Parametric Modeling and Evaluation of Departure and Arrival Air Routes for Urban Logistics UAVs

Abstract

With the rapid development of the low-altitude economy, the intensive take-offs and landings of Unmanned Aerial Vehicles (UAVs) performing logistics transport tasks in urban areas have introduced significant safety risks. To reduce the likelihood of collisions, logistics operators—such as Meituan, Antwork, and Fengyi—have established fixed departure and arrival air routes above vertiports and designed fixed flight air routes between vertiports to guide UAVs to fly along predefined paths. In the complex and constrained low-altitude urban environment, the design of safe and efficient air routes has undoubtedly become a key enabler for successful operations. This research, grounded in both current theoretical research and real-world logistics UAV operations, defines the concept of UAV logistics air routes and presents a comprehensive description of their structure. A parametric model for one-way round-trip logistics air routes is proposed, along with an air route evaluation model and optimization method. Based on this framework, the research identifies four basic configurations that are commonly adopted for one-way round-trip operations. These configurations can be further improved into two optimized configurations with more balanced performance across multiple metrics. Simulation results reveal that Configuration 1 is only suitable for small-scale transport; as the number of delivery tasks increases, delays grow linearly. When the task volume exceeds 100 operations per 30 min, Configurations 2, 3, and 4 reduce average delay by 88.9%, 89.2%, and 93.3%, respectively, compared with Configuration 1. The research also finds that flight speed along segments and the cruise segment capacity have the most significant influence on delays. Properly increasing these two parameters can lead to a 28.4% reduction in the average delay. The two optimized configurations, derived through further refinement, show better trade-offs between average delay and flight time than any of the fundamental configurations. This research not only provides practical guidance for the planning and design of UAV logistics air routes but also lays a methodological foundation for future developments in UAV scheduling and air route network design.

1. Introduction

In recent years, Unmanned Aerial Vehicles (UAVs) have demonstrated great potential in urban logistics due to their high automation, speed, and flexibility, gradually becoming an integral part of urban freight transportation. Several companies, including Meituan (a technology retail company), Antwork (a technology enterprise committed to developing urban aerial logistics networks), and Fengyi (a subsidiary of SF Express focused on UAV logistics and delivery services) have launched commercial UAV delivery operations. Urban logistics UAVs are typically small, multi-rotor aircraft operating at low altitudes within densely built environments. Their operations are constrained by low-altitude obstacles, turbulent wind fields, noise, and privacy concerns, necessitating precise planning of urban logistics air routes (hereafter referred to as logistics air routes) to ensure safety and efficiency [1]. Thus, scientifically designing logistics air routes has become a key issue in ensuring the safe and efficient development of urban UAV logistics.

The academic community has produced a wide range of research outcomes in the field of UAV air route planning. Existing air-route-planning research is typically divided into en route air route planning and departure and arrival air route planning. Existing studies on en route air route planning mostly frame the problem as single-path planning between fixed origin and destination points, considering factors such as obstacles [2,3], wind [4,5], weather [6,7], noise [8,9], privacy [10], and UAV performance [11], and solving it with graph-search algorithms such as Dijkstra [12], A* [13], and their variants [14,15]. Beyond algorithmic planning, real-world operations typically design separated one-way outbound and inbound air routes between vertiport pairs to avoid collision risks.

Beyond the en route air corridor between vertiports, UAV take-off and landing phases are closer to the ground and more affected by environmental constraints and intertwined traffic flows, making departure and arrival air route design more complex. Existing studies have proposed four types of UAV arrival air route designs [16,17,18,19,20,21,22], as illustrated in Figure 1.

