This paper presents a comprehensive approach to the safe motion planning of autonomous unmanned aerial vehicles (UAVs) operating in multi-agent swarm formations. The increasing deployment of UAV swarms in both civil and military domains necessitate robust, scalable, and adaptable control strategies that ensure reliable group behavior under dynamic and potentially adversarial conditions. The proposed architecture integrates a multi-level optimization framework, which combines global trajectory planning with local collision avoidance. It is enhanced by reinforcement learning algorithms and safety-guaranteed maneuvering techniques. A hybrid control architecture is developed, supporting both decentralized and centralized coordination schemes, enabling agents to operate autonomously while maintaining real-time responsiveness to changes in the environment and swarm composition. Inspired by biological systems and competitive behavioral patterns observed in nature, the architecture includes adaptive roles, leader follower dynamics, and swarm clustering for obstacle avoidance and attack-defense positioning. A formal system model is defined, along with simulation algorithms for analyzing various swarm sizes and motion control strategies. The effectiveness of proportional-integral derivative parameter optimization for improving swarm dynamics is also investigated. prevent inter-agent collisions, and maintain formation integrity. The proposed solution lays the groundwork for the development of AI-driven swarm systems that can execute coordinated operations in contested environments.
Countering a large number of unmanned aerial vehicles (UAVs) is a pressing issue in the fields of security and information technologies [1]. The advances in computer electronics and their miniaturization now enable the integration of onboard networked computational and communication systems with specialized artificial intelligence into groups of autonomous unmanned systems [2], facilitating the application of intelligent information technologies to address this problem.
The use of large UAV groups is currently at the stage of empirically accumulating successful field practices, with preliminary computer simulations of group control processes (agents) based on multi-agent system models in virtual environments [3 4], including group competition [4].
Competition for resources and territorial dominance is inherent to many living organ-isms on Earth [5]. Therefore, using conflict behavior patterns from groups of living creatures as simulation scenarios for AI-controlled multi-agent systems is a rational approach that can be further implemented and tested for managing autonomous UAV groups.
In the animal world, flock control is based on a strict hierarchical principle there is a leader and subordinates who perform specific roles within the group. Control structures such as centralized leadership (in animals) and decentralized swarms are both used to model agent group control. Hybrid control models, including temporary leadership and swarm clustering for obstacle avoidance, are also applied [6]. In this paper, we define agents as virtual entities with position, velocity, and radius, following swarm movement algorithms. 1.2.
Drone a mobile unmanned device, such as UAVs, robotic systems, or ground/sea/aquatic unmanned vehicles.
Drone Group a team or swarm of drones.
Flock a group of animals, birds, fish, or other organisms that stay together.
Collective a number of drones (more than one), operating permanently to per-form joint missions/tasks without direct interaction.
Team several drones (more than one) that perform a mission/task without direct interaction.
Swarm a group of drones equipped with swarm intelligence, capable of autonomous interaction, adaptation to changing conditions, and collective decision-making with minimal or no operator intervention. 1.3.
To develop a hybrid control architecture for UAV swarms using reinforcement learning (RL), based on comprehensive multi-level optimization that integrates global trajectory planning and local collision avoidance with formal safety guarantees for emergencies. The architecture should ensure collision-free movement of agents in a dynamic 3D environment through multi-level optimization and cooperative maneuvering. Additionally, the study aims to investigate the optimization of consensus PID (Proportional-Integral-Derivative) controller parameters to improve the dynamic performance of UAV swarms and to develop corresponding algorithmic and software tools for simulating swarm movement of varying sizes under hybrid control systems. 1.4.
Section 2 reviews existing swarm control algorithms and analyzes their limitations. It also presents the general model of swarm agent motion and control, describes individual algorithms Potential Field method (PFM), Vicsek, Particle Swarm Optimization (PSO), Reynolds, and evaluates their applicability to UAV swarm control.
Sections 3 introduces the proposed hybrid architecture with multi-level optimization, including PID parameter optimization.
Section 4 presents mathematical model of a multi-agent system using CBF-based safety mechanisms, RL for emergency cases and adaptive consensus PID controllers, its structural diagram and hybrid architecture.
Section 5 presents proposed hybrid architecture and optimization strategy for UAV swarm control, including structural diagram of a swarm oriented multi-agent system, hybrid strategy and architecture for safe UAV swarm control.
