In recent years, with the rapid development of national defense and unmanned aerial vehicle（UAV）technology, UAVs have been widely applied in various combat scenarios such as target tracking, intelligence reconnaissance, aerial refueling, and precision strikes. These applications impose high demands on the path tracking capability of fixed-wing UAVs. The modern battlefield environment is increasingly complex and variable, where UAVs encounter numerous unknown disturbances. The path tracking controller of a fixed-wing UAV is highly susceptible to these disturbances, potentially causing the flight path to deviate from the preset route and creating safety hazards. Among environmental disturbances, lateral wind fields—consisting of constant wind and turbulence—are the most prominent. Turbulence disturbances can generally be quickly mitigated by the stability augmentation control of the inner loop. However, constant wind disturbances apply a constant side force to the UAV airframe, influencing the long-period motion of the aircraft. Therefore, the study of wind resistance in fixed-wing UAV path tracking primarily addresses the constant wind component of wind fields.
Extensive literature has proposed various algorithms for UAV path tracking. For instance, some researchers applied proportional guidance for dynamic obstacle avoidance, while others used field-of-view guidance to achieve path tracking with parameter-dependent stability. PID controllers combined with neural networks offer good performance for simple paths but are verified only in windless conditions. Vector field methods provide high precision but are computationally complex. Most of these methods do not account for lateral wind interference. In practical flight control systems, the primary strategies to handle crosswind are the crabbing approach and the sideslip approach. The crabbing method adjusts the heading angle to produce a yaw angle that counteracts the crosswind, aligning the velocity direction with the desired track. The sideslip method controls the UAV to roll at a specific angle to balance the lateral force from the wind, but it is unsuitable for long-duration missions due to the constant roll angle required under steady winds.
Some recent algorithms combine field-of-view guidance with pursuit guidance to reduce wind-induced deviations. Nonlinear guidance using a virtual target point has been demonstrated feasible on real fixed-wing UAVs, with further improvements to reduce tracking errors during turns under wind. Integral vector field methods using state feedback compensation have also been introduced to solve the static deviation problem. However, these approaches all adopt the crabbing anti-wind strategy. They focus on the effect of crosswind on velocity direction but neglect the lateral force that causes a side-slip angle, which leads to a mismatch between the control command and the actual flight state. Consequently, the steady-state error remains unresolved.
To address these issues, this work proposes a wind-resistant path tracking algorithm for fixed-wing UAVs based on the nonlinear guidance principle. The algorithm ensures stable tracking of a predefined path under lateral wind conditions, reduces the tracking error caused by wind, and is significant for real combat missions. Simulation results demonstrate the feasibility and effectiveness of the proposed method.
System Model
Motion Model of Fixed-Wing UAV in Wind Field
The object of this research is a fixed-wing UAV. To study the impact of crosswind, we first establish its motion model. Since path tracking mainly concerns planar motion, only the two-dimensional horizontal motion is considered. The motion model of a fixed-wing UAV in a wind field is summarized in Table 1. In the figure,
the wind speed vector is denoted by $ \mathbf{v}_w $, the airspeed vector by $ \mathbf{v} $, and the ground speed vector by $ \mathbf{v}_g $. Before wind disturbance, $ \mathbf{v} $ and $ \mathbf{v}_g $ have the same direction and magnitude. The angle between the airspeed vector and the body axis is the sideslip angle $ \beta $. Under crosswind, the ground speed rotates by an angle $ \beta_w $ relative to its original direction. The approximate relationship is given by:
$$
\beta_w \approx -\frac{v_w}{v},
$$
where $ v_w $ is the wind speed magnitude. The relationship between airspeed and ground speed is:
$$
\mathbf{v}_g = \mathbf{v}_w + \mathbf{v}.
$$
By definition, the heading angle $ \Psi_s $ is the angle between the ground speed and the inertial x-axis, while the yaw angle $ \Psi $ is the angle between the body axis and the inertial x-axis. Under crosswind, the relation is:
$$
\Psi_s = \Psi + \beta + \beta_w.
$$
For a fixed-wing UAV flying in a horizontal plane (pitch angle $ \theta = 0 $), the kinematic equation simplifies to:
$$
\begin{cases}
\dot{x} = v_g \cos \Psi_s, \\
\dot{y} = v_g \sin \Psi_s, \\
\dot{z} = 0.
