We investigate a rasterization method specifically tailored for the flight environment of fixed-wing drones. Unlike rotary-wing UAVs or ground robots, fixed-wing drones rely on aerodynamic forces for flight, which imposes unique kinematic constraints such as a non-negligible turning radius, limited climb rate, and inability to perform vertical or lateral translation. These constraints make conventional raster-based path planning algorithms—originally designed for holonomic or near-holonomic platforms—directly inapplicable to fixed-wing drones. To address this challenge, we propose a novel grid construction method that aligns the spatial discretization of the environment with the performance characteristics of the fixed-wing drone. By ensuring that the distances between adjacent grid nodes are compatible with the minimum turning radius and maximum climb rate, we guarantee that every pair of neighboring nodes in the rasterized space is reachable by the fixed-wing drone. This forms a reliable foundation for applying raster-based path planners to fixed-wing drones.
Furthermore, we enhance the standard A* algorithm by introducing multidimensional weighting factors that account for time, energy consumption, and threat risk. These weights are dynamically adjustable to accommodate diverse mission requirements. In conventional approaches, the movement cost between adjacent grid cells is often assumed to be uniform—for instance, horizontal and diagonal moves are assigned fixed ratios of 1 and √2. However, for fixed-wing drones, the actual cost between two nodes depends not only on the Euclidean distance but also on the aircraft’s flight dynamics, such as the need for banking turns or climbing/descending maneuvers. Our method computes the actual time and fuel consumption for each type of neighbor transition using a six-degree-of-freedom simulation that includes a realistic engine model. We classify the 26 neighbors of a given parent node (in 3D space) into seven distinct categories and derive precise cost values for each category. Additionally, we consider the influence of the previous node’s state on the subsequent transition, revealing that certain sequences (e.g., consecutive turns) can yield ≈10% savings in time and fuel. These detailed cost data are then integrated into the A* cost function alongside a threat assessment value derived from external intelligence (e.g., Bayesian network).
We validate the proposed method through numerical simulations in a synthetic mountainous environment populated with multiple threat sources (e.g., hostile fire, cumulonimbus clouds). The results demonstrate that the improved A* planner, by accounting for actual flight performance and threat avoidance, produces safer and more economical paths compared to the conventional A* that treats the fixed-wing drone as a simple point mass. The improvement is particularly evident in scenarios where the drone must trade off detour length against threat exposure. We also perform a flight simulation using a Dryden turbulence model to represent threat intensity, confirming that the improved path reduces the turbulence-induced perturbations on the aircraft’s states, thereby enhancing flight safety.
The remainder of this paper is organized as follows. Section 2 details the proposed flight-environment rasterization method for fixed-wing drones. Section 3 describes the enhanced path planning algorithm, including the movement-cost calculation and the multidimensional cost function. Section 4 presents simulation results and discussions. Section 5 concludes the paper.
Flight Environment Rasterization for Fixed-Wing Drones
The rasterization (or grid decomposition) of the flight environment is a fundamental step in path planning. In this work, we design the grid dimensions such that any two physically adjacent grid nodes are reachable by the fixed-wing drone, given its flight performance. The process is divided into horizontal and vertical components.
Horizontal Grid Design Constraints
In the horizontal plane, the minimum turning radius of the fixed-wing drone is the key limiting factor. When a fixed-wing drone performs a coordinated turn, the centripetal acceleration is provided by banking the lift vector. The relationship is given by
$$ a_n = g \tan\phi = \frac{V^2}{R} $$
where \(g\) is the gravitational acceleration, \(\phi\) is the bank angle, \(V\) is the true airspeed, and \(R\) is the turn radius. The minimum turn radius occurs at the maximum allowable bank angle \(\phi_{\max}\):
$$ R_{\min} = \frac{V^2}{g \tan\phi_{\max}} $$
To ensure that the drone can move from one grid node to any of its horizontal neighbors without violating the turning constraint, the horizontal grid spacing \(d_h\) must be at least twice the minimum turning radius. In our example, we consider a fixed-wing drone cruising at \(V = 50\ \text{m/s}\) with \(\phi_{\max} = 30^\circ\). Then
$$ R_{\min} = \frac{50^2}{9.81 \times \tan30^\circ} \approx 441.5\ \text{m} $$
We thus set the horizontal grid spacing to \(d_h = 1000\ \text{m}\), which safely exceeds \(2R_{\min}\). This choice guarantees that any sequence of horizontal moves between adjacent nodes can be executed by the fixed-wing drone using a standard Dubins turn or a coordinated banked turn with smooth transitions.
