The rapid expansion of e-commerce has accelerated demand for urban logistics delivery drones, which reduce delivery times and enhance operational efficiency. A critical technical challenge lies in minimizing flight energy consumption. While hardware optimizations offer potential improvements, they often require substantial R&D investments. Scientific path planning that incorporates multiple factors – including battery capacity, payload weight, and environmental conditions – proves more immediately effective for energy conservation.
Urban wind patterns significantly influence delivery drone performance. Tall buildings create complex wind fields as shown below, where structures of varying heights alter airflow dynamics. Dense architectural layouts further intensify wind effects, particularly in narrow urban canyons where wind acceleration creates hazardous microclimates:
These wind variations directly impact delivery UAV energy expenditure. When buildings are arranged in specific configurations, they intensify wind channeling effects. The resulting wind concentrations create localized acceleration zones that substantially increase propulsion demands for delivery drones navigating these areas.
Multi-Characteristic Objective Function Formulation
Building Threat Penalty Model
In 3D urban environments, building proximity threats are quantified through distance-based penalty functions. Define $d_{ist}$ as the distance between the delivery drone and a building, with $d_a$ as the safety threshold:
$$
\text{Penalty} =
\begin{cases}
0 & \text{if } d_{ist} \geq d_a \\
d_a – d_{ist} & \text{if } 0 < d_{ist} < d_a \\
\infty & \text{otherwise}
\end{cases}
$$
Energy Consumption Model Under Wind Influence
Wind forces alter delivery UAV dynamics. The ground velocity $\mathbf{V_k}$, wind velocity $\mathbf{V_w}$, and air velocity $\mathbf{V_a}$ relate through vector addition:
$$\mathbf{V_k} = \mathbf{V_w} + \mathbf{V_a}$$
Aerodynamic drag and propulsion requirements adapt to wind conditions:
$$F_w = \frac{1}{2} C_D \rho S V_a^2$$
$$T \sin\omega \cos\varepsilon = F_w \sin\zeta \cos\sigma$$
$$T \sin\omega = F_w \sin\zeta + G$$
Propeller power and energy expenditure between nodes $i$ and $j$ become:
$$P_p = \frac{T}{\eta_p}, \quad \eta_p = \frac{C_F}{C_p} \frac{1}{\Omega D}$$
$$H_{ij} = P_p \cdot t_{ij}$$
Delivery UAV Risk Assessment
Four failure modes impact ground safety for delivery drones:
| Failure Mode | Impact Area Calculation | Severity Function |
|---|---|---|
| Vertical Descent | $A_{\text{exp1}} = \pi(r_{\text{uav}} + 1.1r_p)^2$ | $E_1 = f(A_{\text{exp1}})$ |
| Horizontal Impact | $A_{\text{exp2}} = \pi(r_{\text{uav}} + r_p)^2 + 2d(r_{\text{uav}} + r_p)$ | $E_2 = f(A_{\text{exp2}})$ |
| Payload Drop | $A_{\text{exp3}} = \pi X_{td}^2 – \pi(X_{td} – r_p)^2$ | $E_3 = f(A_{\text{exp3}})$ |
| Explosion Fragments | $A_{\text{exp4}} = \pi \left( \frac{V_0 + \sqrt{V_0^2 + 2gh}}{g} \right)^2$ | $E_4 = f(A_{\text{exp4}})$ |
Total risk severity combines probabilities $k_i$ of each failure mode:
$$E_{\text{total}} = k_1E_1 + k_2E_2 + k_3E_3 + k_4E_4$$
Operational Constraints
Delivery UAV operations require multiple physical constraints:
$$\begin{cases}
z_{\min} \leq z_t \leq z_{\max} \\
0 \leq |\phi_1 – \phi_2| \leq \phi_{\max} \\
0 \leq |\theta_1 – \theta_2| \leq \theta_{\max} \\
\sum H_{ij} \leq H_{\max}
\end{cases}$$
where $\phi$ represents yaw angles, $\theta$ denotes pitch angles, and $H_{\max}$ is maximum energy capacity.
Global Path Planning Simulation
Delivery Drone and Urban Parameters
Simulations employed DJI FlyCart 30 specifications representing modern delivery UAVs:
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| Empty Weight | 65 kg | Max Speed | 20 m/s |
| Max Payload | 30 kg | Max Flight Time | 18 min |
| Max Pitch/Yaw | 45° | Propeller Diameter | 1.375 m |
The urban environment featured four zones with distinct characteristics:
| Zone | Function | Building Height (m) | Population Density | Wind Speed (m/s) |
|---|---|---|---|---|
| 1 & 3 & 4 | Residential | 40-100 | High | 4-8 |
| 2 | Commercial | 120-200 | Medium | 2-5 |
Path Optimization Results
Three algorithms were tested for five delivery drones operating between residential zones:
| Algorithm | Base Model Cost | Multi-Feature Cost | Computation Time (s) | ||
|---|---|---|---|---|---|
| Min | Max | Avg | Avg | ||
| Artificial Bee Colony | 0.53 | 0.68 | 0.574 | 0.478 | 441.7 |
| Firefly Algorithm | 0.34 | 0.44 | 0.402 | 0.386 | 221.6 |
| Particle Swarm | 0.53 | 0.65 | 0.602 | 0.538 | 447.4 |
The firefly algorithm demonstrated superior performance for delivery drone path planning, achieving 14.3% lower costs than alternatives while requiring 50% less computation time. Wind-aware paths reduced energy consumption by 18-22% compared to wind-agnostic routes, while safety constraints decreased population exposure to drone operations by 30-35%.
Conclusion
This research establishes a comprehensive framework for delivery UAV path optimization in complex urban environments. By integrating wind-induced energy dynamics with multidimensional risk assessment, the developed multi-characteristic model generates paths that significantly enhance safety and efficiency for logistics operations. The firefly algorithm implementation proves particularly effective for solving this multi-objective optimization problem, balancing computational efficiency with solution quality. These advancements enable more sustainable and reliable urban air logistics operations through physics-aware routing for delivery drones.