| Journal of Information and Communications Technology:
Algorithms, Systems and Applications
Received: 02 May 2025; Revised: 27 May 2025; Accepted: 05 June 2025; Published Online: 09 June 2025.
J. Inf. Commun. Technol. Algorithms Syst. Appl., 2025, 1(1), 25303 | Volume 1 Issue 1 (June 2025) | DOI: https://doi.org/10.64189/ict.25303
© The Author(s) 2025
This article is licensed under Creative Commons Attribution NonCommercial 4.0 International (CC-BY-NC 4.0)
Anti-Collision Drone Traffic Control System Using
Swarm Technology
Sushilkumar S. Salve,*
Sanskruti Y. Chaudhari, Ashwini R. Dandekar and Punam Gaikwad
Department of Electronics and Telecommunications Engineering, Sinhgad Institute of Technology, Lonavala, Affiliated by SPPU,
Maharashtra, 410401, India
*Email: sushil.472@gmail.com (Sushilkumar S. Salve)
Abstract
This study presents a novel anti-collision drone traffic control system designed to prevent mid-air collisions
among autonomous drones. The suggested system facilitates communication between drones, enabling them to
exchange their current location and planned flight path. By working together, drones can anticipate and avoid
potential collisions. The technique utilizes the principle of "repulsion forces," enabling drones to autonomously
alter their trajectories in response to nearby obstacles, such as other drones. The collision avoidance behavior
adapts dynamically to the distance between vehicles, guaranteeing both safety and coordination. Created with
simplicity and computational efficiency in mind, the system is well-suited for lightweight, cost-effective drones.
To assess performance, two simulations were carried out: one with two groups of nine drones approaching each
other, and another with 25 drones executing formation changes. The findings revealed that the system was able
to prevent collisions, maintain appropriate spacing between vehicles, and adjust to different environmental
conditions. This approach improves swarm coordination and shows potential for practical applications like
managing air traffic in cities, delivering packages autonomously, responding to emergencies, and monitoring
defense operations. Future research plans involve carrying out tests in both make-believe and actual situations.
These tests aim to assess how effectively the system performs across a range of working environments. This
approach will help understand the system's strengths and weaknesses, ensuring it functions reliably under
different conditions. The research achieved an accuracy exceeding 97%, indicating high reliability and
performance.
Keywords: Drone traffic control; Collision avoidance; Swarm technology; Multi-drone coordination.
1. Introduction
The rapid progress in drone technology has paved the way for the creation of drone swarmscollections of self-
governing drones that work together to accomplish a shared objective. This collaboration allows drones to
accomplish intricate tasks that surpass the limitations of a single drone.
[1]
In environmental monitoring, groups
of drones are really important. They help find and keep track of wildfires. Drones also check the quality of fluid.
In farming, especially precision agriculture, drones are helpful too.
[2]
During emergencies and crises, these teams
offer medical help to people in remote areas. They also support search and rescue operations.
[3]
Entertainment
sector, they design elaborate formations and visual effects for drone performances. In military operations, they
carry out autonomous reconnaissance and provide support during combat, all while reducing the risks to
human soldiers. Creating systems that enable drone swarms to carry out synchronized and intricate movements
represents a major technological breakthrough.
[4]
The successful implementation of autonomous drone
technology necessitates the development of advanced control systems to address the potential hazards involved
in drone operations. One of the main difficulties in swarm control is maintaining coordination while avoiding
drone collisions. To achieve this goal, drones have to use very advanced and computer-intensive decision-
making processes. These processes rely on data collected from sensors.
[5]
There are different methods for managing swarms, such as algorithms inspired by the behaviours of animals
like birds, fish, and bees. Distributed consensus algorithms are used by drones to work together. They do this
by sharing information with nearby drones. The selection of strategies is contingent upon the task's specific
needs, hardware limitations, communication constraints, and reliability concerns. Just like autonomous
vehicles, drone swarms employ obstacle avoidance algorithms that depend on real-time sensor data to assess
their environment continuously.
This process entails creating an environmental map while simultaneously determining the drone's position
using simultaneous localization and mapping (SLAM) techniques.
[6]
Research also assesses the effectiveness of
slam algorithms across various hardware configurations by examining the accuracy of map navigation.
This research introduces a collision avoidance algorithm specifically developed for drone swarms that utilize a
mesh communication system.
[7]
This system lets all drones talk to each other right away. They share details
about where they are and where they aim to fly. This way, each drone knows what's happening with the others.
The suggested algorithm guarantees collision prevention by constantly tracking the positions of the swarm and
its surroundings. One of the standout aspects efficient, which makes it suitable for managing large groups of
drones. The advanced system safeguards against collisions between drone.
The initial study on how to manage a group of drones so they don't collide with each other was conducted using
simulation software. This method allowed researchers to test and develop techniques in a controlled virtual
setting without using physical drones. This methodology expedites software creation while reducing
operational hazards.
[8]
The research concentrates on the behavior of swarms, with a specific emphasis on developing effective collision
avoidance techniques. The research also examines how different group setups influence the swarm's ability to
work together and avoid accidents when conditions change. Earlier studies have focused on the effectiveness of
the simulation environment. This involves considering how communication delays and the accuracy of the
positioning system can impact performance.
This research is organized to be easy to follow. Section 2 discusses different ways to control groups of drones
and how to prevent them from crashing into one another. Section 3 explains the theory behind research new
algorithm for avoiding collisions. Section 4 describes a simulation environment.
In the wild, numerous animals collaborate to compensate for their individual shortcomings. For instance, wolves
hunt cooperatively in packs, birds travel together in flocks, and ants work collectively in colonies. Researchers
investigate these collective behaviours and develop mathematical models to comprehend how they
communicate and synchronize. These models assist in creating algorithms for solving practical problems such
as planning routes or distributing tasks.
[9]
Particle swarm optimization is a well-known method that takes cues
from the way birds move together in flocks. It uses natural behaviours to solve problems. This makes them very
useful in many different situations.
Nevertheless, as drone swarms expand in size, handling them becomes increasingly intricate. A hierarchical
control system can assist in organizing tasks more effectively and enhancing overall efficiency. According to
experts, addressing the challenge of coordinating vast numbers of swarms necessitates a well-structured, multi-
layered approach to planning.