In Figure 1a, the UAV directly flies over the vertiport and performs a vertical descent after alignment. Considering that vertical descent consumes more energy than inclined descent, PRADEEP et al. proposed the slanted arrival in Figure 1b, adding a holding point to balance vertiport alignment and energy reduction [16]. Building on this, PARK et al. introduced aircraft dynamic models to design more energy-efficient curved departure and arrival air routes [17]. To accommodate multi-directional arrival sequencing, Song et al. introduced holding points and holding rings, requiring inbound UAVs to wait at designated positions until instructed to descend [18], as shown in Figure 1c. To better utilize available positions in the holding ring, Song et al. further proposed circular arrival air route structures [19,20], as shown in Figure 1d. Inbound UAVs circulate in the same direction, shifting inward based on priority until reaching the final arrival point for vertical descent. Building on this, Lei et al. extended the holding point and ring structure to dual-vertiport configurations [21]. Shao et al. expanded the circular air route structure to multiple vertiports [22]. The air route structures in Figure 1a,b are space-efficient and easy to implement but offer limited capacity. The air route structures in Figure 1c,d provide greater capacity but occupy more airspace and are more constrained by ground factors, often requiring size reduction in real-world deployment [23].

As summarized above, significant theoretical progress has been made in UAV logistics air route planning, and a relatively clear structure of en route air routes and departure/arrival air routes (as shown in Figure 1) has been established, laying the groundwork for integrating full-flight logistics air routes from take-off to landing. On the practical side, operators such as Meituan, Antwork, and Fengyi have conducted urban UAV delivery for years. Despite relatively low traffic volumes, they have developed workable end-to-end logistics routing schemes. Building upon both theoretical research and operational practice, this paper first develops a generalized parametric model of logistics air routes, covering the full flight process from take-off to landing and accommodating various levels of traffic flow. In addition, at high altitudes, buildings are sparse and obstacles are relatively simple. UAVs only need to perform simple detour maneuvers, which have minimal impact on the air route structure. Therefore, the focus of the parametric model is placed on the departure and arrival air routes. It then constructs an evaluation method based on the intrinsic relationship between traffic delay and air route capacity. Finally, an optimization method is proposed, yielding a general logistics air route design framework. The research framework is shown in Figure 2.

With the expected growth of urban air cargo demand, UAV hub vertiports and high-density air routes—similar to Beijing Capital Airport or the Beijing–Guangzhou A461 corridor—will emerge, with multiple operators (e.g., Meituan, Antwork, and Fengyi) sharing the same vertiports and flight corridors. Unlike current research, which primarily focuses on micro-level factors such as obstacle placement or wind distribution affecting air route waypoints, this paper presents a more macro-level and generalized parametric model. It emphasizes the overall route configuration—particularly the coupling between departure air routes, en route air routes, and arrival air routes. This provides strong support for coordinated logistics air route planning when multiple operators operate from the same vertiport and along the same air route.

2. Parametric Mode of UAV Logistics Air Routes

2.1. Composition of Logistics Air Routes

In 2022, the Civil Aviation Administration of China (CAAC) released the world’s first industry standard “Route Design Specification of the Light-Small Unmanned Aircraft System for Urban Logistics (MH/T 4054-2022)” [1]. This standard defines logistics air routes as comprising three key components: en route air routes, departure and arrival air routes, and vertiports (including alternate vertiports). By integrating the schemes of Meituan, Antwork, and Fengyi with previous studies, the composition of the UAV logistics air route is illustrated in Figure 3. The meaning of each parameter is listed in

Table 1. Components of urban logistics UAV air routes.

No.	Segment Name	Starting Point → Endpoint	Function	Design Influencing Factors	Parametric Consideration
1	Vertical take-off segment ($r=1$)	Origin vertiport ($p_0$) → Alignment point of the origin vertiport ($p_1$)	Vertical climb.	Obstacles around the vertiports, cruise altitude, etc.	Not included in parametric consideration.
2	Departure holding segment ($r=2$)	$p_1$ → Departure holding point ($p_2$)	Wait before entering the departure segment.	Available airspace, UAV size, number of departing UAVs, safety intervals, etc.	Categorized according to the number of UAVs accommodated, corresponding to the number of holding rings in Figure 1.
3	Departure segment ($r=3$)	$p_2$ or $p_1$ → Departure point ($p_3$)	Climb and enter the en route air route.	Obstacles around the vertiports, UAV performance.	As shown in Figure 1, it can be categorized into horizontal, vertical, and slanted types.
4	Cruise segment ($r=4$)	$p_3$ → Arrival point ($p_4$)	Operate between vertiports.	Airspace restrictions, obstacles, electromagnetic interference, wind fields, noise, privacy, etc.	Classified based on different cruise altitudes.
5	Arrival segment ($r=5$)	$p_4$ → Arrival holding point ($p_5$) or alignment point of the destination vertiport ($p_6$)	Descend and arrive.	Obstacles around the vertiports, UAV performance, etc.	As shown in Figure 1, it can be categorized into horizontal, vertical, and slanted types.
6	Arrival holding segment ($r=6$)	$p_5$ → $p_6$	Wait before landing.	Available airspace, UAV size, number of arriving UAVs, safety intervals, etc.	Categorized according to the number of UAVs accommodated, corresponding to the number of holding rings in Figure 1.
7	Vertical landing segment ($r=7$)	$p_6$ → Landing vertiport ($p_7$)	Align with the destination vertiport.	Obstacles around the vertiports, UAV positioning and control performance, etc.	Not included in parametric consideration.

