00051001895 distributed control strategies for changing multiple uav formation

00051001895 distributed control strategies for changing multiple uav formation 00051001895 distributed control strategies for changing multiple uav formation

Motivation

Unmanned aerial vehicles (UAVs) have significant potential to assist humans in tasks such as infrastructure inspection in hazardous areas and disaster damage assessment, driving extensive research into UAV mission automation While single UAV systems offer advantages, they are limited by payload capacity, battery life, and coverage range, prompting the development of multi-UAV systems Cooperative multi-drone networks enhance mission efficiency through scalability, redundancy, and faster operation, making them ideal for tackling complex, time-sensitive applications.

Formation control is a critical component of multi-UAV cooperation, enabling groups of UAVs to fly in precise geometric patterns and maintain necessary spatial relationships It plays a vital role in collision avoidance and optimizing mission performance However, navigating through cluttered environments and narrow spaces presents challenges in maintaining stable formations, increasing the risk of collisions Advanced control strategies are required to dynamically adjust UAV formations in real-time, ensuring safety and mission success even in complex terrains.

Reconfiguration control in multi-UAV systems is essential for enabling UAV formations to dynamically adjust their shapes to adapt to environmental constraints and mission demands, ensuring safe navigation through narrow passageways, obstacle avoidance, and operational efficiency Key requirements for effective reconfiguration include real-time communication between UAVs, robust decision-making algorithms, and reliable sensing mechanisms to detect environmental changes and facilitate responsive shape adjustments This capability is crucial for enhancing the safety, flexibility, and effectiveness of UAV swarm operations in complex environments.

Effective reconfiguration control in UAV formations faces significant challenges, including real-time coordination to ensure seamless communication and precise synchronization among UAVs, and the development of robust obstacle avoidance algorithms that enable the formation to detect and navigate around obstacles without losing cohesion Environmental adaptability is crucial, requiring control strategies that can dynamically adjust the formation to changing conditions Scalability is essential to handle different numbers of UAVs without compromising performance, while robustness ensures formation integrity despite issues like communication latency, UAV malfunctions, or sensor inaccuracies Overcoming these challenges is vital for ensuring the reliability and effectiveness of multi-UAV reconfiguration control systems.

This thesis focuses on enhancing autonomous navigation by developing strategies for the coordinated reconfiguration of multiple UAVs It explores formation-changing techniques for robot swarms to adapt their shape based on environmental data, enabling efficient navigation through challenging terrains Special emphasis is placed on navigating narrow, unknown passages, with applications in search and rescue missions The research aims to improve UAV swarm flexibility and resilience, advancing autonomous multi-robot systems for complex environmental exploration.

Approaches and Background

This thesis focuses on enhancing the autonomy of UAV formations by developing effective distributed reconfiguration control strategies based on environmental data Addressing challenges in formation transformation, the research aims to enable UAVs to perform adaptive and coordinated maneuvers automatically Key approaches include innovative control algorithms designed for various formation types, promoting seamless and efficient reconfiguration These advances contribute to the broader goal of improving UAV fleet flexibility and operational effectiveness in complex environments.

Centralized formation control is a common method where a single control unit coordinates the movements of all UAVs, simplifying synchronization and decision-making This approach involves a central controller that collects data from each UAV, processes this information to determine the optimal formation strategy, and sends specific commands to ensure coordinated flight By reducing the coordination to a single decision point, centralized control enhances the efficiency and cohesion of UAV formations.

Centralized formation control offers the key advantage of enabling precise and coordinated movements across the entire formation, thanks to the central controller’s comprehensive system overview This approach allows for optimized performance in parameters such as fuel efficiency, coverage, and collision avoidance Additionally, centralized control simplifies the execution of complex maneuvers and formation changes, as the central controller can effectively manage and adapt the overall strategy for dynamic operations.

Centralized formation control has notable drawbacks, including the risk of the central controller becoming a single point of failure that could cause the entire UAV formation to collapse if it malfunctions or loses contact Additionally, this approach imposes high computational and communication demands on the central controller, especially in large-scale formations, which can lead to delays and bottlenecks These limitations hinder the scalability and robustness of the system, particularly in dynamic and unpredictable environments.

Distributed formation control is widely employed due to its decentralized decision-making approach, where each UAV operates based on local information and interacts with nearby units Instead of relying on a central controller, the formation is maintained through simple local rules and behaviors followed by each UAV This method mimics natural systems like bird flocks and fish schools, where complex group behaviors arise from individual actions.

Distributed formation control significantly enhances scalability and robustness, allowing the system to easily expand with additional UAVs without overloading a central controller This decentralized approach improves fault tolerance, enabling remaining UAVs to operate effectively even if one fails, and offers greater flexibility and adaptability in dynamic environments by allowing each UAV to respond to local changes independently Consequently, designing distributed controllers is essential for achieving scalable, robust, and flexible UAV formations.

In search and rescue (SAR) operations, the V-formation is widely adopted due to its ability to optimize coverage and ensure an even distribution of UAVs, enabling comprehensive searches without gaps This formation enhances line-of-sight communication, facilitating real-time data sharing and coordination crucial for timely decision-making Additionally, the flexibility and adaptability of the V-formation allow UAVs to navigate effectively across diverse and challenging terrains, making it an efficient strategy for locating survivors and assessing disaster areas rapidly While numerous studies explore maintaining V-formation in open environments, research on its maneuverability through narrow and confined spaces remains limited.

To overcome the challenges of V-shape formation movement in constrained environments, we propose an efficient behavioral strategy that automatically observes and self-coordinates robots to maintain the formation This method enables the formation to adapt and expand appropriately according to the shape of narrow spaces, ensuring safe and efficient navigation through complex environments.

Various formation shapes offer greater potential applications compared to the traditional V-formation, highlighting the necessity for a versatile formation control method To address this, Method 2 extends the formation transformation algorithm to support diverse formation shapes Its effectiveness and stability are validated through Lyapunov stability theory, ensuring reliable and adaptable formation control in complex scenarios.

Traditional primitive motion methods often overlook system constraints, relying solely on potential field approaches influenced by numerous parameters, which can complicate control To address these limitations, Method 3 employs model predictive control (MPC), offering optimal control signals while effectively managing system constraints This approach ensures precise and reliable formation control, significantly improving overall performance and adaptability across diverse operational scenarios.

Contributions

Research Contributions

The master's thesis aimed to develop control strategies for guiding multi-robot formations through narrow spaces and confined environments The study focused on designing effective approaches to ensure precise navigation and coordination among robots in restricted areas The proposed methods aim to enhance robotic performance in challenging, narrow environments, facilitating safe and efficient movement These strategies contribute to advancing robotic formation control, particularly in scenarios requiring navigation through tight spaces.

Method 1 Self-Reconfigurable V-Shape Formation of Multiple UAVs in Narrow Space Environments

This work introduces a self-reconfigurable V-shape formation control algorithm for multi-UAV systems navigating through narrow spaces, ensuring the formation can be established and maintained from random initial positions during movement The proposed strategy enables UAVs to autonomously expand or shrink their V-wings, allowing the formation to reconfigure dynamically for obstacle avoidance and safety The primary contribution lies in designing a distributed control approach that allows UAVs to cooperate seamlessly, maintain a precise V-shape, and effectively avoid collisions in constrained environments These behaviors enhance the robustness and safety of multi-UAV operations in challenging narrow spaces.

Method 2 Event-based Reconfiguration Control for Time-varying Formation of Robot Swarms in Narrow Spaces

This work introduces an event-based reconfiguration control strategy based on artificial potential fields (APF) to enable multi-robot formations to adapt to narrow space environments, extending previous methods to various formation types The proposed approach ensures collision-free, time-varying formations in environments without obstacles by maintaining desired configurations and preventing inter-agent collisions Additionally, each robot is equipped with local sensors that detect narrow spaces, allowing automatic adjustments—such as scaling, rotation, or transforming into straight-line configurations—to ensure safe, collision-free motion within confined environments.

Method 3 Predictive Reconfiguration Control for Multi-Robot Formation in Cluttered Environments

This article presents an optimal reconfiguration control strategy designed to enhance the smoothness and motion control of multi-UAV formations in narrow spaces The core innovation is a perceptual reconfiguration approach that enables a decentralized multi-robot team to navigate complex environments safely and efficiently Each robot is equipped with local sensors and communication modules to gather environmental and neighbor information for distributed decision-making This allows the formation to dynamically shrink, expand, or transition into a line formation tailored to environmental constraints The strategy is based on model predictive control to ensure formation maintenance, correct velocity and direction, and effective collision avoidance during navigation.

List of Publications

During my master's studies, I published several valuable research papers with significant contributions from my co-authors and presented some of these works at international conferences These publications are listed in chronological order, showcasing my ongoing academic development and engagement with the global research community.

Publications included in this Thesis

Duy-Nam Bui, Manh Duong Phung, and Hung Pham Duy present a novel approach for the self-reconfigurable V-shape formation of multiple UAVs in narrow space environments, demonstrated at the 2024 IEEE/SICE International Symposium on System Integration (SII) in Ha Long, Vietnam Their research focuses on enabling UAV swarms to adapt their formations autonomously within confined areas, enhancing navigation and operational efficiency The study highlights the importance of robust formation control algorithms for UAV coordination in constrained environments, providing significant implications for applications such as search and rescue, surveillance, and environmental monitoring This innovative formation strategy improves UAV flexibility and safety when operating in tight spaces, contributing to the advancement of autonomous aerial vehicle systems.

