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\Phi$ Clust: Pheromone-Based Aggregation for Robotic Swarms

Authors:
ΦClust: Pheromone-based Aggregation for Robotic Swarms
Farshad Arvin1, Ali Emre Turgut2, Tom´
aˇ
s Krajn´
ık3, Salar Rahimi2,˙
Ilkin Ege Okay2, Shigang Yue4
Simon Watson1, and Barry Lennox1
Abstract In this paper, we proposed a pheromone-based
aggregation method based on the state-of-the-art BEECLUST
algorithm. We investigated the impact of pheromone-based
communication on the efficiency of robotic swarms to locate
and aggregate at areas with a given cue. In particular,
we evaluated the impact of the pheromone evaporation and
diffusion on the time required for the swarm to aggregate.
In a series of simulated and real-world evaluation trials, we
demonstrated that augmenting the BEECLUST method with
artificial pheromone resulted in faster aggregation times.
Index Terms Swarm Robotics, Aggregation, Pheromone,
Bio-inspired.
I. INTRODUCTION
Vast number of collective behaviours such as aggregation,
flocking and schooling have been observed in nature. Among
them, aggregation is one of the most common behaviour
observed from single-cellular organisms such as amoebae [1]
to large mammals [2]. The main reason behind this is
the fact that all animals living in groups need to gather
together in order to increase their chance of survival or in
order to cooperate. Two different types of aggregation are
mainly observed in nature. One is the cue-based aggregation
where species aggregate near some cues such as humidity
or temperature in the environment [3]. The other is the cue-
less or self-organised aggregation where species aggregate
without any cue.
One of the seminal works on cue-based aggregation is due
to Schmickl et al. [4]. They studied aggregation of young
honeybees on the optimal temperature zone and proposed
a very simple algorithm, called BEECLUST, to model this
behaviour. Their algorithm was based on local sensing of the
conspecifics and the environment and it was able to model
the aggregation behaviour successfully.
Using chemicals, called pheromones, specially by the
social insects to communicate either directly or indirectly
through the environment is widely observed in nature.
Pheromone communication is particularly useful in unstruc-
tured environments where other forms of communication
This work was supported by the UK EPSRC EP/P01366X/1,
H2020 STEP2DYNA (691154), and CZ projects: 17-27006Y and
CZ.02.1.01/0.0/0.0/16 019/0000765.
1Robotics for Extreme Environments Lab (REEL), School of Electrical
and Electronic Engineering, the University of Manchester, Manchester, M13
9PL, United Kingdom, farshad.arvin@manchester.ac.uk
2Mechanical Engineering Department, Middle East Technical University,
06800 Ankara, Turkey
3Artificial Intelligence Centre, Faculty of Electrical Engineering, Czech
Technical University, Prague, Czechia
4Computational Intelligence Laboratory (CIL), School of Computer
Science, University of Lincoln, Lincoln, LN6 7TS, UK
does not work. Artificial pheromones were first introduced
by Payton et al. [5]. They developed a messaging scheme
based on hopping which loosely resembles pheromones.
There were also several attempts to mimic pheromones
using chemical counter-parts [6], [7] that turned out to
have many restrictions due to the chemicals. It was very
recent that pheromones were implemented reliably for swarm
robotic systems. The system (COSΦ) consists of an active
ground system having an LCD screen to implement artificial
pheromones visually [8]. In a very recent paper, Valentini
et al. [9] designed an active ground system to implement
artificial pheromones.
It is known that pheromones are involved in most of
the collective behaviours including aggregation. To the best
of our knowledge, aggregation has never been modelled
using pheromones. In this paper, we modify the state-
of-the-art algorithm BEECLUST and investigate for the
first time systematically the effect of pheromones on cue-
based aggregation. We improve the state-of-the-art two
folds: (1) We designed an aggregation model called it as
ΦClust based on BEECLUST using pheromones. (2) We
implemented the new aggregation model using the simulated
version our state-of-the-art pheromone system, COSΦ.
