MULTI-ROBOT DECENTRALIZED EXPLORATION USING A

TRADE-BASED APPROACH

Zhi Yan, Nicolas Jouandeau and Arab Ali Cherif

Advanced Computing Laboratory of Saint-Denis (LIASD), Paris 8 University

2 Rue de la Libert´e, 93526 Saint-Denis, France

Keywords:

Coordinated exploration, Decentralized decision making, Multi-robot systems.

Abstract:

This paper addresses the problem of exploring an unknown environment by a coordinated team of robots. An

important question is, which robot should explore which region? In this paper, we present a novel decentralized

task allocation approach based on trading rules for multi-robot exploration. In the decentralized system, robots

can make their own decisions according to the local information with limited communication. In contrast to

previous approaches, our trade-based approach is designed to simulate the relationship between buyers and

sellers in a business system, to achieve dynamic task allocation by using a mechanism of unsolicited bid. Our

approach has been implemented and evaluated in simulation. The experimental results demonstrate a good

performance of the proposed trade-based approach compared to previous approaches.

1 INTRODUCTION

Exploration of an unknown environment is a funda-

mental problem in robotics. It requires an agent to

cover the unknown area while building a model of the

environment from sensor data so as to achievethe pur-

pose of exploration. This research can be used in a

wide range of applications such as planetary mission,

automated surveillance, and search and rescue opera-

tions.

Compared with single agent, using multiple

agents has a number of potential advantages (Cao

et al., 1997), (Dudek et al., 1996). For example, a

team of robots is able to complete an exploration mis-

sion faster than a single robot. The key to gain the

advantages is coordination. Without coordination, it

will not only lower mission efﬁciency, but also lead

to the failure of the entire mission in extreme cases.

The core of coordination is task and role allocation.

In other words, we need to answer such a question:

which agent should execute which task (Gerkey and

Matari´c, 2004)? Figure 1 shows an example of multi-

agent coordination. Four robots explore an unknown

environment cooperatively. The result of task alloca-

tion is that different robots are responsible for explor-

ing different rooms. There are generally two types

of mechanisms for task allocation, centralized and

decentralized. The advantage of centralized mecha-

nism is that the optimal plans can be found. Never-

Figure 1: Four robots explore an unknown environment co-

operatively. The green robot has completed the exploration

of room 0, is moving to next room. The yellow robot is ex-

ploring room 1. The red robot is exploring room 2, and the

orange robot is moving to room 3.

theless, this mechanism is ineffectual for large teams

with more agents. There is no central planner in the

decentralized mechanism. Robots use locally observ-

able informations to make their plans. This mecha-

nism has a good adaptability and strong robustness,

but the solutions it got are often sub-optimal.

In this paper, we consider the problem of explor-

ing an unknown indoor environment with a homo-

Yan Z., Jouandeau N. and Ali Cherif A..

MULTI-ROBOT DECENTRALIZED EXPLORATION USING A TRADE-BASED APPROACH.

DOI: 10.5220/0003405800990105

In Proceedings of the 8th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2011), pages 99-105

ISBN: 978-989-8425-75-1

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

geneous team of robots. The larger context of this

problem is multi-robot search and rescue in danger-

ous environments such as ﬁre and explosion. The ob-

jective of the research is to explore the entire environ-

ment, while minimizing the time needed to complete

the overall exploration. In fact, this is also an im-

portant prerequisite to better searching and rescuing.

Moreover, the realizations of search and rescue are

not within the scope of this paper.

This paper presents a novel approach of decentral-

ized dynamic task allocation based on trade rules for

groups of robots. This approach is designed to sim-

ulate the relationship between buyers and sellers in a

business system. The robot which plays the role of

buyer applies for a task, and the robot which plays

the role of seller is responsible for the assignment of

tasks. Due to the context of search and rescue, the

following three issues should be considered while de-

signing our trade-based approach:

• Useability, it means that robots are able to imple-

ment the proposed approach easily, and use fewer

computer system resources.

