**1. Introduction**

The daily parcel of e-commerce enterprises has attracted huge attention due to their rapidly growing volume. In 2021, the global parcel shipping volume exceeded 159 billion parcels, which is expected to reach 256 billion in 2027 at a compound annual growth rate of 8.5 per cent [1]. Meanwhile, the variability of customer demand characteristics, such as different service locations and service times, has led to the need for logistic service providers to invest large-scale capacity and resources in "the last mile" transportation of parcels [2]. Thus, more and more companies are trying to find innovative and autonomous delivery methods for "the last mile" transport, such as drone logistics, to improve the quality of logistics. With the development of technology, drones' airworthiness and cargo-carrying capacity have improved significantly. Electric-powered logistics drones are not restricted by road networks and can reduce environmental costs and increase service flexibility [3]. The contactless services provided by drone logistics are also widely recognised due to the coronavirus outbreak [4]. Overall, the above advantages make drone logistics a powerful solution to solving the problems of traditional logistics [5]. Internationally renowned logistics companies such as Amazon, DHL Express, and Jingdong Logistics have begun developing drone logistics versions [6]. Statistics from BusinessWire also show that the global business value of drone package delivery has grown from USD 0.68 billion in 2020 to approximately USD 1 billion in 2021 and is expected to be USD 4.4 billion in 2025 [7].

**Citation:** Shao, Q.; Li, J.; Li, R.; Zhang, J.; Gao, X. Study of Urban Logistics Drone Path Planning Model Incorporating Service Benefit and Risk Cost. *Drones* **2022**, *6*, 418. https://doi.org/10.3390/ drones6120418

Academic Editors: Ivana Semanjski, Antonio Pratelli, Massimiliano Pieraccini, Silvio Semanjski, Massimiliano Petri and Sidharta Gautama

Received: 25 November 2022 Accepted: 13 December 2022 Published: 15 December 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

However, the accident risks associated with the large-scale application of logistics drones must be effectively assessed and managed. The drone would not only threaten the safety of people and vehicles on the ground in urban environments [8], but also may collide with high-rise buildings [9]. To ensure the safety of other aircraft, people, and property after a drone crash, aviation organisations, including the Federal Aviation Authority (FAA), require a risk mitigation assessment in the pre-flight state [10]. Hence, the study of path risk assessment and mitigation methods is a critical technical prerequisite for logistics drone applications.

Throughout the existing research, the vehicle path problem is a classical mathematical model for studying urban last-mile logistics. It is based on the travelling salesman problem (TSP) [11], which ensures the minimum transportation time or cost by planning the service sequence of customers. The existing research evolved on the basis of this problem model. Murray and Chu [12] proposed a collaborative path-planning model for trucks and drones considering drone service range and load capacity constraints. In this work, they reported two new variants of the traditional TSP problem, the flying sidekick travelling salesman problem (FSTSP) and the parallel drone scheduling travelling salesman problem (PDSTSP). Yurek and Ozmutlu [13], Freitas and Penna [14], and Mbiadou Saleu et al. [15] also presented various algorithms for these problems. The above-simplified approaches assumed that the order of customer service at different locations remains consistent with the drone's service path, while ignoring the problem of safety risks inevitably involved in the actual operation. Inspired by this factor, existing studies have started to consider the risk assessment of drone operations. These mainly include the risk of collision in flight and the impact on the ground.

Falling drones would threaten the safety of pedestrians and vehicles on the ground. Mitici and Blom [16] proposed a mathematical model for collision probability estimation, which provides a research solution for the collision risk assessment of drones. Bertrand et al. [17] studied the probability of drone operations threatening road traffic, defined the range of ground a falling drone could affect, and developed a collision probability model to identify high-risk areas in the road network. Koh et al. [18] and Clothier et al. [19] studied the extent of injury to pedestrians struck by drones and proposed weight limits for drones based on the associated injury scales and criteria. Drone aerial collision risks mainly originate from buildings, no-fly zones, unstable weather, and other drones [20]. To assess the risk of aerial collisions, existing studies have established various collision models, mainly including the REICH model, the EVENT model, and the position probability model based on the concept of position error. The REICH model [21] lays the foundation of flight safety interval assessment and is mainly applied to assess the risk of collision between two aircraft in parallel flight paths. It finds that the collision probability and relative velocity in each direction determine the flight collision risk. The EVENT model proposed by Brooker [22] combines radar and controller operations to analyse lateral and longitudinal separation, which can calculate the probability of collision risk in each direction. The probabilistic model based on position error focuses on collecting and processing information about the positioning error and trajectory deviation of the drone, in order to predict the probability of the flight trajectory conflicting with the risk area [23].

