In modern aerospace and defense applications, drone formations have emerged as a pivotal technology for executing complex missions such as surveillance, search and rescue, and coordinated attacks. However, one of the critical challenges in managing drone formations is ensuring reliable inter-drone communication under harsh environmental conditions, particularly in scenarios with strong electromagnetic interference (EMI). Traditional radio frequency (RF) based communication systems are highly susceptible to EMI, which can disrupt data exchange, leading to formation disarray, collisions, or mission failure. To address this, we propose a novel approach leveraging wireless ultraviolet (UV) light communication, which offers inherent advantages like non-line-of-sight (NLOS) capabilities, low background noise, and high resistance to interference. This paper presents a comprehensive method for drone formation assembly using UV relay cooperation, integrating consistency theory and UV-based virtual potential field obstacle avoidance to enhance formation accuracy and communication reliability. Our work aims to provide a robust framework for drone formations to rapidly and accurately assemble into desired geometries, such as quadrilaterals, pentagons, and hexagons, even in electromagnetically contested environments.
The core of our method lies in utilizing UV beacon models mounted on drones to facilitate information exchange and positioning within the formation. Each drone is equipped with a hemispherical UV LED array that emits encoded signals, allowing for precise identification and communication between neighboring drones. By combining this with a relay mechanism where follower drones act as intermediate nodes, we extend the communication range and improve the probability of successful data transmission. This is particularly crucial during the assembly phase, where drones must converge from dispersed initial positions to form a cohesive drone formation. We validate our approach through extensive simulations, demonstrating significant improvements in communication reliability for various formation shapes. The results show that our UV relay cooperative method enhances the robustness of drone formations, making them more resilient to external disruptions and ensuring mission success.
In the following sections, we delve into the technical details of our approach. First, we establish a three-dimensional (3D) motion model for individual drones, which forms the basis for controlling the drone formation. Next, we describe the wireless UV relay cooperative communication model, highlighting how UV signals are used for NLOS communication and relay coordination. Then, we present the formation assembly algorithm, which integrates consistency theory for state synchronization and a UV virtual potential field for obstacle avoidance. After that, we discuss simulation experiments and analyze the results, including communication performance metrics. Finally, we conclude with insights and future directions for enhancing drone formation technologies.
Three-Dimensional Motion Model for Drones
To effectively control a drone formation, it is essential to model the dynamics of individual drones as point masses in a 3D coordinate system. We define a global coordinate frame with origin O arbitrarily placed on the horizontal ground, axes Ox and Oy oriented arbitrarily in the horizontal plane, and axis Oz vertical upward. Each drone in the formation is indexed, and its motion can be described by a set of differential equations that account for position, velocity, and orientation. For the i-th drone in the drone formation, the equations of motion are given by:
$$ \dot{x}_i = v_i \cos \theta_i \sin \phi_i $$
$$ \dot{y}_i = v_i \cos \theta_i \sin \phi_i $$
$$ \dot{z}_i = v_i \sin \theta_i $$
$$ \dot{v}_i = \frac{T_i – D_i}{m_i} – g \sin \theta_i $$
$$ \dot{\theta}_i = \frac{1}{v_i} \left( \frac{L_i}{m_i} \cos \psi_i – g \cos \theta_i \right) $$
$$ \dot{\phi}_i = \frac{L_i \sin \psi_i}{m_i v_i \cos \theta_i} $$
Here, \((x_i, y_i, z_i)\) represents the position coordinates of drone i, \(v_i\) is its speed, \(\theta_i\) is the pitch angle, and \(\phi_i\) is the heading angle. The parameters \(m_i\), \(g\), and \(D_i\) denote the drone’s mass, gravitational acceleration, and aerodynamic drag, respectively. The control inputs are \(U = [T_i, L_i, \psi_i]\), where \(T_i\) is thrust, \(L_i\) is aerodynamic lift, and \(\psi_i\) is the roll angle. These equations allow us to simulate the trajectory of each drone as it moves within the formation, ensuring that we can model complex maneuvers required for assembly.
