Swarm optimization approach for light source detection by multi-robot system
VNU Journal of Science: Comp. Science & Com. Eng., Vol. 32, No. 3 (2016) 1-10
Swarm Optimization Approach
for Light Source Detection by Multi-robot System1
Hoang Anh Quy, Pham Minh Trien
VNU University of Engineering and Technology, 144 Xuan Thuy, Cau Giay, Hanoi, Vietnam
Abstract
Exploration and searching in unknown or hazardous environments using multi-robot systems (MRS) is
among the principal topics in robotics. There have been numerous works on searching and detection of odor, fire
or pollution sources. In this paper, a modified Particle Swarm Optimization Algorithm (PSO) was presented for
MRS on detecting light sources, namely APSO. In the proposed algorithm, an integration of conventional PSO
and Artificial Potential Field (APF) is employed to use swarm intelligence for space exploration and light source
detection. The formulas for APSO velocities are based on those of PSO and APF. Furthermore, each particle is
surrounded by an APF that forms repulsive force to prevent collision while the swarm is in operation. The
simulation results of APSO in Matlab by various scenarios confirmed the reliability and efficiency of the
proposed algorithm.
Received 04 December 2015, Revised 09 January 2016, Accepted 26 September 2016
Keywords: PSO, MRS, APF, APSO, light source detection.
1. Introduction*
because of its efficiency, intuitiveness and
simplicity. Motivated by social searching
Owing to their robustness to local optima,
behavior of natural swarm, PSO is especially
widespread coverage and high degree of
effective in optimization problems and widely
accuracy, multi-robot systems (MRS) are
applied in various fields. Searching tasks of
highly efficient in the tasks of space exploration
MRS are in fact optimization problems, in
and searching in unknown environments. There
which the robots attempt to locate the regions
have been numerous works in which MRS was
or spots of extreme signal intensity.
used to detect fire, pollutant sources and odor
Although the idea of applying PSO to
sources [1, 2, 3].
multi-robot search is not novel, many problems
Among a variety of potential algorithms to
still need to be addressed adequately in order to
implement on MRS, Particle Swarm
put that idea into practice. Some of them are
Optimization (PSO) has become a natural
proneness to collision and premature
choice for MRS in searching tasks. PSO was
convergence. Many of the related works are
first introduced by Russel Ebenhart and James
concerned with improving performance of the
Kennedy in 1995 [4] and has gained popularity
MRS. In [5], the authors concentrated on
among bio-inspired heuristic algorithms
adjusting learning parameters for better results.
In [6] the PSO algorithm was applied to model
multi-robot search and the effects of system
parameters were also evaluated. In [7], Doctor
_______
1 This work is dedicated to the 20th Anniversary of the IT
Faculty of VNU-UET
* Corresponding author. E-mail.: quyha@vnu.edu.vn
1
H.A. Quy, P.M. Trien / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 32, No. 3 (2016) 1-10
2
et al. proposed a two PSO loops model to
deployment of robotic systems, flame detection
or optical wireless charging.
control their robot system. The inner loop was
applied for collective robotic search and the
outer was used to optimize quality parameters
of the inner. In [8], Cai et. al. proposed a
potential field-based PSO algorithm for
cooperative multi-robots in target searching
tasks. The problem of premature convergence,
which may adversely affect performance of
PSO, was addressed in [9], where Nakisa et. al.
applied a method based on PSO and Local
The methodology and simulation are
discussed in detail in part 2, the results and
discussions follow in part 3. Finally, part 4
concludes this paper with main conclusions and
directions for further research.
2. Methodology and simulation
2.1. Methodology
Search.
In spite of various works on
2.1.1. Artificial Potential Field
application of PSO for MRS in the tasks of
exploration or searching in unknown
environments, there has not been a standard
approach with optimal result. All of the PSO-
based algorithms still need further experiments
and improvements.
