POTENTIAL FIELD BASED INTEGRATED EXPLORATION FOR

MULTI-ROBOT TEAMS

Miguel Juli´a, Arturo Gil, Luis Pay´a and

Oscar Reinoso

Miguel Hern´andez University, System Engineering Department

Avda. Universidad s/n. Edif. Torreblanca, 03202 Elche-Alicante, Spain

Keywords:

Integrated Exploration, SPLAM, Potential Fields, Cooperative Mobile Robotics.

Abstract:

In this paper we present an approach for multi-robot cooperative exploration based on the potential ﬁeld

generated by several basic behaviours. When an unknown environment is explored the uncertainty in the

localization normally grows, this fact may cause the failure of the Simultaneous Localization and Mapping

(SLAM) algorithm, and thus constructing an useless and inaccurate map. The exploration algorithm described

here considers the current knowledge of the environment, the location of the robots and the uncertainty in their

positions in order to return to previously explored areas when it is needed. These actions deﬁnitely help the

SLAM algorithm to build a precise map. Several simulations are presented that demonstrate the validity of the

approach.

1 INTRODUCTION

In the last years, a large number of applications have

emerged that require the utilization of cooperative

mobile robots. Most of these applications require the

robot team to be able to explore unknown environ-

ments autonomously. Employing multiple robots in-

stead of a single robot in exploration is an advantage

because the exploration time could be reduced (Cao

et al., 1995).

Simultaneous Localization and Mapping (SLAM)

techniques are generally used to explore an unknown

environment. They allow to build a map that de-

scribes the environment while simultaneously using

that map to localize the robots. However, the result

obtained by the SLAM algorithm strongly depends

on the trajectories performed by the robots (Stachniss

et al., 2005). When the robots travelthroughunknown

environments, the uncertainty over their position in-

creases and the construction of the map becomes dif-

ﬁcult. Returning to previously explored areas or clos-

ing loops reduces the uncertainty over the pose of the

robots and improves the SLAM process.

Typical exploration algorithms do not take local-

ization uncertainty into account and direct the ex-

ploration in order to minimize the distance traveled

while maximizing the information gained. However,

the solution presented here explores the environment

efﬁciently and also considers the requisites of the

SLAM algorithm. Our algorithm considers return-

ing to previously explored places when the uncer-

tainty becomes too large. This idea has been previ-

ously exploited by other authors and is commonly de-

noted as Integrated Exploration or SPLAM (Simulta-

neous Planning Localization And Mapping). A solu-

tion to the SPLAM problem enables a mobile robot to

acquire data from sensors by autonomously moving

through its environment while at the same time build-

ing a map. The main contribution of this paper is a

new technique for Integrated Exploration for multi-

robot teams.

The remainder of the paper is structured as fol-

lows. Section 2 discusses related work and Section

3 presents the behaviour based exploration algorithm.

In Section 4 we explain the active localization state.

Next, Section 5 presents simulation results to test the

functionality of the method proposed. Finally, the

main conclusions and future work are presented.

2 RELATED WORK

Exploration techniques work basically using the fron-

tier concept introduced by (Yamauchi, 1997). He di-

vided the map into a regular grid of cells where to rep-

resent the occupation probability. At the beginning of

the exploration all the cells are unknown, so they are

308

Juliá M., Gil A., Payá L. and Reinoso Ó. (2008).

POTENTIAL FIELD BASED INTEGRATED EXPLORATION FOR MULTI-ROBOT TEAMS.

In Proceedings of the Fifth International Conference on Informatics in Control, Automation and Robotics, pages 308-314

DOI: 10.5220/0001508903080314

 SciTePress

initialized with an occupation probability of 0.5. This

value is updated with the information of the sensors

of the robots during the exploration. Relying on the

occupation probability for each cell, the cells are la-

beled as free, occupied or unknown. Frontier cells are

free cells that lie next to an unknown cell.

