The operational landscape of modern conflicts is rapidly evolving, with intelligent swarm warfare, exemplified by UAV drone clusters, emerging as a pivotal force. Among various platforms, fixed-wing UAV drones hold distinct advantages in scenarios requiring high-altitude, high-speed, and long-endurance capabilities. For such UAV drone swarms operating in contested environments, the fundamental capability to follow pre-planned flight paths while maintaining a precise formation is critical for mission success and effectiveness. This article presents a novel guidance strategy developed to address the specific challenges of coordinating multiple fixed-wing UAV drones along complex flight paths.
Existing methodologies for fixed-wing UAV drone formation path-following often exhibit limitations, including poor adaptability to paths with variable curvature and insufficient accuracy in both path-tracking and formation-keeping. Common approaches such as PID-based lateral error control, vector field methods, or nonlinear control techniques like sliding mode control can struggle with the inherent underactuated dynamics of fixed-wing platforms, where lateral motion is primarily governed by normal acceleration (bank-to-turn maneuvers). Some recent methods employing a front-positioned moving target show promise due to their compatibility with this underactuated nature but have been primarily validated on simple straight or circular paths, revealing significant overshoot and formation distortion during cooperative turns on complex routes.
Drawing inspiration from mature guidance principles in missile systems, which share similar kinematic constraints, we propose an enhanced UAV drone formation guidance method based on an adaptive front-positioned moving-target strategy. The core innovation lies in its two-tiered structure: a robust single-UAV drone path-following law for the leader, and an adaptive extension for followers that accounts for formation geometry and real-time path curvature. This method dynamically adjusts the reference targets for each UAV drone in the swarm, enabling precise formation maintenance even on paths with varying and complex curvature, a significant advancement for real-world deployment of fixed-wing UAV drone clusters in constrained airspace.
Problem Formulation and UAV Drone Modeling
The problem focuses on the cooperative control of multiple fixed-wing UAV drones in the horizontal plane. We consider a swarm consisting of one leader UAV drone (indexed as 0) and N follower UAV drones (indexed i=1,…,N). The primary objectives are twofold: 1) The leader must accurately follow a predefined, continuous planar path $s$; 2) All follower UAV drones must maintain desired relative positions to the leader, forming a stable formation that moves along the path.
The kinematics of a fixed-wing UAV drone in the horizontal plane, considering its underactuated nature, are described. Let $P_i = [x_i, z_i]^T$ denote the inertial position of the i-th UAV drone. Its motion is governed by speed $v_i$, flight path azimuth angle $\psi_i$ (measured from the inertial x-axis), forward acceleration $a_{A_i}$, and normal (lateral) acceleration $a_{N_i}$. The simplified point-mass kinematics are:
$$
\begin{aligned}
\dot{x}_i &= v_i \cos \psi_i \\
\dot{z}_i &= -v_i \sin \psi_i \\
\dot{v}_i &= a_{A_i} \\
\dot{\psi}_i &= a_{N_i} / v_i
\end{aligned}
$$
For formation control, a Formation Coordinate System (FCS) is defined. Its origin $O_F$ is attached to the leader’s position $P_0$, and its axes are aligned with the leader’s velocity vector: the $X_F$-axis points along $v_0$, and the $Z_F$-axis points to its right. The transformation from inertial coordinates $(x, z)$ to formation coordinates $(x_F, z_F)$ is given by the rotation matrix $L_F$:
$$
\begin{bmatrix} x_F \\ z_F \end{bmatrix} = L_F \begin{bmatrix} x – x_0 \\ z – z_0 \end{bmatrix} = \begin{bmatrix} \cos\psi_0 & -\sin\psi_0 \\ \sin\psi_0 & \cos\psi_0 \end{bmatrix} \begin{bmatrix} x – x_0 \\ z – z_0 \end{bmatrix}
$$
Each follower UAV drone $i$ has a constant desired position in the FCS, denoted as $P_{i,d,F} = [x_{i,d,F}, z_{i,d,F}]^T$. The control goal is to generate appropriate acceleration commands $(a_{A_i}, a_{N_i})$ for every UAV drone such that $P_0$ converges to and follows path $s$, and for each follower, its actual FCS position converges to $P_{i,d,F}$.
Single UAV Drone Path-Following via a Moving Target
The foundation of the formation method is a robust guidance law for a single fixed-wing UAV drone. The core idea is to continuously define a moving target point $T$ on the desired path ahead of the UAV drone and command a lateral acceleration that would steer the UAV drone onto a circular arc passing through its current position and that target.