The communication topology within the drone formation is represented using graph theory. We consider N drones as nodes in a directed graph \(\mathcal{F} = (\mathcal{W}, \mathcal{E}, \mathcal{B})\), where \(\mathcal{W} = \{\omega_i | i=1,2,\dots,N\}\) is the set of nodes, \(\mathcal{E} \subseteq \{ e(i,j) | i,j \in \mathcal{W} \}\) is the set of edges indicating communication links, and \(\mathcal{B} = (b_{ij})_{N \times N}\) is the adjacency matrix. The element \(b_{ij}\) is defined as:
$$ b_{ij} = \begin{cases} 1 & \text{if } \omega_j \in \mathcal{N}_i \\ 0 & \text{otherwise} \end{cases} $$
where \(\mathcal{N}_i = \{\omega_j | e_{ij} \in \mathcal{E}, j \neq i\}\) denotes the set of drones that can communicate with drone i. This topology is crucial for coordinating the drone formation, as it determines how information flows between drones during assembly. For instance, in a hexagonal drone formation, the topology might involve bidirectional communication between neighboring drones, as illustrated in the communication graph. A key aspect of our approach is maintaining this topology through UV-based links, which are less prone to interference compared to RF systems.
Wireless Ultraviolet Relay Cooperative Communication Model
Wireless UV communication operates by scattering UV photons off atmospheric molecules and aerosols, enabling NLOS transmission. This property is particularly advantageous for drone formations, as it allows drones to communicate even when not in direct visual contact, such as in foggy or obstructed environments. To implement this, each drone is equipped with a UV beacon guidance device—a hemispherical array of UV LEDs arranged along longitudinal and latitudinal lines. Each LED has a unique ID based on its coordinates, and it can be controlled independently to transmit encoded signals containing position and status information. When a drone needs to communicate, it activates specific LEDs to broadcast data, which can be received by other drones within range using omnidirectional receivers.
The received power in a NLOS UV communication link depends on various factors like distance, transmitter power, and atmospheric conditions. For a link between a transmitter and receiver, the received power \(P_{r,\text{NLOS}}\) is given by:
$$ P_{r,\text{NLOS}} = \frac{P_t A_r K_s P_s \phi_2 \phi_1^2 \sin(\theta_1 + \theta_2)}{32\pi^3 R \sin \theta_1 \left[1 – \cos\left(\frac{\phi_1}{2}\right)\right]} \cdot \exp\left(-\frac{K_e R (\sin \theta_1 + \sin \theta_2)}{\sin(\theta_1 + \theta_2)}\right) $$
In this equation, \(P_t\) is the transmitter power, \(A_r\) is the receiver aperture area, \(K_s\) is the scattering coefficient, \(P_s\) is the scattering phase function, \(\phi_1\) and \(\phi_2\) are the beam divergence angles, \(\theta_1\) and \(\theta_2\) are the elevation angles, \(R\) is the communication distance, and \(K_e = K_a + K_s\) is the atmospheric attenuation coefficient (with \(K_a\) as the absorption coefficient). This model helps us analyze the signal strength and ensure reliable communication within the drone formation, especially when drones are at varying distances during assembly.
To enhance communication reliability, we introduce a relay cooperative mechanism. Consider a scenario with three drones: a leader drone (UAV1), a follower drone acting as a relay (UAV2), and another follower drone (UAV3). If the direct link between UAV1 and UAV3 is weak due to distance or obstacles, UAV2 can serve as an intermediate node to relay messages. This extends the effective communication range and improves the probability of successful data exchange. The relay mechanism is integral to our drone formation assembly method, as it ensures that all drones, even those far from the leader, can receive coordination commands and share state information. The following table summarizes key parameters in the UV communication model used for our drone formation simulations.
| Parameter | Symbol | Typical Value | Description |
|---|---|---|---|
| Transmitter Power | \(P_t\) | 10 mW | Power emitted by UV LED |
| Receiver Aperture Area | \(A_r\) | 1.77 cm² | Area of photodetector |
| Scattering Coefficient | \(K_s\) | 0.5 km⁻¹ | Atmospheric scattering parameter |
| Communication Distance | \(R\) | Up to 1 km | Range between drones in formation |
| Beam Divergence Angle | \(\phi_1, \phi_2\) | 30° | Angular spread of UV beam |
By leveraging this UV relay model, we can establish a robust communication network that supports the dynamic needs of a drone formation during assembly. The encoded signals from UV beacons allow drones to identify each other’s positions accurately, which is essential for forming precise geometric shapes like quadrilaterals or hexagons. This capability is a cornerstone of our method, as it directly addresses the EMI vulnerability of traditional systems.
Drone Formation Assembly Algorithm
The assembly of a drone formation into a desired geometry involves coordinating multiple drones from their initial positions to target locations around a leader drone. Our algorithm combines consistency theory for state synchronization and a UV-based virtual potential field for obstacle avoidance, ensuring that the formation assembles quickly and safely without collisions. The process begins with the leader drone reaching a designated assembly area and hovering in place. Then, follower drones use UV communication to exchange position and velocity information, compute their target points relative to the leader, and navigate toward them while avoiding obstacles (including other drones).
