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IFAC PapersOnLine 53-2 (2020) 9682–9687
Decentralized
Strategy
for
Cooperative
Decentralized
Strategy
for
Cooperative
Decentralized
Strategy
for
Cooperative
Multi-Robot
Exploration
and
Mapping
Decentralized
Strategy
for
Cooperative
Multi-Robot
Exploration
and
Multi-Robot Exploration and Mapping
Mapping
Multi-Robot Exploration and Mapping
Ana
Ana Batinović,
Batinović, Juraj
Juraj Oršulić,
Oršulić, Tamara
Tamara Petrović,
Petrović, Stjepan
Stjepan Bogdan
Bogdan
Ana
Batinović,
Juraj
Oršulić,
Tamara
Petrović,
Stjepan
Bogdan
Ana
Batinović,
Juraj
Oršulić,
Tamara
Petrović,
Stjepan Bogdan
Ana
Batinović,
Juraj
Oršulić,
Tamara
Petrović,
Ana Batinović, Juraj Oršulić, Tamara Petrović, Stjepan
Stjepan Bogdan
Bogdan
University
of
Zagreb,
Faculty
of
Electrical
Engineering
and
Computing,
University of
of Zagreb,
Zagreb, Faculty
Faculty of
of Electrical
Electrical Engineering
Engineering and
and Computing,
Computing,
University
University
of
Zagreb,
of
Electrical
Engineering
and
Computing,
Laboratory
for
Robotics
and
Intelligent
Control
Systems
(LARICS),
10000
University
of
Zagreb,
Faculty
of
Engineering
and
Laboratory
for
RoboticsFaculty
and Intelligent
Intelligent
Control
Systems (LARICS),
(LARICS),
10000
Laboratory
Robotics
and
Control
Systems
10000
University for
of
Zagreb,
Faculty
of Electrical
Electrical
Engineering
and Computing,
Computing,
Laboratory
for
Robotics
and
Intelligent
Control
Systems
(LARICS),
10000
Zagreb,
Croatia
(e-mail:
ana.batinovic@fer.hr).
Laboratory
for
Robotics
and
Intelligent
Control
Systems
(LARICS),
Zagreb,
Croatia
(e-mail:
ana.batinovic@fer.hr).
Zagreb,
Croatia
(e-mail:
ana.batinovic@fer.hr).
Laboratory for
Robotics
and Intelligent
Control Systems (LARICS), 10000
10000
Zagreb,
Croatia
(e-mail:
ana.batinovic@fer.hr).
Zagreb,
Croatia
(e-mail:
ana.batinovic@fer.hr).
Zagreb, Croatia (e-mail: ana.batinovic@fer.hr).
Abstract:
This work
work presents
presents aaa novel
novel approach
approach to
to autonomous
autonomous decentralized
decentralized multi-robot
multi-robot frontier
frontier
Abstract: This
Abstract:
This
work
presents
novel
approach
to
autonomous
decentralized
multi-robot
frontier
This
work
presents
aa unknown
novel
approach
to
autonomous
decentralized
multi-robot
frontier
Abstract:
exploration
and
mapping
of
an
area.
A
mobile
robot
team
simultaneously
explores
the
This
work
presents
novel
approach
to
autonomous
decentralized
multi-robot
frontier
Abstract:
exploration
and
mapping
of
an
unknown
area.
A
mobile
robot
team
simultaneously
explores
the
explorationThis
and work
mapping
of ana unknown
area. Atomobile
robot team
simultaneously
explores
the
presents
novel
approach
autonomous
decentralized
multi-robot
frontier
Abstract:
exploration
and
mapping
of
an
unknown
area.
A
mobile
robot
team
simultaneously
explores
the
environment,
discovers
frontier
points
(points
on
the
border
between
explored
and
unexplored
space),
and
exploration
and
mapping
of
an
unknown
area.
A
mobile
robot
team
simultaneously
explores
the
environment,
discovers
frontier
points
(points
on
the
border
between
explored
and
unexplored
space),
and
environment,and
discovers
frontier
points
(pointsarea.
on theAborder
between
explored
and unexploredexplores
space), and
exploration
mapping
of
an
unknown
mobile
robot
team
simultaneously
the
environment,
discovers
frontier
points
(points
on
the
border
between
explored
and
unexplored
space),
and
shares
information
in
order
to
become
dispersed
throughout
the
environment.
During
the
exploration,
environment,
discovers
frontier
points
(points
on
the
border
between
explored
and
unexplored
space),
and
shares
information
in
order
to
become
dispersed
throughout
the
environment.
During
the
exploration,
shares
information
in
order
to
become
dispersed
throughout
the
environment.
