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Extended Artificial Pheromone System for Swarm Robotic Applications

Authors:
Extended Artificial Pheromone System for Swarm Robotic Applications
Seongin Na1, Mohsen Raoufi2, Ali Emre Turgut3, Tom´
aˇ
s Krajn´
ık4, and Farshad Arvin1
1School of Electrical and Electronic Engineering, The University of Manchester, M13 9PL, Manchester, UK
seongin.na@student.manchester.ac.uk , farshad.arvin@manchester.ac.uk
2Department of Aerospace Engineering, Sharif University of Technology, Tehran, Iran
3Mechanical Engineering Department, Middle East Technical University, 06800 Ankara, Turkey
4Artificial Intelligence Centre, Faculty of Electrical Engineering, Czech Technical University, Prague, Czechia
Abstract
This paper proposes an artificial pheromone communication
system inspired by social insects. The proposed model is an
extension of the previously developed pheromone commu-
nication system, COS-Φ. The new model increases COS-
Φflexibility by adding two new features, namely, diffusion
and advection. The proposed system consists of an LCD
flat screen that is placed horizontally, overhead digital cam-
era to track mobile robots, which move on the screen, and
a computer, which simulates the pheromone behaviour and
visualises its spatial distribution on the LCD. To investigate
the feasibility of the proposed pheromone system, real micro-
robots, Colias, were deployed which mimicked insects’ role
in tracking the pheromone sources. The results showed that,
unlike the COS-Φ, the proposed system can simulate the im-
pact of environmental characteristics, such as temperature, at-
mospheric pressure or wind, on the spatio-temporal distribu-
tion of the pheromone. Thus, the system allows studying be-
haviours of pheromone-based robotic swarms in various real-
world conditions.
Introduction
Social insects are known for conducting complex tasks with
coordination in highly effective ways. They carry out com-
plicated tasks such as food foraging, aggregating, mat-
ing, etc. using limited perception and memory capabil-
ities (Schmickl et al., 2009; Jackson and Morgan, 1993;
Agosta, 1992; Schmickl et al., 2016; Michener and Press,
1974). Those complex tasks require effective communi-
cation mechanisms within a group of insects. As a key
to achieve the effective communication, several social in-
sects use pheromones which is a medium for the stigmergic
behaviours. Stigmergy is an indirect coordination mecha-
nism using a shared communication medium (Theraulaz and
Bonabeau, 1999). A medium created by an agent in the en-
vironment actuates the other agents to perform certain ac-
tions without any direct communication between them (Hey-
lighen, 2016; Marsh and Onof, 2008). As an example of
how stigmergy is used, an ant releases trail pheromone when
it detects food and other ants detect the trail and follow
it (Jackson and Ratnieks, 2006; Wyatt, 2003; Sumpter and
Beekman, 2003).
Figure 1: Artificial pheromone system including a horizon-
tally placed LCD screen, overhead camera for tracking sys-
tem and a computer.
This coordination mechanism has remarkable features
compared with other traditional methods such as direct com-
munication. First of all, it achieves optimisation through
positive and negative feedback (Jackson and Ratnieks, 2006;
Sumpter and Beekman, 2003; Theraulaz and Bonabeau,
1999; Heylighen, 2016). By reinforcing or suppressing the
medium at a position depending on how close it is to the
goal, the agents can carry out the tasks in an optimal man-
ner, e.g. the shortest path for food foraging is created af-
ter multiple iterations with reinforcement and suppression
on the pheromone trail. Secondly, it does not require com-
plex functionality for each agent (Heylighen, 2016). Com-
pared to the conventional methods, stigmergy demands sig-
nificantly lower capability for each agent. For instance,
an agent does not need to save information into its mem-
ory because it is saved in and read from the media. As an
another example, an agent does not have planning or an-
ticipation ability since it performs tasks only based on the
present media. The advantages of stigmergy have inspired
researchers who study swarm robotics especially adopting
pheromone (Fossum et al., 2014; Purnamadjaja and Russell,
608
2007; Font Llenas et al., 2018). Researchers have devel-
oped and implemented artificial pheromone systems with
different means from chemical substances and RFID chips
to light-based means and virtualization system (Arvin et al.,
2018b; Fujisawa et al., 2014; Herianto and Kurabayashi,
2009; Arvin et al., 2015; Valentini et al., 2018; Beckers et al.,
2000). The methods using chemical means duplicate evapo-
ration, diffusion, locality and reactivity which are the char-
acteristics of pheromone in the real world (Fujisawa et al.,
2014). Besides, different kinds of chemical substances can
be used as different kinds of pheromone which have distinct
functionality (Purnamadjaja and Russell, 2007). Although
their similarities to the pheromone in the real world con-
tributes to mimic the important features of the pheromone,
it is difficult to control the properties of the chemical sub-
stances such as evaporation and diffusion rates. Hence, it
is challenging to be used as an experimental tool (Fujisawa
et al., 2014; Sugawara et al., 2004). Additionally, sensing
technology for chemical substances has to be improved to
detect reasonably small amount of chemicals (Purnamadjaja
and Russell, 2010).