Section 6 reports the results of numerical experiments and compares the proposed system with classical swarm control methods.
Section 7 concludes the paper and outlines future research directions, including the study of 1.5.
This paper addresses the problem of safe autonomous UAV swarm control under conditions of aggressive interaction and complex dynamic environments. The key contributions are development of a general model of swarm agent motion based on multi-agent dynamics and inter-agent interaction functions; critical analysis of existing swarm control methods (PFM, Vicsek, PSO, Reynolds) and identification of their limitations with respect to safety and controllability; proposal of a hybrid architecture that integrates Model Predictive Control, Control Barrier Functions, adaptive consensus-based PID controllers, and Reinforcement Learning for emergency maneuvers; design of a multi-level optimization strategy that combines global trajectory planning, local collision avoidance, and cooperative maneuvering with formal safety guarantees and implementation of numerical experiments, confirming zero collisions in dense swarm formations and demonstrating the superiority of the proposed system in swarm vs. swarm" scenarios compared to classical algorithms.
In the field of AI ontology, collective decision-making algorithms are part of swarm intelligence [7]. Computer modeling of UAV collective behavior uses multi-agent technologies, along with Information and Communications Technology solutions, to enable distributed computing.
Competitive behavior of biological collectives in resource and territory conflicts includes: reconnaissance (including combat reconnaissance), deep raids into enemy territory, frontal attacks, flanking and encircling maneuvers, military deception (e.g., diversionary tactics, feigned retreat), enemy force dispersion (multi-directional attacks), wave attacks (rotational assaults), blocking enemy retreat (encirclement or siege) and tactical adaptation via route updates based on information exchange.
Multi-agent AI technologies allow modeling of autonomous agent collectives as self-organizing swarms or leader-controlled flocks using ad hoc radio networks. Agents collaboratively solve tasks such as directional movement, obstacle avoidance, and spatial positioning for attack or defense [8]. Therefore, control of agents in swarm/flock formations requires navigation algorithms that maintain acceptable positioning accuracy to prevent collisions and preserve group cohesion. 2.1.
The basis of agent swarm behavior lies in the principles of cohesion, alignment, and separation (the Reynolds model) [9]. These are supplemented by collision avoidance strategies with static and dynamic obstacles and task-specific behavioral patterns (attack, defense, evasion, reconnaissance, deception, and others).
The swarm consists of N agents A1,A2,...,AN, each of which is characterized at any given moment by:
Position vector:
xi(t)∈R3
vi(t)∈R3
(
The movement of agents occurs in a limited three-dimensional space that may include static and
dynamic obstacles. The motion of the agents is governed by the following differential equation:
˙ = ( , ), (
= ( , ) = ∑ ∈ ( , ) where wi are the weight coefficients, Fi, zi are the forces acting on agent i:
= ∑ ∈ ℎ( ) (
The collective dynamics of a system comprising N agents are described by the following system of differential equations:
˙1 = ( 1, 1)
{ ˙2 = ( 2, 2) (
⋮ ˙ = ( , )
The proposed general model captures the motion of a multi-agent system and the control of a swarm of agents, accounting for both inter-agent interactions and individual dynamics. The functions , , and ℎ are defined according to the specific characteristics of the system and the prescribed interaction rules. Previous studies by the authors [9] have demonstrated that existing algorithms and methods for modeling group agent motion exhibit several limitations, raising concerns regarding their suitability for controlling agent groups in counter-swarm operations. The developed general model of group motion and multi-agent system control is employed to analyze the limitations of existing models describing the motion of agent groups.
Let us examine the limitations of the PFM, the Vicsek algorithm, PSO algorithm, and the
Reynolds algorithm in the context of their application to UAV swarm control under stringent
collision-avoidance requirements.
(
In PFM, each agent is influenced by artificial forces generated by virtual potential fields [10]. An
attractive potential toward the target and repulsive potentials from obstacles and other agents are
for an agent is defined as the gradient of the potential function:
=
+
= −
( ) = − (
( ) +
( )),
(
From the perspective of absolute safety and UAV swarm control, the PFM has inherent limitations. The presence of local minima in the force field can trap agents, preventing target acquisition and increasing the risk of collisions, which in swarm motion may cause delays, formation disruption, or partial immobilization.