The rest of this paper is organised as follows. In the second
section, we discuss related work, briefly. In the third section,
the proposed method is introduced. Following that in the
fourth section, the realisation of the system is explained. In
the fifth section, the results of the experiments is discussed.
Finally in the sixth section, we discuss the future plan and
conclude the study.
II. LITERATURE SURVE Y
One of the earliest cue-based swarm aggregation scenarios
has been implemented by Kube and Zhang [10] by ag-
gregating robots around a light source. Another cue-based
aggregation which robots aggregated around an infra-red
(IR) emitter and started a collective transportation scenario
was proposed in [11]. In case of bio-inspired aggregation,
Garnier et al. [12] used micro robots to implement the
cockroach aggregation behaviour. BEECLUST [4] has been
used in different research studies with real- and simulated-
robots. Follow up studies on BEECLUST focused on: i)
derivation of aggregation model based on the systematic
honeybee experiments [13], [14], [15], ii) modification of
parameters of BEECLUST to improve the performance [16],
iii) macroscopic modelling of the aggregation [17], [18],
iv) fuzzy-based decisioning [19], v) heterogeneity in be-
haviours [20], and vi) recently a bio-hybrid society of robots
Fig. 1. Finite state machine in BEECLUST.
and honeybees [21], [22].
III. MET HO D
We added pheromone communication to the BEECLUST
method and called our new model as ΦClust.
A. Aggregation
In BEECLUST, aggregation behaviour is modelled as a
state-machine, with a few states and transitions shown in
Fig. 1. A robot moves forward until it encounters an object.
If the object is an obstacle, the robot stops, turns to a random
angle, θ[90,+90], and restarts to move forward. If the
object is another robot, the robot stops and measures the state
of a given cue (type of the cue -light or intensity- differs in
different implementations. In this paper, we use light and
measure the intensity of the light) and sets its waiting time
according to the state of the cue [23]:
w(t) = wmax +S2(t)
S2(t) + 25 ,(1)
where, wmax is the maximum waiting time and Sis the cue
intensity. In our case, wmax = 20 s and the intensity of the
cue, quantified on a scale from 0 to 5, is measured by the
robots light sensors.
B. Artificial Pheromone System
The artificial pheromone system, COSΦ, [8] consists
of two components: an accurate external localisation sys-
tem [24], which allows to track the individual robots in
real time, and a horizontal LCD screen, which displays the
pheromones and their combined effect in form of a colour
image. Each robot can sense the displayed pheromones with
its light and colour sensors and release several pheromones
depending on user-specified conditions, e.g. the distance
from another robot or obstacle.
The image displayed on the LCD is modelled as three
matrices I{r,g,b}corresponding to the the red, green and blue
channels of the individual image pixels, which are calculated
from the pheromones as:
Ic(x, y) =
n
X
i=1
sc
iΦi(x, y),(2)
where Φi(x, y)is a matrix representing ith pheromone
strength at location (x, y)and αc
idefines the pheromone’s
influence on colour of a particular pixel, i.e. c∈ {r, g, b}.
Since the values of αc
ican be positive or negative, the
individual pheromones can amplify or suppress each others’
effect.
Apart from the pheromone’s influence on the displayed
image, defined by three constants α{r,g,b}, we model its
behaviour by three additional parameters. These are injection
ι, which determines the pheromone’s current release rate by
a given robot, evaporation eφ, which defines how it fades
over time, and diffusion κ, that models its spread over time.
The strength of each pheromone at (x, y)is continuously
updated by:
˙
Φi(x, y) = e Φi(x, y) + κi4Φi(x, y) + ιi(x, y),(3)
where ˙
Φi(x, y)represents the pheromone change rate caused
by its evaporation e, diffusion κiand injection ιi.
The injection ιi(x, y)of ith pheromone at position (x, y)
is defined by a set of conditions that are typically related to
the positions of the individual robots in the arena. Typically,
a robot at a position (xr, yr)sets the injection within a given
radius to a specified value, i.e.