First, we define a UV virtual potential field to handle obstacle avoidance within the drone formation. Considering other drones as obstacles, the potential field function \(J(\mathbf{p})\) for a drone at position \(\mathbf{p} = [x, y]^T\) is:
$$ J(\mathbf{p}) = \frac{b_0}{\exp\left(\frac{r_{\text{obs}}}{c_0}\right) – \exp\left(\frac{r_{\text{min}}}{c_0}\right)}, \quad \text{for } r_{\text{obs}} \leq r_{\text{max}} $$
Here, \(b_0\) and \(c_0\) are constants that determine the amplitude and shape of the potential field, \(r_{\text{obs}}\) is the distance to the nearest obstacle, \(r_{\text{min}}\) is a minimum safe distance, and \(r_{\text{max}}\) is the maximum influence range of the field. The virtual repulsive force \(\mathbf{F}(\mathbf{p})\) acting on the drone is the negative gradient of \(J(\mathbf{p})\):
$$ \mathbf{F}(\mathbf{p}) = -\nabla_{\mathbf{p}} J(\mathbf{p}) = \frac{b_0}{c_0} \cdot \frac{\exp\left(\frac{r_{\text{obs}}}{c_0}\right)}{\left[\exp\left(\frac{r_{\text{obs}}}{c_0}\right) – \exp\left(\frac{r_{\text{min}}}{c_0}\right)\right]^2} \cdot \frac{\mathbf{r}}{r_{\text{obs}}} $$
where \(\mathbf{r} = [x – x_{\text{obs}}, y – y_{\text{obs}}]^T\) is the vector from the drone to the obstacle. If multiple obstacles are present, the total force \(\mathbf{F}_{\text{tot}}(\mathbf{p})\) is the sum of individual forces, and this force is used as an obstacle avoidance velocity command \(\mathbf{v}_a\) for the drone:
$$ \mathbf{v}_a = \mathbf{F}_{\text{tot}}(\mathbf{p}) = \sum_{l=1}^{m} \mathbf{F}_l(\mathbf{p}) $$
This approach ensures that drones maintain a safe separation during assembly, reducing the risk of collisions in the drone formation.
Second, we apply consistency theory to synchronize the states of drones in the formation. Consistency theory ensures that all drones converge to a common velocity, heading angle, and attitude by adjusting their control inputs based on information from neighbors. For a drone formation with a leader-follower structure, the leader drone broadcasts its target trajectory, and follower drones update their states using a consensus protocol. The state update for drone i can be expressed as:
$$ \dot{\mathbf{x}}_i = \sum_{j \in \mathcal{N}_i} b_{ij} (\mathbf{x}_j – \mathbf{x}_i) + \alpha (\mathbf{x}_{\text{leader}} – \mathbf{x}_i) $$
where \(\mathbf{x}_i\) represents the state vector (e.g., position and velocity) of drone i, \(\mathcal{N}_i\) is its neighbor set, \(b_{ij}\) are adjacency weights, and \(\alpha\) is a gain factor for leader tracking. This protocol drives the drone formation toward consensus, enabling smooth assembly into geometries like quadrilaterals or pentagons. The integration of UV communication ensures that the consensus updates are reliable even under EMI.
The assembly algorithm proceeds in steps: (1) The leader drone reaches the assembly zone and broadcasts its position via UV signals. (2) Follower drones receive this information and compute their target positions based on the desired formation geometry. (3) Each follower drone navigates toward its target using the UV virtual potential field for obstacle avoidance and consistency theory for speed and orientation matching. (4) Once some followers assemble, they act as relay nodes to assist remaining drones, enhancing communication reliability. This iterative process continues until the entire drone formation is assembled. The following table outlines the steps in the assembly algorithm for a drone formation.
| Step | Action | Description |
|---|---|---|
| 1 | Leader Positioning | Leader drone moves to assembly area and hovers, emitting UV beacons. |
| 2 | Information Exchange | Follower drones use UV communication to share positions and energies. |
| 3 | Target Computation | Each follower calculates its target point relative to the leader for the formation. |
| 4 | Navigation and Avoidance | Drones move toward targets using UV virtual potential field to avoid collisions. |
| 5 | Relay Coordination | Assembled drones act as relays to aid others, improving communication. |
| 6 | Formation Locking | All drones reach consensus in state, forming the desired geometry. |
This algorithm ensures that the drone formation assembles efficiently, with minimal energy consumption and high accuracy. The use of UV relays is particularly beneficial in large formations, where direct communication between distant drones might be unreliable.