A group of explorationmethods employ path plan-

ning techniques in order to direct the robots to the

frontier cells (Simmons et al., 2000; Burgard et al.,

2005; Zlot et al., 2002). They differ in the coordina-

tion strategies used to assign a frontier to each robot:

the robots can go to the nearest frontier (Yamauchi,

1997) or they can follow a cost-utility model to make

their assignments. Normally, the cost is the length of

the path to a frontier cell, whereas utility could be un-

derstood in different ways: (Simmons et al., 2000)

consider the utility as the expected visible area be-

hind the frontier. (Burgard et al., 2005) consider in

the utility function the proximity of frontiers assigned

to other robots. (Zlot et al., 2002) suggest using a

market economy where the robots negotiate their as-

signments.

Another group of exploration techniques makes

use of potential ﬁeld methods (Arkin and Diaz, 2002).

Potential ﬁeld based exploring methods take into ac-

count a set of behaviours to generate a resultant po-

tential ﬁeld. The most common behaviours in explo-

ration are attraction to frontiers and repulsion from

obstacles and other robots. This leads to the avoid-

ance of other robots and collisions and also improves

the exploration by dispersing the robots. As stated by

many authors, the main drawback of this technique is

the occurrence of local minima in the potential ﬁeld,

which may trap the robot and block the exploration

process. A common solution to this problem is to plan

a path to a frontier cell in order to get the robot out

from the local minimum (Lau, 2003).

A few authors used integrated exploration in the

last years (Feder et al., 1999; Bourgoult et al., 2002;

Makarenko et al., 2002; Sim et al., 2004; Stachniss

et al., 2005). (Feder et al., 1999) decide the next

movement for robots by optimizing the information

gain of the environment and minimizing the uncer-

tainty in the localization of the robot. (Bourgoult

et al., 2002) and (Makarenko et al., 2002) use a simi-

lar idea including the uncertainty in the localization as

part of the utility function in the assignment of desti-

nations to robots. These 3 techniques are based on the

estimation of landmarks and they try to prevent that

the uncertainty in the pose of the robots grows, by

means of keeping always well estimated landmarks

in the ﬁeld of view. (Sim et al., 2004) recover the

certainty over the pose of the robots during the explo-

ration using a parametric curve trajectory and includ-

ing returning to explored zones when the uncertainty

in the pose of the robot is too high. (Stachniss et al.,

2005) reduce the uncertainty by actively closing loops

with previously explored areas. They create a topo-

logical map of the environment and look for oppor-

tunities for closing loops in it. As we can see, there

are two main approaches to the problem of localiza-

tion during the exploration: to take the uncertainty

in the pose of the robots into account when choosing

the movements for the robots or to explore and re-

turn later to previously explored zones when the un-

certainty is large.

In this paper, a potential ﬁeld based SPLAM tech-

nique is described. It is based on the potential ﬁeld

generated by several basic behaviours designed to

rapidly explore the environment. It also considers re-

turning to previously explored zones when needed.

3 BEHAVIOUR-BASED

EXPLORATION ALGORITHM

In typical environments we can ﬁnd a set of highly

distinctive elements that can be easily extracted with

the sensors of a robot. These elements are typi-

cally called landmarks. In our application, we as-

sume that the robots are able to detect a set of distinc-

tive 3D visual landmarks and they are able to obtain

relative measurements to them using stereo cameras.

These landmarks can be extracted as interest points

found in the images of the environment (Mozos et al.,

2007). The robot team is able to build a map with

a vision-based technique consisting on a particle ﬁl-

ter approach to the SLAM problem, known as Fast-

SLAM (Gil et al., 2007).

Landmark based maps do not represent the free or

occupied areas in the environment. This is the rea-

son why we make use of a grid map to represent free

and occupied cells detected using the information of

the sonar. In addition, all the cells have a numerical

value associated that indicates their degree of explo-

ration, which is increased each time it falls into the

ﬁeld of view of the robot, until it reaches a limit value

when the cell is considered to be fully explored. A

cell with an exploration degree of zero is considered

unexplored. We deﬁne the frontier cells as explored

cells that lie next to an unexplored cell that do not

belong to an obstacle.