.

2.2. Parametric Model of Logistics Air Route

According to the logistics air route structure shown in Figure 3 and the related parameters and parametric considerations listed in Table 1, parametric models are constructed separately for the outbound and inbound air routes.

The decision matrix ${\mathit{C}}_d$ and the state matrix ${\mathit{S}}_d$ for segments of the outbound air route are defined below:

$$\begin{array}{l}{\mathit{C}}_d=\left[\begin{array}{ccccccc}{C}_1& 0& 0& 0& 0& 0& 0\\ 0& C_2& 0& 0& 0& 0& 0\\ 0& 0& C_3& 0& 0& 0& 0\\ 0& 0& 0& C_4& 0& 0& 0\\ 0& 0& 0& 0& C_5& 0& 0\\ 0& 0& 0& 0& 0& C_6& 0\\ 0& 0& 0& 0& 0& 0& C_7\end{array}\right]\\ {\mathit{S}}_d=\left[\begin{array}{ccc}{S}_1& H_1& N_1\\ S_2& H_2& N_2\\ S_3& H_3& N_3\\ S_4& H_4& N_4\\ S_5& H_5& N_5\\ S_6& H_6& N_6\\ S_7& H_7& N_7\end{array}\right]\end{array}$$

where, $C_r$, $S_r$, $H_r$, and $N_r$ represent parameters related to the outbound air route. In the decision matrix, the 0–1 variable $C_r$ is used to indicate whether the segment exists; in the state matrix, $S_r$ represents the segment orientation—horizontal, slanted, or vertical—corresponding to values of 1, 2, and 3, respectively; $H_r$ denotes the altitude of the segment, which can be set to either 1 or 2, corresponding to 70 m and 90 m; $N_r$ denotes the number of UAVs accommodated by the segment during operation. Subscripts of each parameter indicate the corresponding segment. Thus, the decision matrix indicates the existence of segments, the state matrix defines the segment design scheme, and their product represents the outbound air route.

The parametric representation $\mathit{R}\mathit{o}\mathit{u}\mathit{t}{\mathit{e}}_d$ of the outbound logistics air route is outlined below:

$$\mathit{R}\mathit{o}\mathit{u}\mathit{t}{\mathit{e}}_d={\mathit{C}}_d\times {\mathit{S}}_d$$

(1)

The decision matrix ${\mathit{C}}_a$, state matrix ${\mathit{S}}_a$, and parametric representation $\mathit{R}\mathit{o}\mathit{u}\mathit{t}{\mathit{e}}_a$ of the inbound air route follow the definitions used for the outbound air route:

$$\mathit{R}\mathit{o}\mathit{u}\mathit{t}{\mathit{e}}_a={\mathit{C}}_a\times {\mathit{S}}_a$$

(2)

where parameters $C_r^{\prime }$, $S_r^{\prime }$, $H_r^{\prime }$, and $N_r^{\prime }$ represent the corresponding parameters for the inbound route. Since the vertical take-off and landing segments are shared between the outbound and inbound routes, the first row of ${\mathit{S}}_d$ matches the seventh row of ${\mathit{S}}_a$, and the seventh row of ${\mathit{S}}_d$ matches the first row of ${\mathit{S}}_a$.