[10]
This research addresses these limitations by introducing the near future the
world is going to be surrounded by innumerable drone for different conventional and non - conventional
applications, and hence it is an ultimate problem to be solved to avoid a maximum number of accidents that can
happen with the growing number of drones in the open air. The primary objective of this research is to enhance
human safety by minimizing accidents caused by drones.
Swarm robotics is application of collective intelligence. Swarm intelligence (si) is a type of artificial intelligence
that focuses on understanding how groups of individuals can work together without a central authority, by
studying how they behave in self-organized systems. To sum up, this research seeks to create a drone that can
be used in various environments where larger drones are not suitable or safe. By incorporating swarm
technology, the micro drone can navigate securely, minimizing the chances of collisions and broadening its range
of applications. This concept was first introduced in the field of artificial swarm intelligence and has also been
observed in the study of insects, ants, and other natural phenomena. After completing the introduction, we now
proceed to the comparison table, which presents an overview of the communication techniques relevant to
study, highlighting their respective merits and demerits.
Table 1 shows Comparison of different communication technologies swarm technology, decentralized nonlinear
model predictive control (NMPC) provides a more effective solution for managing multiple unmanned aerial
vehicles (UAVs). Nmap enables each drone to autonomously plan its path by anticipating future states and
avoiding potential collisions, without the need for centralized coordination. One of the key advantages of NMPC
is its exceptional flexibility and fault tolerance if one drone malfunctions, the others can continue functioning
autonomously. Nevertheless, its primary disadvantage is the significant computational requirements, which can
hinder real-time performance, particularly when the number of drones or obstacles escalates rapidly.
One coordinating unmanned aerial vehicles (UAVs). DRL enables drones to acquire optimal navigation and
collision avoidance techniques through continuous interaction with their surroundings. One important benefit
of DRL is its capability to adjust and perform effectively in various and unexpected situations. This adaptability
makes it an excellent choice for carrying out complicated tasks in outdoor environments. On the downside, DRL
necessitates a significant amount of training data and time, and it may struggle to ensure consistent and reliable
behaviour in unfamiliar or previously unseen situations, which can be crucial in practical applications.
[11]
Hil simulation platforms offer a reliable approach to test and verify multi-drone systems before their actual
implementation. These platforms combine actual drone hardware with simulated environments, enabling
developers to witness system behaviour in realistic conditions without the dangers of real-world crashes. The
value of Hil simulation lies in its ability to provide accurate and detailed testing, ensuring safety and efficiency
during the development phase. Nevertheless, implementing these systems can be costly and intricate, and
simulations may not always accurately represent real-world uncertainties like sudden gusts of wind or hardware
failures.
Table 1: Comparison of different communication technologies.
Ref. No.
Communication Technique
Merits
Demerits
[1]
Decentralized Nonlinear Model
Predictive Control (NMPC)
High flexibility
High computational load
[3]
Deep Reinforcement Learning
(DRL) for UAV Coordination
Ability to learn and adapt to
a high dynamic.
Requires huge amounts of
training data and time.
[8]
Hardware-in-the-Loop (HIL)
Simulation Platforms
low-risk testing of
algorithms with high
realism
Initial setup cost and
complexity can be high
[9]
LiDAR-Based Detect and Avoid
Systems
Very accurate 3D mapping
of obstacles.
Expensive and heavy sensors
can burden a UAV.
[12]
Multi-Sensor Fusion for
Navigation and Collision
Avoidance
Increases overall system
reliability.
Data synchronization and
sensor calibration are complex.
Lidar-based detection and avoidance systems are a practical option for autonomous unmanned aerial vehicles
(UAVs) navigation. By utilizing laser pulses to create a 3D map of the surroundings, lidar enables drones to
identify obstacles with exceptional accuracy, even in areas where GPS signals are not dependable.
[12]
The key
advantage is the exceptional accuracy and dependability in obstacle detection. Nevertheless, lidar sensors are
generally bulky and costly, which may restrict drone flight duration and payload capacity, particularly for small
or battery-constrained unmanned aerial vehicles (UAVs).
Lastly, multi-sensor fusion for navigation and collision avoidance improves the performance of UAVs by
integrating data from various sensors, including GPS, cameras, lidar, and IMU. By using various sensors together,
this method makes the system more robust. It helps overcome the weaknesses of individual sensors and gives a
clearer understanding of the environment, thus improving the ability to accurately detect and respond to
surroundings. Its primary advantage is enhanced reliability and precision in navigation and collision avoidance.
Conversely, multi-sensor fusion systems necessitate intricate algorithms for data synchronization and
calibration, which can heighten system complexity and introduce delays in decision-making.
[13]
This research is organized to be easy to follow. Section 2 discusses different ways to control groups of drones and
how to prevent them from crashing into one another. Section 3 explains the theory behind research new
algorithm for avoiding collisions. Section 4 describes a simulation environment.
In the wild, numerous animals collaborate to compensate for their individual shortcomings. For instance, wolves
hunt cooperatively in packs, birds travel together in flocks, and ants work collectively in colonies. Researchers
investigate these collective behaviours and develop mathematical models to comprehend how they communicate
and synchronize. These models assist in creating algorithms for solving practical problems such as planning
routes or distributing tasks.
[14]
Particle swarm optimization is a well-known method that takes cues from the way
birds move together in flocks. It uses natural behaviours to solve problems. This makes them very useful in many
different situations.
2. Proposed methodology
The repulsion vectors, which determine the avoidance response, evaluate the degree of immersion in the
protective sphere. The decision is decentralized and remains stable under dynamic conditions. It is effortless to
integrate for collision avoidance, naturally adjusts to the surroundings, and is computationally efficient, making
it ideal for large groups of drones. Furthermore, it aids in the prevention of both stationary and moving obstacles
and employs mesh communication to share position and trajectory information.
[15]
The system also enables the
customization of the collision avoidance intensity. Nevertheless, it necessitates frequent data synchronization,
entails significant communication demands, and poses challenges in implementing large-scale swarm
operations. It is also sensitive to the failure of leading units, restricts the autonomy of other agents, and may
face challenges in maintaining stability in densely packed formations.
[16]
The suggested system utilizes swarm intelligence to empower autonomous drones to navigate shared airspace
without colliding with each other. This method relies on algorithms inspired by nature. It involves using particle
swarm optimization (PSO) and the boids algorithm. These approaches mimic how decisions can be made in a
group without any central leadership or control. They help in understanding how individuals, like birds or fish,
make decisions and act together in a coordinated way.
