In this paper, a hybrid approach for coordinating autonomous agents is proposed, combining swarm intelligence based on the GBestPSO (Global Best Particle Swarm Optimization) algorithm and behavior trees (BTs). This approach aims to solve the problem of balancing global coordination of actions and local autonomy of each agent in dynamic and uncertain environments. The proposed two-level control system architecture consists of a planning level (GBestPSO-Level) for global optimization and a behavior level (BTLevel) for tactical behavior. The results were partially supported by the National Research Foundation of Ukraine, grant No. 2025.06/0022 "AI platform with cognitive services for coordinated autonomous navigation of distributed systems consisting of a large number of objects".
Modern systems with collective interaction of autonomous agents are attracting increasing attention
from researchers due to their ability to solve complex tasks in environments with a high level of
uncertainty [
Traditional centralized approaches, which assume the existence of a single controller, often prove
ineffective in dynamic environments where there is a possibility of communication loss, system
failure, or the emergence of new obstacles. In contrast, decentralized methods inspired by natural
models of collective behavior, such as swarms of insects or flocks of birds, demonstrate significantly
greater resilience and flexibility. One of the most common tools in this class is the Particle Swarm
Optimization (PSO) algorithm, which allows agents to collectively find effective solutions by
exchanging local and global information [
However, PSO alone does not provide a high level of cognition for an individual agent. It allows
determining the direction and trajectory of movement, but does not provide a flexible mechanism
for decision-making in situations where environmental conditions, unforeseen events, or complex
interaction scenarios must be considered. In this context, the use of behavior trees (BT) [
The combination of PSO and BT forms the basis of a hybrid approach in which swarm
optimization is responsible for global coordination and trajectory optimization, while behavior trees
are responsible for local decision-making and tactical responses of agents [
This work pays particular attention to the application of a modified GBestPSO algorithm, which
is supplemented by mechanisms of self-organization and adaptation to the influence of external
factors that disrupt coordination [
To verify the effectiveness of the proposed approach, two application scenarios are considered. ability to coordinate a collective attack, ensuring synchronization of actions and achievement of the goal. The second is reconnaissance of enemy territory, illustrating the effectiveness of the method in space allocation tasks and avoiding duplication of actions while maintaining global coordination. Both scenarios confirm that the integration of PSO with behavior trees creates the basis for a more robust and flexible control architecture in multi-agent systems.
Thus, the research aims to substantiate and demonstrate the capabilities of a hybrid approach combining swarm intelligence and behavior trees as a promising direction for the development of technologies for coordinating autonomous agents in complex and dynamic environments.
Research into the collective behavior of autonomous agents combines biological inspiration,
optimization methods, and engineering approaches. Many models are based on the idea of
selforganization, borrowed from observations of animal-flocks of birds, colonies of ants, or swarms of
insects [
One of the most popular paradigms is Particle Swarm Optimization (PSO), proposed by Kennedy
and Eberhart in 1995 [
Other swarm algorithms, such as Ant Colony Optimization (ACO) [
Further modifications of swarm algorithms, such as Firefly Algorithm [
In the early stages of multi-agent system development, simpler approaches were actively used.
The Boids model, proposed by Reynolds in 1987, was the first simulation of bird flock behavior based
on three simple rules: alignment, collision avoidance, and attraction to the center of the group [
Another direction of development is consensus algorithms, which focus on achieving a coordinated state among all agents through iterative information exchange. They scale well and have proven effective in synchronization tasks but have limited functionality in dynamic environments where not only coordination, but also adaptive strategy change is required.
The leader-follower model, which places responsibility on a key agent, has similar problems [
Recent years have been marked by the active introduction of deep reinforcement learning (DRL)
methods into multi-agent systems [
Despite its high potential effectiveness, DRL faces a few limitations. First, training requires
millions of episodes, making it unsuitable for rapid deployment in the field. Second, the models are
fication of autonomous systems. Third,
high computational costs make them unsuitable for implementation on resource-constrained robots
without powerful GPUs or TPUs [
Behavior trees (BTs) have become one of the most promising methods for building control
architectures in robotics [
BTs allow you to describe behavior through a combination of control nodes and actions that form a tree with a clearly defined execution logic. Their key advantages are: • • • • ease of reusing individual subtrees in different tasks ability to easily extend the structure with new nodes without complete redesign absence of a single critical element, even with the loss of individual agents ability to rebuild behavior logic during mission execution.
In decentralized architectures, BTs allow each agent to make local decisions, coordinating with neighbors only at the level of exchanging minimal information. This makes them suitable for largescale systems where centralized control is impossible.