During
the
exploration,
environment,
discovers
frontier
points
(points
on
the
border
between
explored
and
unexplored
space),
and
shares information
information
in order
order
to become
become
dispersed
throughout
the environment.
environment.
During
thepositions
exploration,
information
exchanged
between
the
robots
limited
containing
robot
and
shares
in
to
dispersed
the
During
the
exploration,
information
exchanged
between
the
mobile
robots
is
limited
to
data
containing
mobile
robot
positions
and
information
exchanged
between
the mobile
mobile
robots is
isthroughout
limited to
to data
data
containing mobile
mobile
robot
positions
and
shares
information
intarget
order
to become
dispersed
throughout
theisenvironment.
During
the
exploration,
information
exchanged
between
the
mobile
robots
is
limited
to
data
containing
mobile
robot
positions
and
current
mobile
robot
points.
The
main
goal
of
the
approach
to
allocate
the
mobile
robots
to
target
information
exchanged
between
the
mobile
robots
is
limited
to
data
containing
mobile
robot
positions
and
current
mobile
robot
target
points.
The
main
goal
of
the
approach
is
to
allocate
the
mobile
robots
to
target
current mobile
robot target
points.
The
mainrobots
goal of
the
approach
is containing
to allocate mobile
the mobile
robots
to target
information
exchanged
between
the
mobile
is
limited
to
data
robot
positions
and
current
mobile
robot
target
points.
The
main
goal
of
the
approach
is
to
allocate
the
mobile
robots
to
target
frontier
points
in
a
way
which
minimizes
the
overall
exploration
time.
Moreover,
a
mobile
robot
team
at
current
mobile
robot
target
points.
The
main
goal
of
the
approach
is
to
allocate
the
mobile
robots
to
target
frontier
points
in
a
way
which
minimizes
the
overall
exploration
time.
Moreover,
a
mobile
robot
team
at
frontier mobile
points in
a way
which
minimizes
thegoal
overall
exploration
time.
Moreover,
amobile
mobilerobots
robottoteam
at
current
robot
target
points.
The
main
of
the
approach
is
to
allocate
the
target
frontier
points
in
a
way
which
minimizes
the
overall
exploration
time.
Moreover,
a
mobile
robot
team
at
the
same
time
creates
a
common
map
of
the
environment.
The
proposed
strategy
has
been
implemented
frontier
points
in
a
way
which
minimizes
the
overall
exploration
time.
Moreover,
a
mobile
robot
team
at
the
same
time
creates
a
common
map
of
the
environment.
The
proposed
strategy
has
been
implemented
the
same
time
creates
a
common
map
of
the
environment.
The
proposed
strategy
has
been
implemented
frontier
points
in
a
way
which
minimizes
the
overall
exploration
time.
Moreover,
a
mobile
robot
team
at
the
same
time creates
creates
a common
common
map of
of the
thewith
environment.
The proposed
proposed
strategy
has been
been
implemented
in
a
simulation
environment
and
compared
with
a
state-of-the-art
exploration
strategy.
Simulation
results
the
same
time
a
map
environment.
The
strategy
has
implemented
in
a
simulation
environment
and
compared
a
state-of-the-art
exploration
strategy.
Simulation
results
in
a
simulation
environment
and
compared
with
a
state-of-the-art
exploration
strategy.
Simulation
results
the
same
time
creates
a
common
map
of
the
environment.
The
proposed
strategy
has
been
implemented
in aa simulation
simulation
environment
andthe
compared
with
state-of-the-art
exploration
strategy. Simulation
Simulation results
demonstrate
the
advantages
proposed
decentralized
multi-robot
strategy.
in
and
compared
aaa state-of-the-art
exploration
strategy.
demonstrate
the
advantages
of
proposed
decentralized
multi-robot
strategy.
demonstrate
theenvironment
advantages of
of
the
proposedwith
decentralized
multi-robot
strategy.
in
a simulation
environment
andthe
compared
with
state-of-the-art
exploration
strategy. Simulation results
results
demonstrate
the
advantages
of
the
proposed
decentralized
multi-robot
strategy.
demonstrate
the
advantages
of
the
proposed
decentralized
multi-robot
strategy.
license
BY-NC-ND
CC
the
under
article
access
open
an
is
This
The Authors.
2020
Copyright ©the
demonstrate
advantages
of the proposed decentralized multi-robot strategy.
Keywords:
Mobile
System,
licenses/by-nc-nd/4.0)
(http://creativecommons.org/
Keywords:
Mobile
Robot,
Multi-Robot
System,
Frontier
Points,
Target
Point,
Decentralized
Strategy,
Keywords:
Mobile Robot,
Robot, Multi-Robot
Multi-Robot
System, Frontier
Frontier Points,
Points, Target
Target Point,
Point, Decentralized
Decentralized Strategy,
Strategy,
Keywords:
Mobile
Robot,
Multi-Robot
System,
Frontier
Points,
Target
Point,
Decentralized
Strategy,
Exploration,
Mapping.