ιi(x, y) = sφifp(xxr)2+ (yyr)2lφ/2
0otherwise,,
(4)
where (xr, yr) is the position of a particular robot, lφis the
width of the pheromone trail and sφis the pheromone release
rate.
Since various robots release pheromones with differ-
ent injection, evaporation and diffusion rates, and these
pheromones suppress or amplify each other differently for
each colour channel, pheromone-robot interaction can result
in a complex swarm behaviours.
C. Pheromone-guided Aggregation
We extend the state-machine in Fig. 1 by adding an extra
state: ‘pheromone gradient following’, which is activated
whenever a moving robot detects pheromone. Moreover, we
added ‘release pheromone’ behaviour to the waiting state.
The finite state machine of the aggregation behaviour in
ΦClust is shown in Fig. 2.
IV. EXP ERI ME NTAL SETU P
We evaluate the performance of ΦClust by comparing
it with BEECLUST. Hence, we performed two different
experimental scenarios: i) aggregation with BEECLUST and
ii) aggregation with ΦClust.
A. Aggregation with BEECLUST
In this experiment, we employed the standard BEECLUST
method. In our implementation of the BEECLUST, we used
a light source (occupies 25% of arena size) as the cue.
The light source has a circular shape and has its maximum
intensity at the centre. The intensity decreases gradually as
we move to the periphery.
Fig. 2. Finite state-machine of ΦClust.
In particular, a robot moves forward with velocity
u=3.5 cm/s until it meets an obstacle or another robot.
If the robot detects or collides with an obstacle, it simply
turns by a random degree and continues to move forward.
However, if the robot detects another robot, it stops and
measures the intensity of the light S, which, in our case,
is a natural number ranging from 0 to 5, i.e. S∈ N and
0S5. The intensity of the cue Sdetermines the time
w(t), which the robot will wait without moving.
We investigate the capability of the aggregation model and
effects of the population size, ns, on the performance of the
aggregation. This set of experiments was implemented both
real-robot “Mona”, and in simulation (the simulator used was
PyCX [25]). Thus, the results of this scenario served not only
to obtain the data quantifying the BEECLUST behaviour
for comparison with the ΦClust one, but also to assess the
fidelity of the simulation compared to the real world.
B. Aggregation with ΦClust
This set of experiments were similar to the previous setup,
with the addition of an external guidance from pheromones
which were released by the robots when were waiting in the
cue (see Fig. 2).
Robots move with velocities of u=3.5 cm/s, in an
environment with a light source S. Apart from being
able to detect collisions with other robots and obstacles,
and measuring the intensity of the cue, they could also
detect the presence of the pheromone from a distance of
rφ. In our experiments, we evaluated several pheromone
detection distances (called pheromone radii), setting rφto
four different values of {3.5,10.5,14,17.5}cm. Thus, while
moving, the robots were able to detect the pheromone
within a radius rφwhenever its intensity exceeded 1. After
detecting the pheromone, the robots were able to locate and
move towards the pheromone intensity maximum within their
sensing radius.
Apart from being able to detect pheromones, the robots
were also releasing it when in waiting mode. The release rate
of the pheromone ιswas set to the intensity of the pheromone
under the robot Φithat would be stabilise at a value Is, which
is proportional to the intensity of the cue S, perceived by the
TABLE I
EXP ERI ME NTA L VALU ES OR R AN GE F OR VAR IA BL ES A ND C ON STAN TS
Values Description Range / Value(s)
nsPopulation size {10 35}robots
AsSize of arena, area of swarm 210 x 210 cm2
rsRadius of temp sensing 3.5 cm
rφRadius of pheromone sensing {3.517.5}cm
IsSensor reading of pheromone 0 to 5
SSensor reading of temperature 0 to 5
uRobot forward velocity 3.5 cm/s
eφEvaporation rate of pheromone {10% 60%}per sec
κDiffusion coefficient {3.517.5}cm/sec
TDuration of experiments 500 sec
w(t)Waiting time 0 to 20 sec
tTime 0 to 500 sec
robot.
In this scenario, we investigated the effects of the
pheromone parameters evaporation eφand diffusion κ,
swarm population size ns, and pheromone sensing range rφ
on the performance of the aggregation.
