With rapid growth in urban logistics, delivery drones represent a transformative solution for last-mile operations. Ensuring operational safety for delivery UAVs in free-flight environments requires robust separation standards. This research develops a comprehensive collision risk assessment model integrating conflict frequency analysis and conditional collision probability, addressing critical gaps in current delivery drone safety frameworks.
Traditional structured route operations prove inadequate for delivery drones due to their high mobility and density. Our model uniquely incorporates Conflict Detection and Resolution (CDR) mechanisms through key parameters:
| Parameter | Symbol | Value |
|---|---|---|
| Positioning error (1σ) | ε | 1.75 m |
| Position update cycle | ttracking | 0.2 s |
| ATC module response | tsep | 0.04 s |
| Flight control response | tpilot | 0.04 s |
| Minimum physical separation | dmin | 5 m |
| Bank angle | θ | 25° |
The collision risk model combines conflict frequency (Fcft) and conditional collision probability (Pcol|cft):
Conflict Frequency (Gas Model):
$$ \sigma_{cft} = \pi D^2 $$
$$ v_{rel} = \sqrt{v_{host}^2 + v_{intruder}^2} $$
$$ \rho_0 = \frac{N}{V_{airspace}} $$
$$ F_{cft} = \frac{N}{2} \rho_0 \sigma_{cft} v_{rel} $$
Conditional Collision Probability:
$$ D’ = v_{closure}(t_{tracking} + t_{sep} + t_{pilot}) + d_{avoid} + \varepsilon_1 + \varepsilon_2 $$
$$ P_{col|cft} = \int_D^{+\infty} \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}} dx $$
Total Collision Probability:
$$ P_{total} = 2F_{cft} \cdot P_{col|cft} \leq \text{TLS} = 1.5 \times 10^{-8} $$
For delivery UAVs in free-flight within 20km × 10km × 2km airspace (N=2, v=12m/s), avoidance distance is calculated as:
$$ R = \frac{v^2}{g\sqrt{\text{LF}^2 – 1}} = \frac{12^2}{9.8\sqrt{1.1^2 – 1}} = 31.42 \text{ m} $$
$$ \phi = \frac{v}{R} \frac{180}{\pi} = 21.88^\circ/\text{s} $$
$$ d_{avoid} = 25.56 \text{ m (minimum maneuver distance)} $$
Actual required separation follows normal distribution: D’ ∼ N(32.28, 2.472). Solving Ptotal = TLS yields the critical separation standard for delivery drones:
| TLS Variation | Required Separation (m) |
|---|---|
| 1.5×10-8 | 43.3 |
| 1.0×10-7 | 39.2 |
| 5.0×10-7 | 35.6 |
The CDR activation threshold is derived from separation parameters. For delivery UAVs on collision course:
$$ t_{activation} = \frac{D – d_{avoid}}{v_{closure}} = \frac{43.3 – 25.56}{24} = 0.74 \text{ s pre-CPA} $$
Traffic density significantly impacts delivery drone separation requirements. For equivalent safety:
$$ D \propto \sqrt{\frac{\text{TLS}}{N \cdot v_{rel}}} $$
This research establishes that CDR-equipped delivery UAVs require 43.3m separation in free-flight environments at current TLS. The framework enables dynamic adjustment of separation for delivery drones based on:
- Positioning system performance
- CDR response latency
- Regional traffic density
- Acceptable risk thresholds
Implementation requires continuous monitoring of delivery UAV position errors and CDR performance. Future work should validate these separation standards through large-scale delivery drone simulations incorporating wind disturbances and communication failures.