Cooperative Multi-Agent Approach to Dynamic

Coverage in Multi-Robot Activities

Satoshi Kataoka

and Shinichi Honiden

The University of Tokyo,2-1-2 Hitotsubashi, Chiyoda-ku,Tokyo 101-8430, Japan

Abstract. Dynamic coverage is a problem of multi-robot systems based on wire-

less ad-hoc networks. The issue of dynamic coverage occurs notably in post-

disaster survivor rescue, search operation, and planet exploration. In this paper,

we introduce an novel algorithm of dynamic coverage in a realistically restricted

environment for robots.

1 Introduction

We address the problem of deploying a mobile sensor network into an environment with

the task of maximizing sensor coverage of the environment. We restrict ourselves to the

case where every node in the network is a mobile robot. All the robots can calculate

their own the position by dead reckoning and/or GPS (Global Positioning System). All

the robots have wireless communication facilities. Our proposal claims that the robots

make the ﬁeld search as robustly and efﬁciently as they can in the range which they

do not miss each other. Our system is mainly made based on two approaches, Multi-

Agent-System and Dynamic and Distributed Voronoi Diagram. .The ﬁrst one is the

Multi-Agent-System approach.

2 Related Works

Exploration and map building by multi robots in an unknown environments has benn

studied[1]. Although [1] is efﬁcient, the devices of beacon are needed for others with

the robot which searches. And Voronoi Diagram is the algorithm often used in a sensor

coverage problem, and hos been studied by several authors[2,3].

3 Deﬁnition of Coverage Problem Solution

In this section we present a formal description of the planar boundary coverage problem

and provide high efﬁcient solution of the problem compared with the existing research.

We then provide a solution based on Voronoi Overlay, with complexity (n log n), as-

suming that all the robots in the network have the sensing range which is deﬁned for

every robot and knows its own range with each robot. We also make the assumption

that each device knows its two dimensional location. This is a reasonable assumption

since in the absence of this information, the boundary of coverage cannot be uniquely

Kataoka S. and Honiden S. (2006).

Cooperative Multi-Agent Approach to Dynamic Coverage in Multi-Robot Activities.

In Proceedings of the 2nd International Workshop on Multi-Agent Robotic Systems, pages 93-98

DOI: 10.5220/0001224500930098

 SciTePress

determined (i.e., from topological information alone). Moreover, the technology of the

position acquisition system which does not need a global system is realizable. We now

formally describe the coverage of a device. And parameters which used in this paper

are deﬁned below. We use the notation dist (p1; p2) to denote the Euclidean distance

between two points p1 and p2.

3.1 Deﬁnition

Deﬁnition 1 The communication range of a robot agent RA with planar coordinates

(x ,y) and sensing range R (which is graphically explained in Figure ??) is a disk with

center ( x, y)and radius R. R is the greatest range with which each robot can commu-

nicate. A robot determines the division which he should patrol within the limits of this

area. Moreover, in order that he may not separate with other robots completely, the

guarantee other robots are within the limits of this periodically is required.

Deﬁnition 2 The base position VP (voronoi position) of each robot agent on the ﬁeld is

held for every robot agent, and determines a search area by VP. That is, each robot agent

collects the bases of other agents within the communication limits = R, and calculates

a search area using Voronoi Diagram. Each robot changes each base by negotiation.

Deﬁnition 3 The search area VA (voronoi area) of each robot agent on the ﬁeld is

calculated by itself, and holds it. A robot searches by moving the inside of this area.

Moreover, a robot holds the information on the obstacle of the range which searched

once. Each robot determines this area using Voronoi Diagram from VP of each robot of

his communication within the limits.

Deﬁnition 4 Each agent has the obstacle information OI, and this information is up-

dated as it develops the ﬁeld. By using this information, each agent calculates ignore

area ID dynamically so that its area in its duty may not be divided. That is, in this

agent’s ID, other agents calculate VA as if this agent did not exist. An agent can de-

termine ID for every renewal of obstacle information without other agents information.

With our algorithm, only from other agents’ VP and ID, each agent can predict other

agents’ VA and can determine his VA. Since each agent does not need to re-calculate

VP and ID for every request from other agents, he can hold down the amount of com-

munications to minimum.