[17]
Each drone functions as a self-sufficient entity,
equipped with the ability to perceive its environment and share only essential data with nearby drones. This
group behavior allows for dynamic path planning and real-time traffic adjustments based on local information,
which helps reduce the chances of mid-air collisions.
To ensure strong collision avoidance, the system combines onboard sensors like lidar, ultrasonic rangefinders,
and GPS modules. These sensors constantly transmit environmental information to the drone's processing unit,
which analyzes the drone's proximity to other drones and potential obstacles. When predetermined safety limits
are exceeded, a collision-avoidance protocol is activated using a priority matrix and threat estimation.
[18]
This
protocol guarantees that drones can swiftly change their course without causing traffic disruptions or
jeopardizing their mission goals.
A combination of methods is utilized for efficient collaboration. It integrates direct drone-to-drone
communication with a central monitoring node to facilitate better traffic management at a higher level. This
node gathers telemetry data and keeps track of drone positions to help identify and alleviate potential traffic
congestion. Nevertheless, decision-making at the small scale remains decentralized, mirroring swarm principles
to guarantee scalability and fault tolerance, even in situations with intermittent connectivity.
Simulation and real-world testing are conducted to verify system performance across different traffic densities
and environmental conditions. The simulations are conducted using software tools such as MATLAB and
Gazebo, where the algorithms and sensor integration are assessed. Subsequently, physical models of the
hardware are subjected to testing in outdoor settings to evaluate their real-time responsiveness and overall
stability.
[19]
These iterative tests assist in refining the algorithms and enhancing safety margins, guaranteeing
that the drone traffic control system meets the reliability standards required for practical implementation.
Several drones are equipped with GPS, IMU sensors, and onboard processors to enable real-time positioning
and movement tracking. Swarm intelligence algorithms, such as flocking behaviour, collision avoidance, and
consensus decision-making, are utilized. A network of interconnected mesh communication allows drones to
exchange real-time information about their location, speed, and any potential obstacles.
[20]
Each drone
autonomously modifies its trajectory based on shared data to prevent collisions. An optional ground control
station keeps an eye on the swarm without having direct control over each individual drone.
Fig. 1: Block diagram.
The Fig. 1 diagram illustrates the structure of a drone swarm system, where numerous drone units are arranged
and synchronized through a well-defined flow of information. The heart of every drone unit lies in crucial GPS,
which enable the drones to determine their location, orientation, and motion in three-dimensional space. The
onboard processor processes the sensor data received by the swarm, which is then used to manage swarm
intelligence algorithms, navigation rules, and trajectory calculations essential for the autonomous operation of
the swarm.
[21]
Drone communication network of interconnected drones, enabling seamless communication and coordination.
This system enables the drones to exchange crucial real-time data, including their current location, speed,
intended flight routes, and potential obstacles in their vicinity. By utilizing mesh networking, the system
guarantees that each drone is conscious of its neighbouring drones, which is crucial for maintaining a safe and
synchronized movement within the swarm.
[22]
The decentralized structure of the mesh network enhances the
swarm's resilience and flexibility, as it does not depend on a single communication hub.
The core of swarm control lies within swarm intelligence. This core is responsible for more complex decision-
making tasks, such as coordinating the movement of drones in a flock, maintaining a safe distance between them
while moving in the same direction, and avoiding collisions by using repulsion vectors.
[23]
It also employs
consensus algorithms, guaranteeing that the swarm can collectively decide on a new destination point if
obstacles are encountered.
The mesh communication network serves a dual purpose: it connects individual drones and establishes a
connection between them and the swarm intelligence core. This ongoing flow of information allows the swarm
to adjust to changing surroundings without any human interference.
[24]
Mesh networking enables drones to
seamlessly join or leave the swarm, ensuring the system remains scalable and resilient. Although the drones
and the swarm core can function autonomously, the ground control station serves as a platform for overseeing
the swarm's operations, receiving real-time updates on their status, and potentially issuing mission-level
directives. Nevertheless, it does not have direct control over the drones, ensuring that the swarm remains
decentralized.
[25]
The Fig. 1 shows block diagram showcases a drone swarm architecture that is well-organized, with intelligence
distributed among individual drones but coordinated centrally using smart algorithms and mesh networking.
This configuration allows for smooth, self-directed, and dependable group actions, It's useful for many tasks. It
can be used to watch over areas to keep them safe. It's helpful in search and rescue missions to find and save
people. It can also monitor the environment, like tracking weather changes or spotting pollution. There are
many other ways it can be used too.
[26]
2.1 Hardware description
The hardware described is based on the Ten silica Xtensa LX6 dual-core 32-bit MCU, capable of achieving up to
600 DMIPS performance. 802.11 b/g/n Wi-Fi standards HT40, enabling high-speed wireless connectivity.
Bluetooth functionality is provided up to version 4.2 and below, wireless communication applications. The
microcontroller typically operates at a frequency of 160 MHz, ensuring efficient performance across tasks. It
includes 512 Kbytes of SRAM for fast data processing and temporary storage, while external SPI flash memory
support is available for up to 16 MBytes, allowing for substantial program and data storage.
For hardware interfacing, the device offers 36 GPIO (General Purpose Input/Output) pins, providing flexibility
for various input and output operations. Pulse Width Modulation (PWM) is supported with 1 hardware PWM
channel and up to 16 software-controlled PWM channels, which is particularly useful for applications requiring
precise signal control, for example, controlling motors or changing how bright LEDs are. In terms of
communication interfaces, the MCU is equipped with 4 SPI, 2 I2C, 2 I2S, and 2 UART modules, enabling versatile
connections with sensors, peripherals, and other microcontrollers. Overall, this hardware platform provides a
powerful, flexible, and highly connected foundation for embedded and IoT applications.
[27]
2.2 Software description
Development in Embedded C
Implementation of BLE using RTOS
Use of Arduino IDE
Blynk Cloud IoT Platform for App Development
The flowchart illustrates a system created to predict and avoid possible collisions UAVs, ensuring safe navigation
towards a goal while avoiding obstacles. The process begins with predicting potential collisions by analyzing
reachable sets up to the goal point. If a collision is anticipated, the system promptly engages in generating a
suitable avoidance path.
