Urban logistics delivery drones face operational challenges between increasing flight density and low airspace utilization in segregated route systems. This study develops a safety-centric separation model for same-altitude crossing operations of delivery UAVs using Event methodology. We address collision risks through lateral/vertical overlap probabilities and longitudinal proximity rates while incorporating failure probabilities of Conflict Detection and Resolution (CDR) systems.
The crossing scenario involves two delivery drones on intersecting paths at angle $\omega$ with separation $S_c$ defined as the distance between the crossing point and trailing drone when the lead drone reaches the intersection. The collision risk $N_c$ is modeled as:
$$N_c = 2 \times Q \times P_y(S_y) \times P_z(0) \times \left(1 + \frac{2v\lambda_x}{2u\lambda_y}\right) \times \left(1 + \frac{2w\lambda_x}{2u\lambda_z}\right)$$
Where $Q$ is the longitudinal collision rate, $P_y$ and $P_z$ are lateral/vertical overlap probabilities, $u/v/w$ are relative velocities, and $\lambda_x/\lambda_y/\lambda_z$ represent delivery drone dimensions (length/wingspan/height). Core parameters derived from empirical delivery UAV data include:
| Parameter | Value | Description |
|---|---|---|
| $\sigma_y^2$ | 1.5753 m² | Lateral error variance |
| $\sigma_z^2$ | 1.3895 m² | Vertical error variance |
| $E(0)$ | 0.01 | Longitudinal proximity rate |
| $V$ | 12 m/s | Cruise speed |
Lateral overlap probability considers navigation errors in delivery drones:
$$P_y(S_y) = \frac{1}{2\pi(\sigma_{yA}^2 + \sigma_{yC}^2)} \int_{-q}^{q} \exp\left(-\frac{(s – S_y)^2}{2(\sigma_{yA}^2 + \sigma_{yC}^2)}\right) ds$$
Vertical overlap probability accounts for altitude deviations:
$$P_z(0) = \frac{1}{2\pi(\sigma_{zA}^2 + \sigma_{zC}^2)} \int_{-\lambda_z}^{\lambda_z} \exp\left(-\frac{l^2}{2(\sigma_{zA}^2 + \sigma_{zC}^2)}\right) dl$$
Delivery UAV CDR systems undergo event tree analysis for failure probability assessment:
| Module | Failure Probability | Impact |
|---|---|---|
| ATC Processing | $P_1$ (94%) | Full separation |
| Maneuvering | $P_2$ (3%) | Partial loss |
| Flight Control | $P_3$ (2%) | Partial loss |
| Complete Failure | $P_4$ (1%) | Maximum loss |
The comprehensive separation model incorporating CDR failures becomes:
$$N’_c = P_1P_2P_3N_c(S_c) + P_1P_2\bar{P_3}N_c(S_c – V_r t_3) + P_1\bar{P_2}\bar{P_3}N_c(S_c – V_r(t_2 + t_3)) + \bar{P_1}\bar{P_2}\bar{P_3}N_c(S_c – V_r(t_1 + t_2 + t_3))$$
For delivery drones with dimensions 2.5m × 2.5m × 0.6m at 60° crossing angle:
| Safety Target Level (TLS) | Basic Separation | CDR-Adjusted Separation |
|---|---|---|
| 1.5×10⁻⁸ | 156 m | 158 m |
| 1×10⁻⁶ | 153 m | 155 m |
Separation requirements increase with crossing angle, showing significant growth near 180° (head-on scenarios). This trend demonstrates how delivery UAV operational constraints intensify in opposing flow configurations:
$$S_c(\omega) = k \cdot \exp(\omega/90^\circ) \quad \text{for} \quad \omega > 90^\circ$$
Optimal delivery drone separation balances safety targets with urban airspace efficiency. The Event-based approach provides methodology for determining operationally viable crossing configurations while maintaining TLS compliance through CDR-aware modeling.