\end{cases}
$$
Decomposing the wind disturbance along the x and y axes, the equation becomes:
$$
\begin{cases}
\dot{x} = v \cos(\Psi + \beta) + v_{wx}, \\
\dot{y} = v \sin(\Psi + \beta) + v_{wy},
\end{cases}
$$
where $ v_{wx} $ and $ v_{wy} $ are the wind speed components along the x-axis and y-axis, respectively.
Path Tracking Control System Architecture
The path tracking capability of a fixed-wing UAV depends on the path tracking control system, which generates navigation commands and implements attitude control. A common design splits the system into an outer navigation control loop and an inner attitude control loop. This structure is simple, physically interpretable, and easy to implement. The outer loop computes required control commands (typically the roll angle) based on the current position and desired path, while the inner loop executes attitude control via actuators such as elevators, ailerons, and rudders. To achieve path tracking under crosswind, this work designs a new path tracking algorithm for the outer loop without modifying the inner loop.
Path Tracking Control Algorithm
Principle of Nonlinear Guidance Method
The nonlinear guidance method introduces a virtual target point on the desired path at a fixed look-ahead distance $l$ from the UAV. This target point pulls the UAV toward the path. The method is illustrated conceptually: the distance $l$ is the straight-line separation between the UAV and the virtual target point, $ \mathbf{v}_g $ is the ground speed vector, $ \eta $ is the angle between $ \mathbf{v}_g $ and the line segment $l$, and $a$ is the required lateral acceleration. The virtual target point moves along the desired path with the UAV, always maintaining distance $l$ from the UAV.
Assuming the UAV performs a coordinated turn at every instant with radius $r$, the lateral acceleration $a$ is also the centripetal acceleration. From geometry,
$$
r = \frac{l}{2\sin \eta}.
$$
The required lateral acceleration becomes:
$$
a = \frac{v_g^2}{r} = \frac{2 v_g^2}{l} \sin \eta.
$$
Thus, the magnitude of $a$ depends only on $v_g$, $l$, and $\eta$, while its sign depends on the sign of $\eta$. When the UAV is on the desired path, $\eta = 0$, and $a = 0$. The UAV then continues along the path.
Computation of Roll Command
To compute the roll command, the lateral acceleration $a$ must be converted to a roll angle $ \phi $. During a coordinated turn with constant altitude, the lift force $L$ provides both vertical and horizontal components. The horizontal component equals the centripetal force:
$$
mg \tan \phi = m a,
$$
where $g$ is gravitational acceleration. Therefore, the roll angle command is:
$$
\phi = \arctan\left(\frac{a}{g}\right).
$$
Substituting the expression for $a$ gives the final roll command:
$$
\phi = \arctan\left( \frac{2 v_g^2 \sin \eta}{g l} \right).
$$
The look-ahead distance $l$ must be adapted to the flight speed. A common adaptive rule is:
$$
l’ = l + k_l (v_g’ – v_g),
$$
where $k_l$ is a proportional coefficient, and $(l, v_g)$ is a reference pair for the UAV.
Wind Resistance Analysis and Improvement
Wind Resistance Analysis of Nonlinear Guidance
The roll command $ \phi $ depends on $v_g$ and $\eta$, where $\eta$ itself depends on the direction of $v_g$. Since $v_g = v_w + v$, the wind directly affects $v_g$ in both magnitude and direction. Therefore, the algorithm inherently accounts for wind effects on velocity; the roll command can adjust automatically with wind changes, providing a certain degree of wind resistance.
