Multi-mobile Robot and Avoidance Obstacle to Spatial Mapping in

Indoor Environment

Luis Piardi

1,2 a

, Jos

e Lima

1,3 b

and Andr

e Schneider de Oliveira

2 c

Research Center in Digitalization and Intelligent Robotics (CeDRI), Instituto Polit

ecnico de Braganc¸a,

Campus de Santa Apol

onia, 5300-253 Braganc¸a, Portugal

Universidade T

ecnol

ogica Federal do Paran

a - UTFPR, Avenida Sete de Setembro 3165,

80230-901 Curitiba, Paran

a, Brazil

INESC, Technology and Science, Porto, Portugal

Keywords:

Autonomous Mobile Robot, Gas Sources Detection, Avoidance Obstacle, Fuzzy Control.

Abstract:

The advancement of technology and techniques applied to robotics contributes to increasing the quality of life

and safety of humanity. One of the most widespread applications of mobile robotics is related to monitoring

indoor environments. However, due to factors such as the size of the environment impacting the monitoring

response, battery autonomy, and autonomous navigation in environments with unknown obstacles, they are

still signiﬁcant challenges in the diffusion of mobile robotics in these areas. Strategy adopting multiple robots

can overcome these challenges. This work presents an approach to use multi-robots in hazardous environments

with gas leakage to perform spatial mapping of the gas concentration. Obstacles arranged in the environment

are unknown to robots, then a fuzzy control approach is used to avoid the collision. As a result of this paper,

spatial mapping of an indoor environment was carried out with multi-robots that reactively react to unknown

obstacles considering a point gas leak with Gaussian dispersion.

1 INTRODUCTION

In the past years, academic research has focused on

the development of autonomous mobile robots. In

this context, several approaches have been explored,

for example, robots in the indoor or outdoor environ-

ment, using representations with static or dynamic ob-

stacles and total, partial or unknown representations

of the environment in which the robot is allocated.

Technological advances and the development of new

techniques and approaches have disseminated mobile

robotics into real problems. Autonomous vehicles are

becoming an essential tool in a wide range of environ-

mental applications that include ambient data acquisi-

tion, remote sensing, and mapping of the spatial ex-

tent of gas leakage (Bayat et al., 2017). The applica-

tions of these mobile agents in inspection of industrial

plants, search for environmental pollutant sources, ex-

plosives, and drugs at airports and harbors are already

realities (Braun et al., 2019; Baetz et al., 2009).

https://orcid.org/0000-0003-1627-8210

https://orcid.org/0000-0001-7902-1207

https://orcid.org/0000-0002-8295-366X

The present work contributes to the research’s ten-

dency in mapping environments contaminated with

toxic substances or harmful gases using mobile robots

to locate the source of leakage or emission, avoiding

the exposure of humans in hazardous environments.

For this, a group of four robots will be used, equipped

with a sensor and moving collectively towards the in-

door source location in a cooperative manner. Obsta-

cles in the environment are unknown, i.e., the robot

does not have information about the obstacles’ layout

and size. The robot control and avoidance obstacle are

performed through a controller based on fuzzy logic.

During the set of robots navigating the indoor envi-

ronment with dynamic obstacles, carrying out the ac-

quisition of the gas concentration, the data is analyzed

to estimate the leak source position.

The Robot Operating System (ROS) was used to

perform tests and validate the proposal of this work. It

is a framework that contains a wide range of libraries

and tools to develop applications for robots(Martinez

and Fern

andez, 2013). All the development of this

work was carried out in a simulation environment, us-

ing the Stage Simulator, the C ++ software library that

simulates multiple mobile robots with a low compu-

Piardi, L., Lima, J. and Schneider de Oliveira, A.

Multi-mobile Robot and Avoidance Obstacle to Spatial Mapping in Indoor Environment.

DOI: 10.5220/0010509200210029

In Proceedings of the 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2021), pages 21-29

ISBN: 978-989-758-528-9

tational cost (Vaughan, 2008).

