In the evolving landscape of modern warfare, intelligent collective operations, epitomized by drone swarms, are emerging as a pivotal combat force. Among various platforms, fixed-wing Unmanned Aerial Vehicles (UAVs) hold significant advantages in scenarios demanding high-altitude, high-speed, and long-endurance operations. For such drone formations to execute missions effectively, their ability to navigate predefined paths while maintaining a precise formation is paramount. However, existing guidance methods for fixed-wing drone formation path-following often exhibit poor adaptability to complex paths and suboptimal accuracy in both path tracking and formation keeping, limiting their operational utility in realistic, constrained environments.
Our work proposes a novel guidance method based on a front-positioned moving-target strategy to address these shortcomings. This method is inspired by guidance principles in missile systems, which share similar maneuvering characteristics with fixed-wing UAVs. We begin with a strategy for a single UAV, which is then extended to coordinate an entire drone formation. The core idea involves generating lateral acceleration commands by constructing a guidance arc towards a dynamically selected target point ahead on the desired path. For formation control, this logic is adapted for each follower UAV, with its target point strategically placed to reflect the desired formation geometry. Furthermore, an adaptive law for the desired target distance is introduced to account for path curvature, ensuring stable formation keeping during cooperative turns.
Problem Formulation for Drone Formation Flight
The challenge of drone formation path-following for fixed-wing UAVs can be decomposed into two interrelated sub-problems: the control of the drone formation itself, and the accurate tracking of a predefined path by this formation. We address the problem in the horizontal plane, assuming altitude is controlled by a separate loop.
Fixed-Wing UAV Dynamics
The planar kinematics of a fixed-wing UAV, considered as a controllable point mass, are given by:
$$
\begin{align*}
\frac{dx}{dt} &= v \cos \psi \\
\frac{dz}{dt} &= -v \sin \psi \\
\frac{dv}{dt} &= a_A \\
\frac{d\psi}{dt} &= \frac{a_N}{v}
\end{align*}
$$
where $P = [x, z]^T$ is the vehicle’s position in an inertial frame, $v$ is its speed, $\psi$ is its heading angle, $a_A$ is the acceleration along the velocity vector (controlled primarily by thrust), and $a_N$ is the acceleration normal to the velocity vector (controlled primarily by bank angle via lift). The normal acceleration $a_N$ is the primary means for lateral maneuvering in a fixed-wing drone formation.
Drone Formation Definition
A stable drone formation implies the existence of a moving Formation Coordinate System (FCS) in which each member maintains a constant relative position. The FCS is defined such that its origin $O_F$ coincides with the position of a designated leader UAV, its $X_F$-axis aligns with the leader’s velocity vector, and its $Z_F$-axis completes the right-handed system. The transformation from inertial coordinates $(x, z)$ to formation coordinates $(x_F, z_F)$ is:
$$
\begin{bmatrix} x_F \\ z_F \end{bmatrix} = \mathbf{L}_F \begin{bmatrix} x – x_0 \\ z – z_0 \end{bmatrix} = \begin{bmatrix} \cos\psi_0 & -\sin\psi_0 \\ \sin\psi_0 & \cos\psi_0 \end{bmatrix} \begin{bmatrix} x – x_0 \\ z – z_0 \end{bmatrix}
$$
where $\psi_0$ and $v_0$ are the leader’s heading and speed.
Drone Formation Path-Following Objective
We employ a leader-follower structure for the drone formation. The leader (UAV 0) is tasked with precisely following a predefined continuous path $s$. Each follower UAV $i$ ($i>0$) has a desired position in the FCS, denoted as $\mathbf{P}_{i,d,F} = [x_{i,d,F}, z_{i,d,F}]^T$. The control objective is to design acceleration commands $a_{A_i}$ and $a_{N_i}$ for all UAVs such that: 1) The leader converges to and tracks the path $s$, and 2) Each follower’s position in the FCS converges to its desired $\mathbf{P}_{i,d,F}$, thereby maintaining the prescribed drone formation geometry while following the path.
The Proposed Formation Path-Following Guidance Method
The proposed method is developed in two stages: first, a strategy for a single UAV, which is used by the leader; second, an extension of this strategy to manage the entire drone formation.
Single UAV Path-Following Strategy
This strategy provides the lateral acceleration command for a single UAV to follow a path $s$. A fixed look-ahead distance $D$ is chosen. At each instant, a target circle $C_t$ of radius $D$ is drawn centered at the UAV’s current position $P$.
