*3.1. Risk Assessment Model*

This section presents a quantitative model of the integrated risk cost. We analyse the risks derived from the operation of drones in an urban environment. Figure 2 depicts the

impact of considering risk cost mitigation on path planning results. The environment is divided into equal-sized grids, and the risk cost within each grid is calculated according to the integrated risk model. The colours in the map show the distribution of risk cost, with red representing areas of high risk cost and blue representing areas of low risk cost. The dashed line indicates the path with the shortest distance from the starting point to the end, and the solid line is the path that considers risk cost mitigation, which chooses the area with lower risk cost to pass, and the final path has a much lower risk cost than the shortest path.

**Figure 2.** Risk cost mitigation affects path planning results.

3.1.1. Quantifying the Risk Cost Associated with Pedestrians

The risk cost of a drone striking a pedestrian is modelled according to the three components of collision [45,46]: (a) a drone crash, (b) a drone striking pedestrians, and (c) resulting in the death of pedestrians, as shown in Figure 3.

**Figure 3.** Drones and pedestrians.

We quantify the risk cost due to drones affecting pedestrians by potential fatalities as in Equation (1): *Cost*<sup>1</sup> <sup>=</sup> *Costp* <sup>=</sup> *PcrashSdρpPd* (1)

$$^{144}$$

where *Cost*<sup>1</sup> is the quantified value of pedestrian risk cost, *Pcrash* is the probability of a drone crash, *Sd* is the exposed area of the ground impacted by the falling drone, *ρ<sup>p</sup>* is the population density, and *Pd* is the fatality rate associated with the kinetic energy of the drone. The speed of the drone hitting the ground is shown in Equation (2):

$$v\_d = \int\_0^t (g - f)dt = \int\_0^t \left(g - \frac{f\_d \mathcal{S}\_d \rho\_A v\_{d-\text{real}}^2}{2m}\right) dt = \sqrt{\frac{2mg}{f\_d \mathcal{S}\_d \rho\_A} \left(1 - e^{-\frac{Hf\_d \mathcal{S}\_d \rho\_A}{m}}\right)}\tag{2}$$

where g = 9.8m/*s*2, *f* is the resistance acceleration, *fd* is the drag coefficient, *ρ<sup>A</sup>* is the air density, *vd*−*real* is the actual airspeed of the falling drone, *<sup>m</sup>* is the mass of the drone, *<sup>H</sup>* is the height of the drone falling point. The energy generated by the descending drone is shown in Equation (3)

$$E\_{fd} = \frac{1}{2} m v\_d^2 \tag{3}$$

Considering that the buffering effect of buildings and trees can mitigate the injury of falling drones to pedestrians, a sheltering factor *Sf* , *Sf* <sup>∈</sup> (0, 1] is introduced to consider this sheltering effect when calculating risk costs. A higher value implies a better sheltering effect and a lower probability of death. By combining the sheltering element into the kinetic energy equation, the lethality *Pd* of a falling drone can be obtained as shown in Equation (4):

$$P\_d = \left(1 + \sqrt{\frac{\mu}{\nu}} (\frac{\nu}{E\_{fd}})^{\frac{1}{4S\_f}}\right)^{-1} \tag{4}$$

where *μ* is the energy that might cause a 50% fatality with *Sf* = 0.5, *ν* is the impact energy threshold required to cause fatality as *Sf* approaches zero. The values of *Sf* for different environments are shown in Table 1.

**Table 1.** Sheltering coefficients [47].


3.1.2. Quantifying the Risk Cost Associated with Vehicles

Vehicles are another key element in the urban environment that can shelter falling drones; different from buildings and trees, the sheltering effect of vehicles mainly occurs while driving. Similar to the modelling of drone strikes on pedestrians, falling drones cause road traffic accidents in three components [17]: (a) a drone crash, (b) a drone striking vehicles, (c) resulting in traffic accidents, and (d) causing human fatalities, as shown in Figure 4.

Quantify the risk cost due to drones affecting vehicles by potential fatalities, as shown in Equation (5) *Cost*<sup>2</sup> <sup>=</sup> *CostV* <sup>=</sup> *PcrashPVNV* (5)

$$\text{Cost}\_2 = \text{Cost}\_V = P\_{\text{crssh}} P\_V \text{N}\_V \tag{5}$$

where *PV* is the probability of a falling drone hitting a vehicle, proportional to the traffic density, and *NV* is the average number of fatalities caused by a crash. The probability of a drone hitting vehicles on the ground is defined as the ratio of the total area occupied by vehicles to the entire scope of the road, as shown in Equation (6)

$$P\_V = \frac{\overline{S\_V} \rho\_V}{D\_{road}} \tag{6}$$

where *SV* is the average projected area of the vehicle, *ρ<sup>V</sup>* is the traffic density, and *Droad* is the road width.