C. Implementation Details of Swarm Aggregation
The proposed aggregation scenarios were implemented
using real- and simulated-robots. The real robots were
deployed in the no-pheromone aggregation scenario and the
simulated robots were utilised in both pheromone-guided and
no-pheromone aggregation scenarios. The standard values
of the constants and variables which were used in the
experiments are listed in Table. I.
1) Mona Robot: Mona [26] (shown in Fig. 3) was the
mobile robot platform which was utilised in this work. Mona
is an open-source and open-hardware platform developed at
the University of Manchester for Education and Research
purposes. It uses five IR proximity sensors at the front of
the robot, which can detect obstacles within distance of
2±0.5 cm and other robots within distance of 5 cm. The
robot developed is based on Arduino architecture (Arduino
ATMega 328 Mini/Pro) hence Arduino IDE and all available
libraries are being used for programming of Mona.
The Mona robot used two micro DC motors with gear-
head and encoders with resolution of 250 pulses per
revolution which provided sufficient motion accuracy for
a miniature-sized robot. Mona was initially developed for
research on Perpetual Swarm Robot proposal [27]. Using
Mona, it is feasible to implement very long-term experiments
using the combination of pheromone which can play role of
food, source of energy, or a complex communication method
in an evolutionary scenario.
Since the robot is a modular robotic platform, other mod-
ules e.g. bio-inspired vision [28] and ROS integration [29]
can be easily utilised.
2) Simulated Robot: The proposed scenarios were sim-
ulated using Python-based open-source library, named
PyCX [25]. The PyCX application has a GUI (graphical
user interface) which makes it possible for the user to run
the simulation while visually investigating the simulation
progress. PyCX consist of three major parts: i) init that
initialises the program, ii) draw that updates the GUI
Fig. 3. Mona, an open-source and open-hardware swarm robotic platform.
after each step, and iii) step which changes status of the
simulation after each run.
The simulated robots in this work were carefully modelled
based on physical properties of the Mona robot with diameter
of 7cm. Apart from Mona’s kinodynamics, the simulator
also modelled the IR sensors, cue perception and pheromone
detection at different ranges. Unfortunately, due to the time
constraints, we were not able to implement the pheromone
detection capabilities on the real robot. To avoid the potential
effects of delays caused by rendering the graphical output
on the experimental results, the graphical interface was
deactivated during the experiments described.
D. Arena Configuration
A square arena with size of 210 ×210 cm2was provided
for the experiments. The environmental cue had its centre in
the middle of the arena and its radius was 60 cm – in the
case of the real arena, the cue was realised by means of a
video projector.
Fig. 4 illustrates the evolution of randomly selected experi-
ments from both aggregation scenarios – these pictures were
taken every 60 seconds during 240 sec long experimental
runs. In the BEECLUST experiments, the cue is indicated
in blue colour. In the ΦClust experiments, the cue is not
displayed and the red colour is used to indicate of the
pheromone intensity.
E. Statistical Analysis
To analyse the observed results from experiments and
study on the effectiveness of the parameters, the analysis of
variance (ANOVA) was utilised. The F-test method was used
to disprove the null hypotheses, which states that the means
for different conditions are the same. In result of ANOVA
for a factor, a higher F-value (>1) and a lower p-value
(<0.05) show the factor significantly affects the results.
In case of aggregation without pheromone, the effects
of population on the performance of the aggregation was
investigated. However, in the scenario of aggregation with
pheromone, effects of four factors (evaporation eφ, diffusion
κ, population size ns, and radius of pheromone sensing rφ)
were investigated.
V. RE SULTS AN D DISCUSSION
A. Aggregation without Pheromone
1) Results with Simulated Robots: The aggregation sce-
nario without presence of pheromone were implemented
using simulated robots with different population sizes of
ns∈ {10,15,20,25,30}robots. The size of aggregates in
different populations during 450 sec of each experiment is
shown in Fig. 5(a). In general, an increase in population
size, increases the performance of the aggregation due to
increase in number of inter-robot collisions. Time, t, also
had positive impact on the performance of the aggregation
with increasing number of aggregated robots. The similar
results were also reported in previous works on the cue-based
aggregation in [4], [19], [23].
