In recent years, unmanned aerial vehicles (UAVs) have experienced rapid technological development, with significant improvements in endurance, payload capacity, stability, and autonomy. These breakthroughs have enabled UAVs to perform complex tasks autonomously, such as agricultural spraying, power line inspection, and military reconnaissance, thereby freeing human operators from tedious workflows and greatly enhancing operational efficiency. However, achieving full autonomy for onboard unmanned systems remains challenging due to the inherent uncertainty of dynamic environments and the complexity of mission requirements. Among the key enabling technologies—environmental perception, target recognition, flight control, and path planning—path planning serves as a critical bridge between perception and control. It processes environmental information and computes a feasible or optimal trajectory that satisfies mission objectives while respecting the vehicle’s dynamic constraints.
Path planning methods that are widely applied to multi-rotor UAVs and ground robots often fail when directly transferred to fixed-wing drones. Unlike rotary-wing platforms, a fixed-wing drone relies on aerodynamic lift and cannot hover, translate laterally, or ascend/descend vertically. It has a non-negligible minimum turning radius and a finite climb rate, which impose strong kinematic constraints on the connectivity between waypoints. Therefore, we must tailor both the environmental representation (rasterization) and the planning algorithm to the specific flight performance of fixed-wing drones. In this paper, we systematically analyze the motion characteristics of fixed-wing drones and propose a novel grid‑based environment modeling method that guarantees kinematic reachability between adjacent nodes. We further introduce a multi‑criteria cost function that incorporates time, fuel consumption, and threat risk, and we develop an improved A* algorithm that dynamically adjusts these weights to suit diverse mission profiles. Extensive simulations demonstrate that the proposed approach yields safer, more economical, and more efficient paths for fixed-wing drone operations.
1. Rasterization of Flight Environment for Fixed-wing Drones
The first step in any grid‑based path planning method is to discretize the continuous three‑dimensional flight space into a set of nodes (voxels) and edges. For a fixed-wing drone, the grid resolution cannot be chosen arbitrarily; it must be derived from the vehicle’s performance envelope to ensure that every transition between adjacent nodes is dynamically feasible.
1.1 Horizontal Grid Spacing Constrained by Minimum Turning Radius
When a fixed-wing drone turns, it banks to generate the centripetal acceleration required for a curved trajectory. The centripetal acceleration is given by:
$$ a_n = g \tan\phi = \frac{V^2}{R} $$
where V is the flight speed, g is the gravitational acceleration, ϕ is the bank angle, and R is the turn radius. The minimum turn radius R_min is achieved at the maximum allowable bank angle ϕ_max:
$$ R_{\min} = \frac{V^2}{g \tan\phi_{\max}} $$
To enable a smooth transition from one grid node to its horizontal neighbor, the distance between two adjacent nodes must be at least twice the minimum turning radius; otherwise, the drone would be forced to overshoot or violate the bank‑angle limit. In our example, the fixed-wing drone cruises at V = 50 m/s and has a maximum bank angle of 30°. The minimum turning radius is then:
$$ R_{\min} = \frac{50^2}{9.81 \times \tan 30^\circ} \approx \frac{2500}{9.81 \times 0.577} \approx 441 \, \text{m} $$
Thus, we set the horizontal grid spacing to 1000 m (approximately 2.3 × R_min) to ensure that even the tightest possible turn can be completed within one grid step without exceeding the roll limit.
1.2 Vertical Grid Spacing Constrained by Climb Rate
In the vertical plane, a fixed-wing drone climbs by increasing its pitch angle while maintaining a constant speed. The steady‑climb force balance is:
$$ T\cos(\alpha) – D – W\sin\gamma = 0 $$
$$ T\sin(\alpha) + L – W\cos\gamma = 0 $$
where T is thrust, α is angle of attack, D and L are drag and lift, W is weight, and γ is the flight‑path angle. Using the known thrust‑versus‑altitude characteristics of a typical jet engine, we compute the maximum climb rate at different altitudes. For a fixed-wing drone cruising at 50 m/s, the climb rate decreases with altitude as shown in Table 1.
Table 1. Maximum climb rate of a fixed-wing drone at various altitudes (V = 50 m/s)
| Altitude (km) | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| Climb rate (m/s) | 10.36 | 8.80 | 7.26 | 5.88 | 4.64 | 3.53 | 2.53 |
Given the horizontal grid spacing ΔL = 1000 m, the time required to traverse one horizontal step at cruise speed is Δt = ΔL/V = 20 s. Over this time, the maximum vertical ascent that the fixed-wing drone can achieve is Δh = climb_rate × Δt. Therefore, the vertical spacing between consecutive altitude layers is not constant but is set equal to the altitude‑dependent climb capability. For example, at sea level, Δh = 10.36 × 20 ≈ 207 m; at 6 km altitude, Δh = 2.53 × 20 ≈ 51 m. This non‑uniform layering guarantees that the fixed-wing drone can always move from one altitude layer to the adjacent higher (or lower) layer within one horizontal step without exceeding the maximum climb / descent rate. The resulting vertical stratification is illustrated conceptually in our earlier figure (not inserted here but referenced in the original work).