The Vicsek model was developed to simulate the collective behavior of self-propelled particles in a simple way [11]. Each particle moves at a constant speed and, at each step, changes its direction by averaging the directions of its neighbors within a given radius, with the addition of random noise. The swarm influence vector is defined as the sum of forces acting on the agent, including alignment force and random noise:
= , + = ∑ ∈ ( − ) + , (
The Vicsek model of swarm motion, when applied to UAV swarm control, has several inherent limitations. It is primarily oriented toward achieving global order through direction alignment and lacks explicit rules or mechanisms for preventing physical collisions between agents. As a result, collisions remain possible, particularly at high agent densities or in conditions with substantial noise. 2.4.
PSO PSO is a metaheuristic optimization algorithm inspired by the social behavior of birds in flocks or fish in schools. PSO algorithm has been applied to a wide range of optimization problems and can be adapted for swarm control applications [12]. Each agent in the swarm moves under the influence of a balance between its best-found position and the best position found by the entire swarm for that agent.
In PSO algorithm, the sum of the force vectors acting on each agent can be explicitly expressed. These forces include the inertia force, the attraction force toward the personal best position, and the attraction force toward the global best position.
For each agent , the resulting control force is the sum of three components: = , + , + ,
(
In the Reynolds algorithm, each agent is influenced by three main forces: Separation force sep: determines the intensity of collision avoidance with neighbors. Alignment force align
Cohesion force coh: attracts the agent toward the center of mass of its neighbors to maintain swarm cohesion.
The resulting force acting on an agent can thus be expressed as:
= , +
, +
,
(
Let us consider the main disadvantages of the Boids algorithm from the perspective of UAV swarm control. The standard Boids model exhibits several limitations with respect to absolute safety in UAV swarm control. Its reactive nature means that agents respond only to the current positions, velocities, and proximity of neighbors, without predicting future motion trajectories, which can be insufficient to prevent collisions in dynamic environments with high speeds or complex maneuvers. Additionally, groups of agents governed solely by Boids rules may become trapped in locally stable configurations that carry latent collision risks. Conflicts between cohesion and alignment rules may further compromise safety, particularly if rule parameters are not optimally tuned. Finally, the standard Boids model lacks explicit mechanisms for predicting collisions and planning avoidance maneuvers.
In summary, while each of the considered algorithms offers advantages in specific contexts, their direct application to UAV swarm control, where zero-collision performance is critical, presents significant challenges. PFM may lead to agent trapping and does not guarantee safety. The Vicsek model focuses on global alignment, ignoring collisions. PSO is an optimization algorithm and requires specific extensions to enable motion control with real-time safety guarantees. Achieving zero collisions in a dynamic UAV swarm, while preserving controllability and task performance efficiency, is not feasible using algorithms based solely on simple reactive rules or general optimization approaches. This requires the development of hybrid approaches or specialized algorithms that combine proactive prediction, formal safety assurance methods, e.g., Control Barrier Functions (CBF), Reachability Analysis (RA) with optimization of UAV motor controller parameters, enabling the implementation of effective cooperative maneuvering strategies.
A key challenge in integrating multiple real-world technical systems is the potential degradation of their original qualitative and quantitative performance metrics and characteristics. For UAV swarms, such subsystems include the flight controller and the PID controller [14], which directly controls the motors, as well as the autonomous swarm navigation program. Simulation of flight simulation software.
For initial flight performance testing of UAVs, three test trajectories are used: a circle, a figureeight (lemniscate), and a zigzag. Numerical experiments have shown that the relative deviation values for the lemniscate and circle are approximately the same. For the zigzag trajectory, its step and amplitude must be known precisely, as they are specific to the motion of certain UAV types and are useful for determining UAV inertial characteristics during sharp maneuvers a task outside the scope of this work. Accordingly, in the subsequent discussion, PID controller parameter optimization will be tested for simulated agent motion along a circular path.
To demonstrate the effect of PID controller parameter optimization on deviations from the ideal 3.1.
The mathematical model of the drone motor controller is described by second-order differential equations for coordinates x and y. Let the drone move in a circle of radius r and angular velocity . Then, the equations for the ideal trajectory (circle) are as follows [14]: ( ) = ( ), ( ) = ( )
The optimization criterion consists of minimizing the RMSD from the ideal trajectory, described by the following loss function [15]:
= ∫0 {[ ( ) − ( )]2 + [ ( ) − ( )]2} and is defined as [14]: (23) (34) (56) where ex(t) and (t) are the position errors of the drone in space relative to the values obtained from the solution of the problem.