• Duy-Nam Bui, Manh Duong Phung, and Hung Pham Duy “Event-based Recon- figuration Control for Time-varying Formation of Robot Swarms in Narrow Spaces,”

• Duy-Nam Bui, Manh Duong Phung, and Hung Pham Duy “Predictive Reconfig- uration Control for Multi-Robot Formation in Cluttered Environments,” submitted in IEEE Transactions on Control of Network Systems, 2024.

Duy-Nam Bui, Thuy Ngan Duong, and Manh Duong Phung (2024) present an innovative approach to cooperative inspection path planning utilizing Ant Colony Optimization (ACO) algorithms for multiple unmanned aerial vehicles (UAVs) Their research, showcased at the IEEE/SICE International Symposium on System Integration in Ha Long, Vietnam, focuses on enhancing the efficiency and coordination of UAVs during inspection missions By applying ACO techniques, they optimize the route planning process, leading to improved coverage and reduced mission time, which is crucial for industrial and infrastructure inspections This study offers valuable insights into deploying intelligent algorithms for autonomous UAV operations, contributing significantly to advancements in aerial inspection and surveillance technology.

• Duy-Nam Buiand Manh Duong Phung, “Radial Basis Function Neural Networks for Formation Control of Unmanned Aerial Vehicles,” in Robotica, vol 42, pp. 1842–1860, 2024.

• Duy-Nam Bui, Thu Hang Khuat, Manh Duong Phung, Thuan-Hoang Tran, Dong

LT Tran, “Optimal Motion Planning for Unmanned Aerial Vehicles in Unknown En- vironments,” 2024 International Conference on Control, Robotics and Informatics (ICCRI), Da Nang, Vietnam, 2024.

Thi Thuy Ngan Duong, Duy-Nam Bui, and Manh Duong Phung published a 2024 study in Neural Computing and Applications, introducing a novel navigation approach using variable-based multi-objective particle swarm optimization for UAV path planning Their research addresses the challenges of designing efficient UAV routes while respecting kinematic constraints, enhancing the reliability and effectiveness of autonomous aerial navigation This innovative optimization method improves path planning accuracy and performance, making significant contributions to the field of UAV navigation systems and autonomous flight technologies.

Self-reconfigurable V-shape Formation of Multiple UAVs in

Introduction

Unmanned aerial vehicles (UAVs) have gained significant attention in recent years for their diverse applications such as surveillance, search and rescue, and infrastructure inspection [26], [27] Effective navigation and formation maintenance are critical for UAV operations, particularly in complex, obstacle-rich environments The coordination of multiple UAVs through formation control is essential to ensure efficient mission execution and reliable performance in challenging conditions [24], [28].

Formation control in multi-robot systems refers to the coordination and control strategies used to form, maintain, and transform formations among a group of robots [7], [29].

In environments with dense obstacles or narrow passages, UAV formations must adapt and reconfigure their shape to navigate effectively, as illustrated in Figure 2.1 This self-reconfigurable ability allows UAVs to overcome challenging terrain, complex structures, and tight spaces, improving their maneuverability and mission success The V-shape formation is a popular configuration that enhances stability, visibility, and aerodynamic efficiency For example, a formation control algorithm in [21] enables multi-UAV systems to autonomously adjust their positions within a V-shape to avoid obstacles Additionally, methods like the splitting and merging algorithm introduced in [23] facilitate dynamic formation adjustments in environments with static and moving obstacles.

Figure 2.1: The self-reconfigurable V-shape formation can adjust its shape and navigate through narrow passages.

The work in [32] presents a switching strategy of a region-based shape controller for a swarm of robots to deal with the obstacle-avoidance problem in complex environments.

Recent advancements in path planning and obstacle avoidance techniques have significantly contributed to the development of self-reconfigurable formation control algorithms for UAVs For example, the angle-encoded particle swarm optimization algorithm enhances multi-UAV formation for vision-based infrastructure inspection by integrating flight safety and visual constraints to generate trajectory and velocity profiles Additionally, innovative optimization methods enable rapid and accurate UAV formation reconfiguration in response to random attacks, improving system resilience However, many studies primarily focus on maintaining fixed formation shapes, with less emphasis on self-reconfiguration capabilities in obstacle-rich environments.

This work presents a self-reconfigurable V-shape formation control algorithm enabling multiple UAVs to operate effectively in narrow spaces The algorithm facilitates formation formation, maintenance, and reconfiguration by expanding or shrinking the V-wings, allowing UAVs to avoid obstacles and maintain safe distances It supports dynamic behaviors such as opening or closing wings and merging into a straight line, enhancing navigation through tight passages and obstacle avoidance The key contributions include developing a self-reconfiguration strategy for narrow environments and implementing reconfiguration behaviors that ensure UAVs can maneuver efficiently while maintaining their formation.

V-Shape Formation Design

The V-shape formation is chosen due to its advantages in improving maneuverability and enhancing visibility for UAVs Its modeling and design principles are presented as follows.

Figure 2.2: The sensing range r s and alert ranger a (r a < r s ) of a UAV R i

Figure 2.3: Illustration of the V-shape formation

The formation consists of n identical UAVs, each equipped with sensory modules such as Lidar, GPS, and IMU for accurate positioning and navigation These UAVs also feature a communication module enabling peer-to-peer connectivity At a height h, each UAV R_i is modeled as a particle moving in a 2D plane with position p_i and heading angle ψ_i The UAVs follow a single-integrator kinematic model where the velocity vector v_i defines their movement, with v_i = [v_ix, v_iy]^T The heading angle ψ_i is derived using the arctangent function: ψ_i = atan2(u_iy, u_ix).

The communication range of each UAV R i is divided into two areas including the sensing areaS s with radius r s and the alert area S a with radius r a < r s so that S a ⊂S s , as illustrated in Figure 2.2.

In this work, the V-shape formation is constructed by two wings [21], as shown inFigure 2.3 The wings are described by the desired distances between consecutive UAVs,

(a) Disruption in formation (b) Obstacles from one side (c) Obstacles from both sides

Figure 2.4 illustrates the self-reconfiguration process of the V-shape formation, inspired by the mechanical motions of pliers or scissors, with the bearing angle α between the formation heading and each wing In this formation, UAV Rl is designated as the leader UAV, positioned at the front, with l = ⌈n/2⌉ to ensure a balanced leadership role The formation maintains specific parameters, such as the desired distance di and the angle αi, between each follower UAV R i (where i ≠ l) and the leader, ensuring coherent and adaptive collective movement This approach enhances formation stability and maneuverability, essential for efficient UAV coordination.

R l are determined as follows: d i =d|l−i|, α i ( ψ l +α if i < l ψ l −α if i > l

Thus, the desired position of UAV R i can be obtained as follows: p d i =p l +d i

Distributed Formation Control Strategy

The formation control strategy enables UAVs to form, maintain, and self-reconfigure a V-shape formation during navigation, especially when encountering obstacles or narrow passages This adaptive approach involves expanding or shrinking the two wings of the V-shape, allowing the UAV formation to safely maneuver in confined spaces without collisions The proposed algorithm leverages distributed behavior-based control and artificial potential field methods, empowering individual UAVs to make decisions and adjust the formation dynamically The strategy focuses on two key aspects: maintaining the V-shape formation and reconfiguring it as needed for safe and efficient navigation in complex environments.

Behavior-based control is a decentralized approach that uses multiple control modules, known as behaviors, to accomplish specific objectives [7], [35] In this study, UAV formation is maintained through the integration of various behaviors, enhancing coordination and stability This method leverages distributed control strategies to ensure reliable UAV operations and robust formation management.

The formation behavior directs UAVs to reach their designated positions within a predefined formation, ensuring coordinated movement Based on equation (2.4), the desired position \( p_{d_i} \) of UAV \( R_i \) can be determined, facilitating precise formation control Inspired by prior research [21], [36], the formation behavior is mathematically defined as \( v_{f_i} = -k_f (p_i - p_{d_i}) + v_l \), where \( k_f > 0 \) is a positive formation gain that influences the velocity adjustment to achieve accurate positioning.

This behavior guides the formation toward the desired location by utilizing a target-tracking controller based on the relative position between the leader UAV and the goal The goal position, denoted as p_g, represents the target the formation aims to reach The goal-reaching behavior is implemented through a control law defined by v_gi = -k_g (p_i - p_g), where k_g > 0 is a positive tracking gain that adjusts the responsiveness of the movement toward the goal.

During operation, the formation must avoid obstacles present in the environment Let p io h be the closest point on the boundary of obstacle o h within the sensing range of UAV

R i When that UAV senses obstacle o h , it will create a thrust to maneuver and avoid the obstacle The thrust is directed as follows: v o ih 

0 otherwise (2.7) where k o > 0 is a positive gain; d io h is the distance between UAV R i and obstacle o h When considering all obstacles, the obstacle avoidance behavior of UAV R i are obtained as follows: v o i = X m h=1 v ih , (2.8) wherem is number of observable obstacles within the sensing range of UAV R i

Apart from avoiding obstacles, the control algorithm also needs to adjust the UAV positions to avoid collision among them To address this, we propose that UAVs R i and

UAVs that are not in the same wing but within each other's sensing range (i.e., when the distance ∥p_ij∥ is less than the sensing radius r_s) generate a repulsive force to prevent entry into the alert area S_a Here, p_ij represents the position difference between UAV i and UAV j, calculated as p_i − p_j The collision avoidance behavior is defined by the repulsive velocity v_c_ij, which is proportional to an exponential function: v_c_ij = k_c * e^(-β_c * (∥p_ij∥ − r_a)), ensuring effective separation between UAVs within their sensing zones.

∥p i −p j ∥, (2.9) wherek c >0 is a positive collision gain.