Simulation Experiments and Results Analysis
To validate our method, we conducted simulation experiments using a 3D environment modeled in software. The simulations involved drone formations with one leader drone and multiple followers assembling into quadrilateral, pentagonal, and hexagonal geometries. The initial positions of drones were set randomly within a defined volume, and the leader drone either hovered or performed circular motions to test dynamic assembly. Key parameters for the simulations are summarized in the table below.
| Formation Type | Number of Followers | Leader Speed | Formation Distance | Simulation Environment |
|---|---|---|---|---|
| Quadrilateral | 4 | 300 m/s | 300 m | 3 km × 3 km × 6 km |
| Pentagonal | 5 | 300 m/s | 300 m | 3 km × 3 km × 6 km |
| Hexagonal | 6 | 300 m/s | 300 m | 30 km × 30 km × 60 km |
The assembly process was simulated over time, with drones updating their positions based on the motion model and control inputs from our algorithm. We monitored metrics such as position errors, velocity convergence, and communication reliability. For instance, in a hexagonal drone formation, the followers started from dispersed locations and gradually converged to points around the leader, forming a hexagon at a height of 50 km. The position changes in x, y, and z directions showed that all drones reached stable states within approximately 5 seconds, indicating rapid assembly. Similarly, velocity plots demonstrated that drones synchronized their speeds in horizontal and vertical directions, achieving consistency by 35 seconds into the simulation.
A critical performance measure is the communication reliability of the drone formation, defined as the probability that all drones correctly assemble at their target positions. We compared scenarios with and without UV relay cooperation. The results showed that UV relay significantly improved reliability across all formation types. Specifically, for quadrilateral formations, reliability increased from 72% to 78%; for pentagonal formations, from 77% to 85%; and for hexagonal formations, from 81% to 90%. This corresponds to relative improvements of 7.69%, 9.41%, and 10.0%, respectively. The enhancement is attributed to the relay mechanism, which boosts the discovery probability between adjacent drones and ensures robust information flow during assembly.
To quantify the communication performance, we analyzed the received UV signal power under different distances and atmospheric conditions. Using the NLOS power equation, we computed that for a typical drone separation of 500 m, the received power remains above the detection threshold, enabling reliable data exchange. Furthermore, the relay mechanism extended the effective range to over 1 km, which is essential for large-scale drone formations. The following formula illustrates the signal-to-noise ratio (SNR) improvement with relaying:
$$ \text{SNR}_{\text{relay}} = \frac{P_{r,\text{NLOS}}}{\sigma^2} + \gamma \sum_{k=1}^{M} \frac{P_{r,k}}{\sigma^2} $$
where \(\sigma^2\) is noise variance, \(\gamma\) is a relay gain factor, and \(M\) is the number of relay nodes. This shows how multi-hop UV communication enhances overall link quality in a drone formation.
We also tested the algorithm in dynamic scenarios where the leader drone performed circular motions. The followers successfully assembled into the desired geometries while maintaining formation during motion, demonstrating the robustness of our approach. Trajectory plots revealed smooth paths with no collisions, thanks to the UV virtual potential field. These simulations confirm that our method enables rapid and accurate drone formation assembly, even under challenging conditions like EMI or obstacle-rich environments.
Conclusion
In this paper, we have presented a novel method for drone formation assembly using wireless ultraviolet relay cooperation. By integrating UV communication with consistency theory and virtual potential field obstacle avoidance, we address the critical issue of electromagnetic interference that often plagues traditional RF-based drone formations. Our approach allows drones to assemble into precise geometric shapes, such as quadrilaterals, pentagons, and hexagons, with enhanced communication reliability and formation accuracy. The simulation results validate the effectiveness of the method, showing significant improvements in assembly success rates for various formation types.
The key contributions of this work include: (1) a robust UV beacon model for inter-drone positioning and communication, (2) a relay cooperative mechanism that extends communication range and improves data exchange, (3) an integrated algorithm combining consistency control and obstacle avoidance for safe and efficient assembly, and (4) extensive simulations demonstrating performance gains in realistic 3D environments. These elements collectively advance the state-of-the-art in drone formation technologies, particularly for applications in contested electromagnetic spectrums.
Future work will focus on optimizing the algorithm for larger-scale drone formations, incorporating machine learning techniques for adaptive relay selection, and testing in real-world outdoor environments with varying atmospheric conditions. Additionally, we plan to explore energy-efficient protocols to prolong drone endurance during extended missions. Overall, our method provides a solid foundation for developing resilient and autonomous drone formations capable of operating under adverse conditions, paving the way for more reliable and versatile aerial systems.