A review of the literature shows that none of the approaches is universal. Swarm optimization algorithms are good at global planning and search, but do not provide flexible reactive behavior. Conversely, BTs make it easy to model local adaptability and cognitive autonomy but lack mechanisms for global optimization.
That is why modern research shows a tendency toward integrating different methods. For
example, PSO or GBestPSO can determine the optimal location or distribution of tasks among agents,
after which local execution is coordinated through BTs [
Thus, the current state of research in the field of collective behavior of autonomous agents can be characterized as a gradual transition from monolithic approaches to composite architectures that 129 combine the strengths of different methods. Among them, the integration of GBestPSO for global search and BTs for local autonomy attracts particular attention. This approach not only solves the problems inherent in each of the methods separately but also forms a new level of stability and adaptability necessary for building multi-agent systems capable of functioning in real, unpredictable conditions.
Effective coordination of autonomous agents in a dynamic and resource-constrained environment requires a multi-level control system capable of combining global planning with local reactive behavior. The proposed architecture is based on the integration of two approaches: Behavior Trees (BTs), which provide modularity and flexibility at the tactical level, and the GBest Particle Swarm Optimization (GBestPSO) algorithm, which is responsible for the strategic coordination of the entire system.
The architecture has a two-level structure (Fig. 1): the planning level (GBestPSO-Level) and the behavior level (BT-Level).
The planning level (GBestPSO-Level) acts as a global optimizer that forms the strategic basis of the mission. Its main functions are:
Optimization of the global configuration of the swarm. The GBestPSO algorithm periodically calculates the best location of agents in space, considering goals and constraints. Distribution of tasks and roles. Each agent is assigned a subtask that corresponds to its capabilities and the strategic goals of the system.
Scenario planning. In complex missions, it is possible to form several scenarios of events with the subsequent selection of the optimal one.
Replanning. In the event of significant changes in the environment (for example, the emergence of new threats or obstacles), GBestPSO is restarted to correct the strategic plan. the group of agents and coordinates their actions. Unlike centralized approaches, the architecture ly sent to agents, rather than as a real-time directive. This allows the system to remain stable even during temporary communication failures.
The behavior level (BT-Level) determines the individual tactical behavior of each agent, which is equipped with a behavior tree. This level includes the following modules: • • • • •
Behavior Manager. Performs real-time interpretation of the behavior tree, activates local actions, and rebuilds logic when conditions change.
Perception Module. Provides sensor data processing, object recognition, and local environment mapping.
Local Planner. Responsible for low-level navigation obstacle avoidance, local SLAM, trajectory correction.
Adaptation Module. Allows dynamic restructuring of the behavior tree in case of agent loss, role change, or communication interruption.
Communication Module. Implements information exchange with other agents, including the transmission of states, positions, and parts of the behavior tree.
BT-level provides instant responsiveness to environmental events and allows agents to remain operational even when communication with the planning level is lost.
Thus, GBestPSO provides global coordination, while BTs ensure local autonomy. Their interaction is organized through standardized messaging protocols, allowing the system to remain functional even in the event of partial communication loss.
The connection between the planning and behavior levels is organized in such a way as to avoid agents' dependence on a single source of information. The algorithm can be described as follows: Swarm Optimizer (at the GBestPSO level) calculates the globally best strategy (gBest) and transmits it as a message, and BT-level perceives this information as external mission conditions, which are reflected in the tree branches.
In the event of a change in global strategy, the local behavior of agents is automatically adjusted. If communication with the planning level is lost, agents act based on the last received reference point, maintaining the ability to complete the mission. To distinguish between critical and auxiliary data, channels with different priority levels are used: messages about strategy changes have a higher : agents remain autonomous but can quickly integrate new information when it becomes available.
The proposed two-level architecture has some key advantages: • • • • •
Each agent can work without being constantly connected to the global planner.
Behavior trees are easy to modify and scale for different missions.
The system remains operational even if individual agents are lost or communications are temporarily disrupted.
The architecture allows new algorithms to be integrated without the need for a complete system overhaul.
It is suitable for a wide range of applications, from reconnaissance and escort to attack scenarios or search and rescue operations.
Thus, the architecture based on the combination of GBestPSO and BTs provides a balance between global optimization and local adaptability. It demonstrates the ability to work effectively in conditions of uncertainty, high environmental dynamics, and limited resources. The use of a hierarchical approach makes the system fault-tolerant, modular, and suitable for a variety of collective interaction scenarios.
