This study proposes a dual-layer path planning framework for delivery drones operating in complex urban low-altitude environments. The methodology enhances safety and public acceptance by integrating third-party risk assessment with dynamic conflict resolution strategies for drone swarms.
Urban Low-Altitude Environment Modeling
We model urban airspace as a 3D grid using Digital Elevation Models (DEM) with 5m resolution. The environment is classified into free grids and obstacle grids:
$$
\zeta(x_i, y_i, z_i) = \begin{cases}
1 & \text{static obstacle present} \\
0 & \text{free grid}
\end{cases}
$$
Dynamic obstacles are represented using temporal occupancy indicators:
$$\phi(x_i, y_i, z_i, t) = \begin{cases}
1 & \text{grid occupied at time } t \\
0 & \text{vacant}
\end{cases}$$
Third-Party Risk Quantification
Comprehensive risk assessment combines safety and noise impacts:
$$
R(x_i, y_i, z_i) = \sum_{j=1}^{N} \sigma_j \omega_j c_j(x_i, y_i, z_i)
$$
Safety risk includes pedestrian and vehicle collision probabilities:
$$
c_{death}(x,y,z) = P_{UAV} \times N_{hit}^p(x,y,z) \times R_p(x,y,z) + P_{UAV} \times N_{hit}^v(x,y,z) \times R_v(x,y,z)
$$
Noise risk modeling considers population exposure and attenuation:
$$c_{noise}(x,y,z) = (L_s – \Delta L) \times [1 – 0.8G(x,y,z)] \times N_{noise}^p(x,y,z)$$
$$\Delta L = 10 \log_{10}(4\pi h^2)$$
Dual-Layer Path Planning Framework
Upper-Layer: Pre-Tactical Planning
Optimizes individual delivery UAV trajectories minimizing time and risk:
$$
\min C_{up} = \tau_1 \sum_{i=1}^{n} \frac{\sqrt{(x_i-x_{i-1})^2 + (y_i-y_{i-1})^2 + (z_i-z_{i-1})^2}}{v_{i-1}} + \tau_2 \sum_{i=0}^{n} R(x_i,y_i,z_i)
$$
Subject to:
- Maximum range: $\sum_{i=1}^{n} \sqrt{(x_i-x_{i-1})^2 + \cdots} \leq L_{max}$
- Altitude constraints: $H_{min} \leq z_i \leq H_{max}$
- Turning/pitch limits: $\beta_i \leq \beta_{max}, \mu_i \leq \mu_{max}$
Implemented with improved A* algorithm using heuristic:
$$f(x) = \underbrace{\tau_1 C_t^S(x) + \tau_2 C_r^S(x)}_{g(x)} + \underbrace{\tau_1 C_t^D(x) + \tau_2 C_r^D(x)}_{h(x)}$$
Lower-Layer: Tactical Conflict Resolution
Manages delivery UAV swarm conflicts in real-time through deviation minimization:
$$\min \Delta C = | C_{down} – C_{up} |$$
Conflict resolution strategies include:
| Strategy | Application Scenario | Cost Factor |
|---|---|---|
| Yaw Maneuver | Lateral separation | 17.07m deviation avg |
| Hover | Head-on conflicts | 0.5-3s delay |
Experimental Validation
Simulations conducted in campus environment (261×295×20 grids) using DJI Phantom 4 parameters:
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| Grid size | 5m | $v_{cr}$ | 20m/s |
| $L_{max}$ | 5000m | $v_{cl}$ | 6m/s |
| $H_{max}$ | 120m | $v_{des}$ | 4m/s |
Performance Comparison
| Model | Risk Cost | Time Cost | Distance |
|---|---|---|---|
| TPFD (Time-optimized) | 279.03 | 52.34 | 966.81m |
| TPRC (Risk-optimized) | 230.63 | 58.85 | 928.82m |
| Proposed TPCC | 236.85 | 52.61 | 920.01m |
The delivery drone TPCC model reduced risk by 15.12% versus TPFD and flight time by 10.61% versus TPRC.
Swarm Conflict Resolution
For 50 delivery UAVs + 100 non-cooperative drones in 10-minute simulation:
$$
\begin{array}{c|c}
\text{Metric} & \text{Result} \\
\hline
\text{Conflicts resolved} & 60 \\
\text{Resolution rate} & 100\% \\
\Delta\text{Risk} & +1.05\% \\
\Delta\text{Flight time} & +0.95\% \\
\Delta\text{Distance} & +1.09\% \\
\end{array}
$$
Conclusion
The dual-layer framework enables efficient and safe operation for urban delivery drones. Key innovations include:
- Third-party risk quantification integrating safety/noise impacts
- Improved A* algorithm for time-risk balanced trajectories
- Differentiated conflict resolution maintaining <3% deviation from optimal paths
This approach significantly advances urban air mobility safety for logistics UAV operations while maintaining operational efficiency. Future work will integrate weather uncertainty and communication delays.