Our approach to the problem of multi-robot explo-

ration consists of ﬁve basic behaviours whose com-

position results in the trajectory of each robot in the

environment:

Go to unexplored Areas: Each cell attracts each

robot with a force that depends on the degree of ex-

POTENTIAL FIELD BASED INTEGRATED EXPLORATION FOR MULTI-ROBOT TEAMS

309

Table 1: Forces deﬁned for each behavior.

Go to unexplored areas:

∑

i=1

ν−e

−~p

i,k

Go to frontier:

∑

i=1

−~p

i,k

Avoid other robots:

∑

j=1

−

−~p

j,k

Avoid obstacle:

∑

i=1

−

−~p

i,k

Improve imprecise landmarks:

∑

l=1

−~p

l,k

M: Number of cells in the map.

: Number of frontier cells.

: Number of obstacle cells in the range.

X: Number of robots.

: Current number of imprecise landmarks.

: Exploration level of cell i.

ν: Maximum exploration level.

: Landmark position measure uncertainty.

: Position vector of the i-th cell.

: Position vector of the j-th robot.

: Position vector of the k-th robot.

: Position vector of the l-th landmark

i,k

: Distance from i-th cell to robot k.

j,k

: Distance from robot j-th to robot k.

l,k

: Distance from l-th landmark to robot k.

ploration of the cell.

Go to Frontier: This behaviour attracts the robots

to frontier cells since these are the cells that give way

to areas of interest.

Avoid other Robots: This behaviour results in a

repulsive force between robots that normally allows

to spread the robots around the environment.

Avoid Obstacle: Each cell within a speciﬁc range

that is identiﬁed as belonging to an obstacle, applies

a repulsive effort over every robot. This range allows

to easily adjust the system.

Improve imprecise Landmarks: This behaviour

tries to improve the quality of the exploration of those

areas where some landmarks have been extracted but

whose accuracy is not high enough.

Table 1 shows how the forces are calculated for

each behaviour. This way, the resulting force of the

combination of those ﬁve behaviours on each robot

constitutes a vector that indicates the trajectory of the

robot to optimize the exploration process as follows:

= k

+ k

. (1)

−2 0 2 4 6 8 10 12 14 16

(m)

Go To Unexplored Areas

Go To Frontier

Avoid Obstacles

Avoid Other Robots

Go To Imprecise Landmarks

Current Heading

Resultant Force

Figure 1: Weighted outputs of the behaviours and resultant

force in an exploring situation. Also, the landmarks that

have been detected until that moment are shown.

The composition of the behaviours is carried out

taking into account a set of weights k

whose value is

deduced experimentally. Fig. 1 shows the bird’s eye

view of an exploring situation with three robots.

Potential ﬁeld methods have a main disadvantage:

when exploring complex environments, a robot may

be trapped at local minima in the potential ﬁeld and

may not move, thus stopping the exploration process.

To solve this problem, we assume that we are able to

detect the situation in which the robot is trapped at a

local minimum. In this case, a new state is triggered

that enables the robot to escape from the local mini-

mum by planning a path to the nearest frontier cell.

4 INTEGRATED EXPLORATION

As an unknown environment is explored the uncer-

tainty in the localization of the robot grows. When

the uncertainty over the pose of the robots is high,

it is difﬁcult to generate a correct map, and thus the

exploration process is inefﬁcient. If the error in the

localization is very high, some frontiers and obstacles

could be added to the grid map erroneously and some

zones could remain unexplored. The perceptions of

the robots in a given moment can be in conﬂict with

past perceptions or with perceptions of other robots

because of a deﬁcient localization.

Figure 2 shows an example of an extremely de-

ﬁcient exploration caused by a large error in the lo-

calization. It can be observed how the wrong loca-

tion of some obstacles obstructs the corridor and part

of the environment remain unexplored. The error in

the map of landmarks created is considerably high.

All the landmarks in the map should appear over the

walls but they are situated erroneously. These are the

reasons we introduce new techniques to improve the

localization.

