In the field of autonomous unmanned systems, path planning serves as the critical bridge between environmental perception and flight control. For fixed-wing UAVs, which possess advantages such as high speed, long endurance, and large payload capacity, the path planning problem becomes more challenging due to inherent kinematic constraints. Unlike multi-rotor drones or ground robots, a fixed-wing UAV cannot hover, move laterally, or climb vertically; it relies on aerodynamic forces and requires a minimum turning radius and a finite climb rate. Many existing path planning algorithms designed for rotorcraft or mobile robots fail to produce feasible or optimal routes when directly applied to fixed-wing UAVs.
In this work, I propose a novel flight environment rasterization method tailored to the performance characteristics of fixed-wing UAVs. The method ensures kinematic accessibility between adjacent grid nodes, thereby providing a reliable foundation for grid‑based path planning algorithms. Furthermore, I introduce a multi‑dimensional cost function that incorporates time, fuel consumption, and safety risk into the path planning process, enabling the algorithm to adapt to diverse mission requirements by dynamically adjusting the weighting factors. Comprehensive simulation experiments demonstrate the effectiveness and superiority of the proposed approach.
1. Rasterization Method for Fixed-wing UAV Environments
1.1 Horizontal Grid Design Constraint
When constructing a grid map of the flight environment, the distance between adjacent horizontal nodes must be compatible with the minimum turning radius of the fixed-wing UAV. The turning motion relies on banking the lift vector to provide the required centripetal acceleration:
$$ a_n = g \tan \phi = \frac{V^2}{R} $$
where \( \phi \) is the bank angle. Given a maximum bank angle \( \phi_{\max} \) and a cruise speed \( V \), the minimum turning radius is:
$$ R_{\min} = \frac{V^2}{g \tan \phi_{\max}} $$
To guarantee that the UAV can sequentially fly from one node to a neighboring node without violating its turn capability, the horizontal grid spacing \( D_h \) should satisfy \( D_h \ge 2 R_{\min} \). For example, with \( V = 50 \, \text{m/s} \) and \( \phi_{\max} = 30^\circ \), we obtain \( R_{\min} \approx 441 \, \text{m} \), and accordingly set \( D_h = 1000 \, \text{m} \).
1.2 Vertical Grid Design Constraint
In the vertical direction, the ability to change altitude is limited by the maximum climb rate of the fixed-wing UAV. Assuming a steady climbing flight, the force balance in the vertical plane gives:
$$
\begin{aligned}
T \cos \alpha – D – W \sin \gamma &= 0 \\
T \sin \alpha + L – W \cos \gamma &= 0
\end{aligned}
$$
where \( T \) is engine thrust, \( \alpha \) the angle of attack, \( D \) and \( L \) the drag and lift, \( W \) the weight, and \( \gamma \) the climb angle. Using a typical jet engine thrust model, the maximum climb rate at different altitudes can be calculated. For a fixed-wing UAV cruising at 50 m/s, the climb rates at altitudes 0–6 km are shown in Table 1.
| Altitude (km) | Climb Rate (m/s) |
|---|---|
| 0 | 10.36 |
| 1 | 8.80 |
| 2 | 7.26 |
| 3 | 5.88 |
| 4 | 4.64 |
| 5 | 3.53 |
| 6 | 2.53 |
To guarantee that a fixed-wing UAV can ascend from one altitude layer to the next within one horizontal grid step, the vertical spacing between layers should be no larger than the product of the climb rate and the time required to traverse one horizontal grid. Since the horizontal spacing is 1000 m and the cruise speed is 50 m/s, the traversal time is 20 s. Therefore, the allowable altitude gain in one step is:
$$ \Delta z = \text{climb rate} \times 20 \, \text{s} $$
This results in a non‑uniform vertical stratification: at lower altitudes the layers are thicker, while at higher altitudes they become thinner. Such a design ensures that every pair of adjacent grid nodes is kinematically reachable by the fixed-wing UAV, avoiding infeasible transitions.
2. Path Planning Method in a Threat Environment
2.1 Node Movement Cost Calculation
When applying an A*‑like search on the three‑dimensional grid, a parent node can expand to up to 26 neighboring nodes (including those on the same layer and the layers above and below). Based on the flight characteristics of a fixed-wing UAV, these 26 neighbors can be classified into seven categories (Case 1 to Case 7), as illustrated conceptually: Case 1 – straight horizontal; Case 2 – horizontal with climb; Case 3 – diagonal horizontal with climb; Case 4 – diagonal horizontal; Case 5 – straight horizontal with descent; Case 6 – diagonal horizontal with descent; Case 7 – vertical climb/descent (via spiraling).
Using a six‑degree‑of‑freedom flight simulation with an embedded engine model, the time and fuel consumption for each case were computed. The results are summarized in Table 2.
| Case | Time (s) | Fuel (kg) |
|---|---|---|
| Case 1 | 21.6 | 0.20 |
| Case 2 | 23.0 | 0.35 |
| Case 3 | 29.6 | 0.41 |
| Case 4 | 29.2 | 0.28 |
| Case 5 | 23.2 | 0.20 |
| Case 6 | 28.2 | 0.24 |
| Case 7 | 61.7 | 0.74 |
It is noteworthy that Cases 1 and 5 (straight horizontal vs. straight with descent) have nearly identical horizontal projections yet different fuel consumption due to the descent. Similarly, Cases 4 and 6 differ in fuel while sharing the same horizontal distance. Case 7 (vertical climb/descent) requires the longest time and highest fuel consumption because the fixed-wing UAV must spiral to change altitude, making it the least desirable option.