The remainder of this paper is organized as fol-

lows: the next chapter presents a brief review of state

of the art considering methods for the spatial map-

ping of the environment and ﬁnding gas leaks, and

then a brief presentation of approaches that use mo-

bile robots with fuzzy logic control to avoid obsta-

cles. Chapter 3 presents the system architecture and

the simulation environment used in this work. Chap-

ter 4 describes the approach adopted to perform the

spatial mapping, namely the robot’s trajectories, the

fuzzy controllers, and the calculations to estimate the

gas’s position. In chapter 5, the results are presented,

and ﬁnally, in chapter 6, the conclusions, limitations,

and future work are realized.

2 RELATED WORK

In this section it will be summarized the brieﬂy review

of two topics that this work addresses. The ﬁrst of

these will be indoor gas mapping and detection. The

second topic deals with fuzzy logic for the control and

avoidance of dynamic and unknown obstacles using

mobile robot.

2.1 Distribution Mapping and Gas

Leakage Detection

There are several ways to get the gas or toxic distribu-

tion map in a determined contaminated environment.

The most common approach uses stationary sensors,

installed in strategic locations, ﬁxed to posts or walls

(Kroll et al., 2009). It is a standard approach for mon-

itoring environments that have the risk of gas leak-

age and can be found even in homes and other build-

ings (propane and butane based gas detection and

smoke detection). Therefore, the gas distribution in-

formation is only valid for a limited space around the

gas sensor’s location. For this approach’s efﬁciency,

many sensors are required to cover a relatively large

indoor environment efﬁciently (Fort et al., 2004). An-

other methodology adopted to carry out the gas distri-

bution mapping is to use specialized and adequately

equipped technicians carrying sensors to detect the

harmful substances. In this approach, humans are in

a contaminated environment to explore and map the

substance to locate the emission source.

Considering the limitations of ﬂexibility, robust-

ness and to avoid exposure of humans to high-risk

environments, approaches using autonomous mobile

robots to perform spatial mapping and leakage focus

detection are great alternatives. Therefore, the aca-

demic community has been developing robot proto-

types to explore contaminated environments, such as

(Zakaria et al., 2017; Lilienthal et al., 2009). In this

line of research, numerous works study and present

in detail a spatial dispersion model of gases, as can

be analyzed in (Kowadlo and Russell, 2008; Lilien-

thal and Duckett, 2004; Loutﬁ et al., 2009; Lilienthal

et al., 2006).

The need for the use of mobile robots occurs

mainly when the gas source is composed of toxic or

explosive gases, need for ﬂexibility or replacement of

sensors, when the gas source occurs in an inaccessi-

ble location, or when a continuous veriﬁcation of the

environment is necessary (Gongora et al., 2017). Ap-

proaches that use a mobile robot with a gas sensor at-

tached are found in the literature (Piardi et al., 2017;

Braun et al., 2019). However, these have limitations

for large environments due to battery limitations and

delay in the response of gas detection given the size

of the environment. Strategies based on genetic algo-

rithms seek to optimize the robot’s route to perform

more efﬁcient monitoring, however for dynamic envi-

ronments, changes in the environment demand time to

re-calculate the ideal route (Piardi et al., 2018). Multi-

robot approaches for monitoring can map larger en-

vironments and be more responsive to detecting gas

leakage sources.

2.2 Fuzzy Logic Control

Mobile robots have a wide range of use and can be

controlled using telemetry or semi-autonomous and

autonomous approach. For a robot to be fully au-

tonomous and therefore independent of human oper-

ators or users’ decisions, controllers that operate at

their motors’ speeds are required, usually feedforward

controller or feedback controller. In (Pandey et al.,

2017) it is possible to obtain information of different

techniques used to equip robots of autonomy, such as

neural networks, genetic algorithms, and fuzzy con-

trollers. Sensors with a high amount of environment

information have been widely used to avoid collision

with obstacles, as presented in (Morais et al., 2017),

which uses an RGB-D sensor (e.g kinect or intel

real sense) applying Artiﬁcial Potential Field to avoid

nearby obstacles. However, approaches based on

RGB-D sensors demand a high computational power

to process all environment around the robot, identify

obstacles and execute a path free of collision.