The methods using RFID chips have advantages in swarm
robotics because they use low-cost data carriers and it is
free from batteries. However, the fixed size of data carri-
ers does not allow this method to be used with different res-
olutions (Herianto and Kurabayashi, 2009). Virtualization
system is a relatively new method implementing pheromone
communication which reads data from robots, sends the data
to virtual map for mapping and sharing to the robots in the
swarm. In spite of its bidirectional communication and ca-
pacity for large-scale swarm robotics application, the virtu-
alisation of sensors and actuators are restricted by the reso-
lution of the grid (Valentini et al., 2018). Light-based meth-
ods have a number of advantages which cover certain limi-
tations present in the other methods (Arvin et al., 2015; Gar-
nier et al., 2007). The characteristics of pheromone such as
evaporation and diffusion are easily controllable. Further-
more, light-based methods have significantly higher resolu-
tion than the methods using RFID chips or virtualization en-
vironment. Moreover, different types of pheromone can be
implemented since various colors of light can be used (Arvin
et al., 2018a; Jackson and Ratnieks, 2006).
One of the light-based artificial pheromone communica-
tion systems, COSΦ, (Arvin et al., 2015) has four advan-
tages as follows: (1) Precise pheromone trail can be cre-
ated by using high-resolution horizontal LCD screen as an
arena to project light-based artificial pheromones. (2) Char-
acteristics of pheromone such as evaporation and thickness
are easily and precisely modified. (3) Pheromone can be
overlapped or suppressed so that positive feedback and neg-
ative feedback can be implemented. (4) Numerous types of
pheromone can be generated using RGB colors. Although
the system has advantageous features listed above, there are
points which can be developed for more diverse functions
and applications.
The goal of this work is extending COSΦsystem to
cover its limitation. Although evaporation and injection
of pheromones was clearly replicated in the system, diffu-
sion was not implemented whereas it is a necessary fea-
ture of temporal pheromone development (Herianto and
Kurabayashi, 2009; Sugawara et al., 2004; Ji et al., 2013).
Furthermore, the mathematical model of the pheromone up-
dating is expanded. Therefore, it includes advection of the
pheromone by the wind and the advection effect is applied
in the system. This expanded system is expected to offer
more options to users for bio-inspired swarm robotic stud-
ies (Figure 1). Adding the two phenomena has the meaning
described below.
Diffusion is the movement of molecules from the area of
higher concentration to those of lower concentration. So-
cial insects follow pheromone trail, they detect diffused
pheromone rather than contacting to the trail and moving
directly along it (Wyatt, 2003). Despite its importance,
it was not modelled and implemented in the previous re-
search. Therefore, it is meaningful to apply diffusion ef-
fect.
Advection is the transfer of substances or any quantity by
the flow of a fluid, like wind. In fact, pheromone, as a
substance, is transported by wind which is the flow of the
air. Through applying the advection effect with different
velocity and direction, we have a more reliable model and
figure out how wind influences to the pheromone commu-
nication.
This paper is arranged as follows: Section II presents ar-
tificial pheromone system, COSΦ, Section III presents the
proposed extended properties of the COSΦ, Section IV pro-
vides experimental configurations, and Section V presents
the results from experiments and discusses the outcomes.
