In modern battlefield and complex electromagnetic environments, ensuring safe flight operations and reliable communication within drone formation is paramount. The advent of swarm drone formation, comprising numerous unmanned aerial vehicles (UAVs) with varied payloads and types, has revolutionized missions such as covert reconnaissance and targeted penetration. These formations are characterized by high inter-drone density and stringent real-time environmental awareness requirements. Traditional radio frequency communication systems are susceptible to electromagnetic interference and detection, prompting the need for alternative covert communication methods. Wireless ultraviolet (UV) light, particularly in the solar-blind spectrum, offers a compelling solution due to its low background noise, anti-electromagnetic interference capability, non-line-of-sight (NLOS) communication, low power consumption, and ease of integration onto drone platforms. This paper presents a novel cooperative obstacle avoidance algorithm designed for drone formation leveraging wireless UV communication. We integrate the coverage characteristics of wireless UV to devise a virtual fencing strategy and enhance the traditional Vector Field Histogram (VFH) method by incorporating motion state prediction via an Unscented Kalman Filter (UKF). Our approach aims to achieve smooth, efficient, and collision-free navigation within dense drone formation.
The core of our strategy lies in the wireless UV virtual fence model. We define three concentric zones around each drone in the formation based on different UV wavelengths, each serving a distinct function for establishing communication and triggering avoidance maneuvers. The innermost zone, the Link Establishment Zone (radius $R_1$), uses wavelength $\lambda_1$ and represents the critical safety distance where collision is imminent. The intermediate Communication Zone (between $R_1$ and $R_2$) employs wavelength $\lambda_2$ for stable data exchange, including the broadcast of timestamped motion states. The outermost Warning Zone (between $R_2$ and $R_3$) utilizes wavelength $\lambda_3$ to detect nearby drones and initiate the communication link setup. The inter-drone distance $\rho_{ij}$ is calculated based on the received UV signal power, which for NLOS conditions is given by a complex model involving the scattering phase function and geometric parameters. A simplified form for aligned devices can be expressed as:
$$ \rho_{ij} = \sqrt{ \frac{P_t A_r K_e}{P_{r-NLOS}} \cdot \text{lambertw}\left( \frac{P_t A_r K_e}{P_{r-NLOS}} \right) } $$
where $P_t$ is transmit power, $A_r$ is receiver aperture area, $K_e$ is atmospheric extinction coefficient, and $P_{r-NLOS}$ is received non-line-of-sight power. Based on the predicted future positions of neighboring drones, three threat states are defined: Safe Flight (drone moving away within $R_1$), Potential Danger (drone predicted in Communication Zone), and Emergency Avoidance (drone predicted in Warning Zone), which triggers immediate local path replanning.
Our enhanced algorithm builds upon the VFH* framework but is tailored for dynamic drone formation. The environment around a drone is discretized into a histogram grid within the UV virtual fence. Each grid cell $m_{ij}$ is assigned a certainty value influenced by the proximity and predicted state of neighboring drones. Instead of a linear influence, we model the certainty to reflect the curved motion of UAVs:
$$ m_{ij} = C \cdot (\zeta_{ij})^2 $$
The influence function $\zeta_{ij}$ is a monotonic decreasing function of the inter-drone distance $\rho_{ij}$ and a threshold $\rho_n$, defined as:
$$ \zeta_{ij} = \begin{cases}
1 & \text{if } \rho_{ij} \leq r_{r+s} \\
\frac{a(\rho_n^2 – \rho_{ij}^2)}{\rho_n^2 – r_{r+s}^2} & \text{if } r_{r+s} < \rho_{ij} \leq \rho_n \\
0 & \text{if } \rho_{ij} > \rho_n
\end{cases} $$
Here, $r_{r+s}$ is the inflated drone radius for safety, and $a$ is a constant. The key innovation is the integration of real-time trajectory prediction for all agents in the drone formation. We model each drone’s motion as a nonlinear system with Gaussian noise and employ an Unscented Kalman Filter (UKF) for state prediction. The state vector at time $k$, $S(k)$, includes position, velocity, and acceleration components. The state transition and observation equations are:
$$ S(k) = \Phi S(k-1) + W(k) $$
$$ Z(k) = h(S(k)) + V(k) $$
where $W(k)$ and $V(k)$ are process and observation noise with covariances $Q$ and $R$, respectively. The UKF generates sigma points to approximate the state distribution, enabling accurate prediction of neighboring drones’ future positions over a horizon. This prediction is crucial for evaluating potential collisions and selecting the optimal avoidance maneuver within the drone formation.
The local path planner samples feasible velocity and direction pairs $(v, \theta)$ from the set constrained by kinematic limits:
$$ v \in [v_{\text{min}}, v_{\text{max}}], \quad \dot{v} \in [\dot{v}_{\text{min}}, \dot{v}_{\text{max}}], \quad \omega \in [\omega_{\text{min}}, \omega_{\text{max}}] $$
For each candidate motion primitive, the algorithm checks for intersection with predicted trajectories of other drones in the formation and computes a cost function $B(c)$ to select the best option:
$$ B(c) = \mu_1 \cdot \sigma_t(c, k_t) + \mu_2 \cdot \sigma_v(v, \omega) + \mu_3 \cdot \sigma_h(c, \frac{\phi_i}{\phi_{i-1}}) + \mu_4 \cdot \sigma_d(c, k_{n,i-1}) $$
where $\sigma_t$ penalizes deviation from the global goal direction, $\sigma_v$ penalizes high speeds and turn rates, $\sigma_h$ penalizes change from the current heading, and $\sigma_d$ penalizes deviation from the previous direction to ensure smoothness. The weights satisfy $\mu_1 > \mu_2 + \mu_3 + \mu_4$ to prioritize goal directedness. This cost function, evaluated over the predicted horizon, allows the drone formation to maintain cohesion while avoiding collisions efficiently.
