My research focuses on the challenging problem of rapid formation assembly and precise consistency control for small fixed-wing drone swarms launched sequentially from a single platform. The core contribution of my work is a two-phase strategy that combines a rapid, loose formation assembly phase using Dubins path planning with a fine formation control phase based on distributed consensus algorithms. This approach effectively addresses the critical issues of assembly time efficiency and formation geometry accuracy which are particularly difficult for fixed-wing drones due to their inherent constraints such as limited thrust-to-weight ratios, narrow speed ranges, and minimum turning radii.

Problem Formulation for Fixed-Wing Drones

I consider a scenario where multiple small fixed-wing drones are catapult launched from the same ground platform at fixed time intervals. After climbing to a specified altitude and stabilizing in level flight, the formation assembly process begins. For the purpose of my modeling and control design, I make several key assumptions. First, I assume that the drones operate in an ideal environment with no communication delays or wind disturbances. Second, I model each drone as a point mass for control purposes. The underlying kinematic and dynamic model for a single fixed-wing drone in a 3D inertial coordinate system is given by the following equations:

$$
\dot{x}_i = V_{gi} \cos \chi_i \cos \gamma_i
$$

$$
\dot{y}_i = V_{gi} \sin \chi_i \cos \gamma_i
$$

$$
\dot{z}_i = -V_{gi} \sin \gamma_i
$$

$$
\dot{V}_{gi} = \frac{T_{hi} – D_{gi}}{m_i} – g \sin \gamma_i
$$

$$
\dot{\gamma}_i = \frac{L_{fi} \cos \phi_i – m_i g \cos \gamma_i}{m_i V_{gi}}
$$

$$
\dot{\chi}_i = \frac{L_{fi} \sin \phi_i}{m_i V_{gi} \cos \gamma_i}
$$

In these equations, the subscript $i$ denotes the $i$-th drone in the swarm. The state variables include position $(x_i, y_i, z_i)$, ground speed $V_{gi}$, flight path angle $\gamma_i$, and heading angle $\chi_i$. The control inputs are thrust $T_{hi}$, bank angle $\phi_i$, and lift $L_{fi}$. The parameters $m_i$ and $g$ represent mass and gravitational acceleration. For the formation control problem, I simplify this 3D model to a 2D model under the assumption of constant altitude and zero flight path angle. This simplification is valid for the steady, level flight phase of the mission. The critical input constraints for fixed-wing drones are:

$$
0 \leq V_{gi} \leq V_{max,i}
$$

$$
|a_i| \leq a_{max,i}
$$

$$
|\dot{\psi}_i| \leq \dot{\psi}_{max,i}
$$

where $a_i$ is the acceleration and $\dot{\psi}_i$ is the yaw rate. The maximum yaw rate, $\dot{\psi}_{max,i} = V_{gi} / r_{min,i}$, defines the minimum turn radius $r_{min,i}$, a crucial parameter for the motion planning of fixed-wing drones.

Phase 1: Rapid Loose Formation Assembly with Dubins Path Planning

The first phase of my strategy focuses on rapidly bringing the sequentially launched fixed-wing drones into a common area to achieve a loose formation. I employ Dubins curves for path planning. The fundamental idea is that each drone, traveling at a constant cruise speed, will follow a path composed of a Circular arc (C), a straight Line segment (L), and another Circular arc (C), commonly known as a CLC path. This path type is optimal for fixed-wing drones as it respects their minimum turn radius constraint. The geometry for a single CLC path is defined by its initial and final states (position and heading). The path length $l_{si}$ for drone $i$ is:

$$
l_{si} = r_{i1} \phi_{i1} + d_i + r_{i2} \phi_{i2}
$$

where $r_{i1}$ and $r_{i2}$ are the radii of the first and second turns, $\phi_{i1}$ and $\phi_{i2}$ are the turn angles, and $d_i$ is the length of the straight segment.

