=Paper=
{{Paper
|id=Vol-3382/Paper5
|storemode=property
|title=Movement Coordination of Swarm Robotic Systems
|pdfUrl=https://ceur-ws.org/Vol-3382/Paper5.pdf
|volume=Vol-3382
|authors=Abzal E. Kyzyrkanov,Sabyrzhan K. Atanov,Shadi A. Aljawarneh,Nazira A.Tursynova
|dblpUrl=https://dblp.org/rec/conf/dtesi/KyzyrkanovAAT22
}}
==Movement Coordination of Swarm Robotic Systems==
https://ceur-ws.org/Vol-3382/Paper5.pdf
Movement Coordination of Swarm Robotic Systems
Abzal E. Kyzyrkanov1,2, Sabyrzhan K. Atanov2, Shadi A. Aljawarneh3, and Nazira A.
Tursynova2
1
Astana IT University, Astana, 010000, Kazakhstan
2
L.N. Gumilyov Eurasian National University, Astana, 010000, Kazakhstan
3
Jordan University of Science and Technology, Irbid, 22110, Jordan
Abstract
This paper considers the motion of a swarm of self-organizing autonomous robots. An
algorithm for controlling the motion of such systems, with a behavior-based approach, is
proposed. To coordinate the movement of the robots in the swarm, a leader-follower approach
with a virtual leader has been used.
Keywords 1
Robotic swarm, behavior-based approach, leader-follower
1. Introduction
Robotics is an extremely evolving area of modern industrial science. With the help of robots people
solve various problems in different areas of life.
A great deal of work has been conducted in the history of robotics to improve robot performance
and solve various specific problems of the robotics industry, such as communication approaches [1, 2],
building an indoor navigation system [3], development of simplified encryption algorithms to deal with
resource limitations on IoT devices [4], automatic control of a vehicle [6], etc.
One such solution is using a group of the multiple simple robots to solve a single complex problem.
This approach is commonly referred to as group robotics. In recent years, research in the group robotics
systems domain has attracted special attention of researchers. One of the main tasks of group robotics
is to coordinate and control robots in a group so that they can interact effectively and without interfering
with each other to achieve a common goal. Group robotics can have a huge impact on robotics by
letting simple machines solve problems that they would not be able to solve alone and thus easing the
entire development process. The idea of using a few simple cheap robots which are simple to develop
has been considered by researchers for a long time. The first group robotics applications were already
presented three decades ago [6]. Nowadays, group robotics is widely used in the development of mobile
robots[7, 8, 9], UAV [10, 11, 12], satellites [13, 14], sensor networks, power grids, etc.
Recently, many researchers have been increasingly focusing on the swarm of robots. A robot swarm
refers to a group of robots of the same type that are designed to perform a single complex common task.
And, if we have to combine a large number of robots to solve a problem, the problem of organizing the
interaction of these robots is reduced to the problem of coordinating the same type of robots, since the
development of a large number of varieties of robots for only one task makes no sense.
One of the most important problems of Swarm Robotic Systems is the coordination of movement.
Here it is necessary to solve several problems, such as preventing collisions with each other or with an
obstacle, etc. There has been a lot of work in this area [15, 16, 17, 18].
Proceedings of the 7th International Conference on Digital Technologies in Education, Science and Industry (DTESI 2022), October 20-21,
2022, Almaty, Kazakhstan
EMAIL: kyzyrkanov.abzal@astanait.edu.kz (Abzal E. Kyzyrkanov); atanov5@mail.ru (Sabyrzhan K. Atanov); saaljawarneh@just.edu.jo
(Shadi A. Aljawarneh); ntursynova000@gmail.com (Nazira A. Tursynova)
ORCID: 0000-0002-8817-8617 (Abzal E. Kyzyrkanov); 0000-0003-2115-7130 (Sabyrzhan K. Atanov); 0000-0003-3972-5300 (Shadi A.
Aljawarneh); 0000-0002-1857-9028 (Nazira A. Tursynova)
©️ 2022 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
2. Problem statement
This paper considers a swarm robot system with decentralized control. Unlike centralized systems,
in such systems the agents are not controlled by a center unit of control. Here, each robot can use signals
received from each other or from external sources, but mostly makes decisions independently based on
its observations (i.e., sensor data) and state. To maintain motion a behavior-based algorithm and a
leader-follower method with a virtual leader has been used.
2.1. Behavior-based algorithm
The core idea of a behavior-based approach is that robots move according to several required
behaviors. Each behavior corresponds to a particular problem the robot is trying to solve. In this case,
the required behaviors of the robots may be as follows:
• Target retrieval and attainment;
• Collision avoidance with an obstacle or with each other.
The main benefits of this algorithm is that it allows more than one problem to be solved
simultaneously, simply by adding a behavior for each task.
