The coordinated flight of unmanned aerial vehicle (UAV) clusters is a cornerstone of modern aerial systems, finding critical applications in surveillance, logistics, and large-scale environmental monitoring. Among these, the visually stunning and technically demanding formation drone light show represents a pinnacle of precision coordination, requiring dozens or hundreds of UAVs to trace complex paths while maintaining exquisite relative positions. While most formation drone light show systems utilize agile multi-rotors, fixed-wing UAVs offer superior endurance and speed for extended, large-area operations. This work addresses the fundamental challenge of guiding a fixed-wing UAV formation to accurately follow a predefined, potentially complex flight path—a capability essential not only for tactical missions but also for enabling dynamic, high-speed aerial displays that could redefine the scale of formation drone light show.
Existing methods for formation path-following, such as PID-based position control or vector field approaches, often struggle with the inherent constraints of fixed-wing dynamics. These aircraft are underactuated, primarily maneuvering through lateral acceleration (bank-to-turn), and cannot instantly change heading. This leads to poor adaptability to paths with varying curvature and compromises the precision of both path-tracking and formation-keeping. Inspired by guidance principles from missile systems and prior work on moving targets, I propose a novel formation guidance method. The core idea is to use a dynamically calculated point ahead on the path—a “front-positioned moving target”—to generate natural, physically feasible lateral acceleration commands for each UAV, ensuring stable convergence to the desired formation geometry along the path.
1. Problem Formulation and System Modeling
We consider the problem of controlling a group of $N+1$ fixed-wing UAVs, indexed $i=0,1,…,N$, to follow a desired planar path $s$ while maintaining a specified formation. UAV $0$ is designated as the leader, responsible for accurate path-following. The followers ($i>0$) must maintain specific relative positions with respect to this leader. The kinematics of each UAV in the horizontal plane are given by:
$$
\begin{aligned}
\frac{dx_i}{dt} &= v_i \cos \psi_i, \\
\frac{dz_i}{dt} &= -v_i \sin \psi_i, \\
\frac{dv_i}{dt} &= a_{A,i}, \\
\frac{d\psi_i}{dt} &= \frac{a_{N,i}}{v_i}.
\end{aligned}
$$
Here, $P_i = [x_i, z_i]^T$ is the inertial position, $v_i$ is the speed, $\psi_i$ is the heading angle, $a_{A,i}$ is the longitudinal acceleration (from thrust), and $a_{N,i}$ is the lateral acceleration (from lift component during a turn). The primary control objective is to compute $a_{N,i}$ and $a_{A,i}$ for all UAVs such that the leader perfectly tracks $s$ and each follower converges to its designated position within a moving formation frame attached to the leader.
The formation is defined in a Formation Coordinate System (FCS) $\mathcal{F}$. Its origin $O_F$ is at the leader’s position $P_0$, its $X_F$-axis is aligned with the leader’s velocity vector $\mathbf{v}_0$, and its $Z_F$-axis points to the leader’s right. The desired position of follower $i$ in $\mathcal{F}$ is a constant vector $\mathbf{P}_{i,d}^\mathcal{F} = [x_{i,d}^\mathcal{F}, z_{i,d}^\mathcal{F}]^T$. The transformation from inertial coordinates to $\mathcal{F}$ is:
$$
\mathbf{P}^\mathcal{F} = \mathbf{L}_F (\mathbf{P} – \mathbf{P}_0), \quad \text{where} \quad \mathbf{L}_F = \begin{bmatrix}
\cos \psi_0 & -\sin \psi_0 \\
\sin \psi_0 & \cos \psi_0
\end{bmatrix}.
$$
The goal is to achieve $\mathbf{P}_i^\mathcal{F} \rightarrow \mathbf{P}_{i,d}^\mathcal{F}$ for all followers while $P_0 \rightarrow s$.
