In the field of unmanned aerial vehicles, fixed-wing drones have been widely employed in both civilian and military applications due to their long endurance and high speed. One of the core capabilities required for autonomous flight is precise path following, which ensures that the drone adheres to a predefined trajectory even under external disturbances such as wind. Traditional path following methods often rely on PID-based lateral guidance, which can suffer from slow convergence and poor robustness in windy conditions. To address these issues, this paper presents a novel lateral guidance algorithm based on the vector field method for fixed-wing drones. The proposed algorithm generates real-time course angle commands solely as a function of cross-track error, thereby replacing the conventional PID lateral controller. By integrating with a PID longitudinal controller, the overall guidance system demonstrates superior performance in both straight-line and circular arc path following tasks. Extensive digital simulations and hardware-in-the-loop experiments confirm that the vector field method significantly enhances the path following accuracy and wind disturbance rejection capability of fixed-wing drones.
This study begins by modeling the flight dynamics of a typical small-to-medium fixed-wing drone. The lateral-directional and longitudinal control loops are simplified as second-order systems, where the roll angle command is derived from course angle error and cross-track error in the PID scheme, and from the vector field in the proposed scheme. The mathematical formulation of the path following problem is then established for both straight segments and circular arcs. For straight-line path following, the cross-track error is defined as the perpendicular distance from the drone to the desired line. For circular arc following, the error is the difference between the actual distance to the arc center and the desired radius. These definitions are essential for designing the vector field guidance law.
The core idea of the vector field method is to assign a desired course angle at every point in the plane, such that the drone is automatically guided toward the desired path. For a straight line with direction angle χq, the desired course angle χc is given by:
$$
\chi_c(e_{Py}) = -\arctan(k_m e_{Py}) + \chi_q
$$
where ePy is the cross-track error and km is a positive constant that determines the rate of transition from a heading perpendicular to the line (when far away) to the line direction (when on the path). For circular arcs with radius ρ and center, the desired course angle becomes:
$$
\chi_c(d,\rho,\lambda) = \lambda \arctan\left( k_n \frac{\|d\|-\rho}{\rho} \right) + \chi_o
$$
Here d is the distance vector from the drone to the arc center, λ = +1 for clockwise orbit and λ = -1 for counterclockwise, and χo is the tangent direction of the arc at the closest point. These vector field formulations ensure that when the drone is far from the path, it heads directly toward the path, and as it approaches, the heading smoothly transitions to follow the path. No additional PID terms on cross-track error are needed; the vector field acts as a pure geometric guidance law.
To evaluate the effectiveness of the proposed vector field guidance, we conducted a series of digital simulations comparing it with the conventional PID lateral guidance. The drone model parameters were set as aχ = 0.732, aẋ̇χ = 5.968. The PID gains were kχP = 0.105, kDP = 1.815, kDI = 0.006. For the vector field, we chose km = 0.05 and kn = 8. Wind disturbance of 6 m/s from 315° was applied in all cases. Three scenarios were tested: close-range straight line, long-range straight line, and circular arc path.
The first scenario involved a straight-line path (y = 0) with initial cross-track error of 100 m. Table 1 summarizes the key performance metrics. The vector field method achieved convergence (error < 2.1 m) in 30 s with a steady-state error of 2.1 m, while the PID method required 54 s and exhibited oscillatory behavior. The course angle and roll angle responses were smoother with vector field, indicating less actuator stress.
| Method | Settling Time (s) | Steady-State Error (m) | Course Angle Oscillation |
|---|---|---|---|
| PID | 54 | 2.1 | High |
| Vector Field | 30 | 2.1 | Low |
In the second scenario, the initial cross-track error was increased to 400 m. The vector field method guided the drone to the path in 46 s with an error of 3.5 m, whereas the PID method took 77 s and gave an error of 5.5 m. The advantage of the vector field becomes more pronounced with larger initial offsets, as it provides a more direct approach angle.
| Method | Settling Time (s) | Steady-State Error (m) | Maximum Roll Angle (°) |
|---|---|---|---|
| PID | 77 | 5.5 | 35 |
| Vector Field | 46 | 3.5 | 28 |
The third scenario was a circular arc path composed of two semicircles of radius 200 m. The vector field method completed the arc in 74 s with minimal overshoot, while the PID method took 81 s and exhibited significant oscillation in the second half. The cross-track error during the arc was bounded within 5 m for vector field and up to 15 m for PID.
| Method | Completion Time (s) | Max Cross-track Error (m) | Roll Angle Oscillation |
|---|---|---|---|
| PID | 81 | 15 | High |
| Vector Field | 74 | 5 | Low |
These simulation results clearly demonstrate that the vector field guidance outperforms the PID lateral guidance for fixed-wing drones in terms of convergence speed, accuracy, and smoothness. The vector field inherently accounts for the geometric relationship between the drone and the path, leading to more efficient trajectory shaping.
To further validate the algorithm in a realistic setting, we conducted hardware-in-the-loop (HIL) simulations. The HIL platform included a mathematical model of the fixed-wing drone with six-degree-of-freedom dynamics, an autopilot module, and a simulated GPS/IMU sensor suite. The takeoff was simulated as a catapult launch with a 15° pitch angle. Constant wind of 6 m/s from 45° was injected. The vector field lateral guidance was integrated with a PID longitudinal controller for altitude hold. The flight path consisted of multiple straight and circular segments. The results showed that the drone tracked the planned trajectory with high fidelity. The lateral deviation never exceeded 10 m, and the altitude error remained within 5 m throughout the flight. The roll and pitch commands were smooth, indicating that the vector field method does not induce unnecessary oscillations.
One practical issue encountered during arc following is the potential for 2π jumps in the course angle command when the drone passes through certain angular positions. We resolved this by adjusting the phase angle φ using the formula:
$$
\varphi = \arctan(p_e – c_e, p_n – c_n) + 2\pi n
$$
where n is chosen such that |χc – χ| < π. This ensures that the autopilot receives a continuous command without sudden reversals.
In summary, the vector field method offers a simple yet powerful alternative to traditional PID lateral guidance for fixed-wing drones. Its key advantages include automatic tuning of approach angle based on cross-track error, inherent protection against wind-induced drift, and reduced actuator wear due to smoother control signals. The method requires only two parameters (km and kn) that have intuitive interpretations related to the aggressiveness of the convergence. Furthermore, the vector field framework can be extended to three-dimensional path following by combining with altitude control, as demonstrated in our HIL tests.
The contributions of this work are threefold. First, we derived a vector field guidance law tailored for fixed-wing drones that explicitly accounts for both straight and curved paths. Second, we provided a rigorous comparison with the PID method under wind disturbance, quantifying the improvements in settling time and steady-state accuracy. Third, we validated the algorithm on a realistic HIL platform, confirming its feasibility for practical deployment. Future work will focus on adaptive tuning of the vector field parameters based on wind estimation and the integration of obstacle avoidance capabilities.