The solution to the optimization problem is a set of PID controller parameters ( , , ) that minimize the loss function , thereby achieving the smallest possible RMSD from the ideal trajectory. The algorithm for solving the PID parameter optimization problem was based on the gradient descent method. The results of the numerical experiments are summarized in Classical
Classical PID controller, circular motion, parameters, deviation Non-optimized PID parameters
Kp=2.0,Ki=0.1,Kd=0.5 Mean deviation: 0.4475 Max deviation: 1.0101 Kp=10.0,Ki=0.0,Kd=5.0
The left graph illustrates the movement without optimization, while the right graph shows the movement with optimization according to the RMSD criterion. The optimization significantly reduces the deviation from the ideal trajectory. Similar numerical experiments were conducted for fractional and robust controllers [16]. The average error before optimization was about 15%, and after optimization 2.5%. Thus, PID parameter optimization reduced the trajectory deviation by approximately a factor of 6. This means that developing a multi-level algorithmic framework for group agent control without consensusbased PID parameter tuning can degrade the controllability and safety of flock movement or cooperative swarm maneuvering when implemented on real UAVs.
However, this may still be insufficient. To ensure collision avoidance within the swarm, additional safety mechanisms must be implemented, in particular, the CBF method.
Performing rapid aerodynamic maneuvers in swarm movement scenarios target pursuit or swarm-scale evasive action
requires a theoretically guaranteed ability to minimize collisions, i.e., ensuring that agents never leave the set of safe states. 4.1.
Since the 2010s, Barrier Functions (BFs) have been used in robotics to mathematically formalize safety in terms of maintaining minimum distances between agents in constrained systems [17]. CBFs are an extension of these functions for controlled systems, where the motion controller actively maintains safety [18]. The concept of combining CBFs with Model Predictive Control (MPC) for robotics [19] gained traction in 2018, and CBFs became widely integrated into modern robotics between 2020 2023, with applications in autonomous vehicles, robotic manipulators, and swarm robotics.
Functionally similar to CBFs are Optimal Reciprocal Collision Avoidance (ORCA) algorithms, which provide weaker mathematical guarantees and are therefore considered as auxiliary solvers in cases where the CBF method cannot find a feasible solution.
We now present a mathematical model and a concise problem formulation for applying CBFs to ensure the safety of UAV motion. For each pair of neighboring UAVs, a barrier function is defined that becomes zero when the distance between them reaches a predefined safety threshold. The safety condition (imposed on the derivative of the barrier function) constrains the set of admissible control actions for each UAV, guaranteeing that the safety distance will never be violated.
Problem statement for optimizing the movement of a group of agents. 4.2.
We consider a multi-agent system with N agents, where each agent ∈ } has: State ( )=[ ( ), ( )] (position and velocity of the agent at time ); Local PID controller with parameters =[ , ,
, , , ] ;
Data exchange with neighboring agents through a network described by an undirected connectivity graph =( , ), where is the set of vertices and is the set of edges, }. 4.3.
The objective function describes a joint minimization of the deviation of the current state of each parameters from the consensus values, according to a quadratic criterion:
= ∫ [∑ =1 ( ‖ ( ) − , 0
2 ‖ + ‖ ( )‖2 + ‖ ( ) − ~( )‖2)] (17) (18) (19) (20) where , , are weighting coefficients; xi,goal is the target position of agent ; ( ) is the control input; is the planning horizon; (t) is the consensus PID parameter vector: ~( ) = 1 ∑
=1 ( ) 4.4.
enforcement using CBF.
The agent dynamics are described by: where The PID control law is: where ( ) is the control error.
Constraints include agent motion dynamics, PID parameter adjustment, and safe motion ˙ = ( , ), =
( , ) ( ) = ( ) + ∫0 ( ) 4.5.
The barrier function ensuring a minimum safe separation to avoid collisions: ℎ¨ ( , ) + ℎ˙ ( , ) + ℎ( , ) ≥ 0
2 ℎ¨ ( , ) = 2‖ − ‖ + 2( − ) ( − ) problem feasibility: where are adjacency matrix elements of , >0 is the learning rate, and ˙ = − ∑⬚=1 ( − ) +
( , , ) ( , , ) = ‖ ‖2 + ‖ ‖2 + ‖ − ~‖2 i, i >0 are regularization coefficients. 4.6.
