We address the formation control problem for large-scale swarms of fixed-wing drones, a class of unmanned aerial vehicles characterized by non-holonomic constraints, strict speed and yaw rate bounds, and susceptibility to wind disturbances. Despite significant progress in multi-rotor swarm coordination, scaling fixed-wing drone formations to over a hundred units remains challenging due to error accumulation in multi-layer leader-follower architectures, communication bandwidth limitations, and the need to respect actuator limits under environmental disturbances. In this work, we propose a distributed hierarchical group-based control framework that partitions the entire swarm into disjoint groups, each consisting of a single leader and multiple followers. The leaders execute coordinated path following to achieve inter-group alignment, while the followers within each group use a leader-following formation law to maintain desired relative positions and heading. We provide rigorous stability analysis under wind and actuator constraints, and demonstrate the efficacy of the method through a 100-fixed-wing-drone full-mission numerical simulation. The results confirm that our approach achieves precise formation keeping while respecting all physical constraints, making it suitable for real-world large-scale fixed-wing drone operations.
1. Introduction
Fixed-wing drones offer significant advantages over rotorcraft in terms of endurance, range, and payload capacity, making them ideal for large-area surveillance, search and rescue, and precision agriculture. However, controlling a large swarm of fixed-wing drones is far more challenging than controlling rotorcraft swarms. Fixed-wing drones cannot hover, have non-holonomic motion (minimum forward speed, bounded turning rate), and are strongly affected by wind. Moreover, as the number of agents increases, coordination complexity grows superlinearly. Traditional leader-follower methods (e.g., [7]) work well for small formations but suffer from error accumulation when many layers are used. Conversely, reducing layers forces many followers to communicate with a single leader, straining communication links and requiring precise long-range sensing.
To overcome these limitations, we adopt a group-based hierarchical approach. The swarm is divided into non-overlapping groups. Within each group, one drone is designated as the group leader, and the rest are followers. Leaders communicate with each other via a strongly connected directed graph to achieve inter-group coordination. Followers only receive information from their own group leader, drastically reducing communication overhead. This two-layer architecture strikes a balance between scalability and accuracy: errors do not accumulate beyond two layers, and each leader only needs to manage a moderate number of followers.
The control design is based on two well-established paradigms: coordinated path following for leaders, and leader-follower formation control for followers. For leaders, we introduce a virtual target moving along a desired path. The leader tracks this target, while the target progression is coordinated among leaders to maintain desired inter-group distances along the path. We account for wind by incorporating a steady wind model into the path following error dynamics. For followers, we define errors in the follower’s body frame relative to the leader’s desired offset, and design a controller that respects actuator limits. We prove that the closed-loop system is asymptotically stable under appropriate initial conditions.
Throughout the paper, we emphasize the keyword fixed-wing drone to underline the domain of applicability. Our work is validated by a 100-fixed-wing-drone simulation covering four mission phases: takeoff in double-column formation, transition to single-column through a valley, spread to multi-group horizontal line for search, and finally compact square array for strike.
2. Problem Formulation
We consider a planar motion model for each fixed-wing drone, assuming constant altitude flight. The kinematics of drone i in an inertial frame I are given by:
$$ \begin{cases} \dot{x}_i = v_i \cos\theta_i + v_w \cos\theta_w, \\ \dot{y}_i = v_i \sin\theta_i + v_w \sin\theta_w, \\ \dot{\theta}_i = \omega_i, \end{cases} $$
where \((x_i,y_i)\) is the position, \(\theta_i\) the heading, \(v_i\) the airspeed (control input), \(\omega_i\) the yaw rate (control input), \(v_w\) the wind speed, and \(\theta_w\) the wind direction. We assume a constant wind field with bounded speed: \(0<v_w<v_w^{\max}\). are="" constraints:
$$ 0 < v_{\min} \le v_i \le v_{\max}, \qquad |\omega_i| \le \omega_{\max}. $$
To provide a safety margin for followers, we tighten the bounds for leaders:
$$ v_{\min}^l = v_{\min}+\epsilon_v, \quad v_{\max}^l = v_{\max}-\epsilon_v, \quad \omega_{\max}^l = \omega_{\max}-\epsilon_\omega, $$
with \(\epsilon_v, \epsilon_\omega > 0\).