The effects of population size on the performance of the
aggregation scenario was statistically analysed. The results
from ANOVA showed that population size significantly
impacts the performance of the aggregation during 450 sec
of the all experiments with p <0.05 and 84 F140.
2) Results with Real Robots: We also implemented the
BEECLUST aggregation scenario with real robots however
with limited number of robots (ns∈ {10,15,20}robots).
The size of aggregates in different population sizes is shown
in Fig. 5(b). Similar to the simulation experiments, firstly,
an increase in population size improves performance of the
aggregation, and secondly, the performance was improved
when the experiments were carried out for a longer period
of time. However, the results from real- and simulated-robots
had slight differences which were expected due to differences
in physical properties.
We statistically analysed the results of the real-robot
experiments with ANOVA test with the population size as
the main factor. The results of ANOVA showed that the
population size had significant impact on the performance
of the aggregation with p <0.05 and 94.51 F120.86
at t= 50,150,250,350,450 sec.
3) Validation of Simulation Platform: To validate the fea-
sibility of using the simulated robot and simulation platform
in the rest of the experiments with higher population sizes,
results of the aggregation with three different population
sizes of ns∈ {10,15,20}were statistically analysed using
two-way ANOVA test. Therefore, Population size and type
of platforms (real-world and simulated) were two factors
which were studied in the statistical analysis to find the most
effective factor. The results of ANOVA showed that type of
platforms did not have significant impact (p= 0.40) on the
performance of the aggregation. Hence, it was statistically
demonstrated that, implementing the aggregation scenario
using the real robots and the simulation software generated
a similar results. On the other hand, population size had
significant impact (p= 0.00 and F= 73.40) on the
aggregation size during experiments.
Fig. 4. Randomly selected samples of aggregation with 20 robots in two configurations: (up) BEECLUST (with gradient light shown with blue colour)
and (down) ΦClust (with pheromone indicated in red and invisible gradient light). The green spots indicate robots and doted circles indicate the aggregation
zone.
Fig. 5. Results of aggregation without pheromone configuration using (a) simulated robots and (b) real robots. Aggregation size with different population
sizes, ns∈ {10,15,20,25,30}robots, in different time steps of t= 50,150,250,350,450 sec.
B. Aggregation with ΦClust
In this set of experiments, effects of pheromone properties
on the performance of the aggregation have been inves-
tigated. Fig. 6 shows the size of aggregates in different
population sizes (ns∈ {10,15,20,25,30}robots) during
T= 450 sec experiments. The diagram depicted using
the data observed from all experimental configurations with
different pheromone properties. With comparison to the
Fig. 5(a), results demonstrated a clear improvement on
the performance of the aggregation with higher number of
aggregated robots at the optimal zone.
The first 50 sec of the experiments showed that the
external guidance of pheromone had slight improvement
on the performance, however, the performance dramatically
improved during 50 t100 sec due to larger amount of
pheromone released by the aggregated robots attracting the
other robots to the cue zone.
Fig. 6. Results of aggregation with ΦClust configuration. Aggregation
size as a function of population size, ns∈ {10,15,20,25,30}robots, in
different time steps of t= 200,300,400,500 sec.
Fig. 7. Effects of evaporation rate, eφ∈ {10%,60%}per sec, on
aggregation size during 450 sec experiments. Boxes with light colour
indicate eφ= 10% per sec and dark colour indicate eφ= 60% per sec.
1) Effects of Evaporation: Fig. 7 shows the size of
aggregates during T=450 sec of experiments with two
evaporation rates of eφ∈ {10%,60%}per sec. The
experiments were conducted with different population sizes
of ns∈ {10,15,20,25,30}and size of aggregate was
recorded every 50 sec. The results showed that an increase
in the evaporation rate reduces the performance of the
aggregation. It was because of reducing pheromone intensity
faster with the high evaporation rate. The similar behaviour
of evaporation rate on the performance of the system was
also reported in [8].