The safety conditions are based on the second-order derivative of the CBF:
Since the safety inequality is linear in and , it can be solved as a quadratic programming problem to find safe control inputs. 4.7.
Developing hybrid and specialized algorithms that guarantee safe agent motion is a complex interdisciplinary task involving control theory, optimization theory, formal verification methods, and swarm dynamics. This approach is key to achieving the ambitious goal of guaranteeing zero collisions in autonomous UAV swarms.
The basis of proposed hybrid architecture is the structural diagram of a swarm oriented multiagent system for a multi-agent control.
where where 5.1. multi
Data received from other agents is used to check global trajectory compliance, build a shortterm motion prediction model, and update the group PID consensus algorithm. With it: other swarm agents. Low threat: PID parameters are synchronized with nearby agents using a swarm consensus algorithm. Medium threat: PID parameters are optimized using CBFs, local routing, trajectory prediction, and obstacle motion prediction algorithms.
ℎ( , ) ≤ 0, ∀( , ), ≠ ℎ( , ) = ‖ − ‖ − ( + + 2
2 ) ≥ 0 ri, rj are the safety radii of agents and , and safe is the minimum safe distance.
Consensus conditions for PID parameters have lower priority than safety constraints to ensure (21) (22) (23) (24) (25) (26) Agent sensors
Low Collision risk assessment algorithm High Agent PID controller
Agent Group PID Consensus Algorithm
Average CBF, local routing, trajectory prediction Wireless Multi-Agent System
Agent
i Data exchange algorithm in a
group of agents Checking compliance with the global trajectory Local agent motion prediction model
Global level trajectory planning using MPC and Rapidly-exploring Random Tree Star (RRT*). Local level collision avoidance based on CBFs and adaptive PID controllers.
Emergency level RL, specifically Q-learning, for critical maneuvers.
The safety system classifies situations into four risk levels: Normal, Warning, Threat, and Critical.
Main modules and algorithms: 1. Trajectory prediction: Estimates future UAV positions over a 5-step horizon considering control actions and neighbor responses.
Multi-level safety logic: Risk levels determined based on predicted minimum distances, ensuring early responses without false alarms.
Adaptive PID tuning: , , dynamically change according to risk and past maneuver efficiency, preventing conflicts between trajectory tracking and collision avoidance.
Cooperative maneuvering: Coordinated changes in altitude or direction based on priority (agent ID, threat detection time, etc.).
Communication loss handling: In case of signal loss, the agent continues with avoidance maneuvers based on the last known neighbor data, preserving formation after reconnection.
Boundary reaction: Instead of abrupt stopping, UAVs smoothly change direction while staying inside operational space, coordinating maneuvers with other agents.
The proposed hybrid architecture enables a comprehensive multi-level optimization strategy for the safe movement of agent groups. 5.3.
Global planning MPC and RRT* build trajectories considering speed constraints and obstacles.
Local optimization CBF ensures safe distances, while PID provides stabilization and trajectory tracking.
Emergency maneuvers RL Q-table controls discrete actions in critical situations.
Cooperative coordination Control parameters are collectively tuned via consensus mechanisms to improve robustness and energy efficiency.
The implemented technologies are summarized in Table 3 for a better understanding of the levels of comprehensive optimization for group safety.
It is also necessary to determine which trajectory computation approach should be used. Both centralized and decentralized computation can be applied, so both are considered:
Centralized A single controller calculates all trajectories (using MAPF: Multi-Agent Path Finding) to coordinate movement. This is suitable for small swarms but lacks scalability.
Decentralized Each agent plans its motion using local data and partial information from neighbors. This approach provides scalability and fault tolerance but makes it harder to guarantee global route optimality.
A compromise between centralized and decentralized approaches can be achieved through hierarchical coordination: Global planning sets goals and routes.
Local agents adapt movement in real time according to threats.
Subgroups of agents coordinate actions via elected leaders.
We now present numerical experiments for the multi-level agent motion control system and compare its performance with established algorithms and methods for group control. The study multi-level optimization of safe UAV motion was performed in a "swarm vs swarm" scenario. 6.1.
Assess the efficiency of the combined multi-level optimization strategy for safe and coordinated drone movement in an environment with an opposing swarm. 6.2.
Number of drones: 10 in each swarm.
Simulation field: 100×100 units.
Blue swarm objective: reach a gathering point in sector B, avoiding collisions, threats, and detection.