Case 1 (Close to Path): If $C_t$ intersects $s$ at two or more points, the intersection farthest along the path direction is selected as the moving target point $T$.
Case 2 (Far from Path): If $C_t$ has no intersection with $s$, its radius is virtually increased until the enlarged circle $C’_t$ is tangent to $s$. The intersection between the line $PT’$ (where $T’$ is the tangent point) and the original circle $C_t$ is selected as the target $T$.
Once $T$ is located, a command arc $A_{cmd}$ is constructed. This arc passes through $P$ and $T$, and is tangent to the UAV’s velocity vector $\mathbf{v}$ at $P$. The radius $R$ of this arc and the commanded normal acceleration $a_{Nc}$ are calculated as follows, where $q$ is the line-of-sight angle between $\mathbf{v}$ and the vector $\mathbf{D} = T – P$:
$$
R = \frac{|\mathbf{D}|}{2 \cos(\pi/2 – q)} = \frac{|\mathbf{D}|}{2 \sin q}, \quad a_{Nc} = \frac{2 v^2 \sin q}{|\mathbf{D}|}
$$
This $a_{Nc}$ is the centripetal acceleration required to follow the instantaneous command arc. The leader UAV uses this strategy to track the desired path, thereby defining the motion of the drone formation’s reference frame.
Multi-UAV Drone Formation Path-Following Strategy
This strategy generates commands for the follower UAVs to maintain the drone formation while the leader tracks the path.
1. Follower Target Point Planning
A Target Coordinate System (TCS) is established at the leader’s current target point $T_0$, with its $X_T$-axis aligned with the path tangent $\psi_{T_0}$ at $T_0$. The target point $T_i$ for follower $i$ is placed in the TCS such that its coordinates match the follower’s desired coordinates in the FCS. It is then transformed to the inertial frame:
$$
\mathbf{T}_i = \mathbf{L}_T^{-1} \mathbf{P}_{i,d,F} + \mathbf{T}_0, \quad \text{where } \mathbf{L}_T^{-1} = \begin{bmatrix} \cos\psi_{T_0} & \sin\psi_{T_0} \\ -\sin\psi_{T_0} & \cos\psi_{T_0} \end{bmatrix}
$$
This creates a “target formation” that mirrors the desired drone formation geometry, anchored ahead on the path.
2. Lateral Formation Keeping (Normal Acceleration Command)
Each follower $i$ applies the single-UAV strategy from Section 2.1, but uses its own target point $T_i$. The lateral acceleration command is computed based on its own position $P_i$, velocity $v_i$, and the vector $\mathbf{D}_i = T_i – P_i$:
$$
a_{Nc_i} = \frac{2 v_i^2 \sin q_i}{|\mathbf{D}_i|}
$$
This command drives the follower laterally to track its moving target, thus maintaining the relative cross-track position within the drone formation.
3. Longitudinal Formation Keeping (Target Distance & Forward Acceleration)
To maintain accurate along-track spacing in the drone formation, especially during turns, the follower’s desired distance to its target $D_{i,d}$ must be adapted based on path curvature. Assuming the path segment near $T_0$ has a constant radius of curvature $R_0$, and the desired formation offset is $z_{i,d,F}$, the desired target distance is:
$$
D_{i,d} = D \frac{R_0 + z_{i,d,F}}{R_0}
$$
For a straight path ($R_0 \to \infty$), $D_{i,d} = D$. A dedicated target distance control loop (e.g., a PID controller) acts on the forward acceleration $a_{Ac_i}$ to regulate the actual distance $|\mathbf{D}_i|$ to this desired value $D_{i,d}$, ensuring proper longitudinal spacing in the drone formation.