Once a collision is predicted, two possible scenarios are considered: if the UAV is close to an obstacle, it must
take reactive action immediately, or if there is time and space, it can plan an avoidance path more smoothly. This
dynamic decision-making ensures the UAV adapts its strategy based on real-time proximity to obstacles and
environmental changes.
After generating an avoidance path, the UAV and obstacle states are updated accordingly, verifying whether any
constraints (like kinematic or dynamic limits) are violated. If no critical constraints are violated, the new
avoidance path is sent to the UAV, allowing it to continue safely toward the goal without incidents.
The flow chart shown in Fig. 2. begins with the estimation of collisions using reachable sets. Reachable sets are
the set of all possible states the drone can reach given its dynamics and constraints. By researching these sets
towards the goal, the system anticipates whether any potential collision with obstacles is likely to happen during
the flight.
[28]
When a collision is anticipated, the system takes appropriate action to manage it. There are two primary routes:
if the drone is close to an obstacle, the situation is critical, and it must take immediate action, often a rapid
maneuver or emergency stop, to prevent a collision.
[29]
This reactive path is faster but often less efficient than a
planned path. If the drone is not near an obstacle, it can create an avoidance path in a more organized and
efficient way. This route is determined by taking into account the UAV's movement limitations, the presence of
obstacles, and the mission's objective to reach the destination while ensuring safety and efficiency.
Fig. 2: Flow chart.
After the avoidance path is created, the system modifies the states of both the unmanned aerial vehicle (UAV)
and the challenges it encounters. These challenges include avoiding obstacles that might be in its path. This
guarantees that the new route takes into consideration any changes or movements of the obstacles, such as
other drones or vehicles.
Following the update of the states, the system verifies if any constraints are breached along the newly
established path. Constraints may include restrictions on the speed, acceleration, turning radius, energy
consumption, or proximity to no-fly zones for the UAV. If any constraint is not met, the system may initiate a
replanning process or modify the path accordingly.
If the conditions are met, the avoidance path is transmitted to the unmanned aerial vehicle (UAV) for execution.
This command instructs the drone to change its flight path based on the newly calculated safe trajectory,
enabling it to avoid obstacles and progress towards the objective. Finally, with the revised route, the drone
proceeds to reach its destination.
[30]
By combining prediction, reactive and planned actions, constraint
validation, and continual updates, this modular approach enables the building of a strong, reliable, and flexible
UAV that can handle various conditions and tasks. navigation system that can safely navigate in dynamic and
unpredictable environments.
The diagram depicts the step-by-step process for an anti-collision system in unmanned aerial vehicles (UAVs),
employing both predictive and reactive approaches. The procedure commences with the estimation of possible
impacts.
[31]
This is accomplished by employing reachable sets calculations that predict all potential future
positions of the drone while moving towards its objective. If a set that can be reached from a starting point
intersects with an obstacle's path, the system anticipates a potential collision early, allowing for timely
preventive measures.
When a collision is anticipated, the system splits into two potential courses of action. If the drone comes within
proximity to an obstacle, an immediate reactive response is initiated.
[32]
This enables the drone to swiftly change
its course, evading any potential threats without the need for intricate planning. This component of the system
guarantees a prompt response, which is vital in real-world situations where obstacles can suddenly emerge or
change their position unexpectedly.
If there is sufficient distance and time, instead of an immediate response, the system gradually progresses
towards creating an avoidance path. This avoidance path is meticulously calculated to guide the UAV away from
the obstacle while still moving closer to the ultimate objective. When determining the optimal path for a UAV, it
is crucial to take into account several dynamic factors, such as the speed of the aircraft, the characteristics of the
obstacle, and the prevailing environmental conditions.
[15]
Following the creation of the avoidance path, the subsequent step involves modifying the states of both the
unmanned aerial vehicle (UAV) and the obstacle, aligning them with the newly planned route.
[33]
Updating the
states involves continuously recalculating the drone's position, velocity, and trajectory in real-time, ensuring
that it stays on the intended safe path and adapts to any changes in the obstacle's behavior.
[34]
Nevertheless, as the system updates, it constantly verifies if any constraints are being violated. These limitations
could encompass safety buffers around obstacles, flight path restrictions, speed limits, or energy consumption
boundaries. If any constraint is not met during the planned avoidance path, the system either adjusts the plan
or initiates alternative manoeuvres to ensure safety. If there are no constraints, the avoidance path is sent to the
UAV controller for execution.
Finally, after skillfully navigating the avoidance path, the UAV proceeds towards its intended destination. This
systematic approach guarantees that drones can autonomously and intelligently navigate around obstacles
without human assistance, enhancing the safety and dependability of autonomous drone flights, especially in
complex or cluttered surroundings.
[35]
A drone's movement in three-dimensional space can be described using a basic model known as a kinematic
model. Instead of illustrating the position and speed as smooth, continuous lines over time, we use what are
called motion primitives. These are like short, specific paths that the drone can take, and each one is created by
a particular control signal. This results in a limited number of paths that the drone might follow. Because
quadcopters, a common type of drone, usually fly in smooth patterns, we can use a kind of math equation called
a polynomial function to predict where the drone will go.
󰇛
󰇜
   (1)
Equation is used to find ck, which are the coefficients in a polynomial. The letter k shows the order or degree of
the polynomial. Motion primitives are useful because they make describing paths in complex areas easier. They
achieve this by breaking down the area into a grid-like pattern. Each path segment takes into account certain
limits for control, such as top speed and how fast a vehicle or object can accelerate. This ensures that the planned
path can actually be followed safely and realistically.
󰇛
󰇜
󰇧
󰇻
󰣛󰳗
󰇻
󰇨 
󰣛
(2)
Equation Instead of handling complex mathematical equations that involve continuous numbers, planning a
drone's path is tackled like exploring a map. In this method, we use specific terms and paths to help avoid any
crashes while ensuring the drone follows its intended route. To put it simply, imagine pi and pj as the current
positions of the drone. The term vd refers to the speed we want the drone to achieve, and λ helps find a balance
between avoiding collisions and keeping to the planned path. Think of each location as a state, and the lines
connecting them as the possible moves the drone can make. Equation specifically aims to prevent collisions and
keep the drone on its designated course. This balance enhances both the safety and the success of the mission,
so the drone can operate effectively without deviating from its path.