Unmanned Aerial Vehicles (UAVs) were selected as autonomous agents for the study. The simulation model is based on a hybrid architecture that combines swarm optimization methods (GBestPSO) for dynamic modelling of drone trajectories and the Behavior Trees (BT) framework for implementing adaptive and fault-tolerant control logic. Each UAV functions as an autonomous agent controlled by its own behavior tree, which cyclically processes the current mission status and external influences. 4.1.
This scenario simulates a coordinated attack by a swarm of drones on a stationary target, consisting of two consecutive phases: approach and formation of a ring of fire.
In the initial stage, the drones move toward the target using a modified swarm optimization algorithm (GBestPSO). The main difference between this algorithm and others is that the acceleration coefficients that regulate the influence of the leader ( 1) and the target ( 2) are not constants but are linearly dependent on the current distance of the drone from the corresponding object.
The equation for updating the speed of drone in direction is as follows: ( + 1) = ( ) + 1 ( ( ( ), ( ))) ∙ 1( ) ∙ [ ( ) − ( )] +
+ 2 ( ( ∗( ), ( ))) ∙ 2( ) ∙ [ ∗( ) − ( )], where coefficients 1 and 2 are calculated using the following formulas:
− 1 1 ( ( ( ), ( ))) = 2 ( ( ∗( ), ( ))) = 1 ‖ (0) − (0)‖ 2 − 2 ‖ ∗(0) − (0)‖ ∙ ( ( ) − ( )) + 1 ∙ ( ∗( ) − ( )) + 2
The UAVs follow these routes until the leader of the swarm (the UAV closest to the target) reaches the specified attack radius 0.
Once the leader reaches the target's vicinity with a radius of 0 (100 200 m), the swarm enters the phase of rotation around it. Movement in this phase is described in a polar coordinate system relative to the target, which is considered the center.
The coordinates of the leader in the Cartesian system can be calculated based on its angular position ( ) and radius 0: 1 ( ) = 0 ∙
( ( )) { 2 ( ) = 0 ∙ ( ( )) The angular position is updated at each step of the simulation using the following formula: ( + 1) = ( ) + ( )∆ where ( ) is the angular velocity of rotation. (1) (2) (3) (4) (5)
The synchronization stage of the attack is critically important and is provided through the Decorator~ node in the Behavior Tree. This node allows the final attack to begin only after a certain minimum number of UAVs ( ∗) reach orbit, ensuring a simultaneous and effective strike.
The simulation settings for this scenario are shown in Table 1.
This scenario demonstrates the capabilities of a swarm for autonomous reconnaissance, where UAVs effectively divide the search area among themselves. The simulation scenario involves coordinating a swarm of autonomous agents to conduct reconnaissance of enemy territory. Each UAV is assigned a specific area for reconnaissance. The results from all areas are combined into a common map of the terrain, which significantly speeds up the process. The main goal is to ensure complete coverage of the designated area and localization of reconnaissance targets, considering possible UAV losses and route replanning.
Let the surveyed area be defined as a rectangular region with coordinates:
The swarm consists of agents, each of which receives an individual area for exploration. Each area is defined by a strip along the -axis:
This data is transmitted to agents via a communication system.
A hybrid GBestPSO+BTs algorithm is used to plan trajectories, where: { ( + 1) = ( ) + 1( )∆ ( + 1) = ( ) + 2( )∆ where ⃗⃗⃗⃗(⃗⃗⃗⃗⃗) = ( 1( ), 2( )) is the velocity vector of UAV at iteration , and ∆ is the time step. , = + ( − 1)∆
+ ∆ , =
The swarm supervisor evaluates the coordinates of the target areas and optimizes the routes to avoid collisions and ensure minimum arrival time.
UAVs move along strips with a width of = 2 0, where 0 is the observation radius of the UAV. Movement along the axis is defined by the equation:
After reaching the upper limit of the survey area, the UAV shifts along by and returns in the 2 opposite direction to survey the adjacent strip.
Conditions for completing the survey of the area: ( + 1) = ( ) + ( )∆ ( + 1) +
≥ , 2 coefficient ( 1( ))
Communication )
) ( ) , ,
were varied. The main performance metrics were:
If some UAVs are lost or an area remains unexplored, the hybrid algorithm determines which UAVs should perform a re-survey. To do this, the position update rule is used: ( + 1) = ( ) + 1( ) 1( , − ( )) where 1( ) is the cognitive influence coefficient, and 1 ~ (0,1) is a random variable. After completing the survey, the UAVs return to their initial coordinates ( 0, 0). The simulation is configured using the parameters described in Table 2. • • • time to attack initiation (number of iterations until the minimum number of UAVs entered orbit) total attack completion time (number of iterations until all UAVs targeted the object) UAV loss during approach and attack
Value 6-12 2 0 (12)
uniformity of UAV placement in orbit (average distance between UAVs in orbit).