Artificial Pheromone System, COSΦ
In the previous project (Arvin et al., 2015), COSΦ(Com-
munication System via Pheromone) was introduced. It has
a software system and a robotic platform. The software sys-
tem consists of two major parts. The first part is a visual
localization system, SwarmCon (Krajn´
ık et al., 2014). It
reads the position of robots using a camera attached above
the arena and sends their information to the pheromone re-
leasing system which displays light on the LCD screen. The
second part is a pheromone releasing system. After re-
ceiving the position data from the localisation system, the
pheromone releasing system computes where and how much
the pheromone will be injected accordingly. The system also
repetitively updates the obtained pheromone data reflecting
the development of released pheromone over time in reality.
The system subsequently displays a gray-scale image based
on the pheromone data on the LCD screen.
609
COSΦhas three remarkable features which make this
system more reliable and user-friendly to be used as an
experimental platform for researchers in the field of biol-
ogy, swarm robotics or other related disciplines: i) It pro-
vides highly precise location data of robots and pheromone
through SwarmCon system. Moreover, its resolution is equal
to that of the LCD screen; hence, the smallest controllable
size of the pheromone is equivalent to a pixel of the screen.
ii) It has high flexibility allowing the users to change exper-
imental conditions, settings and even initial characteristics
of the pheromone in order to fit their needs. iii) It is a low-
cost platform. COSΦrequires only a low-cost USB camera,
an LCD screen as an arena, and the low-cost micro-robots,
Colias (Arvin et al., 2014).
Pheromone Model
The gray-scale image displayed on the LCD screen com-
puted by the system based on Equation 1.
I(x, y) =
n
X
i=1
ciΦi(x, y)(1)
The brightness of a pixel at a position (x,y), I(x, y)is de-
termined by the multiplication of Φi(x, y)which represents
ith pheromone intensity and ciwhich denotes how strong
the ith pheromone is displayed on the screen. Since the
system can use multiple different types of pheromone, the
brightness of a pixel is the sum of the effect of ndifferent
pheromones released at a position.
In the previous project (Arvin et al., 2015), the change in
the intensity of pheromone at a position (x,y) at a time, ˙
Φi,
is defined by
˙
Φi=ln 2
eiΦ
Φi(x, y) + κiΦi(x, y) + ιi(x, y )(2)
where eiΦ, κiare the evaporation constant and diffusion
constant respectively and ιi(x, y)denotes the amount of in-
jected pheromone at a time. In the previous study (Arvin
et al., 2015), only evaporation and injection terms were ap-
plied into the development in the pheromone concentration.
The two phenomena influence the pheromone in the ways
explained in the below two subsections. Diffusion model is
described in the next section.
Evaporation
Evaporation of the deposited pheromone in the real world
is a fundamental feature of pheromone as a chemical sub-
stance. The intensity of pheromone decays over time due to
evaporation. This model exhibits that the pheromone expo-
nentially decays over time without spreading to the adjacent
positions. Figure 2 shows how the pheromone evaporates
with eiΦ= 20 at t={0,1,2,3}s illustrated by the black,
red, green and blue line respectively. The pheromone is ini-
tially released from x[200,300] with the intensity of 255.
Figure 2: Evaporation of pheromone over time t= 0s
(black), t= 1s (red), t= 2s (green) and t= 3s (blue).
Its horizontal axis denotes the x position of the pheromone
in the 2-D arena with the size of 500×500 pixels, and the
vertical axis is the intensity of the pheromone between 0 and
255.
Injection
The injection ιi(x,y) represents the amount of the newly in-
jected ith pheromone at the position (x,y). In the system,
ιi(x,y) is defined by
ιi(x, y) = (sΦ,if p(xxr)2+ (yyr)2lΦ/2
0,otherwise
(3)
where, (xr, yr) is the position of the robot, lΦis the diam-
eter of the pheromone injected at the time and sΦis the
pheromone release rate.
Extended Pheromone System
Based on the previous model of the pheromone temporal
development and the mathematical model of moving sub-
stances through the fluid proposed in (Stam, 2005), the evo-
lution of the pheromone intensity field is developed as fol-
lows:
˙
Φi(x, y) = u· ∇Φi(x, y)ln 2
eiΦ
Φi(x, y)+
κi2Φi(x, y) + ιi(x, y),
(4)
where, uis a two-dimensional vector field which represents
the wind velocity field. This equation stems from Navier-
Stokes equation which illustrates the motion of fluids. It
is assumed that the pheromone is a non-reactive substance.