Deﬁnition 5 VP changes with negotiations between each agent. A robot moves simi-

larly to change of VP until each robot agent’s VA is decided. That is, VP cannot change

by the width of the velocity VEL more than a robot’s top velocity. Therefore, the high-

est of the VEL of VP is restricted by MAXVEL (max velocity).And we deﬁne the move

vector of VP in one step as VVECTOR.

Deﬁnition 6 An EVALUATION VALUE is used in the case of VVECTOR determination.

Since each agent calculates VVECTOR based on the EVALUATION VALUE acquired

from other agents, an EVALUATION VALUE can interfere in other agents’ action. In

other words, negotiation is performed through an EVALUATION VALUE.

Deﬁnition 7 The Dynamic Coverage Problem Given a set of n robots in the plane, each

with a sensing range r, patrol a plane with a random obstacle and acquire the state of

the plane on real time. Figure ?? expresses ﬁgure-description of Coverage Problem.

And take notice of two points which the next raises. The ﬁrst point EXPANDING TIME

is time until a robot’s area is spread and decided in the ﬁeld to the maximum extent.

The other point PATROLLING TIME is time concerning a robot patrolling VA.

3.2 Solving the Coverage-Boundary Problem with Voonoi Overlays

We divide each robot’s area in his duty (A) for the ﬁeld using voronoi overlays. The time

concerning a robot going round is proportional to VA. PATOROLLING TIME which

described our point is equal to the largest time of all robots. That is, making VA equal

as much as possible leads to improvement in PATROLLING TIME. Theoretical most

efﬁcient PATROLLING TIME can be expressed as follows.

P T min =

Sa − So

Numa

(1)

Sa · · · sizeoffield

So · · · sizeof obstacles

Numa · · · numberofagents

Our purpose is moving VP (the greatest move width of VP is equal to MAXVEL)

so that PATROLLING TIME may be brought close to PTmin as quickly as possible.

And this time is just EXPANDING TIME by convergence of VP.

We developed new approach of Voronoi Overlay of dynamic and a complete distributed

type. This approach has the low amount of communications, and is efﬁcient (EXPAND

TIME is small) compared with ordinary approach.

4 Architecture

The agent carried in each robot acts using a technique which is described below. More-

over, the technique is taking into consideration restrictions of a realistic robot which

stated by deﬁnition, and is the general-purpose thing which can set up each parameter.

4.1 Algorithm Description

Distributed and Dynamic Voronoi Overlay. As for each agent, each calculates its

VA. An agent takes only a disk of a radius R focusing on its VP into consideration in

that case. VA is calculated using Voronoi Overlay from VP of other robot agents who

are inside the disk. Although the agent besides a disk is disregarded here, since VA is

a set of the point that the agent is the nearest, even if it does not take a far point into

consideration, a bad inﬂuence does not give calculation of VA. And it becomes clear

also from the result of a simulation experiment that this thinking is right. Moreover,

by this, since it communicates only with other robots of communication within the

limits, there is no necessity of doing the communication work of multi-hop etc., and the

amount of communications can be stopped low.

The ﬂow of VA calculation. Each agent calculates VA by the ﬂow shown below. Si-

multaneously, the EVALUATION VALUE used in the case of negotiation with other

agents is also calculated.

Step 1 Obstacle Prediction

The agent predicts the obstacle of non-searched area by using from the obstacle infor-

mation and exploitation information in his communication area. And the agent deter-

mines the area which he divides.

Step 2 Information acquisition

The agent acquires VP and a ignore area ID from other agents within the communication

limits.

Step 3 Voronoi Overlay

The agent divides the area calculated at step2 by Voronoi Overlay using VP and ID

which were acquired at 1.

Step 4 Calculation of EVALUATION VALUE

An agent computes an EVALUATION VALUE using the size of VA and other agents’

VP which were acquired at step3. This value is used by the negotiation explained later.

5 Expelimental Result

We performed comparison with DDVAS which we developed, the existing distributed

approach (molecular algorithm), and the theoretical optimal value paying attention to

EXPANDING TIME and PATROLLING TIME which are two points shown in Cov-

erage Problem Deﬁnition. Moleculer Algorithm which is the existing research that we

compare doesn’t guarantee that PT becomes below ﬁxed. So we cann’t measure spec for

every PT. Then, we measure PATOROLLING TIME and EXPANDING TIME of the

present Moleculer Algorithm and compare with the value. And each robot’s parameter

was divided into two portions, the parameter to ﬁx and the parameter to change. The

ﬁxed parameters are the things which we judged that it is realistic and it is not necessary

to make it change.