To focus on the matching relationship between departure/arrival segments and cruise segments, the parametric model constructed in this paper adopts the following simplifications: capacities for all segments other than cruise segments are set to 1; cruise segment capacities, being related only to segment length and not central to this paper, are thus omitted. All variable parameters for the outbound and inbound air routes are listed in

Table 2. Variable parameters in the parametric representation of logistics UAV air routes.

Segment Index ($\mathit{r}$)	$\mathbf{Variable}\mathbf{Parameters}({\mathit{S}}_{\mathit{r}}$$,{\mathit{S}}_{\mathit{r}}^{\prime }$)	Meaning
3	$S_3$, $S_3^{\prime }$	Departure segments’ orientation
5	$S_5$, $S_5^{\prime }$	Arrival segments’ orientation
2	$C_2$, $C_2^{\prime }$	Existence of holding segments
6	$C_6$, $C_6^{\prime }$	Existence of holding segments
4	$H_4$, $H_4^{\prime }$	Cruise segments’ altitude

.

3. Evaluation Model of UAV Logistics Air Routes

To evaluate the effectiveness of parametric design, this paper develops an air route evaluation model aimed at minimizing average delays. An integer programming model is formulated to represent conflict-free UAV operation, constrained by UAV passing times at waypoints, segment occupancy times, and air route capacities. The model is solved using an exact solver algorithm.

3.1. Objective Function

The evaluation criterion is the average delay, defined as the average take-off delay at the origin vertiport and the average arrival delay at the destination vertiport, expressed as follows:

$$\begin{array}{ll}\min {\displaystyle \sum _{i\in U}Dela{y}^i}& =\min (Dela{y}_1+Dela{y}_2)\\ & =\min {\displaystyle \frac{1}{N_m}}({\displaystyle \sum _{i\in U}(t_1^i-ET{D}^i)}+{\displaystyle \sum _{i\in U}(t_8^i-t_{all}^i-ET{D}^i))}\end{array}$$

(3)

where $U$ denotes the set of UAVs assigned to tasks; $N_m$ is the number of tasks; $ET{D}^i$ is the expected departure time for the i-th UAV, coinciding with task arrival at the delivery center; $Dela{y}_1$ is the take-off delay at origin vertiport $p_0$, reducing $Dela{y}_1$ can decrease the number of UAVs remaining on the ground; $Dela{y}_2$ is the arrival delay at destination vertiport $p_7$, minimizing $Dela{y}_2$ enables customers to receive their packages more quickly; $t_{all}^i$ is the nominal flight duration for the i-th UAV between origin vertiport $p_0$ and destination vertiport $p_7$; $t_1^i$ and $t_8^i$ denote the actual take-off and landing times of the i-th UAV at origin and destination vertiports, respectively.

Decision variables in the model include departure times of UAVs from the start and end points of each segment.

3.2. Constraints

The constraints are categorized into fundamental constraints and conflict-free constraints. Fundamental constraints are mandatory requirements for UAVs transiting through waypoints. Conflict-free constraints are defined to enforce exclusive operation of segments and compliance with capacity limitations.

3.2.1. Fundamental Operational Constraints

Departure constraints require UAVs to take off only after task arrival at the origin vertiport, expressed as detailed below:

$$t_1^i-ET{D}^i\ge 0\forall i\in U$$

(4)

where $U$ is the set of UAVs assigned to the task; $t_1^i$ is the take-off time of the i-th UAV from the origin vertiport $p_0$; and $ET{D}^i$ is its actual arrival time of the i-th task.

Operational constraints ensure the interval between consecutive waypoints exceeds or equals the required segment traversal time at constant speed. Constraints are formulated as follows:

$$t_{r+1}^i-t_r^i\ge {\tau }_r\forall i\in U,\forall r\in R$$

(5)

$$t_{r+1}^{i^{\prime }}-t_r^{i^{\prime }}\ge {\tau }_r^{\prime }\forall i\in U,\forall r\in R$$

(6)

where $R$ are sets of segments in the outbound and inbound air routes, the definitions of segment start and end points follow Table 1; $t_r^i$ and $t_r^{i^{\prime }}$ denote departure times of the i-th UAV from start points of segments $r$ in the outbound and inbound air routes, respectively; $t_{r+1}^i$ and $t_{r+1}^{i^{\prime }}$ denote departure times of the i-th UAV from start points of segments $r+1$ in the outbound and inbound air routes, respectively; ${\tau }_r$ and ${\tau }_r^{\prime }$ denote the time required for the UAV to traverse the segment in the outbound and inbound air routes at constant speed, determined by the UAV’s operational speed and the segment length.