2. Guidance Method Design
2.1 Single UAV Path-Following via a Moving Target
The foundation of the formation method is a strategy for a single UAV (the leader) to follow a path. For a given constant “target distance” $D$, we define a “target circle” $C_t$ of radius $D$ centered at the UAV’s current position $P_0$. The moving target point $T_0$ is selected as the intersection of this circle with the desired path $s$ that is farthest ahead along the path’s direction. If the UAV is far from the path and no intersection exists, the circle radius is virtually increased until it is tangent to the path, and the tangent point is used. An “command arc” $A_{cmd}$ is then constructed, which is the unique circular arc that passes through $P_0$ and $T_0$ and is tangent to the UAV’s velocity vector $\mathbf{v}_0$ at $P_0$. The lateral acceleration command is set to the centripetal acceleration required to follow this arc:
$$
a_{Nc,0} = \frac{2 v_0^2 \sin q_0}{D}.
$$
Here, $q_0$ is the angle between $\mathbf{v}_0$ and the line-of-sight vector $\mathbf{D} = T_0 – P_0$. This command continuously steers the UAV toward the moving target, which in turn slides along the path, creating a smooth pursuit and convergence. This principle is directly applicable to orchestrating the lead UAV in a formation drone light show, ensuring the entire group’s trajectory foundation is accurate.
2.2 Formation Extension: Follower Target Assignment and Control
To extend this to a formation, each follower must be guided to its slot in the formation frame. The key innovation is to create a “virtual target formation” that moves ahead of the real UAVs. Using the leader’s target point $T_0$ and the path’s tangent direction $\psi_{T_0}$ at that point, we define a Target Coordinate System (TCS) $\mathcal{T}$. The target point for follower $i$ in this TCS is set equal to its desired formation position: $\mathbf{T}_{i}^\mathcal{T} = \mathbf{P}_{i,d}^\mathcal{F}$. It is then transformed back to the inertial frame:
$$
\mathbf{T}_i = \mathbf{L}_T^{-1} \mathbf{P}_{i,d}^\mathcal{F} + \mathbf{T}_0, \quad \mathbf{L}_T^{-1} = \begin{bmatrix}
\cos \psi_{T_0} & \sin \psi_{T_0} \\
-\sin \psi_{T_0} & \cos \psi_{T_0}
\end{bmatrix}.
$$
This creates a phantom formation of target points $\{T_i\}$ that perfectly mirrors the desired UAV formation and moves along the path ahead of the group. Each follower $i$ then uses the same moving-target logic as the leader, but now chasing its own assigned target point $T_i$. Its lateral acceleration command becomes:
$$
a_{Nc,i} = \frac{2 v_i^2 \sin q_i}{D_i},
$$
where $q_i$ is the angle between $\mathbf{v}_i$ and $\mathbf{D}_i = \mathbf{T}_i – \mathbf{P}_i$, and $D_i = \|\mathbf{D}_i\|$ is the instantaneous distance to its target.
2.3 Longitudinal Formation Keeping via Adaptive Target Distance
A critical aspect for maintaining formation geometry on curved paths is the expected distance $D_{i,d}$ between a follower and its target. On a straight path, all UAVs should have the same target distance $D$. However, on a curved path with radius $R_0$, followers on the inside and outside of the turn must trace circles of different radii to maintain their lateral offset. Assuming the formation is purely lateral ($x_{i,d}^\mathcal{F} \approx 0$), the expected target distance for follower $i$ is adaptively calculated based on the path curvature:
$$
D_{i,d} = \frac{D (R_0 + z_{i,d}^\mathcal{F})}{R_0}.
$$
For a straight path ($R_0 \to \infty$), $D_{i,d} = D$. This adaptive calculation is crucial for eliminating steady-state lateral error during turns. A separate longitudinal acceleration command $a_{Ac,i}$ is generated by a PID controller to drive the actual distance $D_i$ to this desired value $D_{i,d}$.
The complete guidance system structure is summarized below:
| Module | Inputs | Output | Function |
|---|---|---|---|
| Leader Target Calc. | Path $s$, $P_0$, $D$ | $T_0$, $R_0$, $\psi_{T_0}$ | Finds leader’s moving target and path curvature. |
| Follower Target Calc. | $T_0$, $\psi_{T_0}$, $\mathbf{P}_{i,d}^\mathcal{F}$ | $\mathbf{T}_i$ | Computes each follower’s moving target. |
| Lateral Guidance | $\mathbf{P}_i$, $\mathbf{v}_i$, $\mathbf{T}_i$ | $a_{Nc,i}$ | Generates lateral accel. command (Eq. for $a_{Nc,i}$). |
| Target Distance Control | $D_{i,d}$, $D_i$ | $a_{Ac,i}$ | Generates longitudinal accel. command via PID. |
3. Stability Analysis
Under the assumptions of a constant-curvature path (radius $R_0$), an ideal leader perfectly on path, and small formation errors, the stability of the follower’s closed-loop system can be proven using Lyapunov’s second method. The follower’s dynamics in polar coordinates $(r, \chi, v_t, v_n)$ centered at the turn circle’s center are considered. The desired equilibrium state $\mathbf{X}_{2,d}$ corresponds to the follower being at its correct formation position with the appropriate speed. Defining a Lyapunov function candidate $V(\mathbf{X}_2) = K_p (R_i – r)^2 + v_n^2$, where $R_i = R_0 + z_{i,d}^\mathcal{F}$ is the follower’s desired turn radius and $K_p > 0$, and following the derivative analysis, it can be shown that $\dot{V}(\mathbf{X}_2) \le 0$ in a neighborhood of the equilibrium, with $\dot{V} = 0$ only at the equilibrium. This proves local asymptotic stability for the formation-keeping on any constant-curvature path, including straight lines. This theoretical robustness is vital for a reliable formation drone light show, where smooth, stable transitions between patterns are mandatory.