In particular, for this work, the fuzzy control ap-

proach will be used, which was introduced by Zadeh

(Zadeh, 1975). It is widely adopted to control the

speed applied to the robot’s wheels to control three-

dimensional coordinates involved i.e. [x, y, θ]. Fuzzy

logic is especially useful for robot controllers, and re-

SIMULTECH 2021 - 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

searchers present different approaches to control the

robot with fuzzy logic (Vinogradov et al., 2019; Ave-

lar et al., 2020; Mousavi, 2015). The approach pro-

posed in this work uses two fuzzy controls to oper-

ate the wells robot speed, one without the presence of

obstacles whose input is the position of the robot ob-

tained from optometry and the second is active when

an obstacle is detected near to the robot, whose input

is the distance and direction of the obstacle.

3 SETUP AND SYSTEM

ARCHITECTURE

For the present work, the ROS was used as the frame-

work to control four mobile robots Pioneer model

P3-DX with a differential drive. Each robot was

equipped with Hokuyo laser scanner model URG-

04LX to obtain information about the environment

and unknown obstacles. The test and validation en-

vironment was developed in the Stage simulator. This

software presents a realistic model of the 3D environ-

ment, representing the dynamic constraints in real ap-

plications. This environment has 400 squared meters

where it is distributed different unknown obstacles by

the robots. Figure 1a shows the simulation environ-

ment where the blocks in black are walls, in blues are

obstacles that can be moved and in red arranged in

the corners of the environment are the robots. Figure

1b shows the proposed system architecture describing

the data ﬂow.

The data obtained from the simulator (pose from

dead reckoning, gas data and laser scan data) are pro-

cessed in a project developed in python. The multi-

robots are controlled to perform a deﬁned trajectory,

aiming the exploration of the environment and ac-

quisition of gas concentration data. At the end of

the trajectory, the stored gas data are plotted show-

ing the gas concentration at the points visited by the

robots. As the objective of this work is not to propose

a new method for gas dispersion, the adopted model is

generic and simpliﬁed (Kowadlo and Russell, 2008),

not taking into account wind intensity and orientation,

temperature and chemical characteristics of gas parti-

cles. Equation (1) presents the model of gas disper-

sion in the adopted environment, whose behavior is a

Gaussian function.

Z(x, y) = A ·e

−

(x−x

)

+(y−y

)

2·σ

(1)

The variable Z indicates the concentration of gas,

while (x;y) the position of the robot. The variable A

represents the height of the curve’s peak. The leakage

position is described as (x

) and σ (the standard

(a) Stage simulation environment.

CONTROL

POSE

SCAN DATA

GAS DATA

STAGE

SIMULATOR

SETUP

SCRIPT CONTROL

(b) System Architecture.

Figure 1: (a) Simulation environment and (b) architecture

proposed.

deviation) the parameter to control the width of the

“belt”.

4 PROPOSED APPROACH

In this section it will be presented the approach devel-

oped to perform a spatial mapping of gas distribution

in an indoor environment. Initially, the robot’s tra-

jectory will be described, covering a region enough

to map the environment. Then, the approach of the

fuzzy controller to follow the path and avoid the un-

known obstacles is presented and ﬁnally a mathemati-

cal model to estimate the position of the source of gas

emission.

Multi-mobile Robot and Avoidance Obstacle to Spatial Mapping in Indoor Environment

4.1 Robot’s Trajectory

Considering that performing a complete coverage of

the environment with a large size may require a sig-

niﬁcant amount of time and is limited to battery ca-

pacity of the mobile robots. The proposed trajectory

aims at an alternative to perform the data acquisition

for spatial mapping. The simulation environment has

the dimension of −10 to 10 meters in both the X coor-

dinate and the Y coordinate. Table 1 shows the initial,

intermediate and ﬁnal position for each robot. With

this trajectory, the robots tend to perform a diagonal

crossing in the environment and then move clockwise

direction, ending the trajectory, illustrated by the Fig-

ure 2.