4. Algorithm Summary for the Drone Formation
The complete guidance logic for the drone formation is summarized in the table below:
| Agent | Inputs | Core Guidance Logic | Outputs |
|---|---|---|---|
| Leader | Path $s$, its state $(P_0, v_0, \psi_0)$, fixed $D$. | 1. Find moving target $T_0$ on $s$ using Algorithm 1. 2. Compute $a_{Nc_0} = 2 v_0^2 \sin(q_0) / |\mathbf{D}|$. 3. Use speed controller for $a_{Ac_0}$. |
$a_{Nc_0}$, $a_{Ac_0}$ |
| Follower i | Leader’s $T_0$, $\psi_{T_0}$, $D$, $R_0$; its own state $(P_i, v_i)$; desired $\mathbf{P}_{i,d,F}$. | 1. Compute target: $\mathbf{T}_i = \mathbf{L}_T^{-1} \mathbf{P}_{i,d,F} + \mathbf{T}_0$. 2. Compute lateral command: $a_{Nc_i} = 2 v_i^2 \sin(q_i) / |\mathbf{D}_i|$. 3. Compute desired distance: $D_{i,d} = D (R_0 + z_{i,d,F}) / R_0$. 4. Use target-distance controller for $a_{Ac_i}$. |
$a_{Nc_i}$, $a_{Ac_i}$ |
Stability Analysis Under Constant-Curvature Paths
We analyze the local stability of the proposed drone formation guidance method using Lyapunov’s second method, under assumptions of a constant-curvature path and small errors.
Lemma: For a constant-curvature (circular or straight) path, with an ideal leader and a pure cross-track formation ($x_{i,d,F} \approx 0$), if a follower’s desired target distance satisfies $D_{i,d} = D (R_0 + z_{i,d,F}) / R_0$ and its normal acceleration is commanded as $a_{Nc_i} = 2 v_i^2 \sin(q_i) / |\mathbf{D}_i|$, then the desired formation position is an equilibrium point. Furthermore, the system is locally asymptotically stable around this equilibrium.
Proof Sketch: The follower’s kinematics are expressed in a polar coordinate system centered at the center of its desired circular trajectory (radius $R_i = R_0 + z_{i,d,F}$). The state vector is $\mathbf{X}_2 = [r, \chi, v_t, v_n]^T$, representing radial distance, angle, tangential and normal velocity. The desired equilibrium state is $\mathbf{X}_{2,d} = [R_i, \chi_d, v_t, 0]^T$.
Under small-error assumptions ($|e| = |r-R_i| \ll R_i$, small heading error), the normal acceleration command simplifies to a form comprising a feedforward term for the circular motion and a PD correction on the cross-track error $e$:
$$
a_{Nc_i} \approx \underbrace{\frac{v_t^2}{r}}_{a_{Nc_i,0}} + \underbrace{\frac{2 v_t^2 \cos^2 q_{i0}}{D_{i,d}^2}}_{K_p} e + \underbrace{\frac{2 v_t \cos q_{i0}}{D_{i,d}}}_{K_d} \dot{e} + o
$$
where $o$ represents higher-order error terms. Selecting the Lyapunov function candidate $V(\mathbf{X}_2) = K_p (R_i – r)^2 + v_n^2$, which is positive definite, and evaluating its derivative along the system trajectories using the polar kinematic equations yields:
$$
\dot{V}(\mathbf{X}_2) = -2 v_n (o + K_d v_n)
$$
Given $K_d > 0$ and that the higher-order term $o$ is dominated by $K_d v_n$ in a small neighborhood of the equilibrium, we have $\dot{V}(\mathbf{X}_2) \le 0$, with equality only at the equilibrium ($v_n=0, r=R_i$). Thus, the equilibrium is locally asymptotically stable, proving the lemma for the drone formation follower. A similar argument applies to the leader’s path-following stability.
Simulation Results and Comparative Analysis
Numerical simulations were conducted to validate the performance and robustness of the proposed method for drone formation flight, referred to as the Adaptive Front-Target (AFT) method. The UAV model included first-order lags (0.5s for lateral, 0.8s for vertical) to approximate autopilot dynamics. Comparative simulations were run against three established methods: a PID-based position control method (PID), a Vector Field method (VF), and the Existing Front-Target method (EFT).
