**4. Results**

In order to validate the path planning model coupling risk cost and service benefit, we perform simulations and analyses in a constructed urban environment containing pedestrian risk zones, vehicle risk zones, building risk zones, and logistics customers.

First, the urban environment model is constructed based on the modelling of risk areas and customer demands above. Then, we apply the proposed path search algorithm to search the logistics service path with the lowest risk cost and the highest service benefit.

Based on the above, the effect of risk combinations and the dynamic addition in risk areas are investigated to verify the reliability of the model and algorithm, which can mitigate the three risk costs while ensuring the response to the dynamic environment. Next, sensitivity analysis is conducted for the risk and benefit coefficients to study the balance of risk cost and service benefit in path planning. To evaluate the effectiveness of the algorithm proposed in this paper, the three most critical metrics in logistics path planning, namely, service completion, average path length, and average risk, are considered to compare with the A\* algorithm. Finally, simulations and statistical analyses were performed to evaluate the effectiveness of the proposed path planning model for balancing risk cost and service benefit when extended to other urban environments.

### *4.1. Path Planning for Multiple Drones*

The urban environment model proposed in this paper includes pedestrian risk, vehicle risk, and building risk, and it is verified that drones can ensure the completion of customer service while reducing the cost of path risk. In this section, the required parameters for simulation experiments are shown in Table 2 [46,53,54], and the optimisation effect of the model in this study compared with the traditional method is analysed.


**Table 2.** Simulation parameters.

The flight area with a range of 1000 × 1000 m is divided into 50 × 50 grids. In the environment model, we assume that the drone starting points are represented by black circles; the endpoint is represented by a black cross; the building risk zones are randomly generated variance *σ*; the crowd risk zones and the road vehicle risk zones are randomly generated risk radius *r*; the customer zones to be served are assigned random initial demand *dj* <sup>∈</sup> (0, 10].

Considering that the size of the drones is much smaller than the size of the grids, in this paper, we use the integral method to obtain the path risk cost, and the calculation result is not affected by the size of the grids and drones. Therefore, the drone is considered a prime point to simplify the calculation. The drone path planning is guided based on the risk cost distribution consisting of pedestrians, buildings, and vehicles in the environment and the service benefit distribution determined by the customer's location and acceptable service range. The path planning is performed in MATLAB using the algorithm described above. The initial environment modelling and path planning results are shown in Figure 8. The paths of the three drones departing from different locations are represented by three colours. Path group 1 represents the result of path planning considering the balance of service benefit and risk cost, where Drone 1 serves Customers 1, 2, and 3 according to the solid red path, Drone 2 serves Customers 4 and 5 according to the solid blue path, Drone 3 serves Customers 4, 5, and 6 according to the solid green path. Path group 2 is the path only considering customer service without risk. Path group 3 is the path only considering risk without customer service. 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 contour lines represent the distribution of risk cost due to building risk and pedestrian risk, and road 1 and road 2 represent the vehicle risk cost distributed along the road. The specific path parameters are shown in Table 3.

As shown in Figure 8 and Table 3, the result of path planning without considering the risk model (path group 2; no risk considered) traverses the high-risk area to ensure the shortest path to complete the customer service and reach the endpoint, resulting in increased risk cost. The path without considering customer service (path group 3; no customer considered) ignores customers overlapping with the location of high-risk areas for ensuring the shortest length and lowest risk cost path to reach the endpoint. The customers overlapping with high risk cost areas are completely ignored, leading to a decrease in service completion. The model of this paper, which considers both risk avoidance and customer service completion as the driving force, can balance the risk cost and service benefit. Risk cost is reduced by 81.25% compared with path group 2, and service completion is improved by 57.00% compared with path group 3.

**Figure 8.** Environment modelling and path planning.