During each experiment, the launch of UAV from a certain area of the arena was simulated (Fig.
After launch, the UAVs were controlled by the internal BTs mechanism and moved to the target coordinates along the shortest trajectory (Fig. 3). Behavior Trees (BT)
The data shows that increasing the number of UAVs speeds up the start of the attack and reduces the time it takes to complete it due to faster formation of the orbit around the target. UAV losses remain low, indicating the stability of the behavior tree algorithm. The graph shows three stages of UAV behavior: • • •
Approaching UAVs move toward orbit On Orbit UAVs form a circle around the target
Attacking UAVs attack the target.
The next series of experiments was conducted to evaluate the effectiveness of the proposed hybrid consisted of 15 UAVs that took off from an area located on the right side of the arena and had to coordinate and gather around the target at a specified point.
The purpose of the experiment was to measure the swarm's ability to: • form a stable orbit around the target achieve a uniform angular distribution of UAVs in orbit initiate a coordinated attack when the appropriate conditions are met minimize UAV losses.
After the launch of the UAVs, the swarm leader was immediately determined (Fig. 5), which was at the shortest distance to the target's orbit.
During the movement to the target orbit, the UAVs approached the leader, forming a swarm (Fig. 6).
Upon reaching the target orbit, the swarm distributed itself along the orbit (Fig. 7).
The swarm dispersed in orbit until the minimum number of UAVs required for the attack had gathered in orbit. After that, a simultaneous attack from different directions began (Fig. 8).
The key metrics obtained during the experiments are shown in Table 5.
Figure 9 shows the evolution of the number of UAVs in different states (Approaching, Orbiting, Attacking) depending on iterations.
Three distinct phases were observed: • • •
Phase I (0 50 iterations), during which most UAVs approach the target, with a few devices beginning to enter orbit.
Phase II (50 120 iterations), when the number of UAVs in orbit steadily increases, reaching a uniform angular distribution.
Phase III (after ~120 iterations), when a coordinated attack begins, leading to a sharp decrease in the number of UAVs in orbit and an increase in attackers.
The final series of experiments was conducted to simulate a swarm of UAVs for the and was tasked with completely surveying a rectangular reconnaissance area located on the left side of the arena.
The UAVs were assigned individual reconnaissance zones and coordinated their actions using behavior trees (BTs), while their movement and collision avoidance were controlled by the GBestPSO mechanism (Fig. 11).
Upon reaching the reconnaissance zone, each UAV began surveying a separate area (Fig. 12).
After successfully surveying the entire reconnaissance area, the UAVs returned to their permanent deployment location (Fig. 13).
For each simulation run, metrics were recorded that characterized the speed and quality of task execution, as well as the system's resistance to UAV losses.
Based on the research conducted, the following key metric values were obtained (Table 6).
The dynamics of changes in the number of UAVs depended on the corresponding phase of the mission: • • •
Phase I (0 50 iterations) most UAVs move to the areas; the first reconnaissance routes are gradually activated.
Phase II (50 180 iterations) the number of UAVs in Reconnaissance mode increases, gradually covering the entire area.
Phase III (after ~180 iterations) most UAVs complete their survey of the areas and switch to Returning or Awaiting mode.
Experimental investigations confirm the effectiveness of the proposed hybrid approach, which combines swarm optimization (GBestPSO) and behavior trees (BTs). Analysis of the results for two key scenarios
allows us to draw reasonable conclusions about the advantages of this architecture.
A comparison of the results for the attack scenario demonstrates the clear advantage of the hybrid method over a system that uses only behavior trees. Although the BT-based approach provides a 141 faster start to the attack (28 45 iterations versus 121 in the hybrid), it is inferior in terms of coordination quality. Agents controlled only by BTs move toward the target along the shortest trajectory, resulting in a less organized formation in orbit. In contrast, the hybrid system uses GBestPSO to pre-cluster the swarm around the leader, which, although it takes more time in the initial stage, provides significantly better synchronization and uniform angular distribution in orbit. This, in turn, leads to a more effective and simultaneous attack from different directions, minimizing the target's chances of countering.