1. Drone Formation Convergence from Various Initial Conditions
A scenario with 10 follower UAVs starting from random positions and headings around a circular path ($R_0=500$m) was simulated. The desired drone formation consisted of two groups of five UAVs at $z_{F}=\pm50$m. The results are summarized below:
| Metric | Result | Implication |
|---|---|---|
| Convergence | All followers converged to their desired positions in the formation coordinate system within 10 seconds. | The AFT method exhibits stability over a large domain of initial conditions, not just a small neighborhood. |
| Steady-State Speeds | Followers stabilized at two distinct speeds ($\approx$ 49 m/s for outer track, $\approx$ 51 m/s for inner track) compared to the leader’s 50 m/s. | The method naturally induces the required speed differential for steady-state coordinated turns in a drone formation, validating the adaptive $D_{i,d}$ law. |
2. Performance on Complex Paths
A more challenging, realistic path composed of multiple arcs and straight segments with varying curvature (radii from 500m to 2000m) was used. A three-UAV drone formation (leader + two followers at $z_{F}= \pm100$m) was tested. Key performance metrics (RMSE and Max Error) for the leader’s path-tracking and the followers’ formation-keeping are compared in the following table:
| Method | Leader Lateral RMSE (m) | Follower X_F RMSE (m) | Follower Z_F RMSE (m) | Follower Z_F Max Error (m) |
|---|---|---|---|---|
| AFT (Proposed) | 0.081 | 0.788 | 1.762 | 0.096 |
| PID Method | 2.540 | 0.964 | 3.109 | 7.525 |
| Vector Field Method | 0.379 | 1.839 | 3.182 | 15.354 |
| Existing Front-Target | 0.081 | 0.789 | 2.232 | 3.346 |
Analysis of Results:
- Path-Following Accuracy: Both AFT and EFT methods, sharing the same leader strategy, achieved superior leader tracking accuracy (RMSE ~0.08m) compared to PID (2.54m) and VF (0.38m) methods, demonstrating excellent adaptation to curvature changes.
- Longitudinal Formation Keeping (X_F): All methods showed comparable performance in the along-track direction, as this is primarily governed by the inner-loop speed/target-distance controller.
- Lateral Formation Keeping (Z_F): This is the critical metric for dense drone formations. The proposed AFT method significantly outperformed all others, with a near-zero steady-state error and a maximum error of only 0.096m. In contrast, the other methods exhibited significant steady-state errors and large overshoots during curvature transitions. The EFT method, while better than PID and VF, still had a maximum error of 3.35m due to its non-adaptive target distance law.
The drastic reduction in lateral error is the key advantage of the AFT method. It stems from the adaptive calculation of $D_{i,d}$, which allows each follower in the drone formation to automatically adjust its guidance geometry according to the local path curvature, eliminating the steady-state lateral error inherent in other methods. This makes the proposed method particularly suitable for drone formation flight in confined spaces or complex terrains where precise relative positioning is safety-critical.
Discussion and Practical Implementation
The stability proven for constant-curvature paths provides a strong foundation. In practice, paths are piecewise continuous with bounded curvature and curvature rate. The proposed method remains effective if the look-ahead distance $D$ is chosen sufficiently smaller than the minimum path radius, ensuring the local path segment between the UAV and its target is approximately circular. For paths with sudden curvature changes, the use of a filtered or averaged $R_0$ over the look-ahead segment for calculating $D_{i,d}$ can smooth the transition and reduce overshoot.
The choice of $D$ represents a trade-off: a smaller $D$ increases responsiveness and precision but demands higher acceleration capability and may lead to sensitivity to noise; a larger $D$ results in smoother, more sluggish control. This parameter must be tuned considering the dynamic capabilities of the specific UAVs in the drone formation and the aggressiveness of the planned path.
The primary innovation over the Existing Front-Target method lies in two aspects: 1) Aligning the Target Coordinate System with the path tangent at $T_0$ instead of the leader’s velocity, ensuring the target formation geometry is correctly projected onto curved paths, and 2) Introducing the adaptive desired target distance $D_{i,d}$, which is crucial for eliminating lateral steady-state error during turns and is the key to the demonstrated performance superiority.
Conclusion
In this work, we have presented a novel guidance method for fixed-wing drone formation path-following based on a front-positioned moving-target strategy. The method addresses the limitations of existing approaches in adapting to complex, variable-curvature paths. By extending a robust single-UAV path-following law and incorporating an adaptive rule for the desired target distance based on real-time path curvature, the method ensures high-precision tracking and formation keeping. Lyapunov stability analysis confirms local asymptotic stability for constant-curvature paths. Comprehensive simulations demonstrate that the proposed Adaptive Front-Target method significantly outperforms PID-based, Vector Field, and an existing front-target method in both path-following and, more importantly, lateral formation-keeping accuracy. This enhanced precision in maintaining the drone formation geometry, especially during cooperative turns, substantially reduces the risk of intra-formation collisions and increases the viability of deploying dense fixed-wing drone formations in complex, constrained operational environments. Future work will focus on integrating disturbance observers to enhance robustness against wind and model uncertainties.