󰇛 󰇜󰇛󰇜 󰇛󰇜 󰇛󰇜 (3)
󰇛 󰇜󰇛󰇜 󰇛󰇜 (4)
Creating motion steps involves splitting movement into smaller segments and calculating these parts using
control signals over a set period, known as δt. For each segment of the path, we constantly update the position
and speed using specific formulas. These formulas rely on a control vector, called u(t), which stands for
acceleration. By doing this repeatedly, we turn complex equations into simpler, manageable steps. This approach
is really helpful for applications that need to work in real-time, especially in challenging or complex
environments.
󰇛󰇜󰣛󰇛󰇜 󰇛 󰇜 (5)
Equation defines a "safe" intermediate position for the drone. It modifies the current position pi(t)p_i(t)pi(t)
based on the difference between the desired safe distance to the goal (dgoald_{\text{goal}}dgoal) and the
minimum distance to an obstacle (dmind_{\text{min}}dmin). The coefficient ede_ded adjusts how aggressively
the drone should react to maintain a safe distance.
󰇛󰇜󰇛󰇜 󰇛 󰇜 (6)
Equation indicates the vector r(t)r(t)r(t) points from another drone or obstacle pj(t)p_j(t)pj(t) to the current
position of the drones p(t)p(t)p(t). It is used to calculate how close and in what direction another object is,
which is crucial for collision avoidance.
󰇛
󰇜
󰇛
󰇜

󰇛
󰇜
(7)
Equation vector r(t)r(t)r(t) points from another drone or obstacle pj(t)p_j(t)pj(t) to the current position of the
drones p(t)p(t)p(t). It is used to calculate how close and in what direction another object is, which is crucial for
collision avoidance.
 󰇛󰇛󰇜󰇜 (8)
In Equation describe this parameter β\betaβ adjusts the strength of the repulsive force depending on how close
the drone is to an obstacle. When the drone is inside a critical safety zone (dsmd_{sm}dsm), the repulsive force
is strong. wrw_rwr defines how wide the repulsive zone is. When the drone approaches objects that might be in
its way, it detects them more intensely. This detection pushes the drone to steer clear, helping it to avoid any
crashes.
󰇛󰇜󰇛󰇛󰇜󰇛󰇜󰇜 󰇛󰇜 (9)
Equation is the final vector that decides the drone’s next movement. It sums up all the repulsive vectors
rj(t)r_j(t)rj(t) weighted by their corresponding βj(t)\beta_j(t)βj(t) (how dangerous they are), and adds a term
pushing the drone towards its overall desired direction (based on vavg(t)v_{\text{avg}}(t)vavg(t)). This
balances both collision avoidance and goal progression.
3. Result
Every drone is equipped with several tools, including a compass, an IMU (Inertial Measurement Unit), a
barometer, and a precise GPS known as RTK GPS, which allows for very accurate positioning within 5 cm. Fig. 1
shows how this system works to prevent collisions. Drones are constantly checking their location compared to
others in the swarm. The collision avoidance system maintains safe distances between drones, reducing crash
risks and allowing them to move in sync. This system works automatically, ensuring that the drones' movements
stay coordinated even if the environment changes unexpectedly. The drones communicate through a type of
network called a "mesh network," using the MAVLink protocol to share information like their current positions
and travel plans. We conducted tests with 20 actual communication modules in a mesh network, and these tests
showed that data is transmitted with manageable delays and without data loss. The design of this system is
quite flexible, enabling additional components to be added smoothly without trouble.
[36]
The swarm now has fewer drones to make communication more efficient. Fewer drones mean easier
management of challenges and ensure data is exchanged reliably. This reliable data exchange is necessary for
keeping drones close to each other and ensuring the mission goes well. Keeping a smaller number of drones
helps in achieving better coordination and mission success.
Fig. 3: Schematic diagram illustrating the collision avoidance mechanism.
Fig. 3 gives a simple picture of how drones avoid collisions. Drones use a map to help them find their way and
avoid obstacles. This map is available for all drones, helping them plan their paths and avoid crashes. This
ensures drones work efficiently, even in areas with many obstacles or tough flying conditions. To check how well
research collision-avoidance system works, we did some computer-based tests using AirSim, which runs on the
Unreal Engine. We created a simple 3D landscape without obstacles, allowing the drones to fly freely. We made
physical drone models with a Holybro X500 frame and a Pixhawk 6C flight controller. These drones use 2216
kv920 motors, 1045 propellers, a 4s 5000 mah battery, and custom 3D-printed parts like the body, connectors,
and covers for protection.
The study had two different setups. They used a total of 18 drones, split into two groups with nine drones each.
In each group, the drones were placed in a 3 by 3 grid. The leader drone was in the center, with the others lined
up behind. Each drone was 5 meters apart. They could fly up to 5 meters per second. The leaders of the two
groups were set 200 meters apart, and a pretend crash course was made to test their reactions. The drones were
supposed to fly closely behind their leader, so watching the distance between the two leaders helped to see how
they avoided crashing into each other.
[37]
The diagram describes how drones can accidentally fly into each other's routes, especially in busy and
uncontrolled routes. In this diagram, drones are shown moving at different altitudes and bearings. The spots
where their paths overlap are marked as potential collision zones. These spots often happen when drones are
unaware of each other’s place or when there isn't a system to control their routes. This diagram helps us
understand how drone accidents can happen when drones do not collaborate, specifically in assembly zones
like cities or at events with many drones. The diagram also emphasizes the requirement for managing the
system that lets drones communicate. By inspecting airspace paths and length, we can locate exactly where
changes are necessary to prevent crashes. Swarm innovation is useful here, as it allows each drone to know its
location and adjust its speed or bearing to avoid impact.
[38]
This diagram is essential for developing smarter
drone navigation systems that ensure safety and efficiency in shared skies. AirSim, different drone models exist,
but none are exactly like researchs. The settings for these models are in the program's code, making it hard to
change them after setup. To fix this, we moved the settings into a file that can be easily edited, so we don’t have
to redo the whole programming process. In research earlier work, we created the base simulation environment.
We adjusted the drone model in the simulation so that it matches the real drone as closely as possible, including
its weight, size, and the power system. This simulation environment gives us a safe, controlled space for testing
the collision-avoidance systems, which helps lower the chance of unexpected problems or risks.
[39]
Fig. 4: Illustrates the initial drone positions.