Hence, the pheromone does not vary by chemical reaction
but the factors described in Equation 4.
Diffusion
As previously mentioned, diffusion is one of the factors of
the pheromone behaviour. In the Equation 4, diffusion is
described as κi2Φi(x, y). For the sake of computation
610
Figure 3: Diffusion of pheromone over time t= 0 s (black),
t= 1 s (red), t= 2 s (green) and t= 3 s (blue).
simplicity, diffusion is implemented with the approximate
model using the Gaussian filter. It contains analogous fea-
tures to what the actual diffusion model has. i) The to-
tal amount of the pheromone is conserved while it diffuses
ii) The pheromone at a position is distributed to the neigh-
bour positions and the pheromone from surrounding posi-
tions diffuses to the position. Moreover, the intensity of
the pheromone at a position increases if it is surrounded by
greater intensity of the pheromone. Conversely, the inten-
sity decreases if the intensity of the pheromone of its nearby
positions is lower than it.
Φk+1
i(x, y) = ωΦk
i(x, y) =
a
X
s=a
b
X
t=b
ω(s, t)Φk
i(xs, y t),(5)
where ωis a kernel matrix with the size of (2a+1)×(2b+1)
which is convolved with the matrix of the ith pheromone
strength Φk
iat kth iteration, and ωis defined by the equation
below:
ω(x, y) = 1
2πσ2ex2+y2
2σ2, w R2a+1×2b+1,(6)
where the element at ((a+ 1),(b+ 1)) is assigned as (0,0)
of ωand σis the standard deviation of elements of ω. The
elements of the kernel are determined based on the Gaussian
distribution. The further an element from the center of the
matrix is, the smaller value the element has. Figure 3 shows
the diffusion of pheromone at t={0,1,2,3}s illustrated by
the black, red, green and blue line respectively. The axes are
identical to Figure 2. At t= 0 s, the pheromone released on
x= 200300 has the intensity of 255. The arena size is also
500 ×500 pixels and the kernel size is 95 ×95 pixels and
σ= 20. Every time the pheromone is updated with the dif-
fusion, the area where the pheromone is deposited expands
while the maximum intensity of the pheromone decreases.
Figure 4: Advection of pheromone over time t= 0 s (black),
t= 1 s (red), t= 2 s (green) and t= 3 s (blue).
Advection
The change in pheromone intensity at the position (x,y) by
advection is simply described as u· ∇Φi(x, y)in Equation
4. The dot multiplication of the wind velocity field uand
the gradient of the pheromone can be expressed as:
u· ∇Φi(x, y) = ux·Φi(x, y)
∂x +uy·Φi(x, y)
∂y ,(7)
where uxand uyare the x- and y-component of u, respec-
tively. In this project, same magnitude of uxand uyare
applied on the entire field. In other words, the wind with
a given magnitude and direction blows equally at all the
positions. Figure 4 shows the advection of the pheromone
along the x axis where ux= 50, namely, the wind speed
is 50 pixel/s. The pheromone is initially injected from
x[200,300] with the intensity of 255. The black, red,
green and blue lines represent the intensity of the pheromone
on the xposition at t={0,1,2,3}s. It is illustrated that the
wind causes the pheromone to be transferred in the almost
parallel manner without a considerable change in the shape.
Experimental Setup
There are three different experimental configurations to
study: i) effects of diffusion, ii) effects of advection, and
iii) combination of both diffusion and advection on the be-
haviour of the robots. Also, we run a set of experiments
excluding pheromone effects as the control.
A circular cue (with diameter of 25 cm) with a maximum
intensity of pheromone at the centre, source of pheromone
injection, is projected on the right hand side of the area
(screen) and the robots are randomly placed on the left hand
side of the arena. Each experiment takes 5 min and we anal-
yse the collective behaviour of the proposed system with two
metrics which are: i) number of robots at the pheromone
source and ii) average distance of the robots from the centre
of the pheromone source.
It must be mentioned that the robots do not deposit
pheromone during experiments; hence, they only change
611
their direction towards the highest intensity pheromone trail.
The pheromone cue is only injected once at the initial stage
t= 0 s of each experiment.