The SLAM method we use in our experiments is

commonly known as FastSLAM (Gil et al., 2007). It

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310

Figure 2: The upper ﬁgure shows the visual landmark map

created in an exploration with deﬁcient localization. The

trajectories performed by the the robots are indicated in con-

tinuous lines and the estimated trajectories in discontinuous

lines. The landmarks detected are marked in their estimated

position. The bottom ﬁgure shows the grip map generated

for this situation. The grade of exploration is indicated in

gray levels and the obstacles detected in red color. Real ob-

stacle positions are marked in yellow.

consists of a particle ﬁlter, each particle having an es-

timation for the path of each robot and an estimation

of a set of landmarks conditioned to the path. We can

measure the uncertainty on the localization of a robot

by considering the dispersion for all the particles in

the position of the robot. When travelling through un-

known terrain, the dispersion of the particles usually

increases since each is well localized in his own local

map. Since we are using a ﬁnite number of particles

to represent the pose of the robots, this representa-

tion gets worse when the uncertainty is too high. In

this case we consider returning to previously explored

areas to reduce this uncertainty. This idea has been

employed by many authors (Feder et al., 1999; Bour-

goult et al., 2002; Makarenko et al., 2002; Sim et al.,

2004; Stachniss et al., 2005). Avoiding large periods

of time with a high dispersion is a good technique to

avoid the accumulation of error in the global localiza-

tion and an accurate map can be obtained. Thus, our

strategy is to return to positions with low dispersion

when the dispersion in the pose of the robot grows.

This solution produces a better estimation of the map

and the robot’s path.

We denote the model explained in Section 3 as the

Exploration State (StateA). Besides, we introduce an

Active Localization State (StateB). The Exploration

State allows exploring new areas of the map mean-

while the robots are well localized. The Active Local-

ization State intends to lead the robots to previously

explored areas when they have a relatively high uncer-

tainty associated, thus improving their localization.

The transition between both states is made according

to a hysteretic model with two transition thresholds

that are compared with the dispersion in the pose of

the robot.

In the Active Localization State, the control action

of the robot is the composition of Avoid Obstacle, al-

ready presented, and a new behaviour Go to Accurate

Landmarks. This new behavior aims at localizing the

robot returning to previously explored landmarks.

Go to Accurate Landmarks: This behaviour tries

to improve the estimation of the position of the robot,

driving it to landmarks whose position has a robust

estimation. Given a landmark, its position is calcu-

lated for each particle and a measure of its dispersion

is calculated using the correspondent landmarks for

the different particles. The correspondence is done

considering an unique visual descriptor for each land-

mark. Each accurate landmark attracts the robot with

a force inversely proportional to the distance:

∑

l=1

−~p

l,k

. (2)

being n the current number of landmarks in the map,

is the position of the l-th landmark, ~p

is the po-

sition of the robot k and r

l,k

is the euclidean distance

between both positions . Then the trajectory to follow

is pointed by the vector:

= k

+ k

, (3)

where the weights are deduced experimentally.

As stated before, the local minima in the poten-

tial ﬁeld can block the exploration process. In these

cases, we plan a path to the nearest frontier cell. This

solution directs the robots to unknown areas and thus

is only a good solution in the State A. In StateB, local

minima are also likely to appear. In this case, we plan

a path to the last past position in the trajectory of the

robot where the dispersion is low.

POTENTIAL FIELD BASED INTEGRATED EXPLORATION FOR MULTI-ROBOT TEAMS

311

Dispersion > Th A

Local minimum detected

Dispersion < Th B

Target achieved

Local minimum detected

Dispersion > Th A

C’

Target achieved

Dispersion < Th B

(Path to Nearest Frontier)

(Path to low dispersion Pose)

Well Localized

Bad Localized

Figure 3: State transition diagram.