Inspired by the mechanics of pliers and scissors, which change shape through opposing forces on their handles, the V-shape formation can open or close its wings based on external forces In our approach, these forces are generated by differences between the UAVs' current positions and their desired distances, ensuring formation stability When disruptions occur—such as UAVR n deviating from alignment, as shown in Figure 2.4a—these forces work collectively to realign the UAVs and guide them back to their optimal positions.

In the scenario depicted by Figure 2.4b where a force is exerted from one side, UAV

The UAVs respond to potential obstacles by generating a thrust (v_on) to avoid collision, resulting in a control signal (v_n) This control signal prompts other UAVs within the same V-wing, including the leader UAV (R_l), to adjust their positions accordingly through behavior signals (v_ri) As the leader UAV shifts its position, the opposing wing UAVs realign themselves via formation behavior (v_fi), causing the entire UAV formation to move coherently towards the other side.

When obstacles influence both sides of the formation, UAVs R1 and Rn respond with obstacle avoidance behaviors v_o1 and v_on, respectively Simultaneously, other UAVs in the formation generate reconfiguration behaviors v_ir to adapt their positions, allowing the V-shape formation to contract its wings and pass through narrow passages efficiently.

In our work, the aforementioned reconfiguration idea is implemented by the following equation: v r ij =k r |∥p ij ∥ −d ij | β r

∥p i −p j ∥, (2.10) where k r > 0 is a positive reconfiguration gain, β r > 0 is the smoothness factor, d ij is the desired distance between two UAVs R i and R j n the same wing, d ij = d|i−j|.

In section 2.10, the term |∥p_ij∥ − d_ij | allows UAVs to adjust their positions, ensuring that the desired distances between them are maintained This distance regulation is essential for coordinated flight and formation keeping Additionally, this behavior functions as a collision avoidance mechanism among UAVs within the same wing, enhancing safety during autonomous operations.

The overall distributed control strategy is obtained by combining the behaviors from all UAVs as follows: v i ( v g i +v r i +v c i +v o i , if assigned as leader v f i +v r i +v c i +v o i otherwise (2.11)

This function enables autonomous triggering of behaviors in response to external influences or disturbances affecting the UAV formation Once the formation achieves the desired state, these behavioral responses are sustained to ensure stable and reliable operation This adaptive mechanism enhances the UAVs' ability to maintain formation stability under varying environmental conditions.

(a) Trajectories of the UAVs in the formation

(b) Number of UAVs activating reconfiguration behaviors over time

Figure 2.5: Simulation result of the V-shape formation moving through a narrow passage Table 2.1: Statistical evaluation of the proposed strategy for several different scenarios

UAVs d α Average error (m) Min distance

(m) Average distance of consecutive UAVs (m)

Results and Discussion

In this section, we evaluate the performance of the proposed control strategy through different simulation scenarios.

In the simulation, the UAV has the alert radius r a = 0.3 m and the sensing radius r s = 2 m The control period is set at 0.02 s The maximum speed of each UAV is

2.0 m/s The V-shape formation is defined with d = 0.8 m and α = 0.3π/4 rad In our evaluation, 5 UAVs with V-shape formation are operated in the area of 46 m×7 m with two large obstacles arranged to form a narrow passage as shown in Figure 2.5.

Figure 2.5 illustrates the trajectories of UAVs navigating in the environment under the guidance of a proposed distributed controller The UAVs initially start from random positions around a designated point and then self-adjust to form the desired V-shape formation through control signals driven by formation and reconfiguration behaviors Additionally, when encountering obstacles, the UAVs dynamically adjust their formation to maintain collision avoidance and flight stability.

(a) Distances between each pair of UAVs over time

(b) The average distance error of UAV formation

(c) The distance between consecutive UAVs (d) Values of the order metric Φ over time

Figure 2.6: Evaluation of the proposed algorithm

The UAVs deform their formation through steps 414-1035 and then transition to a straight-line formation at step 1242 to navigate narrow gaps effectively After successfully avoiding obstacles, they readjust to the desired V-shape formation and continue toward the target position at step 1656 These formation maneuvers and their effectiveness are demonstrated and verified in the simulation video referenced in footnote 1.

Figure 2.5b illustrates the activation pattern of UAV reconfiguration behavior over time, highlighting that UAVs initiate this behavior during formation shaping at the initial stage Additionally, the reconfiguration process continues as UAVs adjust their formation to effectively adapt to changes in the environmental structure, ensuring optimal operational performance throughout the mission.

The statistical evaluation of the proposed strategy is presented in Figure 2.6, illustrating UAV distance data over time Figure 2.6a demonstrates that the distances between UAVs consistently exceed the alert radius, confirming the control algorithm's effectiveness in preventing collisions and ensuring safe UAV operation.

Figure 2.6b illustrates the average distance error of the UAV formation over time, starting with a large error when the UAVs are not yet aligned After the control algorithm adjusts the UAV positions, the error quickly converges to near zero, ensuring precise formation control During navigation through narrow passages, the error remains minimal, staying below 0.06 meters, indicating stable formation flight Additionally, Figure 2.6c displays the average distance between consecutive UAVs, which fluctuates around the desired 0.8 meters for the V-shaped formation, confirming effective formation maintenance.

To further evaluate the performance of the proposed controller, anorder metric Φ that measures the similarity in the UAVs’ direction is used [37] It takes the values in range

1 Simulation video: https://youtu.be/_6u7yMNOySc

[0,1] and is computed as follows: Φ = 1 n n

The order metric Φ, as described in (2.12), approaches 1 when all UAVs share the same heading angle, indicating a cohesive formation In our simulation (Figure 2.6d), Φ remains close to 1 throughout the UAVs' movement, even during obstacle avoidance and passage through narrow spaces Although heading angles temporarily change when exiting passages to allow re-alignment, the metric quickly returns to 1 as the UAVs restore their desired formation These results validate the effectiveness of the proposed control algorithm in maintaining formation coherence under challenging conditions.

Simulation results demonstrate that the proposed method effectively maintains UAV formations across various challenging scenarios, including narrow passages and dense obstacle areas Adjusting parameters such as the number of UAVs, V-shape configuration, desired distance (d), and bearing angle (α) shows consistent performance, with an average formation error around 0.1 meters, ensuring precise maneuvering in tight spaces Importantly, the minimum inter-UAV distance remains above the collision threshold, confirming collision avoidance capabilities Additionally, the average distance between consecutive UAVs closely matches the desired value, indicating stable formation maintenance Overall, these findings validate the effectiveness and robustness of the proposed control strategy for UAV formation control.

Conclusion

This study introduces a novel behavior-based controller designed for UAV formation in confined spaces, enabling precise navigation in narrow environments By developing specialized behaviors for each UAV and integrating them through a unified function, our approach facilitates the formation of V-shapes with adaptable wing adjustments for obstacle avoidance Simulation results demonstrate that this control strategy effectively enables UAVs to form the desired V-shape, reconfigure to bypass obstacles, prevent collisions, and successfully navigate complex, narrow passages, enhancing UAV operational capabilities in challenging environments.

Event-based Reconfiguration Control for Time- varying Formation of Robot Swarms in Nar- row Spaces

Code: https://github.com/duynamrcv/erc

Video: https://youtu.be/rCIjgSqiWXg

This chapter enhances the previous multi-formation configuration method by addressing navigation in narrow spaces with increased collision risks It introduces an event-based reconfiguration control (ERC) using artificial potential fields (APF) to effectively manage a time-varying robot formation (TVF) in constrained environments The proposed approach is designed to navigate complex, dynamic settings such as forest-like and tunnel-like environments, ensuring safe and efficient movement through limited spaces.

Introduction

Advancements in networked multi-agent technology have propelled the rapid development of autonomous multi-robot systems (MRSs) with diverse applications such as warehouse automation and search and rescue operations [38], [39] A key component of these systems is the formation controller, which coordinates robots to achieve and maintain desired formations, facilitating effective collaboration and system efficiency [4].

In rigid formation control, achieving the desired configuration requires setting precise target distances for each swarm agent However, as the complexity of formation tasks increases, it becomes necessary to adapt the formation configuration to meet specific operational requirements Therefore, time-varying formation (TVF) control has become an essential approach for enabling flexibility and adaptability in swarm robots, ensuring they can dynamically adjust their formations for diverse tasks.

Biological swarm motion is primarily governed by three key behaviors: cohesion, which pulls agents toward their neighbors; repulsion, which prevents collisions by pushing agents away from each other; and alignment, which synchronizes an agent’s heading with that of its neighbors For goal-oriented swarm movement, alignment can be replaced with migration behavior, where agents are directed towards a specific orientation at a preferred speed In complex environments, a fourth behavior—collision avoidance—is essential to ensure safe navigation and obstacle avoidance within the swarm.

(a) Pure formation control (b) Proposed approach

We propose an event-based reconfiguration control (ERC) method to enable a tandem vehicle formation (TVF) to safely navigate through narrow spaces, addressing the limitations of purely behavior-based formation control that can lead to collisions with obstacles Our approach improves upon traditional navigation methods by ensuring collision-free movement, as demonstrated by the comparison of motion paths—one that collides with obstacles using behavior-based control, and another that successfully traverses narrow spaces with our ERC method Behavior-based formation control often utilizes virtual forces within the artificial potential field (APF) to coordinate multi-robot systems around obstacles, effectively managing movements in diverse environments from open areas to complex, concave obstacle settings Additionally, integrating fuzzy controllers into these systems enhances obstacle avoidance capabilities while maintaining swarm connectivity, further increasing navigation robustness.