Based on the conflict risk assessment research, most research on drone path risk mitigation aims to find no-conflict paths. One intuitive approach is geometry-based. The closest proximity point approach is used to solve the potential conflict warning problem by measuring the position between two drones, thus avoiding collision risk and ensuring the safety of the planned path [24,25]. As an improvement to the geometric method, Fan et al. [26] and Tang et al. [27] introduced artificial potential fields (APF) and simulated the environment by designing virtual attractive and repulsive potential fields for autonomous guidance of the drone to avoid obstacles. Driven by efficiency, many researchers have tried to use heuristic search to find the optimal no-conflict path. For example, a node-based optimal algorithm is a special form of dynamic programming. When a map or graph is already constructed, they first define a cost function, and then search each node and arc to find a path with minimum cost. It mainly includes the A\* algorithm [28], Lifelong Planning A\* (LPA) [29], Theta\* [30], Lazy Theta\* [31], D\*-Lite [32], Harmony Search [33], etc. Evolutionary algorithm, which contains genetic algorithm [34], memetic algorithm [35], particle swarm optimisation [36], ant colony optimisation [37], and shuffled frog leaping algorithm [38]. The evolutionary algorithm starts by selecting randomly feasible solutions as the first generation. Then, taking the environment, drone capacity, goal, and other constraints into consideration, the planner evaluates the fitness of each individual. In the next step, a set of individuals is selected as parents for the next generations according to their fitness. The last step is a mutation and crossover step and stops the process when a pre-set value is achieved. The best fitness individual is decoded as the optimal path. Recent studies have treated drones as intelligent agents for stochastic dynamic threats in urban environments and used reinforcement learning to guide drones to avoid collisions [39–41].

Nevertheless, it is still an open problem for drone logistics to plan effective service paths in complex urban environments and ensure service completion based on reducing the threat to pedestrians, vehicles, buildings, etc. Many works focus on only considering obstacles in the environment during the finding phase of collision-free paths, while little attention has been paid to the fact that the risk cost from the threat is simultaneous with the service benefit of providing services to customers. To address the shortcomings in the above studies, we propose an urban environment model considering the coupling effect of customer service requirements and complex risks and develop a path point search strategy for improving the exploration of feasible paths in the environment. We summarise the main contributions of this paper as follows.


The rest of this paper is organised as follows: Section 2 analyses the critical elements affected by drones in the urban environment and illustrates the concept of path planning that combines customer needs and risks. The proposed methodology is described in Section 3, followed by simulation validations and case studies in Section 4. The summary of our work is in Section 5.

#### **2. Problem Definition**

Drones operate at low altitudes below 400 feet above the ground in cities. Once there is a collision, they can cause threats to buildings and other non-cooperative drones in the air. On the other hand, they can threaten pedestrians and vehicles on the ground when a crash occurs [42,43]. We conclude the primary environmental elements threatened by drone operations into four categories as follows.


In this work, we ignore other risk factors, such as noise and privacy impacts on the public, due to their insignificance [44]. Pedestrians, vehicles, buildings, and logistics service customers are randomly dispersed in the city. Therefore, the core problem in logistics drone path planning is quantifying risk cost and service benefit for different locations. The urban environment for drone flight is divided into discrete 2D grids, and each grid's risk cost and service benefit are derived from environmental risk elements and customer demand. The cost-benefit value within each grid is used to guide drones to serve more customers and avoid high-risk areas in the complex urban environment.

The technology framework of the proposed work is presented in Figure 1. There are five steps to quantify risk cost and service benefit in the environment. First, the threat of drone operations to pedestrians, vehicles, and buildings in the city is analysed. Then, we develop three risk cost assessment models to quantify the various types of risk costs from the above elements under threat. Thirdly, we develop a service benefit assessment model based on the characteristics of logistics customers. Fourth, we synthesise the integrated risk cost and service benefit into cost-benefit values. Fifth, we construct the cost-benefit map. The urban environment is gridded, and the cost-benefit value calculation method of the flight path is established. Based on the cost-benefit map, we propose a drone path planning model with energy limitation constraints and a search algorithm with heuristic factors. To explore the effectiveness of the model in this paper, we next simulate and analyse the effects of different risk combinations, unknown risk zones, and risk-benefit preferences on the path planning results. We also compare the algorithm of this paper with the A\* algorithm to verify the solving ability of this paper's algorithm. Finally, the reusability of the method in this paper is demonstrated by statistical analysis.

**Figure 1.** The technology framework of the proposed work.

#### **3. Materials and Methods**