Keywords:
Mobile
Robot,
Multi-Robot
System,
Frontier
Points,
Target
Point,
Decentralized
Strategy,
Exploration,
Mapping.
Exploration,
Mapping.
Keywords:
Mobile
Robot,
Multi-Robot
System,
Frontier
Points,
Target
Point,
Decentralized
Strategy,
Exploration,
Mapping.
Exploration,
Mapping.
Exploration, Mapping.
1.
1.
INTRODUCTION
1. INTRODUCTION
INTRODUCTION
1.
INTRODUCTION
1.
1. INTRODUCTION
INTRODUCTION
Application
of
multi-robot
Application
of
multi-robot
systems
to
solving
core
robotics
probApplication of multi-robot systems
systems to
to solving
solving core
core robotics
robotics probprobApplication
of
multi-robot
systems
to
solving
core
robotics
problems
has
drawn
significant
attention
in
the
last
few
decades.
One
frontier
Application
of
multi-robot
systems
to
solving
core
robotics
problems
has
drawn
significant
attention
in
the
last
few
decades.
One
frontier
lems
has
drawn
significant
attention
in
the
last
few
decades.
One
frontier
Application
of
multi-robot
systems
to
solving
core
robotics
probpoints
points
lems
has
drawn
significant
attention
in
the
last
few
decades.
One
example
is
coordination
of
a
mobile
robot
team
for
exploration
frontier
lems
has
drawn
significant
attention
in
the
last
few
decades.
One
example
is
coordination
of
a
mobile
robot
team
for
exploration
points
frontier
example
is
coordination
of
a
mobile
robot
team
for
exploration
lems
has
drawn
significant
attention
in
the
last
few
decades.
One
frontier
points
points
example
is coordination
coordination
of is
a mobile
mobile
robot in
team
forapplications,
exploration
of
an
unknown
area,
which
encountered
many
example
is
of
a
robot
team
for
exploration
of
an
unknown
area,
which
is
encountered
in
many
applications,
points
of an unknown
area, which
is
encountered
in
many
applications,
example
is
coordination
of
a
mobile
robot
team
for
exploration
filtered
filtered
of
an
unknown
area,
which
is
encountered
in
many
applications,
such
as
search
and
rescue
(Murphy
(2004)),
cleaning
(Endres
filtered
of
an
unknown
which
is
encountered
in
many
applications,
such
as
search
and
(Murphy
(2004)),
cleaning
(Endres
frontier
such
as
search area,
and rescue
rescue
(Murphy
(2004)),
cleaning
(Endres
frontier
of
an
unknown
area,
which
is
encountered
in
many
applications,
filtered
frontier
filtered
such
as
search
and
rescue
(Murphy
(2004)),
cleaning
(Endres
et
al.
(1998)),
(Pinheiro
et
al.
(2015)),
warehousing
(Wurman
points
such
as
search
and
rescue
(Murphy
(2004)),
cleaning
(Endres
et
al.
(1998)),
(Pinheiro
et
al.
(2015)),
warehousing
(Wurman
points
filtered
frontier
ROBOT
et
al.
(1998)),
(Pinheiro
et
al.
(2015)),
warehousing
(Wurman
points
frontier
ROBOT
such
as
search
and
rescue
(Murphy
(2004)),
cleaning
(Endres
ROBOT
et
(1998)),
(Pinheiro
et
al.
(2015)),
warehousing
(Wurman
frontier
al.
(2008))
or
planetary
exploration
(Mataric
and
Sukhatme
points
et
(1998)),
(Pinheiro
et
al.
(2015)),
warehousing
(Wurman
al.
(2008))
or
planetary
exploration
(Mataric
and
Sukhatme
points
ROBOT
et al. (2008))
or
planetary
exploration
(Mataric
and
Sukhatme
ROBOT
(1998)),
(Pinheiro
et
al.
(2015)),
warehousing
(Wurman
points
ROBOT
et
al.
(2008))
or
planetary
exploration
(Mataric
and
Sukhatme
(2001)),
to
aaa few.
to
that
multiet
al.
(2008))
or
planetary
exploration
and
Sukhatme
(2001)),
to
name
few.
Due
to
the
fact
that
autonomous
multi(2001)),
to name
name
few. Due
Due
to the
the fact
fact(Mataric
that autonomous
autonomous
multiet
al.