Evolutionary optimization integrated with behavioral models facilitates stable, decentralized navigation for large-scale aerial robot swarms in confined environments However, relying on a fixed set of behaviors restricts the swarm's flexibility to adapt to sudden environmental changes, which can occur in caves, corridors, and tunnels This limited adaptability increases the risk of collisions and compromises safety in complex, tight spaces.

Formation control strategies can be classified into two main categories: rigid formation and adaptive formation Rigid formations maintain a fixed shape, allowing the swarm to expand or contract while preserving its structure, as demonstrated by models using model predictive control for optimal robot coordination based on shared maps Hierarchical control methods enable obstacle avoidance within confined spaces by guiding robots within a virtual circular region that can contract to navigate around obstacles Additionally, comprehensive control schemes utilizing graph-based path planning and distributed model predictive control facilitate collaborative transport in unknown environments While effective in open spaces, rigid formations face limitations in narrow or cluttered environments, where space constraints and formation contraction increase collision risks among robots, highlighting the need for adaptable formation strategies in complex terrains.

Adaptive formation allows swarm configurations to dynamically change based on environmental conditions, enhancing navigation in complex environments For instance, a reconfiguration strategy combining behavioral control and auction-based market approaches enables swarm movement adaptation in dynamic settings Particle swarm optimization (PSO) techniques are employed to generate reconfigurable UAV trajectories for obstacle avoidance and task execution, though these methods often rely on centralized control with high computational demands Robust adaptive formation control algorithms have been developed to enable UAV groups to switch between different formation patterns for flexible navigation Overall, adaptive formation methods improve robotic navigation through complex environments by facilitating flexible reconfiguration, but there is a significant need for decentralized, partially communicating solutions that ensure safety, efficiency, and effective adaptation to environmental changes.

This study introduces an innovative event-based reconfiguration controller (ERC) designed for safe and efficient navigation of decentralized TVF systems in confined environments, as illustrated in Figure 3.1 Equipped with local sensors and communication modules, the robots effectively gather environmental data and information from neighboring robots, ensuring coordinated movement The primary contributions of this research include the development of a responsive ERC, enabling reliable and collision-free navigation in narrow spaces, and enhancing the overall safety and effectiveness of decentralized robot formations.

1 Define a set of individual behaviors that meet the reconfiguration control requirements, including goal-directed motion, formation maintenance, tailgating, and collision avoidance behaviors Each behavior is designed for convenience in implementation via an artificial potential field.

2 Propose an event-based reconfiguration controller with two modes,“formation” and

“tailgating” capable of adapting the formation shape in response to environmental changes The stability of the proposed approach has been demonstrated via the Lyapunov theorem.

3 Extensive simulations and comparisons have been conducted to evaluate the robustness, scalability, and effectiveness of the proposed controller Software-in-the-loop tests have also been conducted to verify its practical applicability The source code of the proposed controller is publicly available for further research and practical implementation.

This chapter is structured to provide a comprehensive understanding of the proposed approach Section 3.2 details the formation model and its mathematical formulation, laying the foundation for the control strategy In Section 3.3, a novel event-based reconfiguration control method is introduced, highlighting its advantages in dynamic scenarios Section 3.4 presents simulation results, comparative analyses, and software-in-the-loop experiments that demonstrate the effectiveness of the proposed method The chapter concludes with key insights and future research directions in Section 3.5.

Preliminaries

Consider a swarm N consisting of n robots labeled i ∈ {1, , n}, modeled as a directed sensing graph G = (V, E) In this model, the vertex set V = {1, , n} represents individual robots, while the edge set E ⊆ V × V indicates the directional sensing or communication links between robot pairs (i, j) This graph structure effectively captures the interactions and obstacle detection capabilities within the robotic swarm, facilitating efficient coordination and navigation.

Figure 3.2 illustrates a robot equipped with a local range sensor, featuring a sensing area (S s) represented by a solid white circle with radius r s, enabling the robot to detect its immediate surroundings The robot also has an alert area (S a), shown as a dashed gray circle with radius r a, which is smaller or equal to the sensing radius (r a ≤ r s), and defines the zone where the robot activates repulsive forces to prevent collisions The set M i ={o} (highlighted in green) indicates the nearest obstacle point detected by the robot's sensor, facilitating real-time collision avoidance.

Desired time-varying topology TVF reconfigures in narrow spaces TVF Restoration

Figure 3.3: Schematic diagram of time-varying formation in the narrow spaces sense robot j Denote N i ={j ∈ V|(i, j)∈ E} ⊂ V as the set of n i neighbors of robot i inG.

This study involves a swarm of identical robots, each with a body radius r, equipped with IMUs for accurate position and orientation detection, a 360° field-of-view range sensor with radius r_s for obstacle scanning, and wireless ad-hoc modules enabling peer-to-peer communication The communication delay among robots is considered negligible, ensuring seamless information transfer Sensor data collected by each robot at time t(k) is represented as a set of obstacle data points, facilitating effective navigation and collision avoidance within the swarm.

M i (k) = {o} A safe area of radius r a is defined so that repulsive forces are activated when robot i senses obstacles or its neighbors within ranger a

The robot's dynamics are represented in discrete time, with a time step τ, where p_i(k), v_i(k), and u_i(k) denote the position, velocity, and control input of robot i at time t(k) = kτ According to prior research [40], these dynamics can be modeled as a discrete linear system: x_i(k+1) = A_i x_i(k) + B_i u_i(k), where A_i and B_i are system matrices, and the state vector x_i = [p_i, v_i]^T includes both position and velocity To ensure safety and system stability, the velocities and accelerations are bounded, satisfying ∥v_i(k)∥ ≤ v_max and ∥u_i(k)∥ ≤ u_max.

This chapter focuses on time-varying formation (TVF) control for robot swarms operating in narrow spaces The desired formation configuration at time k is represented as δ(k) The TVF problem is formulated based on key definitions outlined in references [40] and [41], providing a foundation for dynamic coordination among swarm robots in constrained environments.

Definition 1 Time-varying formation: Let δ(k) = [δ 1 (k), , δ n (k)] T be a bounded time- varying vector that describes the desired formation configurations The formation is said to achieve a TVF δ(k) if all robots in the formation satisfy: k→∞lim n

(p i (k)−δ i (k)−c(k)) = 0 (3.2) where c(k) is the formation center at time k.

Definition 2 Safe formation: Given the TVF defined in Definition 1, this TVF is said to be safe for any robot i, with i ∈ {1, , n} in the formation if the following conditions are satisfied:

Remark 1 From Definition 1, the robots reach their desired positions, hence achieving the desired configuration In the decentralized approach, when (3.3) is established, the system also ensures convergence to the desired configuration [40] Conditions (3.4) –

(3.5) ensure collision avoidance both among robots within the formation and between any robot and surrounding obstacles.

Formation configurations refer to the shape that the robots form while cooperating and interacting with the environment This work considers two following primary configurations:

Figure 3.4: Overview of the proposed event-based reconfiguration control The proposed strategy is constructed by two primary emergent strategy, including “formation” and

“tailgating”, which are highlighted by red boxes There are five individual behaviors that contribute to the emergent strategy, which illustrated via blue boxes.

1 Desired configuration: The desired configuration represents the arrangement that the robot swarm is expected to maintain to accomplish its task Common desired configurations include shapes such as polygons and V-shapes.

2 Straight line configuration: This formation configuration is employed when the robots do not have enough space to maintain their original configuration It is constructed by having a robot follow and keep desired distance from its leader.

Event-based Reconfiguration Control

To solve the TVF (Transport Vehicle Formation) problem, multiple force-based behaviors are implemented for each robot to synthesize an effective controller These behaviors include emergent strategies designed to navigate narrow spaces while maintaining the shape and safety of the TVF, referred to as “formation” and “tailgating.” In “formation” mode, the TVF preserves its original configuration, ensuring cohesive group movement Conversely, in “tailgating” mode, the TVF realigns into a straight-line configuration for efficient traversal, as detailed in Section 3.2.3 The proposed strategies and behaviors are visually explained in Figure 3.4, providing a comprehensive overview of the control approach for maintaining TVF integrity in constrained environments.

Our approach integrates an event-triggering mechanism into the TVF, enabling the swarm to adapt its formation shape dynamically in response to environmental conditions for safe navigation Initially, the desired formation configuration, denoted as δ₀, is assigned to the TVF, and the formation maintains this topology at time k However, in confined spaces, maintaining the original topology may lead to potential collisions, prompting the system to trigger a new formation topology based on the surrounding environment Once the confined space is no longer detected, the formation reverts to its initial configuration δ₀ The proposed control strategy effectively manages formation adjustments through this adaptive mechanism, with collaborative and collision avoidance controls driven by the Artificial Potential Field (APF) term during movement.

The potential field model is a state-of-the-art approach used to design individual robot behaviors, enabling efficient swarm navigation in confined environments This model incorporates attraction rules to maintain formations, facilitate tailgating, and guide robots toward their goals Additionally, repulsion rules are implemented to prevent inter-robot collisions, ensuring safe operation within the swarm Obstacle avoidance strategies are also integrated to help robots navigate safely around obstacles, enhancing overall navigation performance.

To facilitate goal-directed motion in various environments, a target-reaching behavior is implemented using a preferred velocity vector This vector combines the preferred speed, denoted as v_ref, and the preferred direction, represented by u_ref [44] The migration term, which is consistent across all agents, is calculated as v_m_i = v_ref * u_ref, ensuring smooth and directed movement toward the target.