Figure 3 shows the state diagram for a robot. We

can distinguish two zones of operation: when the

robot is well localized and when it is not. When it is

well localized, it explores the environment by follow-

ing the State A combination of behaviors. If it ﬁnds a

local minimum during the exploration it plans a path

(State C) to the nearest frontier cell. When it arrives

to this cell it returns to the State A. If the dispersion on

the robot position in the particle ﬁlter is over a given

threshold the robot is considered to be bad localized

and it switches to the Active Localization State (B). If

it ﬁnds a local minimum being in this state, it plans

a path (C’) to a past position in the trajectory with

low dispersion. When the dispersion decreases below

a threshold the robot returns to the Exploration State

(A).

5 EXPERIMENTS AND RESULTS

In this section, we analyze simulation results of the

method proposed in this paper. The proposal is tested

in presence of uncertainty in the robots localization to

show the improvement in the quality of the maps gen-

erated and in the estimated path using the techniques

proposed to return to previously explored areas.

The scenarios chosen to test the method are shown

in Figure 4. Scenarios that represent hypothetical real

places like Scenario 1 or Scenario 2 were chosen at

the same time that other artiﬁcial scenarios as for ex-

ample Scenario 3 or a completely random scene as

Scenario 4.

The method proposed is tested with and with-

out considering the uncertainty in the position of the

robots. Besides, it is compared with a pure path plan-

ning approach where the robots always plan a path

to the nearest frontier cell. The mean error per robot

in the estimated trajectories, the exploration time, as

well as the error in the map of landmarks are ana-

lyzed.

The results of the simulation are shown in Figure

Figure 4: Scenarios.

5. On Scenario 1 and Scenario 4, the error on the

estimated path and in the map is smaller with the pro-

posed integrated exploration approach than when not

returning to previously explored zones. This two sce-

narios have large free spaces. When the robots travel

in these zones the measurement of the landmarks is

difﬁcult as they are far away. This makes the dif-

ference between including the Go To Accurate Land-

marks behaviour or not. This large periods of time

with bad localization increases the global localization

error when not considering the dispersion to try to re-

localize the robot.

For Scenario 2 and Scenario 3 we do not observe

an improvement. Note that the global localization er-

ror depends on the form of trajectories and the ex-

ploration time that depend on the structure of the en-

vironments which is unknown. If the measurements

are good enough this other factors affects in a random

way and in average no difference is observed between

the methods.

The exploration time always increases because

this method does not always guide the robots to the

direction of the maximal information gain as it looks

also for the localization. As a conclusion, we think

that a method that only tries to minimize the explo-

ration time produces normally inaccurate maps use-

less for navigation. We consider that taking into ac-

count the requisites of SLAM while exploring the en-

vironment allows to obtain more precise maps.

6 CONCLUSIONS AND FUTURE

WORK

In this paper a method for multi-robot cooperative ex-

ploration has been presented. The method is based

on the computation of a set of behaviours designed

so that we simultaneously consider the necessity of

rapidly exploring the whole environment and the req-

uisite to build an accurate map. In this sense, the

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312

Figure 5: Results with uncertainty in localization: Path er-

ror on x,y and orientation (1st and 2nd graphs), exploration

time (3rd graph) and map error (4th graph).

method directs the robots to return to previously ex-

plored places when the uncertainty on the location

becomes signiﬁcant, and this fact improves the qual-

ity of the resulting map. Several simulation results

demonstrate the validity of the approach. On scenar-

ios with large free space where there is a lack of good

measures of the landmarks the accuracy of the map

improves considerably.

As future works, we consider the extension of

the approach in dynamic environments, adding tech-

niques to learn automatically the multiple settings of

the system. New behaviors that avoid the dispersion

in the localization by trying to keep accurate land-

marks in the ﬁeld of view will be added. Furthermore,

behaviors of attraction between robots will be incor-

porated in order to improve the localization since the

observation of one robot by other member in the team

may improve its localization. Semi-operated models

that integrate the commands expressed by a human

operator in the exploration task will also be studied,

where these commands would be taken as an advice.

ACKNOWLEDGEMENTS

This work has been supported by the Spanish Govern-

ment (Ministerio de Educaci´on y Ciencia). Project:

’Sistemas de percepci´on visual m´ovil y cooperativo

como soporte para la realizaci´on de tareas con redes

de robots’. Ref.: DPI2007-61197.

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