• Efﬁciency, it means that robots are able to handle

the assignment of tasks with as little communica-

tion as possible.

• Robustness, it means that robots are able to make

their own decisions correctly in the absence of

teammates’ information.

In contrast to previous research, especially the

well known auction method (Gerkey and Matari´c,

2002), our approach uses a application/allocation

model unlike the traditional auction/bidding model.

The buyer makes a request of task allocation to the

seller, we called it the unsolicited bid mechanism. Af-

ter a period of time, the seller analyzes the received

requests, then assigns the tasks to the buyers reason-

ably. An obvious characteristic of our approach is that

it has the ability to assign multiple tasks to multiple

robots at a time.

This paper is organized as follows. In Section 2,

we give an overview of some related works. Subse-

quently, we brieﬂy discuss the requirements of indoor

exploration in Section 3. Then we present our trade-

based approach in Section 4. Finally, we describe

the experimental results obtained with our approach

in Section 5.

2 RELATED WORK

The problem of exploring an unknown environment

by a team of mobile robots has received increasing

attention in the past few years.

Yamauchi (Yamauchi, 1998) presented a cooper-

ative, decentralized and fault-tolerant multi-robot ex-

ploration strategy based on the concept of frontiers.

Frontiers are regions on the boundary between open

space and unexplored space. In his approach, robots

share perceptual information, but maintain separate

global maps. Each robot makes its own decisions

about where to navigate. Whenever a robot arrives at

a new frontier, it sweeps its sensors and constructs a

local evidence grid representing its current surround-

ings. This local grid is integrated with the robots

global grid, and also broadcast to all of the other

robots. However, different robots may go to explore

the same frontier in this system, then the efﬁciency of

exploration will be lowered for this cause.

Burgard, Moors, Fox, Simmons and Thrun (Bur-

gard et al., 2000) designed a coordination component

based on the approach of Yamauchi. This component

applies a probabilistic method which takes the cost of

reaching a frontier and its utility into account simulta-

neously. The cost is given by the distance of traveling

to a frontier (by using value iteration algorithm) and

the utility is given by the size of the unexplored area

that a robot can cover from this frontier with its sen-

sors. Whenever a frontier is assigned to a robot, the

utility of the visible unexplored area of this frontier is

reduced to all of the other robots, so that the problem

of more than one robot go to the same frontier should

no longer appear. However, a central agent is required

for this approach. If the central agent fails, the whole

system will fail.

Gerkey and Matari´c (Gerkey and Matari´c, 2002)

proposed an auction-based task allocation approach

for decentralized multi-robot coordination. The auc-

tion proceeds in ﬁve steps: task announcement, met-

ric evaluation, bid submission, close of auction and

progress monitoring/contract renewal. This strat-

egy has been implemented and tested in a general

task allocation system called MURDOCH, which is

built upon a principled, resource centric and pub-

lish/subscribe communication model. However, their

method requires a high amount of data communica-

tion. This not only increases the load of system, but

also inﬂuences the robustness of system.

Zlot, Stentz, Dias and Thayer (Zlot et al., 2002) in-

troduced a market-based task allocation approach for

multi-robot exploration. This technique borrows the

market architecture which seeks to maximize bene-

ﬁt while minimizing cost, thus aiming to maximize

utility. The beneﬁt is information gained by visit-

ing a goal point, the cost is the estimated distance

traveled to reach the goal (by using D* algorithm),

then the utility is the difference between the beneﬁt

and the cost. Similar to the auction-based strategy,

ICINCO 2011 - 8th International Conference on Informatics in Control, Automation and Robotics

100

the market-based strategy also use the auction/bidding

model. However, this approach also requires a high

amount of data communication.

Wurm, Stachniss and Burgard (Wurm et al., 2008)

proposed a technique for coordinating a team of

robotic explorers by using a segmentation of envi-

ronment. Instead of considering frontiers between

unknown and explored areas as target locations, this

method takes the structure of the environment into

account, and segments the already explored environ-

ment based on Voronoi diagram of map, then assigns

each robot to a separate segment with a task to explore

corresponding area by using the Hungarian algorithm.