The APF model is inspired by Artificial
Physics with quadratic function, where the
choice of coefficients is commensurate to the
wireless sensor network of MRS. Myriads of
architectures for APF have been developed in
accordance with users’ definitions and specific
tasks, e.g. deploying mobile sensor networks in
unknown environment [12], controlling and
coordinating a group of robots for cooperative
manipulation tasks [13] or maintaining
connectivity of mobile networks [14]. In any
architecture, magnitude of the potential force
existing around each robot is continuously
updated based on information collected from its
immediate surrounding environment and other
robots via connection network. Therefore, APF
is used to regulate the relation between robots
in term of position. Potential force is
categorized into two main groups: passive force
and active force. Passive force is generated
when robot emit signal and determine distance
to neighboring robots or obstacles by the
magnitude of reflected signal to avoid obstacle
or remain relative position with other robots.
The signal used in the application could be
infrared, ultrasound, laser or camera [15]. On
the contrary, active force is generated from
external signals. These signals are usually
emitted by other robots and transmitted via
communication system [11]. In this research,
APF is only utilized for the purpose of collision
avoidance and only generates repulsive forces
on other particles within repulsive region, as
defined in this formula:
In this paper, we present another approach
and a specific application: detecting light
sources or in other words, searching for the
brightest region in a search space. This method
is then compared with one of those mentioned
above. In our simulations, an MRS is
successfully used to detect light sources (by
gathering all the swarm robots around the area
of highest luminance in the search space). In all
scenarios, each robot (or particle as described in
PSO) has to move towards the mutual target
and meanwhile avoid obstacles. For the robot
swarm to exhibit this behavior, we modified
PSO algorithm by associating each particle with
an artificial potential field (APF) that can exert
repulsive forces to any other particle if their
distance is less than a predetermined value
called repulsive radius. This method of
avoiding collisions is inspired by APF
algorithm, which was proposed by Oussama
Khatib in 1986 for single robot path planning
[10]. APF is widely used nowadays in works on
MRS that demonstrate the interaction between
robots and obstacles in their work space [11].
The proposed PSO algorithm is named APSO,
its details will be presented in the next sections.
The simulation in Matlab shows reliable and
promising results, which could be applied in
various further applications such as dynamic
H.A. Quy, P.M. Trien / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 32, No. 3 (2016) 1-10
3
r
and particles’ positions are updated with the
following formulae:
ij
)
r
ij
FAPFij
=
F
max – kr 2
ij
(1)
(
vinertial = w´ vt- 1 (3)
where Fmax and k are predetermined constants to
regulate the magnitude of potential force, FAPFij
is the APF force exerted on robot i by robot j. rij
is the end-to-end distance vector from robot j to
robot i. rij is the module of rij.
vcognitive = a1 ´ u1 ´ j (pt- 1 - xt- 1)
vsocial = a2 ´ u2 ´ j (gt- 1 - xt- 1)
vt = vinertial + vcognitive + vsocial
(4)
(5)
(6)
Total force exerted on i-th robot of the
xt = xt- 1 + vt
where:
(7)
system is:
N
FAPFi
=
FAPFij (2)
å
j= 1
vt: velocity of the swarm at t (time)
w: inertial factor
where N is the number of robots, FAPFij is zero
if i = j. The impact of FAPFi on overall velocity
is controlled by Fmax and k. As Fmax increases,
the particle is less likely to approach obstacles.
In subsection 2.1.2, this will be discussed
further.
a
1 : cognitive coefficient
2 : social coefficient
1 : random number in [0, 1]
2 : random number in [0, 1]
a
u
u
2.1.2 APSO for MRS
pt: personal best positions at t
gt: global best positions at t
xt: position of the swarm at t
The main contribution of this paper is to
propose and evaluate the efficiency of APSO, a
modified PSO algorithm. In this subsection, we
briefly present principles of PSO and then
explain APSO in detail.
φ(x): a matrix function that returns a row
vector with each element being Euclidean norm
of corresponding column in the matrix
argument.