However, in practice, crosswind not only alters velocity but also exerts a lateral force on the fixed-wing UAV airframe. This force induces a sideslip angle that is not captured by the velocity-only model. Consequently, the roll command computed from $v_g$ and $\eta$ may not match the actual aerodynamic state, leading to a steady-state offset (static deviation) between the actual track and the desired path. To eliminate this offset, an integral term of the track error must be introduced into the outer loop. The improved lateral acceleration is:
$$
a = \frac{2 v_g^2 \sin \eta}{l} + k \int \Delta d \, dt,
$$
where $k$ is an integral gain and $\Delta d$ is the current cross-track error. The corresponding roll command becomes:
$$
\phi = \arctan\left( \frac{2 v_g^2 \sin \eta}{g l} + \frac{k}{g} \int \Delta d \, dt \right).
$$
This feedback mechanism effectively cancels the static error caused by wind-induced side force and also accelerates the convergence rate to the desired path.
Simulation Verification
Simulations were conducted to verify the feasibility and wind resistance of the proposed algorithm. The fixed-wing UAV parameters used in the simulations are listed in Table 1. The initial conditions were: initial position (0 m, 100 m), initial heading angle $\Psi_s = 0^\circ$, and airspeed $v = 40$ m/s.
Table 1 Fixed-wing UAV simulation parameters
| Parameter | Symbol | Value | Unit |
|---|---|---|---|
| Airspeed | $v$ | 40 | m/s |
| Gravitational acceleration | $g$ | 9.81 | m/s² |
| Reference look-ahead distance | $l$ | 200 | m |
| Proportional coefficient for $l$ | $k_l$ | 5 | — |
| Integral gain for cross-track error | $k$ | 0.02 | 1/s² |
Windless Condition
First, the algorithm was tested in a windless environment, tracking a straight line with slope 1. The result showed that the UAV converged to the desired path with negligible overshoot, and the cross-track error quickly became zero. The tracking error is summarized in Table 2.
Table 2 Path tracking error under windless condition
| Flight segment | Maximum cross-track error (m) | Steady-state error (m) |
|---|---|---|
| Initial approach | 60 | — |
| After convergence (distance 500 m) | 0.1 | <0.01 |
Crosswind Condition (Without Improvement)
Next, a constant wind from the east (positive x-direction) was applied at $v_w = 10$ m/s. The UAV was commanded to track a square path with side length 1000 m. Under the original nonlinear guidance without integral feedback, a steady offset appeared on the north-south legs (perpendicular to the wind direction). The measured errors are shown in Table 3.
Table 3 Path tracking error under crosswind (without integral feedback)
| Path segment | Maximum cross-track error (m) | Steady-state error (m) |
|---|---|---|
| North-south leg (wind direction east) | 18 | 15 |
| East-west leg (wind direction east) | 5 | <0.5 |
Crosswind Condition (With Improved Algorithm)
Applying the improved algorithm with integral feedback ($k = 0.02$) under the same wind conditions, the static deviation on the north-south legs was eliminated. The comparison of cross-track error on the north-south leg is presented in Table 4. The improved algorithm also showed faster convergence to the path at the beginning of each leg.
Table 4 Comparison of cross-track errors on north-south leg (wind 10 m/s east)
| Algorithm | Steady-state error (m) | Convergence time (s) |
|---|---|---|
| Original nonlinear guidance | 15 | 25 |
| Improved with integral feedback | 0.3 | 18 |
Simulation results confirm that the proposed algorithm successfully tracks the desired path under wind disturbance. The integral of cross-track error eliminates the static error caused by wind-induced lateral force, demonstrating enhanced wind resistance for fixed-wing UAV path tracking.
Conclusion
In this work, a wind-resistant path tracking algorithm for fixed-wing UAVs is developed based on the nonlinear guidance principle. The algorithm explicitly addresses the impact of crosswind on both the UAV velocity and the additional side force that induces a steady-state offset. By integrating the cross-track error feedback into the roll command computation, the static deviation that persists in conventional nonlinear guidance is effectively eliminated. Simulations in windless and wind-disturbed environments verify that the improved algorithm maintains high tracking accuracy and rapid convergence, making it suitable for fixed-wing UAV operations in complex atmospheric conditions. The approach provides a practical solution for enhancing the autonomous navigation reliability of fixed-wing UAVs under lateral wind perturbations.