Let $P$ be the UAV drone’s current position and $v$ its velocity vector. A fixed, user-defined parameter $L$ (the look-ahead or target distance) is chosen, significantly smaller than the minimum expected path curvature radius. A circle $C_t$ of radius $L$ is drawn centered at $P$.
- Case 1 (Near Path): If $C_t$ intersects the path $s$ at two or more points, the farthest intersection point along the path’s direction is selected as the moving target $T$.
- Case 2 (Far from Path): If $C_t$ has no intersection with $s$, its radius is iteratively increased until the new circle $C’_t$ is tangent to $s$ at a point $T’$. The intersection of line $PT’$ with $C’_t$ (ahead of $P$) is chosen as the effective target $T$.
Once target $T$ is located, a commanded circular arc $A_{cmd}$ is constructed. This arc must satisfy: 1) It passes through $P$ and $T$; 2) At point $P$, the arc’s tangent is parallel to the UAV drone’s current velocity vector $v$. Let $D = T – P$ and $q$ be the angle between $v$ and $D$ (the line-of-sight angle). The radius $R$ of this arc is given by:
$$
R = \frac{|D|}{2 \cos(\pi/2 – q)} = \frac{|D|}{2 \sin q}
$$
The lateral acceleration command $a_{N_c}$ is then set to the centripetal acceleration required to follow this arc at the current speed $v$:
$$
a_{N_c} = \frac{v^2}{R} = \frac{2 v^2 \sin q}{|D|}
$$
This command inherently pulls the UAV drone toward the target point. As the UAV drone moves, $T$ continuously updates, creating a smooth pursuit guidance law. The forward acceleration $a_{A}$ is managed by a separate speed-hold controller. This single-UAV drone law is employed by the leader UAV drone to track the global path $s$, thereby defining the motion of the Formation Coordinate System.
Formation Path-Following Strategy for Multiple UAV Drones
The single-UAV drone strategy is extended to manage the follower UAV drones within the swarm. The key innovation is the creation of a “virtual target formation” that moves ahead of the real UAV drone formation, providing a reference for each follower to track.
Follower Target Point Calculation
For each follower UAV drone $i$, a dedicated moving target point $T_i$ is computed. This calculation uses the leader’s current target point $T_0$ and the path’s local geometry. At $T_0$, the tangent to the path defines the heading $\psi_{T_0}$. A Target Coordinate System (TCS) is established at $T_0$ with its $X_T$-axis aligned with this path tangent.
The desired position of follower $i$ in the TCS is set equal to its desired position in the FCS: $T_{i,T} = P_{i,d,F}$. This effectively creates a virtual formation of target points that mirrors the desired UAV drone formation shape, projected onto the path ahead. The inertial coordinates of follower $i$’s target are then obtained by a simple rotation and translation:
$$
T_i = L_T^{-1} T_{i,T} + T_0 = \begin{bmatrix} \cos\psi_{T_0} & \sin\psi_{T_0} \\ -\sin\psi_{T_0} & \cos\psi_{T_0} \end{bmatrix} \begin{bmatrix} x_{i,d,F} \\ z_{i,d,F} \end{bmatrix} + \begin{bmatrix} x_{T_0} \\ z_{T_0} \end{bmatrix}
$$
where $L_T^{-1}$ is the inverse rotation matrix from TCS to inertial coordinates.
Lateral Formation-Keeping Control
Each follower UAV drone $i$ applies the same moving-target guidance law from Section 2, but now tracking its own assigned target point $T_i$ instead of a path. The lateral acceleration command for follower $i$ is:
$$
a_{N_{c_i}} = \frac{2 v_i^2 \sin q_i}{|D_i|}
$$
where $D_i = T_i – P_i$ and $q_i$ is the angle between the follower’s velocity $v_i$ and the vector $D_i$. This control law drives each follower to intercept its moving target, thereby enforcing the lateral (cross-track) component of the formation geometry.
Longitudinal Formation-Keeping via Adaptive Target Distance
A critical challenge in fixed-wing UAV drone formation turns is coordinating the along-track spacing. Simply using a constant target distance $L$ for all UAV drones leads to distortion because UAV drones on different turn radii require different speeds and therefore different pursuit geometries. Our method introduces an adaptive expected target distance $L_{i,d}$ for each follower.