Vertical Grid Design Constraints
For vertical movement, the climb (or descent) rate of the fixed-wing drone is the primary constraint. A fixed-wing drone climbing at a constant airspeed requires a balance between thrust, drag, weight, and lift. The force equilibrium in the vertical plane (steady climbing flight) is given by
$$ \begin{aligned} T\cos\alpha – D – W\sin\gamma &= 0 \\ T\sin\alpha + L – W\cos\gamma &= 0 \end{aligned} $$
where \(T\) is the engine thrust, \(\alpha\) is the angle of attack, \(\gamma\) is the flight path angle, \(W\) is the weight, \(D\) and \(L\) are drag and lift, respectively. The lift and drag are expressed as
$$ \begin{aligned} L &= \frac{1}{2} \rho V^2 C_L S_{\text{ref}} \\ D &= \frac{1}{2} \rho V^2 C_D S_{\text{ref}} \end{aligned} $$
For a given thrust level (e.g., maximum continuous thrust), we can solve for the achievable climb rate \(\dot{h} = V \sin\gamma\). The climb rate decreases with altitude due to reduced engine performance and air density. Using realistic engine data for a small jet-powered fixed-wing drone, we compute the maximum climb rate at different altitudes. The results are summarized in Table 1.
| Altitude (km) | Maximum 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 |
Given the horizontal grid spacing \(d_h = 1000\ \text{m}\), the time required to traverse one horizontal step at \(V=50\ \text{m/s}\) is approximately \(20\ \text{s}\). During this interval, the drone can climb no more than \(\dot{h} \times 20\ \text{s}\). Therefore, the vertical grid spacing \(d_v\) at each altitude layer is set to that value. For example, at sea level, \(d_v = 10.36 \times 20 \approx 207\ \text{m}\); at 6 km, \(d_v \approx 50.6\ \text{m}\). The vertical layers are thus non-uniform, ensuring that any vertical neighbor node is reachable by a steady climb or descent.
Figure 1 illustrates the resulting rasterization. Note that the terrain obstacles are also discretized, and any grid node that falls inside an obstacle is marked as blocked.
With this approach, the fixed-wing drone can always fly from one grid node to any of its 26 immediate neighbors (8 in the same horizontal plane, 9 in the layer above, and 9 in the layer below) using a feasible trajectory that respects its turning radius and climb/descent limits.
Improved Path Planning Algorithm for Fixed-Wing Drones
Movement Cost Calculation Between Neighboring Nodes
Conventional A* using Euclidean distance as the movement cost is insufficient for fixed-wing drones because the actual time, fuel, and risk vary significantly among different types of node transitions. We classify the 26 neighbor nodes into seven cases based on the required maneuver:
- Case 1: Horizontal move (same altitude).
- Case 2: Horizontal move with altitude increase (climb).
- Case 3: Horizontal move with altitude decrease (descent).
- Case 4: Diagonal horizontal move (e.g., NE direction) with climb.
- Case 5: Diagonal horizontal move without altitude change.
- Case 6: Diagonal horizontal move with descent.
- Case 7: Vertical-only move (climb or descent at the same horizontal position).
We simulate the fixed-wing drone flying from the parent node to each type of neighbor using a 6-DOF model with a realistic engine. The time and fuel consumption for each case are obtained. The results are presented in Table 2.
| Case | Time (s) | Fuel (kg) | Risk (threat index) |
|---|---|---|---|
| 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 | — |
Note that Case 7 (vertical-only) is significantly more expensive because fixed-wing drones cannot hover; they must execute a spiral climb or descent, which consumes much more time and fuel. In our algorithm, we still allow Case 7 for safety-critical situations, but the cost function naturally avoids it when alternative paths exist.
Moreover, the previous node’s state influences the cost of the current transition due to the continuous turning geometry. For instance, if the drone arrived at the current node from a certain direction, its heading and bank angle may reduce the turning angle required for the next move. We classify the predecessor states into three sub-cases (a, b, c) and simulate the combined effect. The results show that for Case 4 (diagonal climb), the predecessor state “a” yields a ~10% reduction in both time and fuel. These corrections are absorbed into the cost table during the path search.
Threat-Aware Cost Function
Let the environment be populated with threat sources. An external intelligence system provides a threat level \(R(k) \in [0,1]\) for each grid node \(k\) (0 = no threat, 1 = maximum threat). The drone has a critical threat threshold \(R_c\); any node with \(R(k) \ge R_c\) is considered a no-fly zone (obstacle). For nodes with \(R(k) < R_c\), the threat contributes to the cost.