For a multi-drone system with a common terminal state, the objective is to coordinate the path of each drone so that they all arrive at the same point simultaneously, given their staggered launch times $\Delta t$. The arrival time constraint for drone $i$ relative to a reference drone is:

$$
\frac{r_{i1} \phi_{i1} + d_i + r_{i2} \phi_{i2}}{V_{gi}} = t_{ref} + \Delta t_i
$$

I solve this coordinated planning problem using two complementary methods and compare their results. The first is an analytical method where I fix the path parameters of one reference drone and then solve for the parameters of others. The second is a numerical optimization method using a Genetic Algorithm (GA). The GA provides a flexible approach to find sub-optimal solutions without the need for a predefined reference. The optimization problem is formulated as:

$$
\min F(X) = \sum_{i=1}^{n} (l_{si} + l_{xi} + l_{yi})
$$

subject to constraints on the variables $X = [dt, dx, dy, r_1, r_2, …, d_1, d_2, …, \phi_1, \phi_2, …]$, which represent the reference flight time, relative positions, and all individual path parameters. The functions $l_{si}$, $l_{xi}$, and $l_{yi}$ are derived from the constraints ensuring that all drones converge to the assembly point with the correct heading and spacing. The GA iteratively optimizes $F(X)$ to minimize the total path length, thereby minimizing the assembly time.

Parameter	Symbol	Value for Fixed-Wing Drones
Minimum Flight Speed	$V_{min,i}$	35 m/s
Maximum Flight Speed	$V_{max,i}$	45 m/s
Cruise Speed	$V_i$	40 m/s
Maximum Acceleration	$a_{max,i}$	0.5 m/s²
Minimum Turn Radius	$r_{min,i}$	200 m
Launch Time Interval	$\Delta t$	2 s
Desired Lateral/Longitudinal Spacing	$(\Delta x_i, \Delta y_i)$	(100, 100) m
Safety Distance	$\rho_0$	25 m

My simulation results for a three-drone scenario comparing the analytical and GA-based methods are summarized in the table below. The analytical method, by searching for the global minimum within a defined variable space, yields a shorter assembly time but requires pre-computation. The GA provides a near-optimal solution faster, making it suitable for real-time or quasi-real-time planning, albeit with a slightly longer path and a small positional error at the assembly point.

Method	Assembly Time $dt$ (s)	Drone 1 Path: ($r_1, \phi_1, d_1$)	Drone 2 Path: ($r_2, \phi_2, d_2$)	Drone 3 Path: ($r_3, \phi_3, d_3$)
Analytical (Optimal)	24.95	(200.0 m, 1.745 rad, 300.0 m)	(221.8 m, 1.579 rad, 217.6 m)	(212.8 m, 1.116 rad, 363.0 m)
Genetic Algorithm (Sub-optimal)	63.8	(628.0 m, 1.67 rad, 452 m)	(653.5 m, 1.58 rad, 412 m)	(677.7 m, 1.43 rad, 453 m)

Phase 2: Fine Formation Control with Distributed Consensus

After the rapid assembly phase, the drones are in a loose formation but may have residual state errors in position and velocity. The second phase of my strategy uses a distributed consensus-based control law to refine the formation into a precise geometric configuration and maintain it. I model the communication topology among the fixed-wing drones using an undirected graph $G = (V, E, A)$, where $V$ is the set of drones, $E$ is the set of edges representing communication links, and $A = [a_{ij}]$ is the adjacency matrix. Each drone is modeled as a second-order integrator system:

$$
\dot{\xi}_i = \zeta_i
$$

$$
\dot{\zeta}_i = u_i
$$

Here, $\xi_i = [x_i, y_i, z_i]^T$ is the position, $\zeta_i = [v_{xi}, v_{yi}, v_{zi}]^T$ is the velocity, and $u_i = [u_{xi}, u_{yi}, u_{zi}]^T$ is the control input for drone $i$. The control input $u_i$ is the command that will be translated into the actual thrust, bank angle, and lift commands for the fixed-wing drone.