Assuming the path segment near $T_0$ has a local curvature radius $R_0$, the expected turn radius for follower $i$ is approximately $R_i = R_0 + z_{i,d,F}$ (for a right turn, $z_{i,d,F}<0$ for an inward follower). To maintain the correct geometric relationship, the expected distance $|D_i|$ for follower $i$ should be proportional to its turn radius:
$$
\frac{L_{i,d}}{L} = \frac{R_i}{R_0}
$$
where $L$ is the leader’s fixed target distance. Therefore, the adaptive expected target distance for follower $i$ is:
$$
L_{i,d} = L \cdot \frac{R_0 + z_{i,d,F}}{R_0}
$$
For straight-line flight ($R_0 \to \infty$), $L_{i,d}$ converges to $L$. A longitudinal controller (e.g., a PID controller) is then used to generate the forward acceleration command $a_{A_{c_i}}$ for follower $i$, regulating the actual distance $|D_i|$ to this adaptive setpoint $L_{i,d}$. This mechanism ensures that during coordinated turns, inner and outer follower UAV drones naturally adopt different effective pursuit geometries, resulting in the necessary speed differential for maintaining the formation shape without steady-state error.
| UAV Drone Role | Lateral Acceleration Command ($a_{N_c}$) | Longitudinal Control Target |
|---|---|---|
| Leader (0) | $\displaystyle a_{N_{c_0}} = \frac{2 v_0^2 \sin q_0}{|T_0 – P_0|}$ | Maintain constant speed $v_{des}$. |
| Follower (i) | $\displaystyle a_{N_{c_i}} = \frac{2 v_i^2 \sin q_i}{|T_i – P_i|}$ | Regulate $|D_i|$ to $L_{i,d} = L \cdot \frac{R_0 + z_{i,d,F}}{R_0}$. |
Stability Analysis Under Constant Curvature Paths
The stability of the proposed formation guidance law is analyzed for the case of a circular reference path (constant curvature) using Lyapunov’s direct method. The analysis assumes the leader is perfectly tracking the path, focusing on the convergence of a follower UAV drone to its desired position in the formation.
Consider a follower UAV drone $i$ with desired formation coordinates $(0, z_{i,d,F})$. Its desired trajectory is a circle with radius $R_i = R_0 + z_{i,d,F}$. We analyze its motion in a polar coordinate system centered at this circle’s center. The state vector is defined as $X = [r, \chi, v_t, v_n]^T$, where $r$ is the radial distance, $\chi$ is the angular position, $v_t$ is tangential speed, and $v_n$ is radial speed. The desired equilibrium state is $X_d = [R_i, \dot{\chi}_d t, v_{t,d}, 0]^T$, where $v_{t,d}$ is the desired tangential speed.
Let $e = r – R_i$ be the radial error. Under small-error assumptions ($|e| \ll R_i$, small heading error), the lateral acceleration command $a_{N_{c_i}}$ can be linearized. After simplification and relating the commanded acceleration to the actual radial dynamics, the expression takes the form of a proportional-derivative (PD) controller with a feedforward term $a_{N_{c_i},0}$:
$$
a_{N_{c_i}} \approx a_{N_{c_i},0} + K_p e + K_d \dot{e}
$$
where $K_p = \frac{2 v_{t,d}^2 \cos^2 q_0}{L_{i,d}^2} > 0$ and $K_d = \frac{2 v_{t,d} \cos q_0 (L_{i,d} – e \sin q_0)}{L_{i,d}^2} > 0$ for small $e$, and $q_0$ is the equilibrium line-of-sight angle.
Consider the Lyapunov function candidate:
$$
V(X) = K_p (R_i – r)^2 + v_n^2
$$
Clearly, $V(X) \ge 0$ and $V(X)=0$ only at the equilibrium $X=X_d$. Taking its time derivative and substituting the simplified system dynamics and the control law yields:
$$
\dot{V}(X) = -2 v_n (o + K_d v_n)
$$
where $o$ represents higher-order terms from the linearization. For a sufficiently small neighborhood around the equilibrium, $|o| < |K_d v_n|$ when $v_n \ne 0$, and $o=0$ at equilibrium. Therefore, $\dot{V}(X) \le 0$ in a neighborhood of $X_d$, and $\dot{V}(X)=0$ only when $v_n=0$, which corresponds to the equilibrium. By Lyapunov’s theorem, this proves that the equilibrium point $X_d$ is asymptotically stable. This result confirms that for any constant curvature path (including straight lines as $R_0 \to \infty$), each follower UAV drone will converge to and maintain its designated position in the formation.