In the reconnaissance scenario, the hybrid algorithm demonstrated high efficiency in solving space allocation and fault tolerance problems. The system successfully distributed the reconnaissance area between UAVs and ensured complete coverage of the territory, even under conditions of simulated agent losses. The two-level architecture plays a key role here: GBestPSO is responsible for strategic zone allocation and replanning in case of losses, while BTs control the tactical behavior of each UAV within its zone. This confirms that the proposed approach not only solves the problem of global optimization but also provides the local autonomy necessary to adapt to unpredictable circumstances.
Thus, the experiments prove the central thesis of the work: the integration of swarm intelligence for global planning and behavior trees for local execution creates a synergistic effect. GBestPSO provides the system with strategic coordination, while BTs provide tactical flexibility and responsiveness. This allows for a balance between global coordination and individual autonomy of agents, making hybrid architecture a promising solution for complex missions in dynamic environments.
The proposed hybrid architecture is not only theoretically sound, but also practically implementable thanks to the use of modern technologies and modularity principles. The implementation is based on a two-level structure that includes planning (GBestPSO) and behavior (BT) levels, which interact through standardized messaging protocols.
The key advantages of the architecture in terms of implementation are modularity and scalability. Behavior trees are modular by nature, which makes it easy to reuse, extend, and modify the behavior logic of agents without having to redesign the entire system. Adding new UAVs to the swarm does not require changing the architecture, as GBestPSO works effectively with different numbers of agents, and each new agent functions as an independent unit with its own BT.
An important practical aspect is fault tolerance. The system is designed according to the principle agent can continue to perform tasks based on the last instructions received. The loss of individual UAVs also does not lead to mission failure, as the system is capable of redistributing tasks among active agents.
Finally, unlike resource-intensive methods such as deep reinforcement learning (DRL), the proposed approach is computationally efficient. This makes it suitable for implementation on UAV onboard computers with limited hardware resources, which is critical for practical application in the field.
The paper investigated and substantiated the effectiveness of a hybrid approach to coordinating autonomous agents, integrating swarm intelligence based on the GBestPSO algorithm and a control architecture based on behavior trees (BTs). The main problem addressed by the study is the need to ensure a balance between global coordination of group actions and local autonomy of each agent in dynamic and unpredictable environments. The hybrid approach was confirmed to be superior. In the attack scenario, the hybrid system, although requiring more time to prepare, provided a significantly higher level of coordination and synchronization of the strike compared to the approach based solely on BTs. Fault tolerance and adaptability were demonstrated. In the reconnaissance scenario, the system effectively distributed tasks among agents, adapted to UAV losses, and successfully completed the mission, confirming its reliability.
The synergy of the two methods was substantiated. It was proven that the combination of global optimization using GBestPSO and local flexibility of BTs allows creating a system that is both purposeful and adaptive.
Thus, the main contribution of this work is to demonstrate that the integration of swarm intelligence and behavior trees is a promising direction for creating a new generation of multi-agent systems. Such systems are capable of functioning effectively in complex real-world conditions, making them suitable for a wide range of applications, from military operations to search and rescue missions.
Despite the successful results, there are several promising areas for further development and improvement of the proposed hybrid approach. Future research may focus on the following aspects:
The proposed two-level architecture, where GBestPSO is responsible for strategic planning and BTs for tactical reactive behavior, demonstrated high efficiency in simulation experiments. Two application scenarios were analyzed: coordinated swarm attack and territory reconnaissance.
Key results of the work: • • •
Expanding the behavior tree library. Creating more complex and versatile sub-trees to implement a wider range of tactical actions, such as evading electronic warfare systems, dynamically changing roles (e.g., from reconnaissance to strike UAV), or cooperative interaction to perform complex tasks.
Intellectualization of GBestPSO. Improving the swarm optimization algorithm by integrating mechanisms for adapting to dynamic changes in the environment in real time. For example, the algorithm parameters could be automatically adjusted depending on the threat level, obstacle density, or communication channel availability.
Heterogeneous swarms. Adapting the architecture to manage heterogeneous swarms consisting of agents with different capabilities (e.g., UAVs for reconnaissance, electronic warfare, and strikes). This will require the development of more complex mechanisms for distributing tasks and roles at the GBestPSO level.
Combination with learning methods. Investigation of the possibilities for synergy between the proposed approach and elements of machine learning. For example, reinforcement learning methods can be used for offline optimization of behavior tree parameters or GBestPSO, which will combine the advantages of transparency and verifiability of classical methods with the high efficiency of data-based models. -in-themodel, followed by a transition to full-scale field tests on real UAVs. This will allow verifying the effectiveness of algorithms in conditions of real communication delays, sensor noise, and other physical limitations.
The authors have not employed any Generative AI tools.