To validate our algorithm, we conducted extensive simulations comparing our method (UAVF) against the standard Vector Field Histogram Plus (VFH+) and the enhanced VFH* (which uses A* for global planning). The simulation parameters for the drone formation are summarized below:
| Parameter | Value Range |
|---|---|
| Drone Speed, $v$ | (0, 10) m/s |
| Acceleration, $a$ | (-6, 6) m/s² |
| Angular Velocity, $\omega$ | (0.1, 4) rad/s |
| Initial Heading | $\pi/2$ rad |
| Influence Constant, $a$ | 1.5 |
| Cost Weight $\mu_1$ | 6 |
| Cost Weight $\mu_2$ | 2 |
| Cost Weight $\mu_3$ | 1 |
| Cost Weight $\mu_4$ | 1 |
The UKF prediction parameters were set with process noise covariance $Q$ and measurement noise covariance $R$ as diagonal matrices reflecting typical sensor inaccuracies in a drone formation. Two complex encounter scenarios were simulated. In Scenario 1, two drones on crossing paths were required to avoid each other and reach opposite destinations. In Scenario 2, multiple drones navigated a cluttered dynamic airspace.
The performance metrics were total path length and total travel time. Our UAVF algorithm demonstrated superior performance in both scenarios within the drone formation. The results are summarized in the following table:
| Scenario | Algorithm | Path Length (m) | Travel Time (s) | Improvement over VFH* |
|---|---|---|---|---|
| 1 | VFH+ | 529 | 31.45 | N/A |
| VFH* | 570 | 36.01 | Baseline | |
| UAVF (Ours) | 398 | 29.23 | Length: -3.02%, Time: -18.82% | |
| 2 | VFH+ | 860 | 42.97 | N/A |
| VFH* | 794 | 47.48 | Baseline | |
| UAVF (Ours) | 763 | 38.43 | Length: -3.90%, Time: -19.06% |
The trajectory plots revealed that VFH+ often exhibited sharp turns and oscillations due to its reactive nature, while VFH* produced longer, sometimes circuitous paths. Our UAVF algorithm generated significantly smoother trajectories with gentle turns, effectively leveraging predictions to anticipate and avoid conflicts early in the drone formation. The absence of jitter and the efficient pathing are critical for maintaining formation integrity and energy efficiency.
The accuracy of the UKF-based trajectory prediction was also analyzed. The average prediction errors for relative distance, velocity, and acceleration over multiple runs were calculated, confirming the filter’s reliability for supporting decision-making in the drone formation.
| Predicted Metric | Average Error (Scenario 1) | Average Error (Scenario 2) |
|---|---|---|
| Relative Distance | 3.07 m | 2.71 m |
| Relative Velocity | 0.61 m/s | 0.57 m/s |
| Relative Acceleration | 0.050 m/s² | 0.069 m/s² |
The mathematical foundation of our motion model is detailed as follows. The transformation from the drone’s body frame $\{P\}$ to the global inertial frame $\{E\}$ is given by the rotation matrix $T(\alpha)$:
$$ T(\alpha) = \begin{bmatrix} \cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha \end{bmatrix} $$
Given an initial global position $G_A = [x_0, y_0, \alpha]^T$ and a movement defined in the body frame by radial distance $r$ and angle $\theta$, the new global position $G_B$ after moving along an arc (assuming constant turn rate) is:
$$ G_B = \begin{bmatrix} x_0 + v \Delta t \cdot \cos\left(\theta + \frac{\Delta \theta}{2}\right) \\ y_0 + v \Delta t \cdot \sin\left(\theta + \frac{\Delta \theta}{2}\right) \end{bmatrix} $$
with $\Delta \theta = \omega \Delta t$. The kinematics for velocity and displacement under constant acceleration are:
$$ V(k) = V(k-1) + T \cdot a(k-1) $$
$$ \rho(k) = \rho(k-1) + T \cdot V(k-1) + \frac{1}{2} T^2 \cdot a(k-1) $$
These equations form the basis for the state prediction within each member of the drone formation. The enhanced histogram construction process involves mapping the inflated drone shapes and their predicted positions onto the polar histogram. The sector $k$ corresponding to angle $\gamma_{ij}$ accumulates a certainty value $m_{ij}$ that dynamically changes with the relative motion in the formation.
In conclusion, we have presented a robust cooperative obstacle avoidance algorithm specifically designed for drone formation operating in electromagnetically contested environments. By synergistically combining wireless UV communication for covert ranging and data exchange, a virtual fence protocol for threat assessment, an enhanced VFH method with a kinematically-aware cost function, and UKF-based trajectory prediction, our algorithm enables safe, smooth, and efficient navigation. Simulation results demonstrate clear advantages over existing methods, including a reduction in total path length by approximately 3.46% and a decrease in total travel time by nearly 18.94% on average. This work provides a significant step towards realizing autonomous, resilient, and collision-free operations for large-scale drone formation, paving the way for their successful deployment in complex mission scenarios. Future work will focus on extending the algorithm to three-dimensional spaces and testing it with physical drone swarms using miniaturized UV transceivers.
The integration of wireless UV technology not only solves the communication problem but also directly feeds into the perception system for avoidance, creating a unified framework for drone formation coordination. The predictive component allows the formation to behave proactively rather than reactively, which is essential for maintaining tight formations at high speeds. The algorithm’s computational efficiency, achieved through careful design of the cost function and the use of efficient sampling techniques, makes it suitable for real-time implementation on the limited processing hardware typical of small drones in a formation. As drone formation become more prevalent in both civilian and military applications, the need for such intelligent, distributed, and secure collaboration mechanisms will only grow, underscoring the importance of continued research in this domain.