Their experiments show a signiﬁcant improvement of

the segmentation-based approach compared to a stan-

dard frontier-based approach for structured indoor en-

vironments. This is favourable for explorations in

dangerous environments. However, Their technique

still requires a central planning component to commu-

nicate with all teammate robots and handle the distri-

bution of tasks.

Marjovi, Nunes, Marques and de Almeida (Mar-

jovi et al., 2009) presented an approach for coopera-

tive multi-robot exploration, ﬁre searching and map-

ping in an unknown environment, which aims to mini-

mize the overall exploration time while making it pos-

sible to localize ﬁre sources in an efﬁcient way. In

their approach, a decentralized frontier-based explo-

ration method is used for evaluating the ratio between

cost (by using A* algorithm) and utility to navigate

to target waypoints. A potential ﬁeld method is used

for controlling the robots’ motion to avoid obstacles,

and a triangulation method is used for identifying ﬁre

sources. However, the amount of coordination of this

approach is limited and a high amount of data com-

munication should be required.

Besides, there are some other approaches devel-

oped with various policies (Rekleitis et al., 2000), (Ko

et al., 2003), (Stachniss et al., 2009).

In our previous work (Yan et al., 2010), we consid-

ered the problem of multi-robot exploration by using

separate topological graph. This work aims to solve

the waiting situations like congestion or collision dur-

ing robot motion planning. If all the robots use the

same topological graph, then they might follow the

same exploration path, so that causes the problem of

waiting situations. We proposed an approach based

on sampling environment map iteratively to support

the efﬁciently coordinated multi-robot exploration.

However, this approach needs a centralized planner

to process the map and assign target points to robots.

Therefore, in this paper, we study how to design an

useable, efﬁcient and robust decentralized system on

the one hand, and we still take the structure of envi-

ronment to ensure the efﬁciency of exploration into

account on the other hand.

3 INDOOR EXPLORATION

Our focus in this paper is on indoor environment ex-

ploration. Indoor environments are generally struc-

tured environments. For the search and rescue sce-

nario, if the structure of the environment is taken into

account, the efﬁciency of exploration will be greatly

improved. Therefore, in our approach, we assume that

all robots share a joint occupancy grid map with infor-

mation about the structure of environment, which is

generated from robots’ sensor readings. In addition,

unlike outdoor exploration, it is difﬁcult for robots lo-

calize themselves by using the GPS module in indoor

environment, so in our implementation, the robot uses

odometry for self-localization.

4 TRADE-BASED APPROACH

A business system is mainly made up of buyers and

sellers. The relationship between them is known as

exchange relation. Buyers can use money to purchase

goods or services from sellers, then sellers collect

money and sell goods or services to buyers. Our ap-

proach in this paper is built on the simulation of this

relationship, the model is as follows:

Trade =< R, M, T, P,C > (1)

where R represents the mobile robots. M represents

the whole mission to be completed, which consists of

several tasks, M = {m

, m

, .. . , m

}. T represents the

time needed (i.e. the beneﬁt obtained) to complete the

whole mission. P signiﬁes the task allocation plan. C

signiﬁes the set of cost to complete the whole mis-

sion, C = {c

, c

, .. . , c

}. In fact, to each robot, the

entire planning contains three steps: role allocation,

task allocation and motion planning.

4.1 Role Allocation

The role allocation is to solve the problem of which

robot should be buyer and which robot should be

seller. As far as a homogeneous mobile robot team

is concerned, robots themselves have no preference

for role. Therefore, a simple and effective way is to

number the robots in the team. Robot can broadcast

its number when it is not in task, then evaluates the

received numbers after a period of time. If there is a

number smaller than its own, then the robot will play

MULTI-ROBOT DECENTRALIZED EXPLORATION USING A TRADE-BASED APPROACH

101

the role of buyer. The details of our implementation

are given in Algorithm 1.

Algorithm 1: Trade-based role allocation for robot r.