The formation behavior is engineered as an attractive force that guides robots to their target positions, ensuring cohesive group movement A scale ratio, denoted as κ ∈ R and detailed in Section 3.3.2, allows for scalable adjustments of the formation To maintain the desired shape and enhance the adaptability of the TVF, a relative position-based controller is employed, with the control input defined as v_fi = k_f n, facilitating scalable and flexible formation control.

(p j −p i −κ(δ j −δ i )) (3.7) wherek f >0 is the formation control gain.

Tailgating behavior in the TVF is designed based on the relative positioning between robots to facilitate navigation through narrow environments Specifically, each robot follows its target robot within a desired distance, \(d_{ref}\), which is greater than twice the robot radius (\(d_{ref} > 2r\)) This behavior is governed by an attractive force field that ensures smooth and safe movement, enabling effective maneuvering in constrained spaces.

The tailgating control gain, denoted as \(k_t\), plays a crucial role in maintaining formation stability To identify the leader robot within the network, the inner product \(\tilde{p}_{ij}\) is calculated between the position difference of neighbor robot \(j\) and robot \(i\), specifically \(p_j - p_i\), and the desired direction \(u_{ref}\) This inner product is expressed as \(\tilde{p}_{ij} = \langle (p_j - p_i), u_{ref} \rangle\), enabling the system to determine the relative alignment and facilitate coordinated movements among robots.

In the swarm, the value of ˜p_ij is positive when robot j is positioned ahead of robot i based on the reference vector u_ref, confirming the relative frontward position of robot j For each robot i, a set P_i is established, containing all ˜p_ij values for neighboring robots j The leader robot l_i for robot i is identified as the closest robot directly in front, determined by selecting the robot with the minimal ˜p_ij value among those ahead This approach facilitates accurate leader selection and spatial awareness within the robot swarm, optimizing coordinated movement and interaction.

 arg min j {p˜ ij ∈ P i |p˜ ij ≥0} ∃ p˜ ij ≥0

To ensure safety, the system incorporates both inter-agent and obstacle avoidance behaviors to prevent collisions The set M_i consists of the closest finite points on the obstacle's boundary to robot i, as shown in Figure 3.2 Repulsive forces are applied based on these points, modeled by the equation v_ii = k_i * n, where k_i is a force coefficient and n is the unit vector directed away from the obstacle This design effectively enhances collision avoidance capabilities in robotic navigation.

X j=1,j̸=i v i ij (3.11) v o i =k o X o∈M v io o (3.12) where k i , k o > 0 is the inter-agent collision and obstacle avoidance gains, respectively. Denotep ij =p i −p j , and ˆp ij = p ij

In robotic navigation, ∥p_ij∥ represents the relative position and the normalized vector between robot i and robot j, facilitating effective collision avoidance Similarly, p_io and ̂p_io denote the relative position and normalized vector between robot i and obstacle o, where o belongs to the set of obstacles M_i The corresponding inter-agent avoidance velocity v_ij and obstacle avoidance velocity v_o_io are derived based on these relative positions and vectors, enabling the robot to navigate safely while avoiding collisions with both other robots and obstacles in its environment.

3.3.2 Event-based Reconfiguration Control strategy

The proposed event-based reconfiguration control, as illustrated in Figure 3.4, employs two emergent strategies to guide the TVF safely through narrow space environments while preserving its shape and ensuring swarm safety At each time step, individual robots autonomously determine their operational mode based on local sensor data, enabling adaptive and coordinated movement Overall, this approach allows the swarm to navigate constrained spaces effectively, maintaining formation integrity and safety throughout reconfiguration.

 v f i +v m i +v c i +v o i if mode = “formation” v t i +v m i +v c i +v o i if mode = “tailgating” (3.15)

To optimize the large parameter space Ξ = {kf, kt, ki, ko} of the controller, evolutionary algorithms are employed to achieve high-order flight performance and minimize collisions The swarm behavior is evaluated using a single fitness function that combines three independent metrics—order, agent safety, and obstacle safety—each contributing to an overall score, ideally less than or equal to 1 This fitness assessment is conducted through simulations where the swarm is randomly initialized in an environment with randomly placed obstacles, ensuring robust parameter tuning For detailed procedures on seeking optimal parameter values, refer to source [12].

An event-based mode switching system is designed to enable robots to navigate narrow space environments effectively This approach allows each robot to adapt its mode dynamically based on its perception of the surrounding environment and its individual behaviors By leveraging emergent strategies, the system ensures that robots can seamlessly switch modes at each time step, enhancing navigation precision and operational efficiency in complex settings This adaptive mode selection is crucial for optimal performance when maneuvering through confined spaces.

Each obstacle point in the set M i is clustered into two clusters on the left and right sides of the robot in u ref direction Denote o l and o r are the nearest obstacle points on the left and right sides, respectively, whose distance to the robotiis minimum If o l and o r exist, the width of the environment can be estimated by the magnitude of the cross product of the vector (o r −o l ) and the desired direction u ref as follows: w e =∥(o r −o l )×u ref ∥ (3.16)The estimation of the environment’s width can be depicted in Figure 3.5 Besides,the formation’s width w f can be easily determined through the predefined formation

Figure 3.5: Environment’s width estimation topology Given the widths of the environment and formation, the scaling factorκ, which contributes to (3.7), can be computed as follows: κ 

Each robot can select its operating mode and determine the appropriate scaling factor κ for computation A threshold value λ > 2 is used to switch between modes, ensuring smooth transitions As detailed in Algorithm 1, the desired velocity ˜v_i corresponding to the selected mode can be accurately calculated, promoting efficient and adaptable robot behavior.

After summing the contributions, we apply a cutoff on the acceleration at u max according to u i = u˜ i

∥u˜ i ∥min(∥u˜ i ∥, u max) (3.18) where ˜u i (k+ 1) = (˜v i (k+ 1)−v˜ i (k))/τ Then, we apply a cutoff on the speed at v max , and get the velocity commandv i as follows: v i = v˜ i

Theorem 1 Given the TVF as described in (3.1), under the control law given in (3.15), the TVF asymptotically converges to the desired configuration.

Results

The proposed strategy is evaluated in a complex environment comprising two distinct areas with different obstacle types The first area simulates a forest-like setting, featuring an obstacle density of 0.05 obstacles per square meter within the range of -12 m to 0 m The second area represents a width-varying cave-like environment, where the narrowest passage measures just 1 meter, spanning from 0 m to 20 m The true value function (TVF) begins to operate within this challenging environment, demonstrating the robustness of the strategy across diverse terrain conditions.

Figure 3.6: Motion paths and velocity profiles of the proposed ERC strategy in multiple configurations.

(b) V-shape configuration Figure 3.7: Theorder values of the proposed ERC strategy

Sc ali ng fa cto r

The study examines the correlation between the number of robots in each mode, represented by a bar chart, and the scaling factor of the proposed ERC strategy, depicted by a black line The robots are randomly initialized on the left side of the environment and tasked with navigating through confined spaces toward the right, following a desired direction u_ref = [1, 0, 0]^T A formation of five homogeneous robots, each with a radius of 0.3 meters, sensing radius of 3.0 meters, and alert radius three times their size, is utilized The formation can adopt two configurations: V-shape and polygon, with the TVF transforming accordingly to adapt to environmental constraints.

In the "tailgating" mode, the robot is programmed to maintain a desired following distance of 1 meter from its leader, with constraints of a maximum speed (v max) of 2 m/s and a maximum acceleration (u max) of 2 m/s² The control system operates with a period (τ) of 0.1 seconds The study compares the proposed control strategy against pure behavior-based control (BC), evaluating performance using metrics such as success rate, mean speed, and mean acceleration cost (calculated as P ∥u(k)∥² / nT, where T is the total travel time) To ensure a fair comparison, identical parameters are used in both methods.

This study demonstrates how the ERC effectively guides a TVF to navigate through confined spaces using optimized motion paths and velocity profiles, as shown in Figure 3.6 Both polygon and V-shape formations successfully maneuver through challenging environments such as forests and tunnels, highlighting the robustness of the proposed strategy Starting from an initial disorganized position on the left, the robots move in the desired direction, form the predefined shape, and activate obstacle avoidance behaviors when encountering obstacles In narrow passages, the formation transitions from “formation” mode to “tailgating” mode, creating a straight-line configuration that facilitates passing through tight gaps Once past the obstacle, the formation reverts to its original shape, ensuring seamless navigation through complex confined spaces The motion paths depicted in Figure 4.4 validate the effectiveness of the proposed method across multiple formation configurations.

To evaluate the effectiveness of the proposed strategy, the order Φ metric is introduced to quantify the heading disturbance of robots in formation during movement This metric ranges from 0 to 1, where higher values indicate a more synchronized heading When the formation lacks a clear heading, the order approaches zero, demonstrating the degree of coordination among the robots.

(3.29) wherev i is the velocity of robot i.

Figure 3.7 demonstrates the heading order of the TVF swarm during movement, indicating a satisfactory formation with an order value of Φ = 1 in both scenarios When encountering obstacles, the heading order briefly changes but the overall formation remains intact However, transitions between “formation” and “tailgating” show increased disorder in heading order due to significant structural changes in the formation This analysis highlights the swarm’s ability to maintain coherence during movement while experiencing temporary disarray during formation transitions.

Figure 3.8 illustrates the relationship between the number of robots in various modes and the scaling factor κ, assessing the effectiveness of the proposed deformation strategy's synthesized controllers When the TVF encounters obstacles, each robot adapts its configuration based on individual observations, resulting in different operational modes across the robot team The scaling factor κ varies between robots depending on their position and observation, influencing their behavior In obstacle-free environments, all robots maintain a "formation" mode, preserving the original configuration and ensuring coordinated movement.