Fig. 4 illustrates the initial drone positions. The arrows indicate the directions of swarm movements. In Fig. 3, a
sequence of the drone formations' movement is shown (two swarms approach each other on a collision course).
Drones belonging to the first swarm are marked in blue, drones belonging to the second are marked in red, and
the arrows indicate directions of swarm movements. As part of the research, a simulation was created with two
groups of nine drones, each flying at a distance of 5 m from one another and at a maximum speed of 5 m/s. The
parameter urr, which determines the strength of the collision avoidance response, had the values of 0.5, 0.75,
and 0.99. When urr = 0.5, it indicates the maximum delay in the reaction of the drones, while urr = 0.99 suggests
a very early response to each other's approach. The simulation outcomes demonstrated that the collision
avoidance mechanism successfully averted collisions in all tested scenarios, irrespective of the value assigned
to the urr parameter. In Fig. 4, the variations in the speeds of individual drones and the minimum distances
between them are depicted. During the experiment, they presented the data between them.
[40]
(a)
(b)
Fig. 5: Change in the formation’s position during mission execution (a) The state before the start, (b) Before the
collision, (c) During movement along the collision course.
Fig. 6: The Speed Chart of selected Drones for both SWARMS (left and right charts) and the minimum distances
(middle chart) for the parameter urr=0.75.
When we set the parameter urr to 0.5, the smallest distance between the drones came to 1.686 meters. This
indicates that the drones took a bit longer to react, but they still successfully avoided a collision. Increasing urr
to 0.75, the gap widened to 1.975 meters, showing the drones reacted more swiftly and evenly. Further adjusting
urr to 0.99, the drones responded even earlier, with the smallest distance growing to 2.621 meters. These
outcomes demonstrate the algorithm's ability to maintain a safe buffer between drones. The simulation
confirms that research collision avoidance system is effective and adaptable to different situations. During tests,
the drones were directed toward each other, which posed a potential risk for collision. However, the system
smartly adjusted the strength of the drones' reactions, steering them away from crashes even in tough
conditions. The findings reveal that regardless of the urr setting, the gap between drones was always sufficient
to prevent collisions. The detail-rich charts on changes in speed and distance underscore the solution’s
effectiveness. Table 2 provides the precise minimum distances between drones on potential collision paths.
Table 2: The minimum distances between drones [m] for urr = 0.5, 0.75, and 0.99.
The Distances
Between Drones
urr= 0.5
urr=0.75
urr=0.99
Drone01Drone11
3.0740
3.1085
4.2240
Drone02Drone12
3.2801
3.5116
4.1203
Drone03Drone13
3.0168
3.3540
4.1241
Drone04Drone14
2.8889
3.3520
4.2383
Drone05Drone15
1.6863
1.9759
2.8827
Drone06Drone16
3.1735
3.0667
4.0470
Drone07Drone17
3.2019
3.1786
3.9095
Drone08Drone18
3.1028
3.2995
4.0981
Drone09Drone19
3.0241
3.4265
4.0682
Fig. 7 shows the changes in distance and speed for the leader drones. The left chart illustrates the distance, while
the right chart indicates the speed. Drone05 is the leader for the first swarm, and Drone15 leads the second
swarm. These graphs display how both distance and speed are affected using three values for the parameter
urr: 0.5, 0.75, and 0.99.
Fig. 7: The speed of the leader drones.
Fig. 7 and 8 illustrate the distance between the leader drones and speed of leader drones. When the parameter
value of urr is set to 0.5, the initial distance between the leader drones decreases rapidly, reaching a minimum
of 1.69 meters. Following that, the increase in distance becomes more gradual. The drones' responses are
delayed here, leading to the smallest safety margin. When urr = 0.75, the minimum distance is larger than when
urr = 0.5. The reaction to getting close to the item happens at a much quicker rate. This enables a more efficient
reaction to a possible accident. When urr = 0.99, the drones respond the quickest. This is evident in the rapid.
Fig. 8: The distance between the leader drones.
The data shows that as the minimum value was reached, the distance between the two points increased. The
smallest separation is 2.88 m. The flight path and the collision avoidance system's reaction are the most
seamless. The examination of the recorded speeds of the leader drones reveals substantial decreases in speed
during the moment of collision avoidance, particularly when urr = 0.5. The mechanism's reaction is postponed.
Producing substantial velocity fluctuations. For a value of urr = 0.75, the drones' speeds decrease, but their
movements are more precise and controlled. The value of Urr = 0.99 has a significant impact on the speed
response, preventing abrupt decreases in speed. The leader drones' velocities remain more consistent. The
obtained results suggest that the parameter urr has a significant impact on the value of urr is 0.99, drones are
best at avoiding collisions because they respond the quickest. This setting helps ensure they don't crash into
obstacles. This enables the driver to maintain a larger minimum distance and more consistent speeds.
Conversely, when urr is lower (around 0.5), the responses are delayed. This leads to a reduced safety buffer and
more significant variations in speed. The values of urr = 0.75 indicate balance between maintaining responding
quickly to changes.
4. Conclusion & future scope
The cutting-edge anti-collision drone traffic control system, employing swarm technology, represents a
breakthrough in ensuring the secure operation of autonomous aerial vehicles. By drawing inspiration from
natural swarms, such as decentralized decision-making, dynamic path planning real-time responsiveness,
system effectively tackles the issues of drone traffic congestion and mid-air collision risks. By incorporating
robust sensing mechanisms, and hybrid communication frameworks, drones have shown that they can work
together efficiently in complex and ever-changing environments, without needing a central control system.
