Urban logistics using delivery drones represents a transformative advancement in transportation. High-density operations demand structured airspace configurations, with parallel routes offering optimal airspace utilization. However, collision risks between adjacent delivery UAVs on parallel routes necessitate rigorous lateral separation standards. This study establishes a safety-focused framework for determining such separation, integrating conflict frequency and collision probability through large-scale Monte Carlo simulations.
Delivery UAV operations face unique safety challenges in congested urban corridors. We adopt the Target Level of Safety (TLS) of $1.5 \times 10^{-8}$ mid-air collisions per flight hour, aligning with ICAO standards for manned aviation. A conflict occurs when adjacent delivery drones on parallel routes breach a 150-meter longitudinal separation. Conflict frequency ($F_{conf}$) derives from Poisson-distributed traffic flow:
$$ F_{conf} = \lambda \int_{0}^{t} \lambda e^{-\lambda y} dy = \lambda (1 – e^{-\lambda t}) $$
where $\lambda=30$ UAVs/hour (mean flow rate) and $t=12.5$ seconds (longitudinal time threshold). This yields $F_{conf} = 0.1$ conflicts per hour.
Collision probability is decomposed into sequential events: conflict existence ($conf$), UAV deviation ($dev$), and collision given deviation and conflict ($TCV$). The baseline probability combines conflict frequency and deviation likelihood:
$$ P_{base} = P(conf \cap dev) = F_{conf} \times P_{dev} $$
Here, $P_{dev} = 1/24,000$ based on operational data. The overall collision risk before mitigation is:
$$ P_{collision} = 2 \times P_{base} \times P_{TCV} $$
where $P_{TCV}$ is determined via Monte Carlo simulation.
Monte Carlo Simulation Framework
We model two delivery drones: $U_i$ (deviating) and $U_n$ (nominal). $U_i$ initiates an unexpected deviation at a random time $t_{dev} \sim U(1,60)$ seconds, maintaining a 45° deviation angle ($\sigma=5°$) for 3 seconds before Conflict Detection and Resolution (CDR) systems trigger a -90° corrective turn. Nominal UAV parameters are:
| Parameter | Symbol | Value |
|---|---|---|
| Longitudinal dimension (m) | $\lambda_x$ | 2.5 |
| Lateral dimension (m) | $\lambda_y$ | 2.5 |
| Vertical dimension (m) | $\lambda_z$ | 0.6 |
| Speed (m/s) | $v$ | 12 |
| Altitude (m) | $h$ | 253 |
| Vertical error SD (m) | $\sigma_z$ | 1.3895 |
| Position error SD (m) | $\sigma_{xy}$ | 2.348 |
Simulation parameters for the delivery UAV scenarios include:
| Parameter | Value |
|---|---|
| $U_i$ initial position | (0, 0, $h$) |
| $U_n$ initial lateral separation ($y_{n0}$) | 1–51 m (tested) |
| Simulations per $y_{n0}$ | 100,000 |
| Simulation duration | 60 s |
| Time step | 1 s |
| Deviation angle ($w$) | $N(45°, 5^2)$ |
Test Criterion Violation (TCV) occurs when all three spatial thresholds are breached simultaneously:
$$ \sqrt{(x_i – x_n)^2} \leq \frac{\lambda_{ix} + \lambda_{nx}}{2}, \sqrt{(y_i – y_n)^2} \leq \frac{\lambda_{iy} + \lambda_{ny}}{2}, \sqrt{(z_i – z_n)^2} \leq \frac{\lambda_{iz} + \lambda_{nz}}{2} $$
Simulation Results and Analysis
Across 5.1 million simulations (51 lateral separations × 100,000 runs), 50,302 TCV events occurred. TCV probability density exhibits a strong negative exponential relationship with lateral separation:
$$ f(x) = 0.062 e^{-0.062x} $$
where $x$ is lateral separation in meters. Representative TCV counts are:
| Separation (m) | TCV Count | Separation (m) | TCV Count |
|---|---|---|---|
| 1 | 3,767 | 26 | 587 |
| 5 | 2,172 | 30 | 451 |
| 10 | 1,808 | 33 | 340 |
| 15 | 1,122 | 40 | 216 |
| 20 | 774 | 50 | 93 |
The baseline collision risk is $P_{collision} = 2 \times (0.1) \times (1/24,000) \times 0.0098 = 8.17 \times 10^{-8}$, exceeding the TLS. The required risk mitigation factor is:
$$ P_{sep} = \frac{\text{TLS}}{P_{collision}} = \frac{1.5 \times 10^{-8}}{8.17 \times 10^{-8}} = 0.1837 $$
Integrating the probability density function solves for the lateral separation ($S$) satisfying this mitigation:
$$ \int_{S}^{\infty} 0.062 e^{-0.062x} dx = 0.1837 $$
yielding $S = 33$ meters. This separation ensures residual collision risk aligns with the TLS for delivery drone operations.
Conclusions
For urban delivery UAVs operating on parallel routes, a 33-meter lateral separation balances safety and airspace efficiency. Our model integrates real-world parameters—UAV dimensions, traffic density, navigation errors, and CDR capabilities—through computationally intensive Monte Carlo simulation. The exponential relationship between collision probability and separation provides a scalable framework. Future work should address heterogeneous delivery drone fleets and refine TLS specifications for urban air logistics. This methodology supports high-density integration of autonomous delivery UAVs in metropolitan skies.