The ﬁxed parameter is created based on the actual robot which is also used in mole-

culer algorithm. These parameters are ﬁxed in order to prevent comparison of perfor-

mance becoming complicated, although it can change arbitrarily inside a program.

5.1 Performance Comparison of PATOROLLING TIME

We measured EXPANDING TIME for every PATOROLLING TIME using parameter

of Table 1. PATROLLING TIME is equal to the time concerning a robot with the biggest

area in his duty in a robot going round. We set EXPANDING TIME that is the time until

PATROLLING TIME becomes below the deﬁned value (MAXPT). MAXPT is based

on the optimal value of PAOROLLING TIME and it can imagine easily that EXPAND-

ING TIME becomes smaller as MAXPT is large. So our approach has guaranteed that

PATROLLING TIME is below arbitrary values, when agents’ VD is converged. The

optimal value of PATROLLING TIME is equal to PTmin shown in Deﬁnition. We cal-

culated the time which it takes when a robot moves the optimal value of EXPANDING

TIME to the optimal arrangement in a straight line for every map. In 6.1 MAXPT is

changed, in 6.2 the number of agents is changed and in 6.3 a time step which is the time

of one cycle of agent action is changed. And the performance was compared every three

maps. We use the value which averaged the result which carried out the simulation 100

times in three different maps of which sizes are 500(m) × 500(m).The ﬁrst map has no

obstacle,the second map has only one obstacle,and the last map has many obstacles.

Table 1. Used Parameters in Comparison of PATOROLLING TIME.

type of parameter parameter name used value at this section

Fixed parameter

R 100(m)

MAXVEL 1(m/s)

map size 500(m) × 500(m)

Number of Robots 10(robots)

Time Step 10(s/cycle)

Changing parameter MAXPT 105% ∼ 200%

Although the number of agents is ﬁxed in 10 here, comparison of this change is

performed.

Result shows that DDVAS shows the outstanding performance compared with mole-

cular algorithm. However, the difference with the optimal value is large as map becomes

complicated. And, as expected, EXPANDING TIME becomes small as MAXPT be-

comes large.

According to simulation,EXPANDING TIME is large when time step is large. There-

fore, as for a time step, it is desirable to make it as small as possible.

6 Conclusions

We have presented a novel distributed solution for solving Dynamic Coverage Problem

that is based on a multi-agent system. In our approach, each robot can act intellectu-

ally, without needing the server of central control. We are making each agent control a

Fig.1. Comperison of PATOROLLING TIME.

motion of each robot, and have realized performance superior to the conventional ap-

proach. Moreover, we veriﬁed that this approach was also excellent also in robustness

as a multi-robot system.

7 Future Work

We introduced the distributed and dynamic approach using Voronoi Overlay for Cov-

erage Problem of strange area. However, still, the environment which we deﬁned is

not realistic enough. As ﬁrst inadequate point, the environment which we assumed is

2D. Naturally the place where a robot works is 3D. Therefore, it is necessary to bring

close more nearly actually by making environment into 3D (a hill, a mountain, etc).

As second inadequate point, an unreal point is that it is completely the same in each

robot’s performance. A robot is considered that each performance (max velocity, com-

munication range, etc) changes according to his feature. Therefore, we should do the

simulation which also took the difference of an each object into consideration. As third

inadequate point, it is that many room for EXPANDING TIME to approach the optimal

value is left behind.

References

1. Maxim A. Batalin, Gaurav S. Sukhatme: Multi-robot Dynamic Coverage of a Planar Bounded

Environment,CRES-03-011, 2003

2. Seapahn Meguerdichian, Farinaz Koushanfar, Miodrag Potkonjak, Mani B. Srivastava: Cov-

erage Problems in Wireless Ad-hoc Sensor Networks, INFOCOM,2001

3. Carbunar, Grama, Vitek: Distributed, Dynamic Voronoi Overlays for Coverage Detection, Dis-