Additionally, the influence of the previous node’s state on the cost of the next transition was analyzed. For horizontal movement, three preceding orientations (a, b, c) were considered. The simulation results show that for Case 1 transitions, the preceding orientation has negligible impact. For Case 4, the preceding orientation can cause a difference of about 10% in time/fuel, which is compensated in the cost function by adjusting the base value accordingly.
2.2 Improved A* Algorithm with Multi‑Dimensional Weighting
The conventional A* algorithm uses a cost function of the form:
$$ f(n) = h(n) + g(n) $$
where \( g(n) \) is the actual cost from the start to node \( n \), and \( h(n) \) is the heuristic estimate to the goal. For fixed-wing UAV path planning in a threat environment, I extend \( g(n) \) to incorporate time, fuel consumption, and risk:
$$ g(n) = W_t \cdot t_{\text{transition}} + W_o \cdot f_{\text{transition}} + W_R \cdot \text{risk}(n) $$
Here \( W_t \), \( W_o \), and \( W_R \) are the weights for time, oil (fuel), and risk, respectively. The risk value \( \text{risk}(n) \) is derived from external threat assessments (e.g., Bayesian networks) and normalized between 0 and 1. When \( \text{risk}(n) \ge R_c \) (a critical threshold), the node is considered forbidden. Otherwise, the risk contributes to the cumulative cost.
The heuristic \( h(n) \) is defined as the three‑dimensional Manhattan distance from node \( n \) to the goal:
$$ h(n) = |x_n – x_{\text{goal}}| + |y_n – y_{\text{goal}}| + |z_n – z_{\text{goal}}| $$
Table 3 provides the set of cost parameters for different node transition cases, including the base time, base fuel, and a risk increment (which is added if the target node lies in a threat zone).
| Case | Time (s) | Fuel (kg) | Risk factor |
|---|---|---|---|
| Case 1 | 21.6 | 0.20 | 1.0 |
| Case 2 | 23.0 (−10%) | 0.35 (−10%) | 1.0 |
| Case 3 | 29.6 | 0.41 | 1.0 |
| Case 4 | 29.2 (−10%) | 0.28 (−10%) | 1.0 |
| Case 5 | 23.2 | 0.20 | 1.0 |
| Case 6 | 28.2 (−10%) | 0.24 (−10%) | 1.0 |
| Case 7 | 61.7 | 0.74 | 1.0 |
The weight factors can be adjusted according to the mission priority. For instance, if safety is paramount, \( W_R \) is increased; if time is critical, \( W_t \) is increased. The algorithm then searches for the path that minimizes the cumulative \( f(n) \).
3. Simulation Verification
3.1 Path Planning Results
A mountainous environment of 20 km × 20 km × 3 km was constructed with multiple threat zones (e.g., anti‑air fire, severe weather). The start point was at grid coordinate (1,1) and the goal at (20,20). Two experiments were conducted: one using the conventional A* algorithm that treats threats above a threshold as obstacles, and the other using the improved A* algorithm with multi‑dimensional weights.
For the conventional A* (weight: only obstacle avoidance), the planned path consisted of 21 nodes with a total cost of 125.1 (in arbitrary units). The path cut through high‑threat regions, leading to higher risk exposure.
For the improved A* (with \( W_t = 0.05 \), \( W_o = 5 \), \( W_R = 5 \)), the planned path consisted of 29 nodes with a total cost of 107.0. Although the path was longer, it circumvented the high‑threat areas, resulting in a significantly lower overall risk level. By adjusting \( W_R \), the algorithm can be tuned to either favor shorter routes or safer routes.
3.2 Flight Simulation Results
To validate the feasibility of the planned paths, a high‑fidelity flight simulation was performed using the fixed-wing UAV dynamics. The threat zones were modeled as regions with atmospheric turbulence (using the Dryden model) whose intensity is proportional to the threat level. The UAV flew along the paths generated by both methods, and the vehicle’s attitude and acceleration responses were recorded.
The results confirmed that the path produced by the conventional A* method subjected the UAV to stronger turbulence disturbances, whereas the improved method’s path resulted in smoother flight with smaller deviations and lower structural loads. This demonstrates that the improved path planning algorithm not only provides a mathematically optimal solution but also enhances real‑world flight safety for fixed-wing UAVs.
4. Conclusions
In this work, I have presented a comprehensive framework for fixed-wing UAV path planning that addresses the unique kinematic constraints of such aircraft. The proposed rasterization method, which aligns the grid dimensions with the minimum turning radius and altitude‑dependent climb rate, guarantees kinematic accessibility between adjacent nodes. The improved A* algorithm incorporates time, fuel, and risk into a unified cost function, allowing the path planner to adapt to various mission scenarios. Simulation results indicate that the new approach yields paths that are safer and more efficient than those generated by conventional methods.
Future work will extend the framework to cooperative multi‑UAV missions and incorporate real‑time re‑planning capabilities in dynamic environments.