The classical behavior-based algorithm can be described by the equation [19, 20]:
⃗ 𝑡𝑜𝑡𝑎𝑙 = ∑ 𝑤𝑏 ∗ 𝑉
𝑉 ⃗ 𝑏, (1)
𝑏∈𝐵
⃗⃗⃗⃗𝑏 is the speed of maintenance of behavior b, which are
Here B is the set of desired behaviors, 𝑉
calculated from sensor data, wb is the weight of the behavior corresponding to the relative importance
of that behavior (Figure 1).
Figure 1: The working principle of the behavior-based approach
Some papers refer to the same approaches as an artificial potential field [26, 27 and 28] or virtual
forces [29]. The classical versions of these algorithm are the identical: the only difference is that instead
of velocities of behavior, they use potential fields or virtual forces that are attracted to desired positions
or repulsed from undesirable positions.
2.2. Leader-Follower approach
The main idea of the leader-follower algorithm is that the followers try to maintain the required
distance during the movement [16]. By representing the Leader and Followers as points in the surface
and having the pose of each point, it is easy to calculate the distance between them. Supposing that the
follower pose is (xF, yF) and the leader pose is (xL, yL), the distance is calculated as:
𝐷 = √(𝑥𝐿 − 𝑥𝐹 )2 + (𝑦𝐿 − 𝑦𝐹 )2 (2)
This distance can be used as a range that the follower tries to keep (Figure 2).
Figure 2: Representation of the robot leader and the robot follower as material points
If some robot from the swarm is assigned as the leader, the robust of the swarm is at serious risk, if
the leader crashes the swarm fully becomes inoperable. To deal with such a challenge, we can assign a
virtual leader and maintain a distance with respect to him [17, 18]. The location of the virtual leader
could be simply marked in the center of the swarm. During the motion, the leader's position can be
calculated as the mean of the positions of the robots in swarm. .
3. Algorithm
The robots of the swarm start motion, updating their velocity vector with time intervals. At each
time interval swarm will perform following steps
• the location of the Leader is estimated;
• the velocity vector for each desired behavior is calculated;
• using calculated in previous step velocities (equation (1)) the total velocity for each robot in the
swarm is calculated.
The location of the virtual leader is estimated using the following equation:
𝑁
1
𝑥𝐿 = ∑ 𝑥𝑖
𝑁
𝑖=1
𝑁 (3)
1
𝑦𝐿 = ∑ 𝑦𝑖
𝑁
𝑖=1
Here, N is the count of the robots in swarm, (xi, yi) is the current location of the i-th robot, (xL, yL)
is the location of the virtual leader.
To calculate the total velocity, a behaviors-based approach is used. In our case, the robots observe
two types of behavior: moving to the target and avoiding collision with each other or with an obstacle.
The value of the collision avoidance speed is inversely proportional to the distance to the closest
obstacle. Any object that in any way may interfere with the robot's movement, including all other robots
in the swarm, is considered an obstacle. The collision avoidance velocity angle is Perpendicular to the
closest obstacle, which way it goes differs depending on which side has more obstacles, because in case
of opposite movement to the obstacle the robots may end up in a deadlock state.
The velocity of movement to the goal is oriented from the virtual leader's position to the target's
position and is the same for all robots in the swarm.
After all, using these velocities (equation (1)), the total velocity can be calculated as:
⃗ 𝑡𝑜𝑡𝑎𝑙 = 𝑤1 ∗ 𝑉
𝑉 ⃗ 𝑎𝑣𝑜𝑖𝑑 𝑐𝑜𝑙𝑙𝑖𝑠𝑖𝑜𝑛 + 𝑤2 ∗ 𝑉
⃗ 𝑚𝑜𝑣𝑒 𝑡𝑜 𝑔𝑜𝑎𝑙 (4)
The flowchart of the complete algorithm is shown in Figure 3.
Start
Retrieving data from sensors
Obtaining the positions of the other robots
Estimating position of the virtual leader
no
Calculating the velocity
movement
Target is reached
yes
end
Figure 3: The flowchart of the complete algorithm
4. Simulation
To examine the work of the algorithm proposed in this paper, we performed experiments with a
swarm robotic system of nine robots. The swarm motion was simulated using a software application
developed in the Python programming language. The Pygame library was used for visualization (Figure
4).
Figure 4: Initial state of the robots in swarm
Each of the robots in the swarm has 12 lidars. The detection radius of all lidars is same. The nearby
lidars are relative to each other at an angle of 30 degrees, so they cover all sides of the robot (Figure 5).
Figure 5: Model of the robot
It is also assumed that each robot in the swarm is aware of the positions of the other robots: in fact,
they can broadcast information about their own location to each other.
At the beginning of the movement the robots in the swarm form a square (Figure 4). Robots move
in the direction of the target (marked in red) avoiding the obstacle.
