretty uniform.

The second experiment is to deploy three Combots follow

one mobile TOI. Figure 8(a) shows the normalized position

deviation which is defined in the similar way as normalized

velocity deviation. It evaluates the deviation from the desired

uniform configuration. Figure 8(b) shows the normalized ve-

locity deviation which is used to evaluate the coincidence of

velocities of sensors and that of TOI. As we can see, the

network configuration reach a steady and uniform state.

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(a) Normalized position deviation

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(b) Normalized velocity deviation

Fig. 8. Deviation analysis.

V. CONCLUSION

In this paper, we discuss two distributed deployment al-

gorithms which are based on first and second-order dynam-

ics. Mobile sensors are required to be deployed around a

TOI which can be stationary or mobile and the network is

regulated to an equilateral triangle tessellation. The second-

order algorithm not only drives sensors to approach the

optimal configuration, but also regulates sensors such that

velocities of sensors coincide with the TOI’s. To demonstrate

the effectiveness of the proposed algorithms, experiments

with a developed platform consisting of seven ComBots are

conducted. Simulations and experimental results demonstrate

the effectiveness and availability of the proposed algorithms.

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(b) Deployment by algorithm(15)

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(c) The deployment around a TOI with time-varyingvelocity by algorithm (16)

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(d) The normalized velocity deviation

Fig. 6. Deployments obtained by proposed second-order algorithms.

(a) Initial deployment (b) Snapshot at t = 15s (c) Snapshot at t = 150s

Fig. 7. Snapshots to monitor a stationary TOI.

ACKNOWLEDGMENT

This work was supported in part by the National Natural

Science Foundation of China under Grant No.61174016and

No.60874054.

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