In PSO, the swarm consists of
homogeneous particles that can explore the
search space collectively. During the
exploration, the movement of a particle is
controlled by a velocity comprised of three
components: inertial, cognitive and social
velocity. Cognitive velocity leads the particle
towards its personal best position and social
velocity leads the particle towards the global
best. Inertial velocity guides each particle
towards their previous directions and thus keeps
particles’ movement smooth [16]. Besides, high
inertial velocity and cognitive velocity at initial
steps make the swarm discover search space
better. The social learning factor should be
increased and cognitive factor should be
decreased throughout the exploration in order to
enlarge the swarm’s coverage at initial steps
and make it converge faster at final steps. The
searching process using PSO is implemented in
four stages: initializing, updating best positions,
updating velocity and position, and finally,
checking for stopping criteria. PSO velocities
In (4), φ(pt-1 – xt-1) returns a vector. Each
element of this vector is distance from a
corresponding particle to its own best position.
It is noteworthy that both position and velocity
are vectors, so in the step of updating position,
they are added directly to get new position,
without any dimensional conflict.
To apply PSO to an MRS, each robot is
modelled as a particle of the swarm and their
movements in the search space resemble those
of ideal particles described above. Actual
implementation of PSO for MRS involves
additional techniques to solve problems which
are not covered in its conventional version,
such as collision avoidance. APSO is developed
to solve that problem. The steps in APSO are
basically the same as those of PSO, but the
velocities and positions are updated with APF-
based formulae. Artificial potential fields are
also created around every particle in the search
space. The repulsive force between a particle
and another particle or an obstacle is given by:
H.A. Quy, P.M. Trien / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 32, No. 3 (2016) 1-10
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F = (Fmax - k´ r2 )´ (H(0)- H(r ))
between two quantities, in which the first
quantity progresses from a small beginning,
then accelerates and approach its climax as the
second quantity increase. There are three
regions on the curve: beginning, acceleration
and saturation region.
(8)
1
where r is the distance between the two objects,
Fmax is the maximum value of the repulsive
force. H(x) is Heaviside step function. r1 is the
radius of separation, i.e., repulsive forces are
only applicable to particles or points whose
distance to each other is smaller than r1. A robot
has a limited sensing range, this range must be
larger than r1. k is a parameter dependent upon
r1, it is calculated so that F is equal to zero
when r = r1. Total repulsive force exerted on a
robot is the sum of all the repulsive forces
exerted by other objects, according to (8).
vseparation is defined as the forth component
velocity, responsible for assuring a collision-
Algorithm: APSO
1.
Initializing
- Generate the population
- Evaluate objective function
2.
Update personal best position
- For each particle, compare fitness of past positions and choose
the optimum position as its new personal best position
3.
Update global best position
- Compare personal best positions of particles and choose the
optimum position as global best position
4.
Update and regulate velocity
- Update velocity using (13)
- Limit velocity if needed
free
exploration
of
the
MRS.
In
implementation, vseparation corresponds to total
repulsive forces on robots in the swarm.
The set of formulae used to update velocity
and position in APSO is:
5.
Update position
- Calculate new position using (14)
- Evaluate objective function for each particle
6.
- Stop if maximum step is reached or the swarm has converged
- Otherwise, come back to step 2.
Check stopping criteria
w = sig(d´ k + l)
(9)
vinertial = w.´ vt- 1 (10)
Figure 1. Implementation of APSO.
(11)
vcognitive = C´ sig(j (pt- 1 - xt- 1)´ u + v)
Fmax
(12)
vsocial = S´ sig(j (gt- 1 - xt- 1)´ u+ v)
vt = vinertial + vcognitive + vsocial + vseparation (13)
xt = xt- 1 + vt
(14)
where:
Fmax/2
d: represents immediate population density
at the position of a robot.