4. Simulation Results and Comparative Analysis
To validate the proposed method, dubbed the Adaptive Front-Target (AFT) method, extensive numerical simulations were conducted and compared against three existing approaches: 1) a standard PID-based position controller (PID), 2) a Vector Field method (VF), and 3) an existing Front-Target method from literature (EFT) which does not adapt the target distance $D_{i,d}$. A challenging path consisting of multiple straight and curved segments with varying curvature (radii from 500m to 2000m) was used, simulating a complex operational route or a dynamic formation drone light show pattern.
A formation of one leader and two followers in a lateral configuration ($z_{1,d}^\mathcal{F}=100$m, $z_{2,d}^\mathcal{F}=-100$m) was simulated. Key performance metrics include the Root-Mean-Square (RMS) and maximum error for the leader’s path-following and the followers’ formation-keeping in the $X_F$ and $Z_F$ axes.
The results are summarized in the table below:
| Method | Leader Lateral RMS Error (m) | Follower 1: $X_F$ RMS Error (m) | Follower 1: $Z_F$ RMS Error (m) | Follower 1: Max $Z_F$ Error (m) |
|---|---|---|---|---|
| Proposed (AFT) | 0.0808 | 0.788 | 1.76 | 4.04 |
| PID Control | 2.540 | 0.964 | 3.11 | 7.53 |
| Vector Field (VF) | 0.379 | 1.839 | 3.18 | 15.35 |
| Existing Front-Target (EFT) | 0.0808 | 0.789 | 2.23 | 3.35 |
The simulations clearly demonstrate the advantages of the proposed method:
- Superior Path-Following: Both AFT and EFT (which share the same leader logic) achieve exceptional leader tracking accuracy, with RMS error an order of magnitude lower than PID and VF methods. This precision is paramount for the reference trajectory in any formation drone light show.
- Excellent Formation-Keeping: The proposed AFT method yields the lowest RMS and maximum errors in the critical lateral ($Z_F$) direction. The adaptive calculation of $D_{i,d}$ effectively eliminates steady-state lateral error during turns, a problem evident in the other methods. The $Z_F$ error for AFT is primarily transient during curvature changes, whereas other methods show significant persistent errors correlated with path curvature.
- Robustness to Curvature Change: The AFT method shows the smoothest transitions and smallest overshoot when the path curvature changes, indicating better adaptability to complex routes. This translates directly to smoother, more graceful shape transitions in a formation drone light show context.
5. Conclusion and Future Work
This work has presented a novel guidance method for fixed-wing UAV formation path-following based on the concept of a front-positioned moving target. By extending a highly effective single-UAV path-following strategy and intelligently assigning adaptive target points to followers, the method achieves simultaneous, high-precision path-tracking and formation-keeping. The local asymptotic stability on paths of constant curvature was formally proven. Comprehensive simulations against established methods confirm that the proposed approach significantly outperforms alternatives in handling complex, variable-curvature paths, offering superior accuracy and stability. The method’s precision and adaptability make it a compelling candidate for advanced fixed-wing UAV applications, including the creation of large-scale, high-speed aerial displays that push the boundaries of what is possible in a formation drone light show.
Future work will focus on integrating disturbance observers to enhance robustness against wind gusts and other environmental uncertainties, further increasing the reliability of formation flight in real-world conditions. Additionally, investigating the integration of collision avoidance protocols within this guidance framework will be essential for deploying dense, safe UAV clusters for complex missions and public performances.