2) Effects of Diffusion: In this set of experiments, two
diffusion speeds of κ∈ {3.5,17.5}cm/sec were studied.
Experiments were conducted with different populations sizes,
ns∈ {10,15,20,25,30}robots. Fig. 8 shows the size of
aggregates during 450 sec of ΦClust aggregation.
The results showed that an increase in diffusion speed
reduces the performance of the aggregation by reducing
number of aggregated robots at the cue zone. This reduction
was higher with large population than the lower population
sizes, since the pheromone trails were expanded to the entire
arena quickly in case of large populations, hence do not lead
free robots to the centre of optimal zone.
3) Effects of Radius of Pheromone Sensing: Fig. 9 shows
the size of aggregates during 450 sec of experiments with
two sensing radii of rφ∈ {3.5,17.5}cm. The results showed
that an increase in the sensing radius of robots increases the
performance of the aggregation due to additional information
and larger amount of data available for the robots to choose
the optimal path towards central location of the cue. The
similar behaviour observed for the all population sizes.
4) Statistical Analysis: We analysed all the data recorded
from pheromone properties in different population sizes
using the multi-factor ANOVA test. Table II shows the
results of analysis of variance on the recorded data from
ΦClust aggregation scenario. Results showed that all the
factors had significant impact on the aggregation size.
However, the most significant factor was the population
Fig. 8. Effects of diffusion, κ∈ {3.5,17.5}cm/sec, on aggregation
size during 450 sec experiments. Boxes with light colour indicate κ=
3.5cm/sec and dark colour indicate κ= 17.5cm/sec.
Fig. 9. Effects of radius of pheromone sensing, rφ∈ {3.5,17.5}cm,
on aggregation performance during 450 sec experiments. Boxes with light
colour indicate rφ= 3.5cm and dark colour indicate rφ= 17.5cm.
size which, demonstrates both aggregation scenarios are
population dependent mechanisms.
VI. CONCLUSION AND FUTURE WO RK
In this paper, an investigation into effects of a bio-
inspired guidance, pheromone, on performance of a cue-
based aggregation behaviour has been carried out. The
aggregation scenario was implemented in two different
phases of with and without presence of pheromone. First
phase of the experiments was implemented with real and
simulated robots. The obtained results validated the feasibil-
ity of the simulation platform on realisation of the proposed
system. Therefore, the second phase of the experiments
was implemented using simulation software only. It allows
faster evaluation of the scenarios to find optimal values
for the pheromone parameters. The results demonstrated
the performance improvement for the aggregation with
pheromone guidance in all the configurations.
For the future work, feasibility of a real-world application
will be studied. In an industrial disaster scenario, where the
operational environment is contaminated with some corrosive
TABLE II
RES ULTS O F ANALY SI S OF VARIANCE, ANOVA
Factors Time
t=50 sec t=250 sec t=450 sec
Population p-value 0.00 0.00 0.00
F-value 751.21 405.26 96.99
Diffusion p-value 0.00 0.00 0.00
F-value 2.52 3.98 21.77
Evaporation p-value 0.00 0.00 0.00
F-value 1.96 4.80 7.95
Sensing Radius p-value 0.00 0.00 0.00
F-value 1.78 2.99 1.36
or radioactive substance. In many of these scenarios, robots
cannot use high-fidelity, range- or visual-based sensing
because the performance of these sensors is negatively
affected in a severe way. One of the possible solutions is
to use a large number of small, expendable platforms with
limited sensing and processing capabilities and apply nature-
inspired, swarm-based methods to identify the sources or
the irradiation. While this would be achievable easily if
the robots could communicate their positions and sensory
information with each other, radio-based communication
in irradiated environments is affected, severely limiting its
range, reliability, bandwidth and power efficiency. Thus,
the inter-robot communication has to be based on another
modality, such as audio or olfaction, and be kept as
simple as possible. Thus, these alternative modalities can be
represented as artificial pheromones.
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