Make drone operations more dependable, able to handle increased tasks or loads efficiently, and capable of
maintaining functionality even when issues or failures occur. System has demonstrated remarkable efficiency
in adapting to different environmental conditions and traffic densities through extensive simulations and
carefully designed field experiments. The incorporation of threat estimation and prioritized collision avoidance
maneuvers significantly improves operational safety, making it a promising solution for future urban air
mobility (UAM) and logistics networks. Additionally, the modular design allows the system to be customized for
drones of various sizes and capabilities. Despite its achievements, certain constraints were identified, such as
the reliance on sensor precision and communication delay, which can affect decision-making speed in heavily
congested areas. Furthermore, unexpected environmental conditions, like sudden weather shifts, can impact
the functionality of onboard sensors and, in turn, the entire system. Overcoming these challenges will
necessitate advancements in sensor fusion techniques, the development of more sophisticated predictive
models, and the incorporation of machine learning approaches to improve adaptability. Anticipating ahead, the
system's domain is vast. By integrating emerging technologies like 5G communication, artificial intelligence-
based predictive analytics, and blockchain for secure data sharing, the efficiency and reliability of the swarm-
based traffic control mechanism can be further improved. Additionally, expanding the system to accommodate
various types of drones, such as fixed-wing and hybrid VTOL (vertical take-off and landing) drones, will greatly
enhance its versatility in sectors like logistics, surveillance, agriculture, and disaster management. One
promising direction is the integration of real-time environmental data, including wind patterns, air pressure,
and temperature, which would allow drones to adapt their flight behaviour in real-time. Furthermore, working
together with smart city systems could help manage drone traffic more effectively in bigger cities, connecting
drones with ground and air transportation networks. Investigating energy-efficient swarm behaviours and
battery optimization techniques would be essential for prolonging mission durations and extending operational
ranges. In summary, the anti-collision drone traffic control system utilizing swarm technology serves as a crucial
initial step towards the creation of autonomous, intelligent, and secure drone ecosystems. Through ongoing
innovation and strategic improvements, this system has the potential to transform aerial transportation and
establish new benchmarks for autonomous traffic management in the skies.
Funding Declaration
This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-
profit sectors.
Data Availability Statement
The datasets and source code used to support the findings of this study are available from the corresponding
author upon reasonable request.
Conflict of Interest
There is no conflict of interest.
Artificial Intelligence (AI) Use Disclosure
The authors declare that artificial intelligence (AI)-assisted tools were used only for language refinement,
grammar improvement, and manuscript structuring purposes during the preparation of this work. All technical
content, experimental implementation, results, and interpretations were independently developed and verified
by the authors.
Supporting Information
Not applicable.
References
[1]
A. Tahir, J. Böling, M. H. Haghbayan, H. Toivonen, J. Plosila, Swarms of unmanned aerial vehicles - a survey,
Journal of Industrial Information Integration, 2019, doi: 10.1016/j.jii.2019.100106.
[2]
M. R. Rezaee, N. A. W. A. Hamid, M. Hussin, Z. A. Zukarnain, Comprehensive review of drones collision
avoidance schemes: challenges and open issues, IEEE Transactions on Intelligent Transportation Systems,
2024, 25, doi: 6397-6426, doi: 10.1109/TITS.2024.3375893.
[3]
E. Şahin, Swarm robotics: from sources of inspiration to domains of application, In Proceedings of the
Swarm Robotics Workshop, Santa Monica, CA, USA, 17 July 2004, Springer: Berlin/Heidelberg, Germany,
2005, 1020.
[4]
L. Bayındır, A review of swarm robotics tasks, Neurocomputing, 2016, 172, 292321, doi:
10.1016/j.neucom.2015.05.116.
[5]
H. Yao, Rongjun Qin, X. Chen, Unmanned aerial vehicle for remote sensing applicationsa review, Remote
Sensing, 2019, 11, 1443, doi: 10.3390/rs11121443.
[6]
V. U. Castrillo, A. Manco, D.Pascarella, G. Gigante, A review of counter-UAS technologies for cooperative
defensive teams of drones, Drones, 2022, 6, 65, doi: 10.3390/drones6030065.
[7]
G. E. M. Abro, S. A. B. M. Zulkifli, R. J. Masood, V. S. Asirvadam, A. Laouti, Comprehensive review of UAV
detection, security, and communication advancements to prevent, Drones, 2022, 6, 68, doi:
10.3390/drones6100284.
[8]
M. Brambilla, E. Ferrante, M. Birattari, M. Dorigo, Swarm robotics: a review from the swarm engineering
perspective, Swarm Intelligence, 2013, 7, 141, doi: 10.1007/s11721-012-0075-2.
[9]
A. Singh, G. Singh Malhi, T. Singh, G. S. Bhatia, Swarm robotics: a review from mechanical engineering
perspective, International Journal of Advanced Engineering Research and Applications, 2020, 5, 120-127, doi:
10.46593/ijaera.2020.v05i11.001.
[10]
S. Min, H. Nam, ACACT: Adaptive collision avoidance algorithm based on estimated collision time for swarm
UAVs, IEEE Access, 2023, 11, 11, doi: 10.1109/ACCESS.2023.3327928.
[11]
G. Vásárhelyi, C. Virágh, G. Somorjai, N. Tarcai, T. Szörényi, T. Nepusz, T. Vicsek, Outdoor flocking and
formation flight with autonomous aerial robots, International Conference on Intelligent Robots and Systems,
2014, 38663873, doi: 10.1109/IROS.2014.6943105.
[12]
Y. Xue, L. Wang, L. Li, Research on automatic recharging technology for automated guided vehicles based
on multi-sensor fusion, Applied Sciences, 2024, 14, 8606, doi: 10.3390/app14198606.
[13]
D. Mahmoud, M. A. Salem, H. Ramadan, M. I. Roushdy, Comparison of Optimization Techniques for 3D
Graph-based SLAM, Proceedings of the 4th European Conference of Computer Science (ECCS '13), Paris,
France, 2013.
[14]
J. Yasin, M-H. Haghbayan, J. Heikkonen, H. Tenhunen, J. Plosila, Formation maintenance and collision
avoidance in a swarm of drones, In Proceedings of the 2019 3rd International Symposium on Computer
Science and Intelligent Control (ISCSIC 2019), Association for Computing Machinery, New York, NY, USA,
Article 1, 16, doi: 10.1145/3386164.3386176.
[15]
G. De Masi, E. Ferrante, Quality-dependent adaptation in a swarm of drones for environmental monitoring,
2020 Advances in Science and Engineering Technology International Conferences (ASET), 2020, 1-6, doi:
10.1109/ASET48392.2020.9118235.
[16]
N. Ashush, S. Greenberg, E. Manor, Y. Ben-Shimol, Unsupervised drones swarm characterization using RF
signals analysis and machine learning methods, Sensors, 2023, 23, 1589, doi: 10.3390/s23031589.
[17]
E. Zaitseva, V, Levashenko, R. Mukhamediev, N. Brinzei, A. Kovalenko, A. Symagulov, A. (2023). Review of
reliability assessment methods of drone swarm (fleet) and a new importance evaluation-based method of
drone swarm structure analysis. Mathematics, 11(11), 2551.