5. Experimental results and discussion
Experimental research was carried out with weights of each behavior ranging from 0.1 to 10. Two
values were observed: the total number of steps to reach the goal and the count of robots reaching the
target.
For a small value of collision avoidance speed weight (w1), the count of agents which reach the
target is very small, for a value less than 0.3 the robots do not reach the target at all. Experimental
results for values less w1 <=1 in which at least one robot reaches the target are presented in Table 1.
Table 1
Experimental results for values less w1 <=1 in which at least one robot reaches the target
The weight of the The weight of the The count of the The total number of
speed of avoiding speed of reaching the robots reaching the steps to reach the goal
collision (w1) target (w2) target
0.3 0.1 4 7049
0.4 0.1 3 7108
0.5 0.1 5 6051
0.6 0.1 7 4785
0.7 0.1 5 4657
0.8 0.1 7 4520
0.9 0.1 6 4863
1 0.1 3 5071
0.6 0.2 6 2307
0.7 0.2 4 2450
0.8 0.2 5 2982
0.9 0.2 5 2679
1 0.2 5 2594
0.8 0.3 2 1525
0.9 0.3 3 1895
1 0.3 4 1714
Also, robots cannot reach target on the large values of the weight of the speed of reaching the target.
For a value w2>2.7 the robots do not reach the target at all. Experimental results for values less w2>2 in
which at least one robot reaches the target are presented in Table 2.
Table 2
Experimental results for values less w2 >2 in which at least one robot reaches the target
The weight of the The weight of the The count of the The total number of
speed of avoiding speed of reaching the robots reaching the steps to reach the goal
collision (w1) target (w2) target
7.8 2 1 225
9.1 2 1 220
9.2 2 1 221
9.5 2 2 222
9.8 2 1 220
9.9 2 2 216
10 2 1 217
9 2.1 1 209
9.1 2.1 2 208
9.4 2.1 2 209
9.8 2.1 1 205
9.9 2.1 1 205
10 2.1 2 206
9.3 2.2 1 200
9.5 2.2 2 197
9.9 2.2 2 197
8.8 2.3 1 199
9.3 2.4 1 186
8.6 2.5 1 181
9.5 2.5 1 180
9.6 2.5 1 182
9.9 2.6 1 175
10 2.6 1 174
As the weight increases, the number of robots reaching the goal gradually decreases (Figure 6). But
the robots reach the goal faster, the number of steps to reach the goal decreases (Figure 7).
Figure 6: The graph of dependence of the count of robots reaching the goal on the goal reaching speed
weight (w2) at the value of the collision avoidance speed weight: w1=4, 6, 8, 10
Figure 7: The graph of the dependence of the number of steps of reaching the goal on the goal
reaching speed weight (w2) at the value of the collision avoidance speed weight: w1=4, 6, 8, 10
As the collision avoidance speed weight increases, the number of robots reaching the target increases
to a maximum and in many cases (especially with a small target speed weight) keeps this position
(Figure 8) But as the weight of the collision velocity grows, the robots cannot always reach the target
fully, they begin to run into each other because of the small sensitivity of the lidar.
Figure 8: The graph of dependence of the count of robots reaching the goal on the collision avoidance
speed weight(w1) at the value of the goal reaching speed weight: w2=0.1, 0.2, 1, 1.5
The number of steps to reach the goal does not depend as much on the collision avoidance speed
weight, only in some cases (especially when the goal speed weight is small) the robots can go around
the obstacle for a long time (Figure 9).
Figure 9: The graph of the dependence of the number of steps of reaching the goal on the collision
avoidance speed weight(w1) at the value of the goal reaching speed weight: w2=0.1, 0.2, 1, 1.5
6. Conclusion
In this paper, we proposed an algorithm to control the motion of a swarm of robots. A behavior-
based approach has been used to control the motion of the robots. This method allows to establish a
movement without a management center, which increases the fault tolerance. In addition, the leader -
follower method was proposed for coordination, which is one of the simplest algorithms to develop.
The presented algorithm was used to simulate the movement of a swarm of 9 robots in size. The
changes in the number of steps to reach the goal and the number of robots reaching the goal were
examined. During the experiments it was found out.
• The number of steps of reaching a goal depends very strongly on the weight of the speed of
reaching the goal. By increasing the value of this weight the robots reach the goal faster.
• The number of robots reaching the goal decreases as the weight of the speed of reaching the
goal increases. For at least one robot to reach the goal, the collision avoidance speed weight must be
at least two and a half times the goal achievement speed weight.
• By increasing the weight of the collision avoidance speed the number of robots reaching the
goal reaches a maximum.
• But as both weights increase, the robots start colliding with each other due to the low sensitivity
of the lidar.
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