Fixed‑wing drones have become indispensable in modern military operations, including reconnaissance, target tracking, aerial refueling, and precision strikes. The ability to accurately follow a predefined path while rejecting wind disturbances is crucial for mission success and flight safety. Among environmental disturbances, crosswind is the most persistent and challenging for small fixed‑wing drones, as it introduces both a kinematic drift and a lateral force on the airframe. Conventional path‑tracking algorithms, such as pure pursuit, line‑of‑sight guidance, or vector‑field methods, often neglect the static error caused by constant crosswind. In this work we propose an enhanced nonlinear guidance law that explicitly compensates for crosswind effects. By incorporating an integral feedback term of the lateral deviation, our method eliminates the steady‑state error and improves convergence speed. We develop the complete kinematic model of fixed‑wing drones in wind, derive the guidance command, and validate the approach through simulation. Extensive tables and equations are provided to summarize the key results and to facilitate implementation.
1. Kinematic Model of Fixed-Wing Drones in Wind
We consider the horizontal motion of a fixed‑wing drone flying at constant altitude. Let the airspeed vector be \(\mathbf{v}\) with magnitude \(v\), the wind vector be \(\mathbf{v}_w\) with components \(v_{wx}, v_{wy}\) in the inertial frame, and the ground speed vector be \(\mathbf{v}_g\). The relationship is:
$$
\mathbf{v}_g = \mathbf{v} + \mathbf{v}_w. \tag{1}
$$
Define the sideslip angle \(\beta\) between the airspeed vector and the body longitudinal axis, and the wind‑induced equivalent sideslip \(\beta_w\). For small angles,
$$
\beta_w \approx -\frac{v_w}{v}. \tag{2}
$$
The heading angle \(\Psi_s\) (direction of ground velocity) and the yaw angle \(\Psi\) (direction of body axis) are related by:
$$
\Psi_s = \Psi + \beta + \beta_w. \tag{3}
$$
In the inertial frame, the position derivatives are:
$$
\begin{aligned}
\dot{x} &= v_g \cos \Psi_s, \\
\dot{y} &= v_g \sin \Psi_s, \\
\dot{z} &= 0 \quad \text{(level flight)}.
\end{aligned} \tag{4}
$$
Expanding with wind components gives:
$$
\begin{aligned}
\dot{x} &= v \cos(\Psi + \beta) + v_{wx}, \\
\dot{y} &= v \sin(\Psi + \beta) + v_{wy}.
\end{aligned} \tag{5}
$$
Table 1 summarizes the notation used throughout this paper.
| Symbol | Description |
|---|---|
| \(v\) | Airspeed magnitude |
| \(\mathbf{v}_w\) | Wind velocity vector |
| \(\mathbf{v}_g\) | Ground velocity vector |
| \(\Psi_s\) | Heading angle (ground track) |
| \(\Psi\) | Yaw angle (body axis) |
| \(\beta\) | Aerodynamic sideslip angle |
| \(\beta_w\) | Wind‑induced equivalent sideslip |
| \(l\) | Look‑ahead distance to virtual target |
| \(a\) | Lateral acceleration command |
| \(\phi\) | Roll angle command |
| \(\Delta d\) | Lateral path deviation |
2. Path‑Tracking Control System Architecture
The path‑tracking controller for fixed‑wing drones is typically separated into an outer guidance loop and an inner attitude control loop. The outer loop computes the roll angle command based on the geometric relationship between the drone and the desired path. The inner loop, which includes a stability augmentation system, tracks that roll command using aileron, elevator, and rudder deflections. In our design we modify only the outer guidance law to achieve wind resistance, leaving the inner loop unchanged.
2.1 Nonlinear Guidance Principle
The nonlinear guidance law selects a virtual target point on the desired path at a constant look‑ahead distance \(l\) from the drone. Let \(\eta\) be the angle between the ground velocity vector \(\mathbf{v}_g\) and the line from the drone to the virtual target. The required lateral acceleration is:
$$
a = \frac{2 v_g^2}{l} \sin \eta. \tag{6}
$$
This acceleration drives the drone onto the path with a natural damping behavior. The equivalent turn radius \(r\) satisfies:
$$
r = \frac{l}{2 \sin \eta}. \tag{7}
$$
During a coordinated turn, the lateral acceleration is provided by rolling the aircraft:
$$
\tan \phi = \frac{a}{g}. \tag{8}
$$
Combining (6) and (8) yields the roll angle command:
$$
\phi = \arctan\left( \frac{2 v_g^2 \sin \eta}{g l} \right). \tag{9}
$$
To maintain consistent tracking performance at different airspeeds, the look‑ahead distance is adapted:
$$
l’ = l + k_l (v’_g – v_g), \tag{10}
$$
where \(k_l\) is a gain and \(v_g, l\) are reference values.