Table 1: Trajectory waypoints (x;y) for each robot.

Robot Initial Position Intermediate position End position

A (-8 ; 8) (7 ; -7) (-6 ; -6)

B (8 ; 8) (-7 ; -7) (-6 ; 6)

C (8 ; -8) (-7 ; 7) (6 ; 6)

D (-8 ; -8) (7 ; 7) (6 ; -6)

ROBOT A

ROBOT B

ROBOT C

ROBOT D

-10 0 10

Figure 2: Trajectories for robots to explore the environment.

It is worth mentioning that deviations from the ini-

tial trajectory can occur due to the existence of un-

known obstacles. With this arrangement, all portions

of the environment will have sample gas concentra-

tion data.

4.2 Fuzzy Logic Control

The goal of fuzzy logic control is to generate linear

and angular velocity, which will be converted through

ROS to velocities for both the mobile robot’s right and

left motor. To the robots navigate and ﬁnd their tar-

get while avoiding obstacles, an approach using two

fuzzy controllers has been developed. This approach

was inspired by (Faisal et al., 2013), changing the use

of a sonar sensor to a LiDAR, making it possible to

extract more information from the environment and,

consequently, completely modify fuzzy memberships

and rules. The ﬁrst one is free path fuzzy control

(FPFC). The second one logic is free obstacle fuzzy

control (FOFC), triggered when the scan laser sensor

detects an obstacle inside a radius of 1 meter from

the robot. Figure 3 illustrates the fuzzy controller of

FPFC and FOFC through a ﬂowchart.

Figure 3: Flowchart of fuzzy logics for robot control.

4.2.1 Free Path Fuzzy Control

FPFC is proposed to move the robot to target points

smoothly. The inputs of FPFC are the distance from

the robot to the target and the angle between the robot

and the target (error angle) as shown in Figure 4.

The outputs of FPFC are linear and angular speed

of the mobile robot. FPFC is implemented with 3

membership functions for each input as illustrated in

Figure 5 and Figure 6. The fuzzy control rules for

these two inputs and two outputs for control the lin-

ear and angular velocity are shown in Table 2.

The velocities (linear and angular) of the mobile

SIMULTECH 2021 - 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

Target

Negative

angle error

Target

Zero angle

erro

Target

Positive

angle error

Figure 4: Cases related to distance and negative, zero and

positive angles for FPFC.

Figure 5: Input membership functions for the distance error

and membership functions for the linear velocity.

robots are calculated using the defuzziﬁcation step.

Note that in this work, the centroid defuzziﬁcation

technique has been adopted.

4.2.2 Free Obstacle Fuzzy Control

The FOFC enters the scene in place of FPFC when

the laser scan detects some obstacle within 1 meter of

the distance around the robot (0 to 180

). In this con-

trol methodology, the robot does not collide with un-

known obstacles in the environment, generating linear

and angular velocities so that the robot’s trajectory is

free of collisions. Figure 7 shows the used method on

how the inputs to the fuzzy logic are obtained.

This logic consists of two inputs and two out-

puts. The ﬁrst input represents the shortest distance

between any obstacle and the robot (yellow line in

Figure 7), while the second input indicates the angle

of the line representing this shortest distance from the

robot and the obstacle. The outputs of FOFC are the

linear and angular velocities. FOFC is implemented

with three membership functions for distance (input

and output) illustrated in Figure 8. For the angular

Figure 6: Membership functions for the angle error and

membership functions for the angular velocity.

Table 2: Fuzzy rules of the linear and angular velocity of

the robot in FPFC.