On the other hand, when narrow space is detected by all robots, the mode transforms to “tailgating”, which forces robots to the straight line configuration to safely navigate

Table 3.1 compares the performance of BC and our innovative ERC method across 10 simulations involving 5 robots in two different configurations The evaluation metrics include success rate, mean speed, and mean acceleration cost, highlighting the effectiveness and efficiency of each approach Our ERC method demonstrates superior success rates and optimized movement costs, establishing its advantages over traditional BC in robotic control tasks These results underscore ERC's potential for enhancing robotic navigation performance in varied configurations.

Configuration Strategy Success Mean speed

(a) Gazebo SIL model (b) Real UAV model [58], [59]

Figure 3.9: Used Hummingbird UAV model through narrow space The value of κ = 0 when all robots in the TVF are in the

The proposed ERC strategy significantly outperforms the traditional behavioral-based control (BC) in success rate, effectively navigating formation passes through confined spaces without collisions, as demonstrated in Table 3.1 and Figure 3.1 Unlike BC, which consistently fails in narrow spaces, ERC successfully manages obstacle avoidance through adaptive configuration, resulting in lower mean acceleration costs and improved energy efficiency Although the mean speed of the TVF is slightly reduced due to the translation mode affecting movement speed, ERC offers an effective and reliable method for obstacle handling and formation navigation in constrained environments.

3.4.2 Validation on the software-in-the-loop Gazebo

We conducted a software-in-the-loop (SIL) validation to assess the effectiveness of the proposed system, focusing on navigating UAV formations through a narrow tunnel-like environment within Gazebo The experiment utilized a Hummingbird quadrotor model, developed based on the Gazebo-based RotorS simulator, as illustrated in Figure 3.9a Three UAVs were deployed in the test to evaluate formation control and navigation performance in confined spaces.

1 Gazebo experiment video: https://youtu.be/AIAAzRiIepg

(b) Random initial positions Figure 3.10: The environment in SIL test

(a) Maintain triangle formation from random (b) Small-scaled triangle formation

(c) Transform to line formation (d) Line formation

(e) Transform back to triangle formation (f) Original triangle formation

Figure 3.11: Validation results captured in the SIL Gazebo step = 1 step = 375 step = 750 step = 1125 step = 1500 step = 1875 step = 2250 step = 2625 step = 3000

In the SIL test illustrated in Figure 3.12, the recorded flight paths of three UAVs are shown from a top view, demonstrating their trajectories at random positions The environment designed for the SIL test features two large obstacles that create a tunnel with varying width, as depicted in Figure 3.10b and 3.10, providing a challenging scenario for UAV navigation and testing the robustness of the flight control system.

The experiment depicted in Figure 3.11 illustrates the formation movement of UAVs, with the paths recorded in Figure 3.12 Initially, at step 1, three UAVs start from random positions before converging to form the desired triangle formation between steps 375 and 750 During navigation through a narrow passage (steps 1125 to 1500), the formation gracefully shrinks to ensure safe passage, as shown in Figure 3.11b When the space becomes too tight for the original formation, the UAVs transform into a straight line formation, allowing them to pass through the narrow area effectively, as demonstrated in Figure 3.11c This adaptive formation control enhances UAV coordination and obstacle navigation efficiency in complex environments.

The UAVs utilize an ERC strategy to navigate through tight spaces, as demonstrated in the experiment where the formation adapts to environmental constraints Once the UAVs detect sufficient space, they smoothly revert to their original formation, as shown in Figure 3.11d and 3.11e Subsequently, the formation advances toward the target location, depicted in Figure 3.11f, during steps 2625 to 3000 This process effectively showcases the ERC strategy's capability to guide UAV formations through narrow passages and achieve accurate target navigation.

Predictive Reconfiguration Control for Multi-Robot Forma-

Introduction

Formation control of multiple robots is crucial for performing complex tasks such as disaster response, search and rescue, target tracking, and swarm reconnaissance, enhancing operational effectiveness in challenging environments [1], [4] It improves system resilience by allowing the swarm to reconfigure its formation in case of malfunctions, ensuring continuous operation Formation reconfiguration enables robots to adapt to cluttered and dynamic environments where static formations are inadequate, making flexible formation control essential for effective swarm navigation and task execution.

In formation control, natural collective behaviors such as schooling fish and flocking birds serve as a foundation, involving simple actions like repulsion from neighbors, cohesion towards the group, migration in preferred directions, and obstacle avoidance These behaviors are often integrated with artificial potential fields (APF) to generate control signals for robot navigation Studies have combined formation and navigational behaviors as concurrent processes to efficiently guide robot swarms toward their goals in specific formations Additionally, fish-inspired underwater robots utilize APF to coordinate behaviors and achieve collective capabilities without direct communication However, behavior-based methods face limitations in complex environments, as fixed behaviors lack the flexibility needed to adapt to abrupt environmental changes.

Recent research highlights the limitations of behavior-based swarm algorithms and proposes hybrid approaches that combine Artificial Potential Fields (APF) with optimization techniques For instance, integrating APF with neural networks allows the adaptation of potential force parameters to changing environmental conditions, thereby improving swarm responsiveness Additionally, evolutionary optimization frameworks are employed to select optimal parameters and fitness functions that enhance swarm velocity and cohesion However, optimizing parameters alone does not fully resolve the core issue of fixed behavior sets in behavior-based approaches, emphasizing the need for more flexible and adaptable strategies.

Recent advancements in swarm management include the use of optimal control techniques to handle constraints and predict agent states for reliable formation control Optimization-based motion planners are employed for point-to-point transitions, ensuring formation integrity and collision avoidance in multi-robot systems Model Predictive Control (MPC) has been introduced for swarm navigation, utilizing cost functions and constraints to regulate speed, enhance safety, and guide drones through complex environments While centralized MPC relies on a primary agent, decentralized approaches offer distributed computation for formation control but are mainly effective in spacious, cluttered environments Maintaining specific formations in tight spaces remains challenging due to the conflicting requirements of shape preservation and collision avoidance.

In another direction, several studies propose control techniques that reconfigure the formation in response to sudden changes in the environment structure [11], [46], [47],

Several methods have been proposed for adaptive robot formation reconfiguration in environments with static and dynamic obstacles For example, a distributed approach computes a movable convex region from robots’ current positions, allowing repositioning within this space based on desired directions, though it relies on reassigning robots to predefined virtual points rather than utilizing environmental information Another technique utilizes affine transformations to modify formation shapes for obstacle avoidance in dense settings, requiring full communication among robots Our previous work introduced a V-shape formation that adapts by expanding or contracting its wings to navigate narrow corridors, but it did not account for the robots' physical constraints, risking infeasible control inputs and collisions Additionally, local decision-making based solely on sensor data remains limited, highlighting the need for more robust, environment-aware formation control strategies.

This work introduces a novel technique called predictive reconfiguration control (PRC) to ensure safe and efficient navigation of decentralized multi-robot swarms in cluttered environments Equipped with local sensors and communication modules, robots gather environmental and neighboring robot information to facilitate adaptive formation control Building on recent advances in multi-robot formation, the PRC enables robots to dynamically reconfigure their formations for improved maneuverability and safety The main contributions include the development of a decentralized control method that enhances obstacle avoidance, coordination, and robustness of robot teams operating in complex environments This approach advances multi-robot formation strategies by providing reliable and flexible navigation solutions for cluttered terrains.

1 Model the formation as a directed sensing graph where each node represents a robot capable of sensing its surroundings and communicating with its neighbors. This representation allows the system to be decentralized and the formation to be formulated as an optimization problem.

2 Define a set of cost functions that represent the formation constraints and performance The functions ensure not only the desired formation shape but also the swarm’s performance, including the desired velocity, direction, and obstacle avoidance The cost functions are designed to be compatible with existing solvers for MPC, thereby simplifying the implementation.

3 Propose a predictive reconfiguration controller with two modes, “formation” and

The "tailgating" controller is capable of adapting the formation shape dynamically in response to environmental changes, ensuring robust and flexible multi-agent coordination Extensive simulations and comparisons confirm its effectiveness, scalability, and robustness in various scenarios Software-in-the-loop tests further validate the practical applicability of the proposed controller for real-world implementations Additionally, the source code is publicly available, promoting further research and practical deployment in autonomous systems.

This chapter is structured into several key sections: Section 4.2 details the formation model, providing the foundational framework for the study Section 4.3 introduces the proposed formation reconfiguration control method, highlighting its approach and advantages Section 4.4 presents comprehensive simulations, comparisons, and software-in-the-loop experimental results to validate the effectiveness of the proposed method Finally, conclusions are summarized in Section 4.5, encapsulating the main findings and future research directions.

Formation Background

Consider a swarm of n robots labeled i ∈ {1, , n}, modeled as a directed sensing graph G = (V, E) In this model, the vertex set V = {1, , n} represents the individual robots, and the edge set E ⊆ V × V includes pairs (i, j) where robot i can sense robot j The set of neighbors for each robot i, denoted as N_i, consists of all robots j for which the sensing edge (i, j) exists in the graph, indicating the robots that robot i can detect and interact with.

This study models robot swarm dynamics in discrete time, where each robot's position, velocity, and control input are represented as p_i(k), v_i(k), and u_i(k) respectively at time t(k) = kτ, with τ being the sampling period Homogeneous robots with a body radius r are equipped with inertial measurement units (IMUs) for precise positioning and orientation, range sensors offering a 360° field of view for environmental scanning, and wireless ad-hoc network modules enabling peer-to-peer communication In this work, communication delays between robots are considered negligible, ensuring real-time data exchange within the swarm.