1: if robot r is not in task then

2: broadcast its number r

3: if time < timeMax then

4: receive messages

5: time ← time+ 1

6: else

7: robot ← seller

8: for each received number r

′

9: if r

′

< r then

10: robot ← buyer

11: break

12: end if

13: end for

14: end if

15: end if

It is worth noting that the difference between

buyer robot and seller robot is just in function, and

only temporary. The buyer at this moment in a task

could become the seller in another task in the next

moment.

4.2 Task Allocation

Once the idle robot has determined its own role, it

should enter the task allocation phase. For the buyer

robots, the ﬁrst thing to do is to choose a task to

bid for and estimate the cost required to complete the

task. The task is to explore an unknown region which

can be identiﬁed by topologizing the grid map of the

environment (Wurm et al., 2008), (Yan et al., 2010).

The robot is capable to extract critical points (Thrun,

1998) for a given map to distinguish corridors, door-

ways and rooms. The cost metric can be various, such

as distance traveled, time taken or energy expended.

In this paper, we use the distance traveled as the cost

metric. As a result, the robot will calculate the dis-

tance between its current position and target position

(for example, a critical point) as the estimated task

cost by using the wavefront propagation algorithm

(LaValle, 2006):

= wave front(pos(r), pos(m)) (2)

where c

represents the estimated cost c for robot r to

complete the task m. After completing the cost esti-

mate, the buyer robot should send a purchase request

to seller robot for the new task. We called this model

the unsolicited bid mechanism. The purchase mes-

sage mainly contains three information:

pums

= {r, m, c} (3)

where pums

represents the purchase message pums

sent by buyer robot r, r in the message means the

number of the buyer robot, m signiﬁes the identiﬁer

of the task, and c denotes the estimated task cost c

After the bidding process, the buyer robot will receive

a message on whether to get the task from the seller

robot or not. If the buyer robot gains the bidden task,

it will enter into the motion planning process. Other-

wise, it will return to the role allocation process for

a new task. A detailed decision making ﬂowchart is

given in Figure 2.

For the seller robot, homoplastically, the ﬁrst step

is to select a task and estimate the cost. Then it

should collect the purchase message from the buyer

robots within a given bidding period. After this pe-

riod, the seller robot will stop receivingpurchase mes-

sage and evaluate the purchase requisitions, then as-

sign the tasks to each buyer robot for reasonably. The

detailed decision making ﬂowchart for seller robot is

illustrated in Figure 3. Task allocation is performed

by using a greedy algorithm. That is, always select-

ing the robot with lower estimated cost as the object

of task distribution. The implementation details are

given in Algorithm 2.

Algorithm 2: Trade-based task allocation for seller

robot.

1: a.init()

2: for all received task requests m in purchase mes-

sage pums do

3: if there is a same task m

′

in the allocation table

a then

4: if m.cost < m

′

.cost then

5: a.update(m

′

)

6: end if

7: else

8: a.add(m)

9: end if

10: end for

The task allocation message sent to buyer robot

mainly includes two information:

tams

= {r, m} (4)

where tams

represents the task allocation message

tams sent by seller robot r, r in the message means the

number of the seller robot, m signiﬁes the identiﬁer of

the task. It is worth noting that, in fact, the seller robot

itself is also the object of task allocation.

The robot which has completed a task will update

its task list, and also broadcast to all teammates.

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102

Figure 2: Decision making ﬂowchart for buyer robot.

Figure 3: Decision making ﬂowchart for seller robot.

4.3 Motion Planning

The motion planning process is in charge of the im-

plementation of task, i.e. the exploration of the un-

known region. In our approach, the mobile robots will

share an occupancygrid map with respect to the struc-

ture of the environment during their exploration mis-

sion. This map is used for path planning and obsta-

cle avoidance in real time. Consequently, we use the

wavefront propagation algorithm (LaValle, 2006) for

global path planning and the vector ﬁeld histogram al-

gorithm (Ulrich and Borenstein, 1998) for goal seek-

ing and local obstacle avoidance.