Input Output

Distance Error Angle Error Linear Velocity Angular Velocity

low zero low zero

low positive low positive

low negative low negative

medium zero medium zero

medium positive medium positive

medium negative medium negative

high zero high zero

high positive high positive

high negative high negative

1 m

don't care

Input Avoid Angle

Input Avoid

Distance

Obstacle

Figure 7: Illustration for the input values for the FOFC.

input, ﬁve membership functions are used, while for

the output, three functions are used illustrated in Fig-

ure 9. The rule of FOFC for these two inputs and

two outputs for control the linear and angular veloc-

ity avoiding obstacle is shown in Table 3.

Figure 8: Input membership functions for the distance to

avoid obstacle and membership functions for the linear ve-

locity.

4.3 Algorithm to Find the Gas Source

Considering equation (1) which simpliﬁes the behav-

ior of the gas dispersion in a Gaussian function and

the fact that the robot, while following its trajectory,

records position data and its gas concentration, math-

ematically it is possible to estimate the position of the

Multi-mobile Robot and Avoidance Obstacle to Spatial Mapping in Indoor Environment

Figure 9: Membership functions for the angle to avoid ob-

stacle and membership functions for the angular velocity.

source with the stored gas concentration data from

each robots. After completing the entire trajectory,

each robot will contribute with the highest gas con-

centration obtained Z and the position (x, y) of this

measurement.

Table 3: Fuzzy rules of the linear and angular velocity of

the robot in FOCF.

Input Output

Distance Angle Linear Velocity Angular Velocity

low zero medium negative

low E medium negative

low D medium positive

low ME medium zero

low MD medium zero

medium zero medium negative

medium E medium negative

medium D medium positive

medium ME medium zero

medium MD medium zero

high zero medium negative

high E medium zero

high D medium zero

high ME medium zero

high MD medium zero

Then, it is possible to use the Linear Least Squares

estimation to ﬁnd the (x

, y

) gas emission origin,

with Z concentration measure.

lnZ = ln A + B(x

− 2xx

+ x

+ y

− 2yy

+ y

) (2)

From equation 2, where B = −

2σ

, and rearrang-

ing the parcels, results on the equation (3)

lnZ = B(x

)−2Bx

x −2By

y +lnA +B(x

)

(3)

The model for the Linear Least Square is found in

equation (4).

w = α

+ α

(4)

The Linear Least Square variables represent the

following system values:

= B

= −2Bx

= −2By

= ln A + B(x

+ y

)

w = ln Z

= x

+ y

= x

= y

= 1

α = (U

.U)

−1

.W (5)

α =





(6)

W =













(7)

U =













(8)

The matrices in equation (5) are deﬁned in equa-

tions (6), (7) and (8) assuming n measures,where n

indicates the number of robots, and in this case n = 4.

After the estimation the gas emission origin (x

, y

)

can be found by the expressions in equation (9).

B = α

, x

= −

, y

= −

(9)

Therefore, after applying the maximum values of

gas concentration obtained by each robot during the

execution of its deﬁned trajectory, in the Linear Least

Square model to obtain the values of α

a1, α

, α

and α

, and substitute these variables in equation 9,

the source of the gas leak x

and y

is estimated.

5 RESULTS

In order to present the results of this work, the ap-

proach described above with four robots was per-

formed in the STAGE simulator, a multi mobile robot

simulator contained in ROS, to obtain samples of gas

concentration data in an environment of 20 X 20 me-

ters. Figure 10 shows the gas distribution in the envi-

ronment according to equation 1 with the gas source

SIMULTECH 2021 - 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

located at the position x

= -2 and y

= 3.It is possi-

ble to observe the Gaussian behavior of the gas con-

centration throughout the environment, which decays

exponentially as it moves away from the source of the

gas leak in any direction.

Figure 10: Gaussian distribution of gas in an indoor envi-

ronment, source of gas located at position x

= -2 and y

Figure 11 shows the gas samples collected by the

robots during their path as described in section 4.1.