By combining the horizontal and vertical constraints, we obtain a three‑dimensional grid that is intrinsically matched to the fixed-wing drone’s performance. All nodes that lie inside terrain obstacles or above the service ceiling are marked as blocked. The rasterized environment not only reduces the computational load but also makes the path planning results directly executable by the autopilot.
2. Node Connectivity and Multi‑Criteria Cost for Fixed-wing Drones
With the grid defined, we must specify which neighboring nodes are reachable from a given parent node and what the transition cost is. Unlike a rotary‑wing UAV that can move in any direction with equal ease, a fixed-wing drone cannot execute a vertical climb or a pure lateral translation without first banking or pitching. Therefore, we classify the 26 possible neighbors in a three‑dimensional grid into seven distinct motion types (Case 1 through Case 7), as summarized in Table 2.
Table 2. Classification of neighbor‑node transitions for a fixed-wing drone
| Case | Horizontal displacement | Vertical displacement | Description |
|---|---|---|---|
| 1 | 1 grid (straight) | 0 | Level straight flight |
| 2 | 1 grid (straight) | +1 layer (climb) | Straight climb |
| 3 | 1 grid (diagonal) | 0 | Level turn (45°) |
| 4 | 1 grid (diagonal) | +1 layer (climb) | Climbing turn |
| 5 | 1 grid (straight) | –1 layer (descend) | Straight descent |
| 6 | 1 grid (diagonal) | –1 layer (descend) | Descending turn |
| 7 | 0 | +1 or –1 layer | Vertical ascent/descent via spiral |
Although Case 7 (vertical motion) is possible for a fixed-wing drone by executing a spiral climb/descent, it is far more expensive in terms of both time and fuel than the other cases. The cost of each transition must therefore be computed using a high‑fidelity six‑degree‑of‑freedom simulation that includes the engine model, aerodynamics, and flight‑control laws. We assume level cruise at constant indicated airspeed (50 m/s). Table 3 presents the computed time and fuel consumption for each case, normalized to Case 1 (which requires 21.6 s and consumes 0.20 kg of fuel).
Table 3. Time and fuel consumption for different neighbor transitions of a fixed-wing drone
| Transition Type | Time (s) | Fuel (kg) | Horizontal projection |
|---|---|---|---|
| Case 1 (level straight) | 21.6 | 0.20 | 1 grid |
| Case 2 (straight climb) | 23.0 | 0.35 | 1 grid |
| Case 3 (level turn) | 29.6 | 0.41 | √2 grid |
| Case 4 (climbing turn) | 29.2 | 0.28 | √2 grid |
| Case 5 (straight descent) | 23.2 | 0.20 | 1 grid |
| Case 6 (descending turn) | 28.2 | 0.24 | √2 grid |
| Case 7 (vertical spiral) | 61.7 | 0.74 | 0 |
It is important to note that Case 1 and Case 5 have nearly identical time and fuel consumption, contradicting the naive assumption that a descending flight should be as costly as a climbing flight when the vertical distance is the same. Similarly, Case 3 and Case 6 share similar horizontal projections but differ in fuel due to the altitude change. The vertical spiral (Case 7) is roughly three times more expensive than a straight‑line move and should be avoided unless no other path exists.
Furthermore, the cost of a move may depend on the previous node’s orientation due to the need to execute a smooth turn. Our analysis of three consecutive nodes (previous, current, next) shows that for Case 1 next moves, the heading history has negligible effect. For Case 4 next moves, however, a favorable previous node orientation can reduce time/fuel by approximately 10%. This effect is incorporated as a small correction in the cost function.
3. Improved A* Path Planning with Threat Environment
The classical A* algorithm uses a cost function f(n) = g(n) + h(n), where g(n) is the accumulated cost from the start to node n, and h(n) is a heuristic estimate of the remaining cost to the goal. For a fixed-wing drone operating in a threat‑populated environment, we extend g(n) to include three weighted terms:
$$ g(n) = W_t \cdot t_{\text{move}}(n) + W_o \cdot o_{\text{move}}(n) + W_R \cdot R_{\text{risk}}(n) $$
where:
- tmove(n) is the time required to fly from the parent node to node n (from Table 3);
- omove(n) is the fuel consumed (from Table 3);
- Rrisk(n) is the cumulative threat risk associated with the path segment, obtained from external intelligence (ranging from 0 = no threat to 1 = maximum threat);
- Wt, Wo, WR are user‑adjustable weights that reflect mission priorities.
Any node whose threat risk exceeds a critical threshold Rc is treated as an obstacle and removed from the open list. For nodes with risk below Rc, the risk term enters the cost linearly with weight WR. The heuristic h(n) is computed as the three‑dimensional Manhattan distance from node n to the goal:
$$ h(n) = |x_n – x_{\text{goal}}| + |y_n – y_{\text{goal}}| + |z_n – z_{\text{goal}}| $$
The overall algorithm proceeds as follows:
Algorithm: Improved A* for fixed-wing drone under threat
- Initialize open list with start node, closed list empty.