Arena Configuration
Arena that is used in this work is analogous to the experi-
mental setup presented in (Arvin et al., 2015). It includes a
horizontally placed 42” flat LCD screen, a USB camera, and
a computer to track the robots and manage the pheromone
system. Figure 1 shows the experimental setup that was used
in this work.
Utilizing this system, we are able to determine whether or
not a robot is reached the cue. In this regard, at the beginning
of each experiment, we store the brightness of each pixel in
a matrix Ia. Then, the localisation system detects the tags of
four corners and calculates the transformation between the
arena and camera coordinate systems. Similarly, it allows
us to detect the robots and measure their positions on the
field. Then, the visual system takes the brightness of the
current image as Icand compares its with Ia.By finding the
largest circular continuous segment in Icand calculating its
position (xc, yc)and average brightness bc, the cue zone is
determined.
Robotic Platform
Colias micro-robot (Arvin et al., 2014) was utilised in this
study to test the feasibility of the proposed extensions (Fig-
ure 5-a). Colias is a low-cost open-source mobile robot uses
an AVR micro-controller as its main processor. It has three
short-range infrared proximity sensors at the front to detect
obstacles and other robots. Colias has two light intensity
sensors (Figure 5-b) at the bottom of the robot, sland sr
on the left and right hand side, respectively. Motors’ rota-
tional velocities, Nland Nr, are directly controlled using
measurements from these two sensors:
Nl=slsr
α+β ,
Nr=srsl
α+β ,
(8)
where, αis the velocity sensitivity coefficient and βis a bi-
asing speed. In this work, βrelies on the average pheromone
intensity, because the higher intensity results in the lower ve-
locity:
β= 100 sr+sl
2.(9)
This relation between βand the sensors measurements is
tuned empirically. The main idea is to reduce the speed of
motion near source of the pheromone to keep the robots at
the high intensity pheromone cue. Therefore, there are two
direct impacts of the pheromone on the robots behaviour
which are: i) controlling angular velocity of the robot to di-
rect robot to the centre of the pheromone and ii) reducing
speed of the robot with increasing pheromone intensity.
Figure 5: (a) Colias micro-robot and (b) bottom of the robot
including light intensity sensors.
Experiments
Three pheromone configurations were implemented. The
first configuration was diffusion speed with two settings:
1. Diffusion-A: pheromones diffuse by a rate which results
in diffusion of 25% of total pheromone till t=300 s (eiΦ=
1000, a, b = 7 and σ= 0.3)
2. Diffusion-B: pheromones diffuse by a rate which results
in diffusion of 50% of total pheromone till t=300 s (eΦ=
1000, a, b = 7 and σ= 6)
The second set of experiments were conducted with various
advection speeds:
1. Advection-A: pheromone spot moves with the wind speed
of 2.27 pixel/s to the left hand side of the arena during
t= 300 s (eiΦ= 1000, ux= 2.27 and uy= 0)
2. Advection-B: pheromone spot moves with the wind speed
of 4.53 pixel/s to the left hand side of the arena during
t= 300 s (eiΦ= 1000, ux= 4.53 and uy= 0)
The third set of experiments were conducted with combin-
ing Diffusion-B and Advection-B. Apart from the 5 distinct
configurations which are already mentioned, we applied a
simple experiment in which the effect of neither diffusion
nor advection is considered. All of these 6 experiments were
conducted with two population sizes of N∈ {4,6}robots.
Moreover, for each configuration, 5 independent runs are ap-
plied.
In order to assess the effect of these two phenomena on
the behaviour of the system, two different variables are de-
fined. The number of robots on pheromone, a dimensionless
variable, is the ratio of number of robots which are located
within the cue to all robots in the arena. The second vari-
able is “coherence distance”, dcoh , indicating the average
distance of all robots to the center of cue, which is defined
by the following equation:
dcoh =1
N
N
X
i=1
k(xi, yi),(xc, yc)k(10)
in which, (xi, yi)and (xc, yc)are the location of i-th robot
and cue center, respectively, and k.kis the Euclidean dis-
tance operator between two points in a 2-D space.
612
(a) (b)
(c) (d)
(e) (f)
Figure 6: The arena, robots and pheromone from the camera
perspective, illustrating the experiments of Advection-B, as
well as Diffusion-B + Advection-B . Each row is related to
a specific time t={0,60,180}s, respectively.