Simulation Results and Comparative Analysis
The performance of the proposed Adaptive Front-Positioned Target (AFPT) method is validated and compared against three existing methods through numerical simulations in a complex path scenario. The comparison methods are:
- PID Method: A cascaded controller using PID for lateral path error (leader) and PID for x/z formation errors in FCS (followers).
- Vector Field (VF) Method: A guidance law that generates desired heading and speed commands based on an artificial vector field constructed from path/formation errors.
- Existing Front-Positioned Target (EFPT) Method: A baseline moving-target method without adaptive target distance adjustment for followers.
The simulation uses a challenging 2D path representative of low-altitude terrain-following, composed of multiple arcs and straight segments with radii varying from 500 m to 2000 m. A formation of one leader and two followers in a lateral configuration (positions in FCS: [0, 100]m and [0, -100]m) is tested. All UAV drones use identical inner-loop dynamics models, including first-order lags to approximate autopilot response for lateral and vertical acceleration channels.
| Parameter | Value | Description |
|---|---|---|
| $v_{des}$ | 50 m/s | Nominal formation speed. |
| $L$ | 50 m | Leader’s target distance. |
| $\tau_N$ | 0.5 s | Time constant for lateral acceleration lag. |
| $\tau_H$ | 0.8 s | Time constant for vertical acceleration lag. |
The simulation results demonstrate the superior performance of the AFPT method. All methods successfully completed the path without divergence. Quantitative error metrics are summarized below:
| Performance Metric | AFPT (Proposed) | PID Method | VF Method | EFPT Method |
|---|---|---|---|---|
| Leader Lateral RMS Error (m) | 0.0808 | 2.5400 | 0.3791 | 0.0808 |
| Follower 1 – X_F RMS Error (m) | 0.7881 | 0.9636 | 1.8390 | 0.7893 |
| Follower 1 – Z_F RMS Error (m) | 1.7618 | 3.1091 | 3.1819 | 2.2324 |
| Follower 1 – Z_F Max Error (m) | 0.0962 | 7.5254 | 15.3543 | 3.3458 |
Key Observations:
- Path Following: Both AFPT and EFPT provide identical, highly accurate leader tracking (RMS error ~0.08 m), significantly outperforming PID and VF methods. This validates the effectiveness of the core moving-target strategy for single-UAV drone path-following.
- Formation Keeping: The AFPT method achieves the lowest formation-keeping errors, particularly in the critical cross-track (Z_F) direction. Its maximum Z_F error is an order of magnitude smaller than other methods.
- Adaptation to Curvature: The AFPT method’s adaptive target distance eliminates steady-state formation error on constant-curvature segments and drastically reduces transient overshoot during curvature changes. The PID, VF, and EFPT methods all exhibit significant and persistent cross-track errors during turns.
- Robustness: The AFPT method maintained stable convergence even when follower UAV drones started with significant initial position and heading offsets in separate tests, confirming stability beyond the small neighborhood assumed in the theoretical analysis.
Conclusion
This article has presented a novel Adaptive Front-Positioned Moving-Target (AFPT) guidance method for fixed-wing UAV drone formation path-following. The method directly addresses the underactuated dynamics of fixed-wing platforms by generating lateral acceleration commands that smoothly steer each UAV drone toward a dynamically calculated target point. Its principal innovation lies in the adaptive extension for follower UAV drones, which calculates an expected target distance based on real-time path curvature and formation geometry. This adaptation is proven, via Lyapunov analysis, to ensure asymptotic stability for any constant-curvature path.
Comprehensive simulations on a complex, variable-curvature path have demonstrated the method’s significant advantages over conventional PID, vector field, and non-adaptive moving-target methods. The proposed AFPT method provides exceptional accuracy in both path-tracking and, more importantly, formation-keeping, especially in the cross-track dimension. This high-precision lateral control is crucial for the safe operation of UAV drone swarms in constrained environments, such as urban canyons or mountainous terrain, where collision risk with obstacles or between UAV drones is a major concern.
The method is computationally efficient, relying on geometric calculations and simple controllers, making it suitable for real-time implementation on typical UAV drone hardware. Future work will focus on integrating disturbance observers to enhance robustness against wind and other environmental uncertainties, further solidifying this approach as a practical and reliable solution for advanced fixed-wing UAV drone swarm operations.