**Figure 4.** Drones and vehicles.

3.1.3. Pedestrian Density and Vehicle Density

The density distribution of pedestrians and vehicles in the urban environment can directly affect the risk cost of drone operations. Their density distribution is highly correlated with attractive facilities [48]. To quantitatively assess this correlation, gravity models are used to calculate pedestrian and vehicle density [49]. Inspired by gravity models, the pedestrian density in urban environments is shown in Equation (7).

$$
\rho\_P = e^{(1-r^2)} \rho\_P^0 \tag{7}
$$

where *ρ*<sup>0</sup> *<sup>P</sup>* is the average pedestrian density, *r* is the distance from the centre of gravity. If there is an increase in *r*, it leads to a decrease in *ρP*, as shown in Figure 5.

**Figure 5.** Gravity model for pedestrian distribution.

Similarly, the road traffic density distribution is shown in Equation (8):

$$
\rho\_V = e^{(1-r^2)} \rho\_V^0 \tag{8}
$$

where *ρ*<sup>0</sup> *V* is the average traffic density.

#### 3.1.4. Quantifying the Risk Cost Associated with Buildings

As shown in Figure 6, the operation of drones in urban airspace inevitably involves potential conflicts with buildings, and this potential conflict incurs risk costs [50]. Considering the overlapping locations of logistics customers and buildings, buildings cannot simply be set up as no-fly grids.

**Figure 6.** Drones and buildings.

The flight risk decreases as the distance between the drone and the building increases. However, due to the different sizes and shapes of buildings in the city, the influence range of buildings on drones is also different. For a normal distribution, setting different variances can reflect the different influence ranges of buildings, which is simple compared to other distributions or describing the shape and dimensions of the buildings. To simplify the model calculations, the distribution of the risk cost due to the influence of the building is assumed to be a normal distribution with different variances [51].

For *n* independent buildings in the map, given the central location *Bi* = (*Xi*,*Yi*) of the *i*-th building, *CostBu*(*x*, *y*) denotes the risk cost of the point (*x*, *y*) when considering the impact of the building *Bi*, as shown in Equation (9)

$$\text{Cost}\_3 = \text{Cost}\_{B\text{ll}}(\mathbf{x}, y) = \frac{1}{\sqrt{2\pi}\sigma} e^{-\frac{d^2}{2r^2}} \tag{9}$$

where *d* = (*<sup>x</sup>* <sup>−</sup> *Xi*) <sup>2</sup> + (*<sup>y</sup>* <sup>−</sup> *Yi*) 2 , *<sup>i</sup>* <sup>∈</sup> {1, 2, ··· , *<sup>n</sup>*} indicates the Euclidean distance between the drone and the centre of the building.

#### 3.1.5. Comprehensive Risk Model

In the previous section, risk cost quantification models were constructed for three elements: pedestrian, vehicle, and building. The different calculation methods would obtain different values of risk cost magnitude, which cannot be measured by the same standard. Therefore, the risk costs of the three elements need to be standardised to describe the total risk cost in the urban environment.

The risk costs of all three elements can be calculated through a particular distribution, and then each type of risk cost contained in a raster would be divided by the maximum risk value generated by the risk source separately. It is guaranteed that all risk cost values for each type are in the range of (0, 1].

The weights of the three risks may vary with the difference in their importance or preference, and the contribution of each risk may also vary with the cost [52]. For example, aviation regulators emphasise the risk of pedestrian fatalities caused by drones. The risk cost of pedestrians will be weighted much more than the other two factors. Traversing the areas with high pedestrian density will result in higher costs, so the planned paths will be more inclined to avoid these areas.

For point (*x*, *y*), its cumulative risk value needs to consider *a* pedestrian risk zones, *b* vehicle risk zones, and *c* building risk zones. The total risk cost of the point (*x*, *y*) is calculated as shown in Equation (10),

$$R\_{\text{total}}(\mathbf{x}, \mathbf{y}) = a\_i \sum\_{i=1}^{a} \frac{\mathbf{C}\_1^i}{\mathbf{C}\_{1-\text{max}}^i} + a\_j \sum\_{j=1}^{b} \frac{\mathbf{C}\_2^j}{\mathbf{C}\_{2-\text{max}}^j} + a\_k \sum\_{k=1}^{c} \frac{\mathbf{C}\_3^k}{\mathbf{C}\_{3-\text{max}}^k} \tag{10}$$

where *αi*, *αj*, *αk* are the weighting factors, *αi* + *αj* + *αk* = 1.

The cumulative risk *Rtotal*(*x*, *y*) of the path *C* is shown in Equation (11)

$$\int\_{(\mathbf{x},\mathbf{y})\in\mathbb{C}} \mathcal{R}\_{total}(\mathbf{x},\mathbf{y}) \tag{11}$$