. ×: element-wise matrix multiplication
sig(x): element-wise sigmoid function on
Fmin
matrix:
0
r1
r2
Distance
1
1+ e- x(i, j)
(15)
sig(x)(i, j) =
Figure 2. Attractive force.
k, l, u, v: adjusting parameters used to adjust
values of quantities of interest.
This property was used to control velocities
in APSO. vcognitive and vsocial are dependent upon
the distances of particle to their personal best
position and global best position. These
velocities are regulated so that their magnitude
and the corresponding distance could be
described by a monotonically increasing
relationship. With k being negative, (9) gives a
C: maximum value of vcognitive
S: maximum value of vsocial
In Figure 1, the implementation of APSO is
presented.
In APSO, sigmoid function is widely used
because of an appropriate property of the
sigmoid curve. It exhibits a relationship
H.A. Quy, P.M. Trien / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 32, No. 3 (2016) 1-10
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lower inertia for a higher population density.
During the exploration, each robot sees the
search space as a potential field, with repulsive
force being proportional to vseparation; attractive
force proportional to a combination of vcognitive
and vsocial. The magnitude of attractive force
could be described by a sigmoid curve (Figure
2.). The potential field is time-varying. As the
position of particles change, global and
personal best positions are always improved.
However, in APSO, such criterion is not
applicable because each particle has to maintain
a distance to other particles. In our simulation,
the two following criteria are used to determine
whether the swarm is converged:
1. Improvement in best fitness: The swarm
is said to be making progress if in 10
consecutive iterations, best fitness is improved
by at least 0.1%.
2. Physical convergence: If in 10
consecutive iterations, the position of the
swarm’s center of mass does not change
considerably (less than the radius of a particle)
and a certain number of particles are at a small
distance from the center, we said that the swarm
has physically converged. The number of
particles and the distance are proportional to
swarm population.
Figure
3
shows the potential energy
configuration for a robot outside of sensing
range of any others. The robot is also not close
to any obstacles and its personal best and global
best positions are respectively (15, 15) and (20,
-20). The search space is confined in x = [-
50,50] and y = [-50,50].
In short, if there is no improvement in best
fitness and the change in the swarm’s position
is inconsiderable, the swarm is considered to be
converged and the searching process is
terminated. It is worth noting that this kind of
convergence criterion is not absolute
convergence since not all particles gather
around the swarm’s center. The operation is
deemed successful if after convergence, the
point of highest luminance is covered by the
swarm and is within a predefined radius from
global best position.
Figure 3. Potential energy configuration.
The main difference between PSO and
APSO is how velocity is updated. In APSO,
vseparation, a new velocity is introduced. Its
inertial value depends on immediate population
density, vcognitive and vsocial are functions of
distance, described by the sigmoid function.
This reduces the possibility of collision,
meanwhile yields a high performance.
2.2. Simulation
2.2.1. Simulation setup and MRS
configuration
In this research, we implement APSO on a
homogeneous MRS in Matlab environment.
The radius of each robot (r) is set as unit of
length. The system has direct communication,
the communication range is unlimited (beyond
the limit of search space). r1 is 5×r, i.e. a robot
can detect obstacles at the distance of 5×r from
its position. Population size varies between 5,
10 and 15. Maximum velocity is 1.5×r/step.
Each robot is able to acquire the illuminance at
its position via a light sensor on top.
2.1.3. Criteria for convergence
We claim that the exploration is success
when the swarm converges atthe point of
maximum illuminance. The criterion for
convergence of the swarm in conventional PSO
is simple and intuitive, as the swarm is said to
be converged when all the particles is within a
given radius, e.g. 10-3 of smallest dimension of
the search space, regardless of population size.