The multiple mobile robots carry out the trajectory

simultaneously. Even robots do not perform all the

scanning of the environment, it is possible to observe

that at some moment of the deﬁned path, some robot

will pass near to a point with a high concentration of

gas (whatever it is), which is enough to estimate the

position of the gas source.

Figure 11: Robots detection of gas in the indoor environ-

ment, source of gas located at position x

= -2 and y

= 3.

Figure 12 divides the trajectory into 6 scenarios.

Scenario 1 shows the start point of robots A, B, C, and

D with the handle sensors (circle in green) according

to Table 1. They start at the intermediate point ac-

cording to the FPFC algorithm. In scenario 2, it is

possible to identify that due to the presence of un-

known obstacles detected by the LiDAR sensor, the

FOFC controller is active, and there were no colli-

sions, and the robots start to bypass the obstacles in

the region of nearly 1 meter of distance. Scenario 3

and 4 is a region that alternates between the two con-

ﬁgurations (FPFC or FOFC) according to the robot’s

position. In scenario 5, all robots are already at the

intermediate point towards the endpoint (scenario 6),

predominantly controlled by the FPFC rules.

Table 4: Data obtained by the robots to estimate the position

of the gas leak.

x [m] y [m]

Gas Conc. (Z) [%]

Robot A 0.939 -1.731 72.861

Robot B -1.430 5.828 91.858

Robot C -3.847 3.399 96.421

Robot D -2.32 4.84 96.490

The complete trajectory executed by the robots to

reach the target avoiding obstacle can be seeing in

the complementary video available at: https://tinyurl.

com/tpysdbf5.

The position (x, y) where each robot detected the

highest gas concentration, as well as the percentage

of this concentration is described in Table 4. After

applying the logarithmic calculation to the Z concen-

tration values and obtaining the w values of each robot

to construct the W matrix (equation 7) and the calcu-

lations with (x, y) positions to obtain the variables u

, u

and u

, doing this for each robot and then ob-

taining the U matrix (equation 8) to result in the val-

ues of α (equation 5 and 6) the system of equation is

then solved (equation 9), resulting in the position of

the gas leak source x

= -2 and y

= 3.

6 CONCLUSIONS AND FUTURE

WORKS

In this work, a multi-robot system was developed in

ROS using STAGE simulator, to carry out the scan-

ning in high risk indoor environments, which objec-

tive is to obtain a spatial mapping of the gas con-

centration. The fuzzy system proposed for the work,

namely FPFC and FOFC based in the Lidar sensor

distance data, proved to be efﬁcient, since the robots

do not collide with unknown obstacles and managing

to cross tight spaces between two distinct obstacles.

Considering the simpliﬁcation of gas dispersion in the

environment, it was possible to simulate its distribu-

tion and, applying the Linear Least Squares model

presented, estimate the position of the gas leak source.

Multi-mobile Robot and Avoidance Obstacle to Spatial Mapping in Indoor Environment

Figure 12: FPFC and FOFC algorithm to multi robot free collisions navigation in the environment with unknown obstacles.

The known limitations of this work will be ex-

plored in future works, such as interference and noise

in the use of several laser sensors with similar char-

acteristics and frequency bands and calibration and

delay correction in multi-robot systems. More com-

plex gas distribution models will also be implemented

in future works, considering the effect of wind, tem-

perature, and particle characteristics, adapting the gas

leak source’s pose estimation technique. Finally, as

the interaction between robots to optimize space ex-

plored and monitored in the indoor environment, task

allocation policies and data exchange regarding gas

concentrations in the scanned area by each robot.

ACKNOWLEDGMENT

This work has been supported by FCT- Fundac¸

para a Ci

encia e Tecnologia within the Project Scope:

UIDB/05757/2020. Additionally, this work was

supported in part by the National Counsel of Techno-

logical and Scientiﬁc Development of Brazil (CNPq),

in part by the Coordination for the Improvement of

Higher Level People (CAPES).

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Multi-mobile Robot and Avoidance Obstacle to Spatial Mapping in Indoor Environment