Constraints: jamming zones, no-fly areas, dynamic obstacles.
The structure of multilevel optimization is presented in Table 3.
Selection of overall swarm trajectory (route segments, target priorities)
Distribution of subgroups and individual drone paths within the chosen route
Real-time obstacle avoidance based on sensor data 6.3.
We used the following metrix: Average distance between drones (swarm cohesion); Number of collisions or entries into risk zones; Time to reach the target; Percentage of detected/intercepted drones; Energy consumption per agent.
The multilevel optimization model, which integrates global strategic planning with local threat avoidance, demonstrates high efficiency in swarm-versus-swarm scenarios. This approach enables drones to achieve mission objectives with a higher probability while simultaneously reducing incidents and resource consumption. Thus, numerical experiments confirmed that the multi-level system achieves zero collisions in dense formations a key indicator of its effectiveness. This is achieved through the integration of MPC, CBF, adaptive PID, and RL, which provide proactive prediction and formal safety guarantees. 6.4.
The analysis identified the limitations of existing group control algorithms (Table 4):
PFM prone to local minima, oscillations near obstacles, and no formal collision avoidance guarantees. Vicsek model lacks explicit collision avoidance, unpredictable behavior due to noise. PSO not a direct control algorithm, lacks collision avoidance mechanisms. Boids model reactive, susceptible to local optima, lacks explicit collision prediction. Unlike these, the proposed system provides formal safety guarantees through CBF and proactive collision avoidance, making it a superior choice for tasks such as "swarm vs swarm". For the simulations conducted in the Google Colab environment, the following algorithms were used: Hybrid CBF-PID algorithm (Control Barrier Function + PID) a collision-avoidance algorithm that uses optimization constraints to guarantee the maintenance of a safe distance, achieved by combining an adaptive PID controller with barrier functions. Classical collision-avoidance algorithms: Boids, Vicsek, PFM, PSO; Algorithms without collision avoidance: Leader-Follower one agent (leader) moves toward the target, while the others (followers) attempt to follow; the algorithm lacks explicit collisionavoidance mechanisms. Random-Walk the simplest algorithm, in which agents move in random directions with speed adjusted to a fixed value. In the simulation, 1,000 agents with movement constraints were used, and 200 steps of the algorithmic suite were executed (Optimization structure in the simulation).
The agents followed the following trajectory models: CBF-PID swarm agents move along smooth parallel lines with guaranteed spacing. Boids random deviations but may create clusters. Vicsek all agents move in the same average direction. Potential Field generates curvilinear paths for agents. Leader-Follower straight-line motion of the leader, with followers trailing behind. Simulation results show that the classical Boids and Vicsek algorithms with collision-control mechanisms can produce high-quality results using minimal computational power in the absence of mobile obstacles. However, they do not provide safeguards against agent collisions. CBF-PID requires significantly higher computational resources but guarantees zero collisions.
The implementation of safe, real-time autonomous big scale UAV swarm control is a critical challenge for practical deployment in complex environments. Abandoning standard Boids rules or significantly modifying them and developing custom swarm control rules is a justified and potentially highly effective approach for achieving zero collisions while maintaining coordinated swarm motion. One scientific problem requiring resolution is the multi-agent modeling of
This work addressed the problem of decentralized collective collision avoidance for a group of agents using predictive planning, adaptive control, and optimization methods with safety guarantees. For the first time, a hybrid control architecture for UAV swarms was proposed, based on comprehensive multi-level optimization that combines global trajectory planning and local collision avoidance with formal safety guarantees. The developed system integrates Model Predictive Control, Control Barrier Functions, adaptive consensus-based PID controllers, and Reinforcement Learning for emergency situations. The proposed approach ensures zero collisions for agent motion in a 3D dynamic environment through multi-level optimization and cooperative maneuvering. We propose a new collision avoidance strategy for swarms of agents that leverages control barrier functions in conjunction with a local adaptive consensus scheme for the dynamic adjustment of PID controller parameters.
In addition, algorithmic and software tools were developed to simulate UAV swarm motion of varying sizes with hybrid control systems. Computational experiments demonstrated zero collisions for tightly packed formations. The result is a comprehensive multi-level optimization system for safe group motion of agents, aimed at solving the collision problem during aggressive maneuvers in contested environments and during obstacle avoidance.
During the preparation of this work, the authors used ChatGPT in order to grammar and spelling
check.
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