H.A. Quy, P.M. Trien / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 32, No. 3 (2016) 1-10
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If we set r = 1, the search space size is
In the next two scenarios, we test with real
light sources. Figure 6. and Figure 7. are
contour maps of light intensity in regions
100×100. In the Cartesian coordinate system,
the ranges of x and y coordinates are both [-50,
50]. We evaluate the effectiveness of the
modified PSO algorithm in three scenarios with
the presence of an isotropic source and two real
light sources: 87517M56FG [17] and
AVL1XMAMDG [18]. In the simulations, all
obstacles in the search space are static
cylindrical obstacles. The radii of cylindrical
obstacles used in all scenarios are 4.
illuminated
by
AVL1XMAMDG
and
87517M56FG, respectively.
2000
4000
6000
8000
10000
12000
50
40
30
20
10
0
-10
-20
-30
-40
-50
-50
0
50
Figure 6. Scenario 2 - AVL1XMAMDG.
In each scenario, three population sizes: 5
robots, 10 robots and 15 robots are simulated. The
results acquired after 1000 runs (for each scenario
and population size) is presented in Figure 9. The
figures are statistical graphs given for analysis of
reliability and effectiveness of APSO.
Figure 4. Scenario 1 - 3D View.
2.2.2. Detection of light sources in different
scenarios
In the first scenario, a single light source is
placed above the search space at (20, -20)
(Figure 5). There are four static obstacles at
(-30, -30), (-20, 30), (0, 0) and (30, 20) as
illustrated in Figure 4.
2000 4000 6000 8000 10000 12000 14000 16000
50
40
30
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045
20
50
40
10
0
30
-10
-20
-30
-40
-50
20
10
0
-10
-20
-30
-40
-50
-50
0
50
-50
0
50
Figure 7. Scenario 3 - 87517M56FG.
Figure 5. Scenario 1 - Single isotropic light source.
H.A. Quy, P.M. Trien / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 32, No. 3 (2016) 1-10
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In a typical run, as the exploration of this
swarm progresses, the robots move towards
global best position. As the population size
increases and the robots have to maintain a
minimum distance from each other, the swarm
covers a large area even after convergence. This
can be seen clearly in Figure 8.
algorithm is used. The same pattern can be
observed in every scenario.
Step: 100 Best Value = 12945.3969
50
40
30
20
10
0
-10
-20
-30
-40
-50
Figure 9. Distribution of SC in scenario 1.
-50
0
50
x coordinator
Figure 8. Final distribution
of robot swarm - scenario 2.
3. Results and discussion
The main results of these simulations are
summarized in the following figures and tables.
The results with MPSO - an algorithm from our
previous work [19] - are also presented for
comparison. Figure 9-11 display the
distribution of step of convergence (SC) in each
scenario after 100 runs. Figure 12-14 show the
cumulative distribution of SC. Only data from
successful operations is included.
Figure 10. Distribution of SC in scenario 2.
From the figures, it can be concluded that as
the swarm population increases, the step of
convergence tends to decrease. However, while
there is a large gap in performance between the
5-robot and the 10-robot swarm, there is not
much improvement when the population
increases from 10 to 15, regardless which
H.A. Quy, P.M. Trien / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 32, No. 3 (2016) 1-10
8
where number of iterations is restricted, due to
constraints on energy consumption or time,
success rate at a given maximum iteration may
become a crucial value to evaluate an
algorithm. Table 1 provides data regarding this
value, with the maximum iteration being 100.
The data in all the figures consistently
indicates low performance of the 5-robot
swarm. Both algorithms are not effective for
swarms of small population. The swarm with
larger initial coverage is less prone to premature
convergence.
APSO is also compared to the multi-search
algorithm inspired by PSO in the work of Pugh
et. al. [6]. With the same constraints and
Figure 11. Distribution of SC in scenario 3.
conditions on the robot system, the respective
results are given in Figure 15. Initially, the
robots are deployed randomly in a square of the
size 8×8. The target is placed in the center of
the square. The realistic conditions here are
wheel slip (10%) and noise (standard normal
distribution). In such conditions, APSO even
yields better results. In every case, the result is
improved when applying APSO.