S s of radiusr s , as shown in Figure 4.1 Its point data obtained at timet(k) is represented by setM i (k) ={m}.

In swarm robotics, each robot can be modeled as a discrete linear system, represented by the equation \( x_i(k+1) = A_i x_i(k) + B_i u_i(k) \) [64], where \(A_i\) and \(B_i\) are system matrices, \(u_i\) is the input acceleration, and the state vector \(x_i = [p_i; v_i]\) includes position and velocity The velocities and accelerations are constrained within specified bounds, with velocity limits \(v_{min} \leq v_i(k) \leq v_{max}\) and acceleration limits \(u_{min} \leq u_i(k) \leq u_{max}\).

Figure 4.1: Illustration of a robot with its range sensor having the scanning area S s

(dashed gray circle) of radiusr s and setM i ={m} (green) of the acquired point data.

Figure 4.2: Diagram of the proposed predictive reconfiguration control strategy.

Predictive Reconfiguration Control

The primary goal of reconfiguration control in robot swarms is to navigate through cluttered environments with narrow passages while maintaining specific constraints These constraints include preserving desired shapes (C1), moving in a prioritized direction (u_ref ∈ R^3) (C2), achieving a desired speed (v_ref ∈ R) (C3), and avoiding collisions with neighbors and obstacles (C4) To accomplish this, a predictive reconfiguration control system has been developed, utilizing inputs such as point cloud data from range sensors and the states of neighboring robots Based on the environmental structure inferred from the point cloud data, the controller can adapt its operation to ensure safe and efficient navigation through complex spaces.

The robot operates in either “formation” mode, which maintains a specific shape, or “tailgating” mode, which transforms the formation into a line for navigating narrow spaces such as valleys or tunnels The control system is designed using a weighted sum of five cost functions to satisfy constraints (C1)–(C4), ensuring effective and safe navigation An optimal solver is employed to generate control signals for the low-level controllers, enabling precise maneuvering in various environments.

In multi-robot formations, δ_ij ∈ R³ represents the desired position of robot i relative to neighbor j The formation is achieved through a constraint ensuring that the difference in positions between robots, adjusted by a scaling factor κ, converges to zero over time: limₖ→∞ (p_j(k) - p_i(k) + κδ_ij) = 0 for all pairs of robots i and j The parameter κ ∈ [0,1] controls the formation's shrinkage level, allowing flexible formation adjustments The desired relative position of each robot i within the formation is denoted as p*_i(k), which is determined by the average position across all robots, facilitating coordinated movement This approach ensures stable and scalable multi-robot formations aligned with specific spatial constraints for optimal coordination. -🌸 **Ad** 🌸 Optimize your multi-robot formation control research with [Claude’s](https://pollinations.ai/redirect/claude) advanced reasoning and massive context capabilities.

During mode transitions, each robot designates a leader to serve as a positional reference, ensuring seamless coordination within the group The leader selection is based on calculating the inner product between the difference in position vectors (p_j − p_i) of neighboring robots and the desired direction, u_ref, as expressed by ˜p_ij = ⟨(p_j − p_i), u_ref⟩ This approach helps robots determine their relative positions and facilitates effective movement alignment during mode changes Implementing this method enhances the accuracy and stability of multi-robot coordination in various operational scenarios.

A positive value of ˜p_ij indicates that robot_j is positioned in front of robot_i in the reference direction Conversely, a negative value signifies that robot_j is behind robot_i The set P_i encompasses all inner products between robot_i and its neighboring robots j within the neighbor set N_i, providing a comprehensive measure of their relative orientations This approach helps in understanding the spatial relationships and alignment among robots, which is essential for coordinated navigation and control in multi-robot systems.

P i ={p˜ ij } Leader robot l i of robot i is chosen as the closest robot in front of it, i.e., l i 

 arg min j {p˜ ij ∈ P i |p˜ ij ≥0} ∃ p˜ ij ≥0

Algorithm 2: Pseudocode of the leader selection

2 Compute inner product ˜p ij ; /* Eq 4.4 */

4 Select leaderl i for robot i to follow; /* Eq 4.5 */

Algorithm 2 presents the leader selection process.

In "tailgating" mode, robot i maintains an optimal distance \( d_{ref} \) from its leader \( l_i \), ensuring precise alignment This behavior is mathematically described by the limit \(\lim_{k \to \infty} \| p_{li}(k) - p_i(k) \| = d_{ref}\), which guarantees that the distance converges to the desired value over time The target position for robot i is then determined by subtracting the reference distance along the leader’s direction, expressed as \( p_i^*(k) = p_{li}(k) - d_{ref} u_{ref} \), enabling effective and coordinated tailgating in robotic formations.

Using equations (4.4) and (4.7), the formation problem is converted into tracking the desired positionp ∗ i , which can be handled by predictive controllers.

The proposed predictive controller leverages the desired position p∗i as a reference point and employs multiple cost functions to ensure formation constraints (C1)−(C4) Key cost functions include tracking cost (Jt,i), direction cost (Jd,i), speed cost (Js,i), obstacle avoidance cost (Jo,i), inter-agent collision cost (Ji,i), and control effort cost (Ju,i) The prediction horizon, denoted as P ∈ N+, is finite and advances at each time step The predicted state at future time step (k + l), given information up to time k, is represented as ã(k + l|k), where l ∈ {0, , P}.

Obstacle points set with left/right clustering Obstacle points set in direction

Obstacle set Obstacle set Obstacle set in left hand side Obstacle set in right hand side

Figure 4.3 illustrates the process of estimating the environment’s width using the robot’s range sensor data The predicted value of (ã)(k+l) is calculated based on information available at time t(k) The sequence of predicted states, denoted as Xi(k), belongs to the R^6P space and represents the predictions x_i(k + l|k) over the horizon l ∈ {1, , P} This approach enables accurate environment measurement and robust localization for the robot.

U i (k) ∈ R 3P be the sequence of the predicted control inputs u i (k) over the horizon l∈ {0, , P−1} The predictive reconfiguration control can be modeled as a non-convex optimization problem as follows:

(4.9) with l∈ {1, , P}, and i∈ N The cost functions are defined as follows.

The tracking term is designed to direct robots toward their respective reference positions, ensuring the formation shape is accurately achieved It is mathematically defined as the squared error between the desired position, p*i, and the predicted position, pi, of robot i This error metric plays a crucial role in guiding robot movements and maintaining precise formation control Optimizing this tracking term helps enhance the accuracy and stability of multi-robot formations in various applications.

∥p ∗ i (k+l|k)−p i (k+l|k)∥ 2 , (4.10) wherew t is a positive tracking weight.

The speed cost is a crucial component in maintaining the desired speed, denoted as v_ref, of the swarm It is calculated based on the squared difference between each robot's actual speed and the target speed, ensuring precise velocity control By minimizing this speed cost, the swarm can efficiently operate at the desired velocity, enhancing coordination and overall performance Incorporating the speed cost into the control algorithm helps optimize robot movement and maintains consistent swarm behavior aligned with mission objectives.

∥v i (k+l|k)∥ 2 −v 2 ref 2 , (4.11) wherew s is a positive weight.

The cost function guides robots to move in the desired direction \( u_{ref} \) by evaluating the normalized dot product between the robot's velocity \( v_i \) and the reference direction When the robot's velocity perfectly aligns with \( u_{ref} \), the cost equals zero, indicating optimal movement As misalignment increases, the cost proportionally rises, reflecting the deviation from the intended direction This calculation ensures precise control of robot navigation, optimizing movement efficiency and accuracy.

, (4.12) wherew d is a positive direction weight.

To prevent collisions, the distance between a robot and any obstacle must be greater than its radius \( r \), and the distance between any two robots must exceed twice their radius \( 2r \) The distance between robots \( i \) and \( j \) is defined as \( d_{ij} = \| p_j - p_i \| \), and the distance between robot \( i \) and obstacle \( m \) is denoted as \( d_{im} \) The collision avoidance constraints are expressed as \( d_{im}(k + l|k) \geq r \) for all robots \( i \) in the set \( N \) and obstacles \( m \) in the set \( M_i(k) \), and \( d_{ij}(k + l|k) \geq 2r \) for all robots \( j \) in the neighborhood \( N_i \).

In this work, constraint (4.13) is represented via obstacle avoidance cost J o,i defined as a logistic function as follows [69]:

1 + exp (α(d min im (k+l|k)−r)), (4.15) wherew o >0 is a constant weight, α >0 is a smoothness parameter, and d min im (k+l|k) = min{d im (k+l|k)|m∈ M i } (4.16)

Similarly, constraint (4.14) is represented via an inter-agent collision cost J i,i defined as follows [7]:

F ij (k+l|k), (4.17) wherew i >0 is a constant weight and

0 if d ij (k+l|k)≥βr βr−d ij (k+l|k) (β−2)r if 2r < d ij (k+l|k)< βr

(4.18) with β >2 being the influence ratio of the neighbors.

The control effort cost is used as a penalty term to minimize the control signal It is defined as:

∥u i (k+l|k)∥ 2 , (4.19) wherew u >0 is a constant control weight.

The control system adapts the formation shape and scaling factor κ based on the environment’s width As shown in Figure 4.3, the environment width estimation process begins with the robot collecting point cloud data M_i (green) from its local sensors The robot then selects a specific point set, M_ui (red), positioned ahead along the movement direction u_ref, to accurately determine the environment’s dimensions and adjust its formation accordingly.