- Set g(start)=0, h(start)=Manhattan distance to goal, f(start)=h(start).
- While open list not empty:
- Select node with minimum f as current.
- Move current from open to closed.
- If current = goal, reconstruct path and return.
- For each neighbor that is not blocked and has risk < Rc:
- Compute tentative g = g(current) + multi‑criteria cost of the transition.
- If neighbor not in open: add to open with computed g, h, f.
- If neighbor already in open and new g is lower: update parent, g, f.
- Return failure if open list empty.
By adjusting WR, we can tune the planner’s behavior. For a time‑critical mission, we set WR small (e.g., 1) to allow the drone to cut through moderate‑threat areas, reducing flight time. For a safety‑critical mission, we set WR large (e.g., 10) to force the algorithm to route around high‑threat zones, even if the path becomes longer.
4. Simulation Results and Validation
4.1 Path Planning in a Threat-Enriched Mountainous Environment
We constructed a 20 km × 20 km × 3 km mountainous environment containing multiple threat sources (e.g., anti‑air fire, thunderstorms, icing clouds). The combined threat risk at each grid node was estimated using a Bayesian network (details omitted here). The start node was at grid coordinate (1,1,1) and the goal at (20,20,1). The fixed-wing drone had the same performance parameters as described earlier (V=50 m/s, ϕ_max=30°, etc.). We compared two methods:
- Conventional A*: only treats nodes with threat risk > 0.8 as blocked; uses Euclidean distance as cost.
- Improved A*: uses the multi‑criteria cost with Wt=0.05, Wo=5, WR=5; threat threshold Rc=0.8.
The image below illustrates the simulation environment and the planned paths.
Table 4 summarizes the key performance metrics.
Table 4. Comparison of conventional and improved A* path planning results
| Metric | Conventional A* | Improved A* |
|---|---|---|
| Number of waypoints | 21 | 29 |
| Total path cost (normalized) | 125.1 | 107.0 |
| Average node threat risk | 0.62 | 0.38 |
| Maximum node threat risk | 0.79 | 0.51 |
The conventional A* produced a shorter path (fewer nodes), but it cut directly through the high‑threat central region. The improved A* deliberately avoided dangerous zones, resulting in a slightly longer route (29 nodes vs. 21 nodes), but the overall path cost was lower because the threat contribution was heavily penalized. The average and maximum threat risks along the improved path were reduced by about 39% and 35%, respectively, demonstrating a much safer trajectory.
4.2 Flight Simulation with Atmospheric Turbulence
To further evaluate the impact of threats on the actual flight, we mapped the threat risk to the intensity of Dryden atmospheric turbulence. A higher threat region corresponds to stronger gusts that perturb the fixed-wing drone’s attitude and position. We ran a six‑degree‑of‑freedom simulation for both planned paths. The root‑mean‑square (RMS) deviations of roll angle and vertical acceleration are shown in Table 5.
Table 5. Flight simulation results under turbulence representing threat intensity
| Metric | Conventional A* path | Improved A* path |
|---|---|---|
| RMS roll deviation (deg) | 4.7 | 3.2 |
| RMS vertical acceleration (m/s²) | 1.8 | 1.1 |
| Maximum lateral deviation (m) | 85 | 52 |
The improved path, which avoided high‑threat areas, experienced significantly smaller gust‑induced disturbances. The smaller roll and acceleration deviations imply improved flight safety, reduced pilot/autopilot workload, and lower structural loads. This confirms that the proposed multi‑criteria planning method not only produces a theoretically safer path but also yields practically better flight behavior for the fixed-wing drone.
5. Conclusion
This paper has presented a comprehensive framework for fixed-wing drone path planning that integrates performance‑aware environment rasterization and a threat‑sensitive improved A* algorithm. By deriving the horizontal and vertical grid spacings from the drone’s minimum turn radius and altitude‑dependent climb rate, we guarantee that every grid‑to‑grid transition is kinematically feasible. We have also established a multi‑criteria cost function that properly reflects the time, fuel, and risk consumed by each type of neighbor movement, accounting for the unique flight dynamics of fixed-wing drones. Simulation results in a complex mountainous threat environment demonstrate that the improved planner yields paths with significantly lower risk exposure and better flight stability compared to a conventional A* planner that ignores motion‑dependent costs. Moreover, the ability to dynamically adjust the weighting factors makes the method adaptable to a wide range of mission requirements, from time‑critical to safety‑critical operations.
Future work will extend this approach to multi‑UAV cooperative scenarios and incorporate real‑time threat updates from onboard sensors. The rasterization principle and cost‑based planning methodology presented here provide a solid foundation for deploying autonomous fixed-wing drones in challenging real‑world environments.