(2008))
or
planetary
exploration
(Mataric
and
Sukhatme
(2001)),
to
name
aaentering
few.
Due
to
the
fact
that
autonomous
multirobot
systems
are
society
and
as
such
will
interact
with
(2001)),
to
name
few.
Due
to
the
fact
that
autonomous
multirobot
systems
are
entering
society
and
as
such
will
interact
with
robot systems
are aentering
society
such
will interactmultiwith
(2001)),
to name
few. Due
to theand
factas
that
autonomous
robot
systems
are
entering
society
and
as
will
interact
with
people
on
basis,
of
efficient
coordination
robot
systems
are
entering
society
and
as
such
will
interact
with
people
on aaa daily
daily
basis, development
development
of such
efficient
coordination
people
on
daily
basis,
development
of
efficient
coordination
robot
systems
are
entering
society
and
as
such
will
interact
with
people
on aabecomes
daily basis,
basis,
development of
of efficient
efficient coordination
coordination
algorithms
becomes
necessary.
people
on
daily
development
algorithms
necessary.
algorithms
becomes
necessary.
people
on
a
daily
basis,
development
of
efficient
coordination
unexplored
explored
unexplored
explored
algorithms becomes
becomes necessary.
necessary.
obstacle
unexplored
explored
algorithms
obstacle
space
space
obstacle
space
space
Like
human
robots
unexplored
explored
algorithms
necessary.
Like in
in the
the becomes
human society,
society,
robots can
can be
be more
more effective
effective when
when
space
space
unexplored
explored
obstacle
Like
in
the
human
society,
robots
can
be
more
effective
when
obstacle
unexplored
explored
space
space
space
space
Like
in
the
human
society,
robots
can
be
more
effective
when
they
work
together.
Moreover,
a
robot
team
can
accomplish
a
obstacle
Like
in
the
human
society,
robots
can
be
more
effective
when
they
work
together.
Moreover,
a
robot
team
can
accomplish
a
space
space
they
work
together.
Moreover,
a
robot
team
can
accomplish
a
Like
in
the
human
society,
robots
can
be
more
effective
when
they
work
together.
Moreover,
aa robot
team
can
accomplish
aa
predefined
task
much
quicker
than
a
single
robot
can
(Dias
and
they
work
together.
Moreover,
robot
team
can
accomplish
predefined
task
much
quicker
than
a
single
robot
can
(Dias
and
predefined
task muchMoreover,
quicker than
a single
robot
can
(Dias anda
they
work together.
a robot
team
can
accomplish
predefined
task
much
quicker
than
aaof
single
robot
can
(Dias
and
Stentz
Another
advantage
mobile
robot
teams
is
the
predefined
task
much
quicker
than
robot
can
(Dias
Stentz
(2000)).
Another
advantage
of
mobile
robot
teams
the
Stentz (2000)).
(2000)).
Another
advantage
ofsingle
mobile
robot
teams
isand
the
predefined
task
much
quicker
than
a
single
robot
can
(Diasis
and
Stentz
(2000)).
Another
advantage
of
mobile
robot
teams
is
the
possibility
of
sensor
fusion,
which
in
turn
can
help
to
compensate
Stentz
(2000)).
Another
advantage
of
mobile
robot
teams
is
the
possibility
of
sensor
fusion,
which
in
turn
can
help
to
compensate
possibility
of
sensor
fusion,
which
in
turn
can
help
to
compensate
Stentz
(2000)).
Another
advantage
of
mobile
robot
teams
is
the Fig.
Fig.
1.
The
environment
is
represented
by
2D
map,
with
an
possibility
of
sensor
fusion,
which
in
turn
can
help
to
compensate
for
sensor
uncertainty
(Wurm
et
al.
(2008)).
If
done
properly,
Fig. 1.
1. The
The environment
environment is
is represented
represented by
by aaa 2D
2D map,
map, with
with an
an
possibility
of
sensor
fusion,
which
in
turn
can
help
to
compensate
for
sensor
uncertainty
(Wurm
et
al.
(2008)).
If
done
properly,
for
sensor
uncertainty
(Wurm
et
al.
(2008)).
If
done
properly,
possibility
of
sensor
fusion,
which
in
turn
can
help
to
compensate
Fig.
1.
The
environment
is
represented
by
a
2D
map,
with
an
occupancy
grid
that
divides
the
map
into
cells:
white
cells
Fig.
1.
The
environment
is
represented
by
a
2D
map,
with
an
occupancy
grid
that
divides
the
map
into
cells:
white
cells
for
sensor
uncertainty
(Wurm
et
al.
(2008)).
If
done
properly,
multi-robot
coordination
can
lead
to
i)
task
accomplishment
in
occupancy
grid
that
divides
the
map
into
cells:
white
cells
for
sensor
uncertainty
(Wurm
et
al.