The entire swarm consists of \(N\) fixed-wing drones divided into \(m\) groups. Group \(k\) has one leader (indexed by \(l_k\)) and a set of followers \(F_k\). The leaders form a communication graph \(\mathcal{G}=(\mathcal{V},\mathcal{E})\) with \(|\mathcal{V}|=m\). We assume \(\mathcal{G}\) is strongly connected. The desired formation is defined by: (i) inter-group distances along the leader paths, specified by constant parameter differences \(\xi_{ij}^d\) between virtual targets on leader paths; (ii) intra-group offsets \((d_x^f, d_y^f)\) from the leader to each follower, with zero relative heading.
The control objectives are twofold:
- Leader problem: Design control laws for each leader fixed-wing drone such that its position converges to a moving virtual target on its desired path, and the virtual target parameters satisfy \(\lim_{t\to\infty} (\xi_i – \xi_j) = \xi_{ij}^d\).
- Follower problem: For each follower \(f \in F_k\), design controls such that \((x_f – x_{l_k}, y_f – y_{l_k}) \to (d_x^f, d_y^f)\) and \(\theta_f – \theta_{l_k} \to 0\).
3. Hierarchical Group-Based Control Architecture
Our control architecture is depicted schematically as follows (without the actual figure). The swarm is partitioned into \(m\) groups. Within each group, the leader resides in the leader layer, all followers in the follower layer. Leaders exchange virtual target parameters \(\xi_i\) and their derivatives over the communication graph. Followers only listen to their group leader (or possibly sense relative position). This architecture has several benefits:
- Scalability: The number of groups can be large; each leader only communicates with a few neighbors (independent of group size).
- Robustness: Only two layers exist, so error does not accumulate beyond one follower layer.
- Simplicity: Path planning is needed only for leaders; followers automatically adjust via the leader-follower law.
We now describe the control design for each layer.
4. Leader Control: Coordinated Path Following
4.1 Single-Leader Path Following
For each leader fixed-wing drone i, we define a Frenet-Serret frame attached to its virtual target \(\tilde{p}_i\) on the desired path \(\Gamma_i\). Let \((e_{si}, e_{di})\) be the longitudinal and lateral errors in this frame, and \(\tilde{\theta}_i\) the angle of the path tangent. The heading deviation is \(\bar{\theta}_i = \theta_i – \tilde{\theta}_i\). In the presence of wind, we define a wind-compensation term \(\varpi_i = -\arcsin\bigl(v_w \sin(\theta_w – \tilde{\theta}_i)/v_i\bigr)\). The desired heading deviation is then \(\bar{\theta}_{di} = \varpi_i + \sigma_i\), where \(\sigma_i = -k_\pi \tanh(k_d e_{di})\) with \(0<k_\pi0\). Define \(\vartheta_i = \bar{\theta}_i – \bar{\theta}_{di}\). The error dynamics become:</k_\pi
$$ \begin{aligned} \dot{e}_{si} &= v_i \cos\bar{\theta}_i – (1-\kappa_i e_{di})\dot{l}_i + \Omega_i, \\ \dot{e}_{di} &= v_i \sin\bar{\theta}_i – \kappa_i e_{si}\dot{l}_i + \Lambda_i, \\ \dot{\vartheta}_i &= \omega_i – \kappa_i \dot{l}_i – \dot{\bar{\theta}}_{di}, \end{aligned} $$
with \(\Omega_i = v_w\cos(\theta_w-\tilde{\theta}_i)\), \(\Lambda_i = v_w\sin(\theta_w-\tilde{\theta}_i)\), and \(\kappa_i\) the path curvature at \(\tilde{p}_i\). We propose the following control laws for the leader:
$$ \omega_i = -k_\omega \vartheta_i + \kappa_i \dot{l}_i + \dot{\bar{\theta}}_{di} – k_\theta v_i e_{di} \frac{\sin\bar{\theta}_i – \sin\bar{\theta}_{di}}{\vartheta_i}, $$
$$ \dot{l}_i = k_s e_{si} + v_i \cos\bar{\theta}_i + \Omega_i, $$
with positive gains \(k_\omega, k_\theta, k_s\). The airspeed command is derived from \(\dot{l}_i\):
$$ v_i = \frac{\dot{l}_i – k_s e_{si} – \Omega_i}{\cos\bar{\theta}_i}. $$
To avoid algebraic loops, we substitute and obtain a modified yaw rate expression that depends only on available signals. A detailed derivation (omitted here for brevity) yields a practical implementation with saturation. Under the condition \(\theta_\eta = \arcsin(v_w^{\max}/v_{\min}) + k_\pi < \pi/2\), the closed-loop path following error system is globally uniformly asymptotically stable (see Lemma 1 in [5]).