When APSO is applied, there are typically
less outliers and IQRs are smaller than when
MPSO is applied. We can come to the
conclusion that APSO is more stable.
Scenario 1
1
0.8
0.6
0.4
5 robots
10 robots
15 robots
0.2
Scenario 2
0
1
20
40
60
80
100
120
140
160
Maximum step allowed - APSO
0.8
0.6
1
0.8
0.6
0.4
0.2
0
0.4
5 robots
10 robots
15 robots
0.2
0
0
50
100
150
200
250
5 robots
10 robots
15 robots
Maximum step allowed - APSO
1
0.8
0.6
0.4
0.2
0
20
40
60
80
100
120
140
160
Maximum step allowed - MPSO
Figure 12. CDF of SC in scenario 1.
5 robots
10 robots
15 robots
Figure 12-14 provide the most accurate way
to evaluate the effectiveness of APSO when
time (or number of iterations) is limited. In
general, to achieve the same rate of success,
APSO requires less iterations than MPSO.
0
50
100
150
200
250
Maximum step allowed - MPSO
Figure 13. CDF of SC in scenario 2.
In any scenario, if the maximum iteration is
100, success rate of APSO approaches 100%
when the swarm population is 10 or 15. The
corresponding values of MPSO are all lower. If
the maximum iteration is less than 50, there is
little possibility that the swarm could converge,
no matter which algorithm is chosen. In cases
H.A. Quy, P.M. Trien / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 32, No. 3 (2016) 1-10
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Table 1. Success rate at 100th iteration
Scenario 3
1
0.8
0.6
0.4
0.2
0
Scenario 1 Scenario 2 Scenario 3
N
A
87
10 98
M
77 70
96 97
A
M
6
A
84
M
58
5
5 robots
10 robots
15 robots
32 100 99
15 100 98 100 95 100 100
0
50
100
150
200
250
D
Maximum step allowed - APSO
1
0.8
0.6
0.4
0.2
0
5 robots
10 robots
15 robots
0
50
100
150
200
250
Maximum step allowed - MPSO
O
Figure 14. CDF of SC in scenario 3.
3
Simplified
Realistic
2.5
2
1.5
1
0.5
0
1
2
3
5
10
20
Number of Robots
a)
b)
Figure 15. Distance to target from the swarm’s point of strongest signal detection,
averaged over 1000 runs a) multi-search algorithm inspired by PSO. b) APSO.
dynamic deployment of robotic systems, flame
detection or optical wireless charging.
However, there are still some drawbacks in
this algorithm, for example, the swarm is
unable to detect multiple sources. Furthermore,
it has yet to be tested in complex scenarios.
In future works, we will focus on dealing
with them and applying the algorithm on a
real MRS.
4. Conclusion and Future works
In this paper, a modified PSO algorithm,
namely APSO, is presented for detecting light
sources. In this algorithm, APF is integrated
into PSO and a new velocity component is
introduced to keep the movement of the swarm
collision-free. Experimental results in Matlab
environment have shown good performance,
compared to previous works. With a high
success rate, this proposed algorithm is
promising for some practical problems
involving the utilization of MRS, such as
H.A. Quy, P.M. Trien / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 32, No. 3 (2016) 1-10
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[9] B. Nakisa, M. N. Rastgoo, M. F. Nasrudin,
Acknowledgements
and M. Z. A. Nazri. "A multi-swarm particle
swarm optimization with local search on
multi-robot search system." Journal of
This work has been supported by Vietnam
National University, Hanoi, under Project No.
QG.15.25. This work is dedicated to the 20th
Anniversary of the IT Faculty of VNU UET.
Theoretical
and
Applied
Information
Technology 71, no. 1 (2015): 129-136.
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manipulators and mobile robots." The
international journal of robotics research 5,
no. 1 (1986): 90-98.
[11] T. D. Ngo. "LinkMind: Link optimization in
swarming mobile sensor networks." Sensors
11, no. 8 (2011): 8180-8202.
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