(2008)).
If
done
properly,
multi-robot
coordination
can
lead
to
i)
task
accomplishment
in
Fig.
1.
The
environment
is
represented
by
a
2D
map,
with
an
multi-robot
coordination
can lead
to (2008)).
i) task accomplishment
in
for
sensor
uncertainty
(Wurm
et al.
Ifmap
done
properly,
occupancy
grid
that
divides
the
map
into
cells:
white
cells
describe
explored
while
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finally
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the
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frontier
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frontier
by
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by
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(Dias
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(2006)).
frontier points
points (green).
(green).
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the
by aaconsider
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etof
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2405-8963 Copyright © 2020 The Authors. This is an open access article under the CC BY-NC-ND license.
Peer review under responsibility of International Federation of Automatic Control.
10.1016/j.ifacol.2020.12.2618
Ana Batinović et al. / IFAC PapersOnLine 53-2 (2020) 9682–9687
CENTRALIZED
Google Cartographer
Map
Laser scan
and
odometry
Map
Ground truth
poses
Frontier
detection
Filter
Frontier points
Filtered frontier
points
Robot localization
Mobile robot 1
DECENTRALIZED
...
Mobile robot n
Path planning
and navigation
Target point
DECENTRALIZED
Decentralized
exploration strategy
Fig. 2. Overall schematic diagram of the decentralized exploration and mapping process for n mobile robots in the
simulator. Google Cartographer SLAM and filter module
(highlighted in red) generate filtered frontier points that are
(currently) the centralized part of exploration and mapping
process. The exploration strategy, path planning and navigation module (highlighted green) are decentralized parts
that generate n outputs and create a common map.
In the next section we describe more thoroughly different parts
of the system, state-of-the-art for each part and algorithms used
in this paper. In Section III we describe the proposed exploration
strategy. Simulation results are presented in Section IV, and in
the final section a conclusion is given.
2. EXPLORATION AND MAPPING OVERVIEW
Overview of the system is given in Fig. 2. The system consists
of a centralized part (Simultaneous Localization and Mapping
(SLAM), frontier detection and frontier points filter), which runs
on a dedicated computer and a decentralized part (Exploration
strategy and navigation), which runs on each robot. In the
folloewing text each part is described separately.
2.1 SLAM
The laser scan and odometry sensor measurements of each mobile robot represent input data for a Simultaneous Localisation
and Mapping (SLAM) module. Most exploration approaches in
the literature use the ROS ’gmapping’ package for generating the
map and localizing mobile robots (Keidar and Kaminka (2012),
Umari and Mukhopadhyay (2017)). The ’gmapping’ package
implements a SLAM algorithm that uses a Rao-Blackwellized
particle filter (Grisetti et al. (2007)).
In this paper, we use a submap-based graph SLAM method
- Google Cartographer (Hess et al. (2016)) for map building,
which in our case generates the ground truth map. This map is
used in simulations to obtain the mobile robot poses (perfect
localization) from the Stage simulator (Vaughan et al. (2012)),
allowing us to eliminate the SLAM algorithm uncertainty in
simulations for algorithm comparison.
9683
The RRT algorithm is biased towards unexplored regions and
provides a general approach which can be extended to higher
dimensional spaces. However, the method has proved not to be
fast enough for a given scenario in instances when larger parts
of the environments were explored, so we opted to use a dense
frontier detection method from Orsulic et al. (2019).
2.3 Filter Module
The filter module receives frontier points from the frontier
detector, clusters the points and stores only the centre of each
cluster (Umari and Mukhopadhyay (2017)). The clustering
process reduces the number of frontier points that are close to
each other. In that manner we avoid unnecessary consumption of
computational resources, without significant loss of information
about the frontier. For clustering we use the Hierarchical
Agglomerative Clustering algorithm (Scikit-learn (2019)), which
does not require a predefined number of clusters. We only need
to set a distance threshold parameter, above which clusters will
not be merged. Taking into consideration a given scenario and a
laser range, the distance threshold parameter is set to 1 meter.
2.4 Exploration strategy
The term exploration strategy considered here includes algorithms for assigning robots to target (frontier) points for environment exploration. Such algorithms can be grouped into
centralized and decentralized algorithms. In the centralized
approach, each mobile robot receives tasks from a single central
leader which runs the overall planning algorithm, and afterwards
the mobile robot sends its info back to the leader. Centralized
assignment may be less practical due to communication limits
(Dias and Stentz (2000)), robustness issues (Dias et al. (2006)),
or time required for algorithm execution and scalability (Juliá
et al. (2012)). An advantage of centralized approach is that
optimal plans can be found (Z. Yan and Cherif (2011)).