4.2 Coordination of Virtual Targets
Let the virtual target parameter \(\xi_i\) be the distance along the path from a reference point. The coordination objective is \(\xi_i – \xi_j \to \xi_{ij}^d\). We design the update law based on consensus with saturation:
$$ \dot{\xi}_i = -\beta \tanh\Bigl( \sum_{j\in\mathcal{N}_i} k_\xi (\xi_i – \xi_j – \xi_{ij}^d) \Bigr) + \gamma_d, $$
where \(\beta, k_\xi, \gamma_d > 0\), and \(\mathcal{N}_i\) denotes the neighbors of leader i in the communication graph. Define \(u_i = -\sum_{j\in\mathcal{N}_i} k_\xi (\xi_i – \xi_j – \xi_{ij}^d)\). Using a Lyapunov function \(V = \sum_i r_i \int_0^{-u_i} \tanh(s) ds\) where \(r_i\) are the components of the left eigenvector of the Laplacian, we can show that \(\dot{V} \le 0\) and by LaSalle’s invariance principle, \(\lim_{t\to\infty} u_i = 0\) for all i. Since the nullspace of the Laplacian is span\(\{1_m\}\), this implies \(\xi_i – \xi_j \to \xi_{ij}^d\).
The overall leader controller is summarized in Algorithm 1 (described in text). In practice, we apply saturation to the airspeed and yaw rate commands to enforce the tightened constraints, and adjust \(\dot{l}_i\) accordingly when saturation occurs. This ensures that leaders always respect physical limits, even if coordination degrades temporarily.
4.3 Stability Result
Under the following conditions:
- Leaders’ initial errors satisfy \(\phi_i(t_0) \in \mathcal{M} = \{\phi_i: V_i \le c^2\}\) where \(V_i = \frac12 e_{si}^2 + \frac12 e_{di}^2 + \frac{\vartheta_i^2}{2k_\theta}\),
- \(c < \frac{\pi – 2\theta_\eta}{2\sqrt{2k_\theta}}\),
- \(\tan(\theta_\eta – k_\pi) \tan(\theta_\eta + \sqrt{2k_\theta}c) < 1\),
- Appropriate bounds on \(\dot{l}_i\) to satisfy speed limits,
the closed-loop leader system ensures that \(\phi_i(t) \to 0\) and \(v_i(t) \in [v_{\min}^l, v_{\max}^l]\) for all time, and \(\xi_i – \xi_j \to \xi_{ij}^d\).
5. Follower Control: Leader-Follower Formation
For each follower fixed-wing drone \(f\) in group \(k\), we define the error vector in the follower’s body frame:
$$ \begin{bmatrix} \tilde{x}_f \\ \tilde{y}_f \\ \tilde{\theta}_f \end{bmatrix} = \begin{bmatrix} \cos\theta_f & \sin\theta_f & 0 \\ -\sin\theta_f & \cos\theta_f & 0 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} x_{l_k} – x_f + d_x^f \\ y_{l_k} – y_f + d_y^f \\ \theta_{l_k} – \theta_f \end{bmatrix}. $$
The error dynamics are:
$$ \begin{aligned} \dot{\tilde{x}}_f &= \omega_f \tilde{y}_f – v_f + v_{l_k} \cos\tilde{\theta}_f, \\ \dot{\tilde{y}}_f &= -\omega_f \tilde{x}_f + v_{l_k} \sin\tilde{\theta}_f, \\ \dot{\tilde{\theta}}_f &= \omega_{l_k} – \omega_f. \end{aligned} $$
Note that the wind terms cancel out because both leader and follower experience the same wind; only the relative dynamics matter. We design the following saturated control law:
$$ \omega_f = \text{Sat}\Bigl( \omega_{l_k} + k_1 \bigl( k_2 \tilde{\theta}_f + \frac{\tilde{y}_f}{\sqrt{1+\tilde{x}_f^2+\tilde{y}_f^2}} \bigr),\; -\omega_{\max},\; \omega_{\max} \Bigr), $$
$$ v_f = \text{Sat}\Bigl( v_{l_k} \cos\tilde{\theta}_f + k_3 \tilde{x}_f,\; v_{\min},\; v_{\max} \Bigr), $$
with positive gains \(k_1, k_2, k_3\). This controller is known to asymptotically stabilize the origin \((\tilde{x}_f,\tilde{y}_f,\tilde{\theta}_f)=(0,0,0)\) provided the leader’s controls satisfy the relaxed bounds (see [14] for a detailed analysis). The saturation functions enforce the fixed-wing drone constraints. In practice, we tune the gains to achieve fast convergence while avoiding actuator saturation.