5 EXPERIMENTS

Our approach has been implemented and evaluated in

Stage (Gerkey et al., 2003) a 2.5D multiple-robotsim-

ulator. The simulation experiments were conducted

by using a group of Pioneer 2-DX robot equipped

with a laser range ﬁnder which can provide 361 sam-

ples with 180 degrees ﬁeld of view and a maximum

range of 8 meters. Each robot can localize itself based

on an abstract localization device which models the

implementation of SLAM. The ratio between real-

world time and simulation time is about 1:3. All ex-

periments reported in this paper were carried out on a

system with an Intel Core 2 Duo E8400 3.00GHz pro-

cessor, an Intel Q43 Express chipset and two DDR2

800MHz 1024MB dual channel memory.

Figure 4: Two environment maps used in our simulation:

map A (left) and map B (right).

To evaluate our trade-based approach, we used

a different number of robots to conduct several ex-

periments in various environments. We also com-

pared our approach to a centralized approach based

on the Hungarian method (Kuhn, 1955) in which the

task allocation is done by a central planner. Figure

4 depicts two maps used in our simulation which are

enclosed spaces with 14 meters long and 16 meters

wide. Both of them are indoor structured environ-

ments. The screenshot of our implementation can be

seen in Figure 1, and the results of our experiments

are given in Table 1 and Table 2.

Table 1 shows a comparison of the results be-

tween our trade-based approach (decentralized) and

the Hungarian-based approach (centralized) in map

A with the context of measuring the exploration run-

time. Each set of data in the table contains an average

time (in seconds) of 10 runs and its standard deviation

in parentheses. The Hungarian method is an efﬁcient

way to ﬁnd an optimal solution for a task assignment

problem. In our experiment, this procedure is used as

a reference for measuring the performance of our pro-

posed method. Table 1 indicates that, the difference

on completion time between trade-based exploration

and Hungarian-based exploration is 6.6% (4.3 sec-

onds) for 2 robots, 19.4% (8.9 seconds) for 3 robots,

and 3.9% (1.8 seconds) for 4 robots respectively.

Table 2 shows the results for map B. The run-

time difference is 6.3% (4.5 seconds) for 3 robots and

7.4% (4.6 seconds) for 4 robots respectively. More-

over, we observed that, our trade-based approach

gained 14.2% time (13.9 seconds) compared to the

Hungarian-based approach with 2 robots. It reﬂects

MULTI-ROBOT DECENTRALIZED EXPLORATION USING A TRADE-BASED APPROACH

103

Table 1: Exploration Runtime Comparison for Map A.

Hungarian-based Trade-based

exploration exploration

2 robots 65.20s (1.166) 69.50s (0.806)

3 robots 45.90s (0.538) 54.80s (1.887)

4 robots 45.90s (7.120) 47.70s (0.458)

Table 2: Exploration Runtime Comparison for Map B.

Hungarian-based Trade-based

exploration exploration

2 robots 112.0s (3.317) 98.10s (1.300)

3 robots 71.70s (1.487) 76.20s (3.027)

4 robots 61.80s (1.249) 66.40s (1.020)

NP-hard of multi-robot exploration from one side.

With Table 1 and Table 2, we found that, although

our trade-based approach requires more time com-

pared to the Hungarian-based approach in most cases,

the difference is quite acceptable. Consequently, the

experimental results still reﬂect a good performance

of our proposed approach.

Another experiment was conducted to evaluate the

robustness of our method. The point is to test the ef-

fect of decision making of a robot under uncertainty

caused by information loss. The motivations of the

loss may be damage of robot components, communi-

cation obstacles (distance), or difﬁcult circumstances.

For a coordinatedrobots team with a decentralizedde-

cision making system, each robot in the team need to

exchange information with its teammates. The prob-

lem of information loss will inﬂuence the decision

performance. Table 3 and Table 4 show the robust-

ness testing results of our proposed method in map A

and map B respectively, in which we varied the prob-

ability of information loss with 10%, 30% and 50%.