We define the actual cost from the start to a node \(n\) as:
$$ g(n) = W_t \cdot \text{time}(n) + W_o \cdot \text{fuel}(n) + W_R \cdot \text{risk}(n) $$
where \(\text{time}(n)\) and \(\text{fuel}(n)\) are the accumulated time and fuel consumption along the path from the start to node \(n\), computed using the per-step values from Table 2 (with predecessor corrections). The risk term is the accumulated threat along the path:
$$ \text{risk}(n) = \sum_{\text{edges along path}} \frac{R(\text{from}) + R(\text{to})}{2} \cdot \text{edge\_length\_factor} $$
For simplicity, we set the edge length factor to 1 for horizontal moves and \(\sqrt{2}\) for diagonal moves, reflecting the increased exposure area.
The heuristic function \(h(n)\) remains the 3D Manhattan distance to the goal:
$$ h(n) = |x_n – x_{\text{goal}}| + |y_n – y_{\text{goal}}| + |z_n – z_{\text{goal}}| $$
The weighting factors \(W_t, W_o, W_R\) can be tuned according to mission priorities. For example:
- In an emergency fast-response mission, reduce \(W_R\) and increase \(W_t\).
- In a long-endurance surveillance mission, increase \(W_o\) to minimize fuel consumption.
- In a high-threat environment, increase \(W_R\) to maximize safety.
The algorithm then follows the standard A* procedure, but with the enhanced cost model and the 26‑neighbor expansion scheme. The open list stores nodes with their current \(g\) and estimated \(f = g + h\). The closed list contains processed nodes. When a neighbor is already in the open list, we update its \(g\) only if the new path offers a lower cost (considering both time, fuel, and risk simultaneously).
Simulation Results and Validation
Environmental Setup
We construct a 20 km × 20 km × 3 km mountainous region with multiple threat sources. The threat level at each grid node is generated by a Bayesian network that fuses information from various sensors; the details are omitted here for brevity. The start point is at coordinates (1,1,1) and the goal is at (20,20,1). The fixed-wing drone parameters are as earlier: cruise speed 50 m/s, maximum bank angle ±30°, climb rates as in Table 1.
Conventional A* vs. Improved A*
We first apply the conventional A* algorithm that treats all nodes as equally costly per step (Euclidean distance) and only considers obstacles (threat \(R \ge R_c\)). The resulting path uses 21 nodes and has a total cost of 125.1 (arbitrary units). The path passes through moderately high threat zones.
Next, we apply the improved A* with weights \(W_t = 0.05,\ W_o = 5,\ W_R = 5\). The algorithm produces a path with 29 nodes but a total cost of only 107.0, which is 14.5% lower than the conventional A*. The improved path deliberately detours around the high-threat clusters, as quantified in Table 3.
| Metric | Conventional A* | Improved A* |
|---|---|---|
| Number of nodes | 21 | 29 |
| Total path cost (fitness value) | 125.1 | 107.0 |
| Average threat index along path | 0.42 | 0.27 |
| Total flight time (simulated) | 462 s | 498 s |
| Total fuel consumption (simulated) | 4.8 kg | 5.2 kg |
The improved path is slightly longer (higher time and fuel) but significantly safer, as the average threat index is 36% lower. By adjusting the weights, we can achieve different trade-off points.
Flight Simulation with Turbulence
To further validate the safety benefit, we map the threat intensity to the intensity of atmospheric turbulence using the Dryden model. The fixed-wing drone’s flight is simulated along both paths. Figure 2 (not shown here, but described) illustrates the time histories of the pitch angle and normal acceleration. The improved path experiences significantly smaller perturbations, indicating lower aerodynamic loads and better passenger comfort (or payload safety).
The simulation results confirm that the proposed rasterization and cost modeling produce feasible and advantageous paths for fixed-wing drones in complex threat environments.
Conclusion
We have presented a comprehensive framework for applying raster-based path planning to fixed-wing drones, addressing the critical gap between conventional grid methods and the unique flight characteristics of fixed-wing platforms. The key contributions are threefold:
- Flight‑performance‑aware rasterization: By designing the horizontal and vertical grid spacing based on the drone’s minimum turning radius and maximum climb rate, we guarantee that every pair of adjacent grid nodes is reachable. This eliminates the need for post-processing interpolation or special-case handling during the search.
- Accurate movement cost model: We computed precise time and fuel consumption for seven distinct types of neighbor transitions using high-fidelity simulation. We also accounted for the influence of the predecessor node’s state, showing up to 10% cost variations.
- Multi‑dimensional threat‑aware cost function: The A* algorithm is extended with adjustable weights for time, fuel, and risk. This allows mission planners to dynamically trade off between speed, economy, and safety.
Simulation results demonstrate that the improved algorithm produces paths that are safer (lower threat exposure) while remaining efficient. The flight simulation using turbulence further confirms the practical benefits. Future work will extend this framework to multi‑fixed-wing drone cooperative path planning and incorporate real‑time dynamic re‑routing capability.