In contrast to centralized approaches, in a decentralized approach, the mobile robots are completely independent throughout the exploration process. Each mobile robot has its own
local knowledge of the world and can decide its future actions
by taking into account its current context and tasks, its own
capacities and the capacities of the other mobile robots, through
a negotiation process (Yan et al. (2013)). Moreover, it typically
has better reliability, flexibility, adaptability and robustness (Zlot
et al. (2002)). Our approach is a hybrid one - the robots can independently decide towards which target point to navigate using an
optimization procedure, while having common knowledge of all
target frontier points and sharing information on their position
and current goals.
In order to determine frontier points we use frontier detection
according to Orsulic et al. (2019). This method, which is an
extension to Google Cartographer, has achieved good results in
terms of wall-time per frontier update, which greatly speeds up
our exploration and mapping process.
Two frontier-based exploration approaches are introduced in
Yamauchi (1998) and Singh and Fujimura (1993). Both approaches are uncoordinated in a sense that robots head to the
closest frontier point. Approaches cover homogeneous and
heterogeneous multi-robot systems, respectively. Authors in Zlot
et al. (2002) use a market-based approach and allow robots to
visit a set of goal points (a tour) while continuously negotiating
with other robots. One approach similar to ours is given in
Burgard et al. (2005), which is a centralized approach that takes
into account the costs of reaching a target and the utility of
reaching that target.
Another detection method, based on Rapidly Exploring Random
Trees (RRTs) is given in Umari and Mukhopadhyay (2017).
With respect to the mentioned approaches our approach is
hybrid and uses slightly different objective functions for frontier
2.2 Frontier Detection
9684
Ana Batinović et al. / IFAC PapersOnLine 53-2 (2020) 9682–9687
points assignment, which are a combination of frontier point
cost, utility of reaching the target point and frontier occupancy
function. We also cluster frontier points to get a problem
of manageable size and thus enable application of known
optimization algorithms. Our approach is hybrid in a manner
that target point assignment process and navigation are fully
decentralized and event-based, that is, each robot team member
makes an individual decision on the next target point each time
it reaches the previous one. On the other side, SLAM extended
with frontier detection and filter module are a centralized part of
the exploration and mapping process (Fig. 2). There are several
approaches that tackle decentralization of the SLAM for mobile
robots (Jiménez et al. (2018), Atanasov et al. (2015)), but this is
out of the scope of the paper. We assume that communication
range is unlimited, however, one approach for dealing with
limited communication range might be to take into account the
last target points, such as in Burgard et al. (2005). Another
workaround might be to implement a multi-hop communication
network.
assigned
frontier point
position ya
ROBOT 1
frontier point
position yj
path
rf
ROBOT 2
Fig. 3. Illustration of the value of the frontier occupancy function
F being different from zero. The mobile robot 1 is assigned
to visit a frontier point a (at position ya ), and follows the
path to reach it. When mobile robot 2 calculates weight
for all the current frontier points (green), F for the frontier
point j is different from zero because j is inside the radius
rf .
With respect to the previous approaches we conduct a realistic
ROS-based simulation suitable for straightforward experimental
deployment. We use state-of-the art frontier detection and map
building software, and provide data to allow for future comparisons of different exploration strategies. Software architecture is
modular, allowing components to be easily changed or extended,
without affecting the remaining processes. Simulation results
given at the end of the paper have shown that the proposed
approach achieves better performance than the state-of-the art
approach selected for comparison.
The utility function U j : (Y × M ) → R+ returns a positive real
number. The cells of the occupancy grid M may be marked
as explored space, unexplored space or obstacle. The utility
function is proportional to the number of the unexplored cells k j
within a fixed distance from the frontier point j in the previously
defined radius r:
3. DECENTRALIZED EXPLORATION STRATEGY
U j = λu k j ,
At the core of our paper is a decentralized strategy for multirobot exploration and mapping. The mobile robots exchange
information about frontier points under the assumption of a
fully connected graph and event-based communication. We
define a mission as a process that starts by getting a target point
and finishes by reaching the target point. Then, event-based
communication is triggered by mission accomplishments, since
all mobile robots communicate with each other in the moments
when the mission for a single mobile robot s over. It means that
the rest of mobile robots should send the data even though their
missions are in progress and they are still navigating to the goal.
The exploration is performed by a team of n mobile robots
R = {1, 2, ..., N}, where the mobile robots do not have prior
knowledge about the environment, i.e., the position of the
boundaries and obstacles. Every mobile robot i gets the list
of frontier points Y = {1, 2, ..., M} from the filter module (Fig.