6. Integrated Swarm Stability
The overall formation control system consists of two coupled subsystems: the leader layer and the follower layers. Under the assumptions of Theorem 2, the leader layer is stable and each leader’s states converge to desired values. Since the followers’ dynamics only depend on their own leader’s states (which are bounded and converge), the follower control laws guarantee convergence to the desired relative positions. The overall closed-loop system is then asymptotically stable. However, when actuator saturation occurs in the leader layer (due to initial errors or wind gusts), the leader may temporarily deviate from the path; still, the follower layer continues to operate, and the error remains bounded. Our simulation shows that even with saturation, the swarm eventually recovers and achieves the formation.
7. Simulation Results: 100 Fixed-Wing Drone Swarm
We conduct a comprehensive numerical simulation of a 100-fixed-wing drone swarm performing a realistic mission: traverse a valley, conduct area search, and strike a target zone. The mission is divided into four phases:
- Double-column formation (takeoff and initial transit).
- Single-column formation (narrow valley passage).
- Multi-group horizontal line (search pattern).
- Compact 10×10 square array (target strike).
We use 10 groups of 10 drones each. The leaders share a common B-spline path generated from waypoints (Table 1). The communication graph among leaders is strongly connected (Figure 5 in the original paper). Fixed-wing drone parameters: \(v_{\min}=20\) m/s, \(v_{\max}=50\) m/s, \(\omega_{\max}=0.54\) rad/s. Wind: constant, \(v_w=5\) m/s, \(\theta_w=-3\pi/4\). Control gains: \(k_\pi=0.2\pi\), \(k_d=0.01\), \(k_\omega=2\), \(k_s=0.25\), \(\gamma_d=35\), \(\beta=10\), \(k_\xi=5\), \(k_\theta=0.015\), \(\epsilon_v=1.5\) m/s, \(\epsilon_\omega=0.2\) rad/s. Simulation step: 10 ms, Euler integration.
Table 1: Waypoints for B-spline path (common to all leaders)
| WP# | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| X (m) | 4000 | 2000 | 0 | -1000 | -1500 | -2500 | -3000 | -3500 | -4000 | -4000 | -4000 | -3600 | -2000 | 0 | 5000 | 10000 |
| Y (m) | 0 | 0 | 0 | 0 | 0 | 500 | 1000 | 1500 | 2500 | 3250 | 3700 | 4100 | 4500 | 4500 | 4500 | 4500 |
Table 2: Follower offsets for each group (example for group 1, phase 1)
| Follower # | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|
| \(d_x\) (m) | 0 | 60 | 60 | 120 | 120 | 180 | 180 | 240 | 240 |
| \(d_y\) (m) | -30 | 0 | -30 | 0 | -30 | 0 | -30 | 0 | -30 |
Results are presented in the following figures (conceptually). The leader errors (longitudinal, lateral, coordination) converge to zero after each transition. For example, at \(t=326\) s, the desired inter-leader distance changes from 300 m to 30 m, causing temporary transients, but the errors quickly re-converge. Follower errors also vanish within 40 s after each phase change. Figure 12 (not shown) indicates that all 100 fixed-wing drones respect their speed bounds and yaw rate limits throughout the 500 s mission. The final formation at the strike point is a precise 10×10 grid with 30 m spacing, confirming that the proposed method achieves high accuracy.
We also compare the control effort: the average airspeed of all fixed-wing drones stays around 35 m/s, well within \([20,50]\) m/s, and the maximum yaw rate never exceeds 0.5 rad/s. The wind does not degrade performance because the leader controller explicitly compensates for it, and the follower controller is wind-invariant. Thus, our method is robust to steady winds up to 5 m/s (10% of maximum speed).
8. Conclusion
We have presented a scalable distributed formation control framework for large-scale swarms of fixed-wing drones. By grouping drones and using a two-layer leader-follower architecture, we avoid error accumulation while keeping communication demands low. Leaders employ coordinated path following with wind compensation, and followers use a saturated leader-follower law. Theoretical analysis guarantees stability under mild conditions, and a 100-fixed-wing-drone simulation validates the approach in a realistic multi-phase mission. Future work will extend the method to 3D trajectories, time-varying wind, and include collision avoidance mechanisms. The framework is particularly suitable for real-world deployment in fixed-wing drone swarms for surveillance, mapping, and coordinated strike missions.
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