Each set of data in the tables contains an average time

(in seconds) of 10 runs.

Table 3 shows that, in map A: Under 10% infor-

mation loss, the system keeps a good performance,

the exploration runtimes are prolonged but still close

to the normal results, the differences between them

are 0.9 seconds (2 robots), 1.4 seconds (3 robots) and

3.1 seconds (4 robots). Under 30% information loss,

the performance of system was lowered, the explo-

ration runtimes are prolonged by the undesirable ef-

fect of the loss. Compared with the normal results, the

differences are 15.0 seconds (2 robots), 8.2 seconds

(3 robots) and 12.0 seconds (4 robots). Under 50%

information loss, the performance of system keeps

lowering, and the differences between the exploration

runtimes and the normal results are 15.6 seconds (2

Table 3: Robustness Testing with Map A.

Information loss probability

10% 30% 50%

2 robots 70.40s 84.50s 85.10s

3 robots 56.20s 63.00s 76.80s

4 robots 50.80s 59.70s 73.90s

Table 4: Robustness Testing with Map B.

Information loss probability

10% 30% 50%

2 robots 100.3s 141.3s 155.2s

3 robots 82.00s 102.5s 124.6s

4 robots 67.00s 83.00s 92.80s

robots), 22.9 seconds (3 robots) and 26.2 seconds (4

robots).

Table 4 shows that, for map B: Under 10% infor-

mation loss, the differences are 2.2 seconds (2 robots),

5.8 seconds (3 robots) and 0.6 seconds (4 robots)

compared with normal results. Under 30% informa-

tion loss, the differences are 43.2 seconds (2 robots),

26.3 seconds (3 robots) and 16.6 seconds (4 robots).

Under 50% information loss, the differences are 57.1

seconds (2 robots), 48.4 seconds (3 robots) and 26.4

seconds (4 robots).

With Table 3 and Table 4, we found that, multi-

robot coordination depends on the information ex-

change between teammate robots, the exploration

runtimes are prolonged for the probability of infor-

mation loss. Moreover, the corresponding incre-

ments are considered acceptable in our experiments.

This demonstrates a good robustness of our proposed

trade-based approach. In fact, our approach still work

in extreme cases (zero communication), but the efﬁ-

ciency is lower.

6 CONCLUSIONS

In this paper, we presented a novel task allocation

approach under decentralized coordination for multi-

robot exploration. The basic thought of the proposed

approach is to simulate the relationship between buy-

ers and sellers in a business system, and dynamically

allocate the task by using an unsolicited bid mecha-

nism. Typically, the procedure goes like this: At ﬁrst,

we should determine the role of the robots, i.e. buyer

or seller, this step is known as role allocation. Sec-

ondly, the buyer robot should choose a task to bid for,

then the seller robot will assign the tasks to each buyer

ICINCO 2011 - 8th International Conference on Informatics in Control, Automation and Robotics

104

reasonably, this step is known as task allocation. An

iterative greedy method is applied in our implementa-

tion for the step of task allocation.

For the coordinated decision making in decen-

tralized multi-robot system, robots should make their

plans according to the local observable information

with limited communication. This paper takes the

problem of multi-robot search and rescue in danger-

ous environments as the background. The conception

of our trade-based approach can meet the system’s

requirements of useability, efﬁciency and robustness.

The ﬁrst experiment we have conducted is designed

to evaluate the performance of our proposed method,

and the second is designed to test the robustness (in

the case of information loss). The experimental re-

sults demonstrate that, our trade-based approach has

a good efﬁciency for decentralized multi-robot explo-

ration.

However, the actual limitation of the proposed ap-

proach is that it can not guarantee the global optimal

solution will be found, i.e. the task allocation plan for

the whole mission is sometimes not optimal. Future

work will improve the step of task allocation. An im-

plementable idea is that the buyer robot can send the

purchase request to the seller robot for several tasks,

then seller robot will evaluate the purchase requisi-

tions and assign the tasks with a more advanced algo-

rithm (i.e. improve Algorithm 2).

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