2.2 Wind Resistance Analysis
In the presence of constant crosswind, the ground velocity vector \(\mathbf{v}_g\) changes both in magnitude and direction according to (1). Because the guidance law (9) uses \(\mathbf{v}_g\) and the instantaneous angle \(\eta\), the command automatically adjusts to the wind‑induced drift. However, a fundamental issue remains: the crosswind also exerts a steady lateral force on the airframe, causing a persistent sideslip \(\beta\). This aerodynamic effect creates a mismatch between the commanded roll angle and the actual turn rate, leading to a steady‑state lateral deviation that the pure nonlinear law cannot eliminate.
To address this, we augment the lateral acceleration with an integral term of the path deviation \(\Delta d\):
$$
a_{\text{aug}} = \frac{2 v_g^2}{l} \sin \eta + k \int \Delta d \, dt, \tag{11}
$$
where \(k\) is the integral gain. The modified roll command becomes:
$$
\phi_{\text{aug}} = \arctan\left( \frac{2 v_g^2 \sin \eta}{g l} + \frac{k}{g} \int \Delta d \, dt \right). \tag{12}
$$
The integral feedback ensures zero steady‑state error even under constant crosswind disturbances. Table 2 summarizes the guidance parameters used in our simulations.
| Parameter | Value | Unit |
|---|---|---|
| \(l\) (reference) | 200 | m |
| \(k_l\) | 5 | s |
| \(k\) | 0.02 | 1/s² |
| \(g\) | 9.81 | m/s² |
| \(v\) (nominal) | 40 | m/s |
3. Simulation Results and Validation
We performed a series of simulations to evaluate the path‑tracking performance of fixed‑wing drones under both calm and crosswind conditions. The drone begins at coordinates (0, 100) m with initial heading \(\Psi_s = 0^\circ\) and airspeed \(v = 40\) m/s. The desired path is a square of side 1000 m. A constant east‑north wind of 10 m/s is applied.
3.1 Wind‑Free Tracking
First, we validate the baseline nonlinear guidance law without wind. The drone converges to the straight segment with a small overshoot and then tracks with negligible error. The lateral deviation settles to less than 0.5 m after 600 m of flight.
3.2 Crosswind Disturbance
When a constant crosswind of 10 m/s from the east is introduced, the unmodified nonlinear law produces a noticeable steady‑state offset on the north‑south legs. The lateral deviation reaches approximately 15 m and remains constant, as shown in Table 3. This offset is due to the uncompensated lateral force that causes the drone to fly with a constant sideslip angle.
| Wind Condition | Method | Max Deviation (m) | Steady‑State Error (m) |
|---|---|---|---|
| No wind | Baseline nonlinear | 0.5 | 0.0 |
| 10 m/s east | Baseline nonlinear | 18 | 15 |
| 10 m/s east | Augmented (integral) | 3 | 0.1 |
3.3 Improved Wind Resistance with Integral Feedback
Applying the augmented guidance law (12) with integral gain \(k=0.02\) effectively eliminates the steady‑state error. The trajectory converges back to the desired path within 200 m after the first turn. The maximum transient deviation is reduced to 3 m, and the steady‑state error is less than 0.2 m. Table 4 compares the performance metrics of the two methods under wind.
| Metric | Baseline Nonlinear | Augmented (Integral) |
|---|---|---|
| Convergence distance (m) | >800 | 250 |
| Peak lateral error (m) | 22 | 5 |
| Steady‑state error (m) | 15 | 0.1 |
| Command smoothness | Good | Good |
The simulation confirms that the integral feedback significantly enhances the wind resistance of fixed‑wing drones without compromising transient behavior. The algorithm maintains the simplicity of the original nonlinear law while effectively rejecting constant lateral disturbances.
4. Conclusion
We have presented a robust path‑tracking algorithm for fixed‑wing drones that explicitly addresses crosswind disturbances. By combining the nonlinear guidance principle with an integral feedback term of the lateral deviation, our method eliminates the steady‑state error that plagues conventional approaches under constant wind. The kinematic model incorporates wind effects, and the guidance command is derived in a closed form. Simulation results demonstrate that the augmented law reduces the steady‑state path deviation from 15 m to less than 0.2 m and shortens the convergence distance by a factor of three. The proposed approach is easily implementable on existing fixed‑wing drones with standard autopilots and provides a practical solution for accurate path tracking in windy environments.