Advection and Diffusion Effects Towards a Bio-inspired Artiﬁcial
Seongin Na, Mohsen Raouﬁ, Ali Emre Turgut, Tom´
ık, Barry Lennox, Farshad Arvin
Social insects are known for conducting complex tasks with
coordination in highly effective ways. As a medium for com-
munication, most of social insects use pheromone. Due to
its effectiveness, researchers have adopted pheromone com-
munication for swarm robotic applications. COSΦ(Commu-
nication System via Pheromone)  is an example of bio-
inspired pheromone system which has been developed for
use in swarm robotic applications. It uses an LCD screen to
display the artiﬁcial pheromone which is a gray-scale image.
The experimental setup is shown in Fig. 1.
COSΦhas remarkable features which make this system
more reliable and user-friendly for researchers in the ﬁeld of
biology, swarm robotics or other related disciplines. It pro-
vides highly precise location data of robots and pheromone.
Moreover, it has high ﬂexibility allowing the users to change
experimental conditions and settings in order to ﬁt their
Despite the advantages of COSΦ, a number of features
are required to be improved so that the system becomes
more realistic . Advection and diffusion are the two
effects that are added to COSΦwhich affect spatio-temporal
development of pheromone in the real world.
In this work, a new model of spatio-temporal development
of pheromone is proposed. The new model of pheromone
development including advection and diffusion is expressed
Φ(x, y) = −u· ∇Φ(x, y)−ln 2
κ∇2Φ(x, y) + ι(x, y),
Φ(x, y)is a temporal development of pheromone at
(x,y), uis a two-dimensional vector ﬁeld which represents
the wind velocity ﬁeld, eis the evaporation constant, , κ
is the diffusion constant and ι(x,y)is a newly injected
pheromone at (x,y).
To test the extended system, Colias  which is an open-
source swarm robotic platform was employed. The robot
is designed to reduce its speed when it detects artiﬁcial
This work was supported by EPSRC RNE (EP/P01366X/1),
EPSRC RAIN (EP/R026084/1), and Czech Ministry of Science
and Education grant ‘Research Centre for Informatics’ number
S. Na, M. Raouﬁ, B. Lennox, F. Arvin are with the School of Electrical
and Electronic Engineering, The University of Manchester, M13 9PL,
Manchester, UK e-mail: firstname.lastname@example.org.
A.E. Turgut is with the Mechanical Engineering Department, Middle East
Technical University, 06800 Ankara, Turkey
ık is with the Artiﬁcial Intelligence Centre, Faculty of Electrical
Engineering, Czech Technical University, Prague, Czechia
Fig. 1. Experimental platform of COSΦincluding a horizontally placed
LCD screen, overhead camera for tracking system and a computer.
Fig. 2. Effect of advection and diffusion on the behaviour of robots. (a)
The number of robots on pheromone and (b) Coherence distance
pheromone and to avoid obstacles. Experiments are con-
ducted by measuring the number of robots and coherence
distance (average distance) on a circular artiﬁcial pheromone
cue to measure the impact of advection and diffusion. Fig. 2
reveals that the greater number of robots are likely to stay on
a pheromone cue and the robots on the pheromone cue stay
closer to each other with advection and diffusion effects. We
can conclude that the implementation of advection and diffu-
sion improved the system since the effects make signiﬁcant
differences on the collective behaviour of a robot swarm.
 F. Arvin, T. Krajn´
ık, A. E. Turgut, and S. Yue, “COSΦ:
artiﬁcial pheromone system for robotic swarms research,” in
IEEE/RSJ International Conference on Intelligent Robots and
Systems (IROS), IEEE, 2015, pp. 407–412.
 Seongin Na, M. Raouﬁ, A. E. Turgut, T. Krajn´
ık, and F. Arvin,
“Extended Artiﬁcial Pheromone System for Swarm Robotic
Applications,” in Artiﬁcial Life, 2019.
 F. Arvin, J. Murray, C. Zhang, and S. Yue, “Colias: An
autonomous micro robot for swarm robotic applications,”
International Journal of Advanced Robotic Systems, vol. 11,
no. 7, p. 113, 2014.