2) in the moments when any of the mobile robots reaches the
target point (when a mission is over). Each frontier point j is
defined with its position in the environment, denoted as y j ∈ R2 .
We define the weight of a mobile robot performing a visit to
frontier point Wi j as a function of cost C, utility U and frontier
occupancy F. Cost function C: (R ×Y ) → R+ returns a positive
real number. If i is the index of the mobile robot, and j is the
index of the frontier point, then C(i, j) (denoted in the remaining
text as Ci j ) describes the cost of ith robot to visit the jth frontier
point. The cost can be a function of time, energy or, like in our
case, the estimated distance travelled by mobile robot to reach
the target frontier point. The estimated distance is approximated
using Euclidean distance between the mobile robot position pi
and the frontier point position y j :
Ci j = d(pi , y j ) =
�
(pix − y jx )2 + (piy − y jy )2 .
(1)
(2)
where λu is a constant determined experimentally. When the
function U j is taken into account, the mobile robot will prefer
frontier points that are surrounded by more unexplored space
even if they are a little bit further. It is assumed that the mobile
robot will detect all unexplored cells around the assigned frontier
point after reaching it.
Another important component is the frontier occupancy function
Fi j : (R × Y ) → R+ , the 2-dimensional Gaussian function with
the position of the mean in a frontier point and with the standard
deviation σ = [r f r f ]T . If the frontier point j, for which the
mobile robot i is calculating the weight, is in the range of radius
r f from the position of an another mobile robot assigned point
(ya ); the value of the frontier occupancy function is calculated
by Gaussian function, and zero otherwise:
�
�

2
2
 − (y jx −y2ax ) + (y jy −y2ay )
2σx
2σy
if d(y j , ya ) < r f ,
Fi j = λ f e
(3)

0
otherwise
where λ f is an experimentally determined constant. An example
of the frontier point position y j , assigned point position ya and
Gaussian function values inside the radius r f is shown in Fig.
3. The function Fi j is used to prevent assigning frontier point to
the mobile robot B if that point is close to a point that is already
assigned to mobile robot A.
For each frontier point j, the weight Wi j of the i-th mobile robot
is calculated as:
Wi j = Ci j −U j + Fi j .
(4)
The weight matrix W (N × M) is formed for N mobile robots
and M frontier points:
Ana Batinović et al. / IFAC PapersOnLine 53-2 (2020) 9682–9687
9685
Algorithm 1: Decentralized strategy for mobile robot i
1 while Unexplored do
2
if Request then
3
Send position and current target point to the other
mobile robots;
4
if Mobile robot i has reached the previous target
point then
5
Request positions and current target points from
other mobile robots;
6
Calculate the weight matrix W ;
7
Hungarian algorithm (W );
8
return Mobile robot i is assigned to frontier
point;

W11 W12 . . . W1 j . . . W1M
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. 
..
 ..
. .. 
WN1 . . . . . . . . . . . . WNM
Robot i reached
target point
YES
Request positions
and current target
points from the
others
Calculate the matrix
W
Hungarian algorithm
Target point
Path planning
and navigation
Fig. 4. Execution of the decentralized part of the Fig. 2. Every
mobile robot explores the environment following the steps
from Algorithm 1. The blue robot accomplished the mission
and requests weights from other team members (red). The
algorithm is the same for all mobile robots and always
executes in the moment when a robot reaches a target point.

(5)
Since mobile robots have the same set of frontier points, the
only information mobile robots share is their position and
current target point, needed to calculate (1)-(3). The amount
of exchanged data is thus reduced, which enables easier and
faster communication. The weight matrix W represents the input
into the Hungarian algorithm that finds an optimal assignment solution in polynomial time. The Hungarian algorithm is described
in Kuhn (1955) and tested in Kulich et al. (2015). Initially, the
Hungarian algorithm assumes that the number of frontier points
is the same as the number of mobile robots. Due to the fact that
there are usually fewer mobile robots than frontier points, virtual
mobile robots are added and then skipped during the process of
assignment and exploration.
Let the matrix X be the matrix of zeros and ones, where Xi j = 1
iff the mobile robot i is assigned to the frontier point j. Then the
optimal task assignment has weight:
�
�
(6)
min ∑ ∑ Wi j Xi j ,
X
i
NO
j
anticipating that minimisation of sum will ensure the dispersion
of the mobile robots in the environment.
All frontier points are visible to all mobile robots. When mobile
robot i is assigned to a frontier point according to line 8 in
Algorithm 1, the mobile robot starts to follow the planned path
and navigates to the target frontier point. At the moment when
the mobile robot i reaches the target point (mission is over), a
request is sent to other mobile robots to get their positions and
current target points, and to fill in the weight matrix W , which is
an input to Hungarian algorithm. The described process executes
until the whole environment is explored and a complete map of
the environment is generated. The Fig. 4 illustrates the described
steps and algorithm lines for a mobile robot team.