The DBSCAN algorithm is employed to segment M ui into two clusters representing the robot's left (blue) and right (yellow) sides The data points M i,l and M i,r, which are closest to a reference point u ref, are selected from these clusters for further analysis Using these points, the environment's width is calculated with the formula w e = ∥(M i,r − M i,l) × u ref∥ The process of estimating the environment’s width is summarized in Algorithm 3.

The formation’s width, denoted as w_f, is predefined for each specific formation shape to ensure accurate scaling The scaling factor, κ, is then calculated based on both the environment’s conditions and the formation’s width This ensures precise adjustment of the formation's size and layout, optimizing performance across different scenarios Properly determining κ is essential for maintaining formation coherence and adaptability in various operational environments.

0 otherwise (4.22) where λ > 2 is a scaling coefficient determining the environment’s width at which the PRC switches its mode.

Algorithm 3: Pseudocode to estimate the environment’s width

1 Get point set M ui in front of robot i in moving direction u ref ; /* Eq 4.20 */

2 Cluster M ui for the left and right sides of the robot using DBSCAN;

3 Find point pair (M i,l ,M i,r ), whose distance to u ref is minimum;

4 Compute the environment’s width w e ; /* Eq 4.21 */

Results and Discussion

A number of simulations, comparisons, and software-in-the-loop tests have been conducted to evaluate the performance of the PRC with details as follows.

The swarm consists of five identical robots, each with a radius of 0.2 meters and a maximum speed of 1.5 meters per second Equipped with range sensors that have a sensing range of 3 meters, these robots are capable of precise environmental awareness The robots are programmed to achieve a pentagon formation shape, with a reference velocity of 1 meter per second and maximum control inputs of 2.0 meters per second squared, ensuring coordinated movement and formation stability.

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(c) Scenario 1 - Correlation between the number of robots (bar chart) in each mode and the scale factor (black line) over time

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(d) Scenario 2 - Correlation between the number of robots (bar chart) in each mode and the scale factor (black line) over time

Figure 4.4 illustrates the trajectories and formation shapes of robots controlled by the Potential Field-based Reinforcement Control (PRC) algorithm across two evaluation scenarios The robots navigate within environments featuring two structures with narrow passages, as shown in the figure The intended movement direction is along the vector [1, 0, 0]ᵗ, highlighting the robots' capability to efficiently maneuver through complex environments with constrained pathways This demonstrates the effectiveness of the PRC method in guiding multi-robot systems in challenging navigation tasks involving tight spaces, ensuring coordinated formation control.

Evaluation of the system's performance is conducted using key metrics such as success rate, mean order (Φ), mean speed (m/s), mean formation error (ε), and acceleration cost (Γ), as outlined in recent studies [73] The order metric [37] specifically assesses the heading consensus among robots, calculated with the formula Φ = 1 These metrics collectively provide a comprehensive understanding of the robots' coordination, efficiency, and accuracy in formation tasks Optimizing these parameters is crucial for improving robotic swarm performance in various applications.

The formation error, which measures the deviation between the desired and actual positions of the robots, is calculated as εi = ∥pi - p*i∥, where its value ranges from 0 to 1; a value of 1 indicates that the robots are moving in the same direction, highlighting the importance of minimizing this error to ensure accurate formation control and coordination in robot fleets.

The acceleration cost indicates the control effort and is given by: Γ = 1 n

The comparing methods include the behavior-based reconfiguration control (BRC) [12] and the predictive formation control (PFC) [66] In evaluation, each method is run 10 times for each scenario.

Figure 4.4 demonstrates the formation process for both scenarios, highlighting how robots rapidly assemble into a pentagon shape after takeoff They then adapt their formation to pass through tight passages before transforming back to the original configuration The figures also illustrate the scaling factor κ and the number of robots involved in each control mode, emphasizing the flexibility and coordination of the robotic system throughout the maneuver.

BRC - Max/Min BRC - Mean PFC - Max/Min

PFC - Mean PRC - Max/Min PRC - Mean

Figure 4.5: Comparison results of three control methods in two scenarios.

Av e for ma tio n e rro r (m )

Figure 4.6: Effect of the swarm size on system performance, including the mean order Φ and formation errorε.

Table 4.1: Comparison between BRC, PFC, and the proposed PRC

Scen Method Success rate Mean order Φ Mean speed

PRC 9/10 0.9830 0.9800 0.3217 21.8559 during operation When the environment’s width is large, the scaling factor κ stays at

The PRC enables a robot swarm to reconfigure and adapt to complex environments by adjusting formation shape As the environment narrows, the parameter κ gradually decreases, causing more robots to switch to “tailgating” mode and the formation to shrink When κ reaches zero, all robots are in “tailgating” mode, allowing the swarm to navigate through tight spaces Upon exiting the narrow corridor, κ increases, restoring the formation to its original shape and size This dynamic reconfiguration capability ensures robust maneuverability of the robot swarm in various environmental conditions.

Figure 4.5 compares the performance of the PRC with other control methods, highlighting its superior stability and accuracy The proposed controller maintains more stable velocities closer to the reference velocity, as demonstrated by the average and maximum/minimum values in Figures 4.5a-4.5b In terms of the order metric, PRC quickly stabilizes after initial fluctuations, reaching a high consensus among robots with an order value of 1, as shown in Figures 4.5c-4.5d Although both BRC and PFC perform well, BRC exhibits greater variation during the transition phase compared to PRC.

The PRC outperforms other formation maintenance methods by achieving the smallest average error, as demonstrated in Figures 4.5e-4.5f and confirmed by the comparison data in Table 4.1 It consistently exhibits high performance across all metrics, with the highest success rate and minimal formation error in both scenarios While the PFC fails in scenario 2 due to its limited reconfiguration capabilities, the BRC shows good speed and mean order performance but incurs high acceleration costs, indicating lower energy efficiency.

Our experiments tested swarm sizes of 4, 5, 7, 10, 15, and 20 robots to evaluate the scalability of the proposed method Results indicate that as the number of robots increases, the PRC maintains strong consensus with a mean order close to 1 Additionally, the formation error remains low, averaging around 0.05 meters, during steady-state operations These findings demonstrate that the PRC approach is scalable and consistently performs well across various swarm sizes.

4.4.3 Software-in-the-loop verification

We conducted software-in-the-loop (SIL) tests to assess the performance of the proposed controller under realistic conditions These tests took place in a narrow environment featuring two large obstacles that create a cave-like structure, as illustrated in Figure 4.7a.

(b) The drone model [58], [59] Figure 4.7: The robot and environment structure used for software-in-the-loop tests.

The reconfiguration process of the robot swarm during a SIL test involves several key steps Initially, the robots are positioned randomly, as shown in Figure 4.8(a) They then collaboratively form a precise pentagon shape to achieve the desired formation, illustrated in Figure 4.8(b) To adapt to environmental constraints, the swarm efficiently shrinks their formation, as depicted in Figure 4.8(c) When navigating through narrow passages, the robots switch to a “tailgating” mode, enabling smooth traversal through confined spaces, as shown in Figures 4.8(d) and 4.8(e) Finally, the swarm transforms back into the original pentagon shape, completing the reconfiguration process, as demonstrated in Figure 4.8(f).

(a) The formation and motion paths

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(b) Number of robots and scaling factor κ

Fo rm at ion er ro r Max/Min

The computational time associated with the SIL tests was analyzed to evaluate performance efficiency Figure 4.9 illustrates the results of these tests conducted on five homogeneous Hummingbird quadrotors simulated using RotorS, with each drone featuring an arm length of 0.17 meters, a mass of 0.716 kg, and a specified rotor thrust constant These findings provide insights into the processing requirements and scalability of the simulation environment for multi-robot systems.

The robot features a rotor drag constant of 8.54858×10⁻⁶ Nm/A, as illustrated in Figure 4.7b, with a rotational speed of 1.6 to -2 N/A Each robot is outfitted with a range sensor for environment point cloud data collection, a positioning module to ensure accurate localization, and a communication module to facilitate interaction and data exchange with other robots, enhancing coordinated navigation and operational efficiency.

Figure 4.8 presents the formation reconfiguration process as the swarm navigates through the environment The robots continuously collect data about the environment and based on it adjust their formation to ensure safe operation Figure 4.9 provides a detailed view of the result Each UAV determines its mode and desired position based on the perception of the surrounding environment and information about its neighbors. The robots together form the relevant shape in a decentralized manner, as shown in Fig- ures 4.9a - 4.9b Requirements for speed, order, and formation accuracy are also met, as depicted in Figures 4.9c - 4.9e Moreover, the computational time per controller iteration, shown in Figure 4.9f, indicates that the system can operate at a sampling rate of 10 Hz in the worst-case scenario, which is sufficient for real-time robot operation.

1 Source code used to setup SIL tests in Gazebo - https://github.com/duynamrcv/hummingbird_ simulator

Evaluation and comparison results show the key properties of the proposed control method as follows:

The PRC is a fully decentralized system where each robot independently makes decisions based solely on its own sensor data and information from neighboring robots Unlike methods that require system-wide communication to gather information from all robots, the PRC employs only one-hop communication between a robot and its immediate neighbors This approach enhances efficiency by enabling localized updates of predictive states without the need for extensive communication networks.

Conclusion and Future Works 47

Tiêu đề	Distributed Control Strategies for Changing Multiple UAV Formation
Tác giả	Bui Duy Nam
Người hướng dẫn	Dr. Pham Duy Hung, Dr. Phung Manh Duong
Trường học	Vietnam National University, University of Engineering and Technology
Chuyên ngành	Electronics Engineering
Thể loại	Master thesis
Năm xuất bản	2024
Thành phố	Hanoi

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Số trang	69
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