Results & Discussion
The results of the above-mentioned experiments are pre-
sented in this section. Figure 6 shows several images from
randomly selected experiments at various times showing the
effect of diffusion and advection on the system. The images
in the left column show an experiment with the configura-
tion of Advection-B with 6 robots, and the images of the
right column have the configuration of mixed Diffusion-B
and Advection-B. In the left column, the effect of wind on
the movement of the cue is shown vividly. The cue starts to
move from the right side toward the left side of the arena due
to advection. In this case, the number of robots which were
able to find and stay at the cue is raised. The effect of diffu-
sion on the pheromone is clearly shown in the right column;
The sharp edge of the cue fades by time, resulting in lower
number of robots remained in the cue. To such an extent that
some of them lost the cue and wander in the arena. On the
other hand, it makes the robots to stay closer to the center of
cue, and as a result, the coherency of the robots increases.
Meanwhile, the advection affects the cue location.
To study the effect of diffusion on the behaviour of robots,
Figure 7 demonstrates the pheromone intensity and coher-
ence distance for three different configurations set of exper-
iments: i) No effects, ii) Diffusion-A, and iii) Diffusion-B.
As shown in Figure 7 (a), the number of robots reached the
(a) (b)
Figure 7: Effect of diffusion on the behaviour of robots. (a)
The number of robots on pheromone and (b) Coherence dis-
tance
(a) (b)
Figure 8: Effect of advection on the behaviour of robots.
(a) The number of robots on pheromone and (b) Coherence
distance
spot in Diffusion-A and B are close to that of with no effect
configuration. However, when time went and the pheromone
diffused to the neighbor areas, the cue shrunk and the robots
left the cue. As what we expected, this separation happened
for Diffusion-B much earlier than Diffusion-A. The diffu-
sion has another impact on the behaviour of robots, which
results in more coherence. Prior to separation, the robots in
the cue stayed closer to the center of cue. This can be seen
not only from Figure 6 (d), but also from the Figure 7 (b).
The effect of advection on the behaviour of robots can be
seen in Figure 8, in which 6 robots are utilized. Compared
to the ‘no effect’ configuration, the number of robots which
were able to find the cue increased when advection is con-
sidered. However, the influence of wind on the coherency is
negligible.
Finally, the result of combination of both concepts are il-
lustrated in Figure 9 besides the result of ’no effect’ case.
We can see that the number of robots on pheromone is gen-
erally more than the simple case, but, same as Figure 7, it
starts to drop after a time called separation time.
To investigate the effects of different factors on collec-
tive behaviour of the swarm, all the results were statisti-
cally analysed using 2-way Analysis of Variance (ANOVA).
Table 1 and Table 2 show the results of ANOVA test for
number of robots on pheromone and coherence distance.
613
(a) (b)
Figure 9: Effect of both diffusion and advection on the be-
haviour of robots. (a) The number of robots on pheromone
and (b) Coherence distance
Table 1: Results of ANOVA test for number of robots on
pheromone
Factors p-value F-value
Exp. Configuration 0.000 132.708
Time 0.000 2.512
Based on the results, both factors, time and experiment con-
figurations, significantly affected the swarm. However, the
configuration was the most significant factor in number of
robots on pheromone (F=132.708) and coherence distance
(F=80.156).
Table 2: Results of ANOVA test for coherence distance
Factors p-value F-value
Exp. Configuration 0.000 80.156
Time 0.000 4.639
Conclusion
This paper added two new properties – diffusion and ad-
vection– to the previously developed artificial pheromone
system, COS-Φ. Three set of experimental configurations
were conducted to investigate the performance of the pro-
posed properties. Coherence distance and number of robots
on the pheromone spot were tracked during experiments.
The results were statistically analysed and the most effec-
tive factor was detected. The future work is to include sev-
eral robots with capability of injecting pheromones and to
study inter- robot interactions using the updated artificial
pheromone communication.
Acknowledgement
This work was supported by EPSRC RNE (EP/P01366X/1),
EPSRC RAIN (EP/R026084/1), and Czech Ministry of Sci-
ence and Education grant ‘Research Centre for Informatics’
number CZ.02.1.01/0.0/0.0/16 019/0000765.
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