I design a distributed control law based on a virtual leader approach. All fixed-wing drones are tasked to follow a virtual leader, identified by the subscript 0. The control law for drone $i$ is:

$$
\begin{aligned}
u_i = &-\alpha \left[ (\xi_i – \xi_0 – d_i) + \beta (\zeta_i – \zeta_0) \right] \\
&-\sum_{j=1}^{n} a_{ij} \left[ (\xi_i – \xi_j – (d_i – d_j)) + \beta (\zeta_i – \zeta_j) \right]
\end{aligned}
$$

where $\xi_0$ and $\zeta_0$ are the position and velocity of the virtual leader. The term $d_i = [\Delta x_i, \Delta y_i, \Delta z_i]^T$ represents the desired relative position of drone $i$ with respect to the virtual leader to form the desired geometric formation. The parameter $\alpha$ indicates whether drone $i$ can receive the virtual leader’s state (I set $\alpha = 1$ for all drones). The parameter $\beta$ is a positive gain that weighs the velocity error; I use $\beta = 2$ in my simulations. This algorithm ensures that the position and velocity differences between drones converge to the desired values, thereby achieving and maintaining a stable geometric formation. The control law inherently corrects the state errors introduced during the Dubins path planning phase.

Simulation Study: Formation Maintenance and Transformation

I conducted comprehensive simulations to validate my two-phase strategy. Starting from the state achieved by the GA-based Dubins path planning, I applied the consensus control law to refine the formation. The target configuration was a diagonal line (skewed one-line) formation with an inter-drone spacing of 100 meters in both the x and y directions. The virtual leader moved at a constant speed of 40 m/s along the x-axis. The simulation results show that the consensus algorithm quickly corrected the initial positional errors, driving the formation to a stable, rigid geometric configuration within approximately 10 seconds, with residual errors on the order of $10^{-3}$ meters. This demonstrates the effectiveness of the consensus algorithm for precise formation control of fixed-wing drones.

After achieving and maintaining the diagonal formation for a period, I initiated a formation change to a “V” shape. The V-formation is defined by three vertices forming an equilateral triangle with a side length of 100 meters. The transition was accomplished by simply updating the desired relative position vector $d_i$ for each drone in the distributed control law. The system then autonomously adjusted the trajectories of all three fixed-wing drones to converge to the new formation geometry. The simulation results show that the transition was completed successfully, with the swarm assuming the V-configuration after approximately 350 seconds. A critical aspect of this transition is the maintenance of inter-drone safety distances. I defined a safety distance $\rho_0 = 25$ meters. Throughout the transformation process, the minimum distance between any two drones never fell below this threshold, confirming the collision avoidance properties inherent in the consensus-based approach.

Conclusion and Future Work for Fixed-Wing Drone Swarms

In conclusion, my research presents an effective two-phase control strategy for the rapid assembly and precise formation control of small fixed-wing drone swarms. The first phase, utilizing Dubins path planning optimized by a Genetic Algorithm, enables the efficient and collision-free convergence of sequentially launched drones. The second phase, based on a virtual-leader, distributed consensus algorithm, robustly corrects initial errors and achieves stable, precise geometric formations. The success of the approach, validated through simulations for diagonal-line and V-formations, demonstrates its potential for real-world fixed-wing drone applications such as cooperative surveillance, search and rescue, and tactical operations.

While the current results are promising, several avenues for future research are apparent. First, the dynamic model should incorporate real-world uncertainties like communication delays, sensor noise, and wind gusts. Second, the distributed control law needs to be extended to handle dynamic and directed communication topologies, enhancing the system’s robustness to node failures. Third, a more sophisticated obstacle avoidance capability is required. I plan to integrate the consensus algorithm with velocity obstacle (VO) methods, which are particularly well-suited for fixed-wing drones as they consider the drone’s velocity vector and the dynamic nature of obstacles. Finally, for extremely tight formations, the aerodynamic coupling between fixed-wing drones becomes significant. Future work will focus on developing consensus protocols that account for these coupling effects to ensure stability and efficiency in close-proximity flight. This will be crucial for maximizing the operational benefits of large fixed-wing drone swarms.