[18]
D. Marek, M. Paszkuta, J. Szyguła, P. Biernacki, A. Domański, M. Szczygieł, M. Król, K. Wojciechowski, General
concepts in swarm of drones control: Analysis and implementation, Proceedings of the 2023 IEEE
International Conference on Big Data (BigData), 2023, 50705077.
[19]
K. Huang, J. Chen, J. Oyekan, Decentralised aerial swarm for adaptive and energy efficient transport of
unknown loads,Swarm and Evolutionary Computation, 2021, 67, 100957, doi:
10.1016/j.swevo.2021.100957.
[20]
Z. Zhang, W. Yang, Z. Shi, Y. Zhong, Hardware-in-the-loop simulation platform for unmanned aerial vehicle
swarm system: Architecture and application, Proceedings of the 2020 Chinese Control Conference (CCC),
2020, 16.
[21]
V. J. Hodge, R. Hawkins, R. Alexander, Deep reinforcement learning for drone navigation using sensor data,
Neural Computing and Applications, 2021, 33, 20152033, doi: 10.1007/s00521-020-05097-x.
[22]
O. Velasco, J. Valente, P. J. Alhama Blanco, M. Abderrahim, An open simulation strategy for rapid control
design in aerial and maritime drone teams: A comprehensive tutorial, Drones, 2020, 4(3), 37, doi:
10.3390/drones4030037.
[23]
E. Bonabeau, M. Dorigo, G. Theraulaz, Swarm intelligence: From natural to artificial systems. Santa Fe
Institute Studies in the Sciences of Complexity, Oxford University Press, 2001, 18.
[24]
F. Ducatelle, G. A. Di Caro, L. M. Gambardella, Principles and applications of swarm intelligence for adaptive
routing in telecommunications networks, Swarm Intelligence, 2010, 4, 173198, doi: 10.1007/s11721-010-
0040-x.
[25]
N. K. Chandran, M. T. H. Sultan, A., Łukaszewicz, F. S. Shahar, A. Holovatyy, W. Giernacki, Review on type of
sensors and detection method of anti-collision system of unmanned aerial vehicle, Sensors, 2023, 23, 6810,
doi: 10.3390/s23156810.
[26]
IEEE/ASME Transactions on Mechatronics, 2021 Index, IEEE/ASME Transactions on Mechatronics, 2021,
26, 14.
[27]
H. Zhu, Y. Ding, Optimized dynamic collision avoidance algorithm for USV Path Planning, Sensors, 2023, 23,
4567, doi: 10.3390/s23094567.
[28]
S. Shah, D. Dey, C. Lovett, A. Kapoor, AirSim: High-fidelity visual and physical simulation for autonomous
vehicles, arXiv preprint, 2017, arXiv:1705.05065, 10.48550/arXiv.1705.05065.
[29]
S. Min, H. Nam, ACACT: Adaptive collision avoidance algorithm based on estimated collision time for swarm
UAVs, IEEE Access, 2023, 11, 120179120191, doi: 10.1109/ACCESS.2023.3327928.
[30]
X. Liu, H. Liu, K. Zheng, J. Liu, T. Taleb, N. Shiratori, AoI-minimal clustering, transmission and trajectory co-
design for UAV-assisted WPCNs, IEEE Transactions on Vehicular Technology, 2025, 74, 10351051, doi:
10.1109/TVT.2024.3461333.
[31]
O. S. Oubbati, M. Atiquzzaman, H. Lim, A. Rachedi, A. Lakas, Synchronizing UAV teams for timely data
collection and energy transfer by deep reinforcement learning, IEEE Transactions on Vehicular Technology,
2022, 71, 66826697, doi: 10.1109/TVT.2022.3165227.
[32]
C. Lee, S. Lee, T. Kim, I. Bang, J. H. Lee, S. H. Chae, Multi-agent deep reinforcement learning-based multi-UAV
Path planning for wireless data collection and energy transfer, 2024 Fifteenth International Conference on
Ubiquitous and Future Networks (ICUFN), Budapest, Hungary, 2024, 500-504, doi:
10.1109/ICUFN61752.2024.10625275.
[33]
C. Qin, A. Robins, C. Lillywhite-Roake, A. Pearce, H. Mehta, S. James, T. H. Wong, E. Pournaras, M-SET: Multi-
drone swarm intelligence experimentation with collision avoidance realism, Proceedings of the 49th IEEE
Conference on Local Computer Networks (LCN), 2024, 17.
[34]
D. Marek, P. Biernacki, J. Szyguła, A. Domański, M. Paszkuta, M. Szczygieł, M. Król, K. Wojciechowski,
Collision avoidance mechanism for swarms of drones, Sensors, 2025, 25, 1141, doi: 10.3390/s25041141.
[35]
E. Ferrera, A. Alcántara, J. Capitán, A. R. Castaño, P. J. Marrón, A. Ollero, Decentralized 3D collision avoidance
for multiple UAVs in outdoor environments, Sensors, 2018, 18, 4101, doi: 10.3390/s18124101.
[36]
E. Aldao, L. M. González-de Santos, H. González-Jorge, LiDAR based detect and avoid system for UAV
navigation in UAM corridors, Drones, 2022, 6, 185, doi: 10.3390/drones6080185.
[37]
X. Lan, W. Chen, J. Huang, Z. Han, Path planning and collision risk management strategy for multi-UAV
systems in 3D environments, Drones, 2022, 6, 35, doi: 10.3390/s21134414.
[38]
M. Manzoni, R. Rubinacci, D. Invernizzi, Efficient motion primitives-based trajectory planning for UAVs in
the presence of obstacles, Drones, 2024, 8, 256, doi: 10.3390/drones8060256.
[39]
C. Wyard, B. Beaumont, T. Grippa, E. Hallot, UAV-based landfill land cover mapping: optimizing data
acquisition and open-source processing protocols, Drones, 2022, 6, 123, doi: 10.3390/drones6050123.
[40]
F. Zhao, Y. Zeng, B. Han, H. Fang, Z, Zhao, Nature-inspired self-organizing collision avoidance for drone
swarm based on reward-modulated spiking neural network, Patterns, 2022, 3, 100611 doi:
10.1016/j.patter.2022.100611.
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