To summarize with respect to the coordinated strategy from
Burgard et al. (2005), the cost function described in (1) is
the same (probability is taken into account through frontier
(a)
(b)
Fig. 5. Maps used for simulation experiments. (a) Original map:
Map from Haehnel (2014). (b) Google Cartographer map:
The map generated using Google Cartographer SLAM
algorithm.
points) and the utility of a frontier point, in contrast to (2),
depends on the number of mobile robots that are moving to that
point. Component (3) is introduced in this paper. Event-based
approach that we use results in less frequent target changes, thus
minimizing the need for re-planning.
4. SIMULATION RESULTS
The proposed strategy is implemented and compared with the
coordinated strategy (Burgard et al. (2005)), one of the first
coordinated approaches which achieved enviable results and is
easy to implement. The frontier detector and filter module are
the same for both algorithm implementations - coordinated and
our decentralized.
4.1 Simulation Setup
Simulations were carried out in well-known robot operating
system (ROS) using the Stage 2D simulator (Vaughan et al.
(2012)), which simulates robot movement and lidar perception
inside a loaded environment map. The ROS Navigation stack is
used to control and direct the mobile robots towards exploration
goals.
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The scenario used in the simulation is the Belgioioso Castle,
available in Haehnel (2014) and shown in Fig. 5. It is a
challenging and a typical office-like scenario with a free space
area of approximately 225 m2 . For the simulation, we use a
model of Pioneer P3-DX with maximum speed of 1.3 m/s, laser
range 20 m and 360◦ laser scan window. The algorithms were
tested with teams of two, three and five mobile robots. In our
case, the number of mobile robots was limited because of the
complex simulation setup and computational requirements.
The robots started off in random positions within this world, but
the initial positions are the same for both algorithms to allow
for comparison. The results are presented as averages of 10 runs
for each set. Constants λu , λ f , r and r f were experimentally
determined considering map dimensions and mobile robot laser
ranges and set to 0.9, 1.2, 0.5, 3.0 respectively. The constant
values are set to give more importance to the frontier occupancy
function than the utility function.
4.2 Simulation Results
The exploration process is visualized using the RViz visualization tool shown in Fig. 6. During the exploration and mapping
process, the covered area as a function of time was recorded. The
comparison of the coordinated and our decentralized strategy is
shown using the Coverage Ratio (CR) indicator which shows the
percentage of the accessible terrain covered by the mobile robot
cells·100
team. It is calculated as: explored
accessible cells , where accessible cells
represent free cells. We report the time it took to cover 50, 75,
90 and 98 percent of the environment. Box plots for coverage
ratio in time measured during exploration are shown in Fig. 7.
As can be observed, the decentralized strategy has an advantage
over the coordinated strategy.
When we compare the average exploration time for both strategies, we conclude that adding mobile robots to exploration team
reduces exploration time. Using our decentralized strategy, it
took 7.8%, 15.3% and 32.6% less time for two, three and five
mobile robots respectively to explore the environment compared
to coordinated strategy. This result shows that our decentralized
strategy (within described setup) performs significantly better
than coordinated, especially for five mobile robots. However,
depending on the area size and configuration, adding of more mobile robots might not pay off in terms of shorter exploration time
due to overcrowding. Additionally, openly available source code
of this work can be found on Github 1 . It includes developed and
implemented decentralized multi-robot exploration strategy as
well as our implementation of the coordinated algorithm. Video
recordings for simulation with multiple mobile robots can be
found on YouTube 2 .
5. CONCLUSION AND FUTURE WORK
In this paper, a modular approach to autonomous decentralized
multi-robot exploration and mapping was presented. This approach is not only restricted to Google Cartographer SLAM and
dense frontier detection, but may also be applied to different
multi-robot systems. This strategy has resulted in improved
behaviour in terms of exploration time compared to a state-ofthe-art strategy in terms of exploration time.
Even though the goals of this paper were shown to be achieved,
the algorithm is open towards improving. Future research
should consider decentralized map creating. Also, a significant
improvement to this strategy would be a simpler simulator, that
would allow for simulation of more robots.
Another research direction can be an extension to the algorithm
to cope with a limited communication range of the mobile robots.
Future work should also consider a multi-robot system which
uses a (not fully) connected communication graph. Finally, we
would like to take into consideration scenarios in which the
robots may fail as well as time-varying environment scenarios.
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(b)
Fig. 6. Decentralized exploration with five mobile robots. In
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