Package unloading constraints mandate UAV dwell times at the destination vertiport $p_7$, expressed below:

$$t_1^{i^{\prime }}-t_8^i\ge {\tau }_T,\forall i\in U$$

(7)

where $t_8^i$ is the landing time of the i-th UAV at the destination vertiport $p_7$ in the outbound air route; $t_1^{i^{\prime }}$ is the departure time of the i-th UAV from the origin vertiport $p_0^{\prime }$ in the inbound air route, $p_7$ and $p_0^{\prime }$ share the same vertiport; ${\tau }_T$ is the dwell time, set as 60 s.

3.2.2. Exclusive Segment Constraints

Segments allowing only one UAV at a time are termed exclusive segments. In practice, all segments near vertiports are exclusive segments.

Exclusive-segment operation constraints require that different UAVs using the same vertical take-off and landing segments must operate sequentially, allowing only one UAV within any given time period. Constraints (8) and (9) apply, respectively, to outbound and inbound UAV operations on segments $1$ and $7$:

$${\alpha }_{1,7}^{i,j}\ge {\beta }_{2,8}^{i,j}+1\forall i,j\in U$$

(8)

$$t_7^j-t_2^{i^{\prime }}+M(1-{\lambda }^{i,j})\ge 0,\forall i,j\in U$$

(9)

where ${\alpha }_{r,r^{\prime }}^{i,j}$ is the maximum of two values: the time at which the i-th UAV leaves the starting point of outbound segment $r$ in the inbound air route, and the time at which the j-th UAV leaves the starting point of inbound segment $r^{\prime }$ in the outbound air route. Meanwhile, ${\beta }_{r,r^{\prime }}^{i,j}$ is the minimum of two values: the time at which the i-th UAV leaves the endpoint of outbound segment $r$ in the inbound air route, and the time at which the j-th UAV leaves the endpoint of inbound segment $r^{\prime }$ in the outbound air route. The term $t_7^j$ is the time when the UAV departs from the start of outbound segment 7. The term $t_2^{i^{\prime }}$ is the time when the i-th UAV leaves the endpoint of inbound segment 1. ${\lambda }^{i,j}$ is a 0–1 variable that equals 1 if the i-th UAV departs the take-off vertiport $p_0$ in the outbound air route before or at the same time as the j-th UAV, and 0 otherwise. $M$ is a sufficiently large positive number.

The sequential exclusive constraint states that if multiple UAVs move through a series of exclusive segments in order, only one UAV can occupy each segment at any time. Its expression is as follows:

$$t_r^j-t_{r+1}^i+M(1-{\lambda }^{i,j})\ge 0\forall r\in R\backslash \{4\},\forall i,j\in U$$

(10)

$$t_r^{j^{\prime }}-t_{r+1}^{i^{\prime }}+M(1-{\lambda }^{i,j})\ge 0,\forall r\in R\backslash \{4\};\forall i,j\in U$$

(11)

where $t_r^j$ and $t_r^{j^{\prime }}$ are the times at which the j-th UAV leaves the starting point of outbound segment $r$ and inbound segment $r$, respectively.

3.2.3. The Air Route Capacity Constraints

The cruise segment capacity constraint dictates that at any moment, the number of UAVs in the cruise segment cannot exceed its capacity $N_4$ or $N_4^{\prime }$. Its expression is outlined below:

$$n_4^t\le N_4\forall t$$

(12)

$$n_4^{t^{\prime }}\le N_4^{\prime }\forall t$$

(13)

where $n_r^t$ and $n_r^{t^{\prime }}$ represent the number of UAVs along outbound segment $r$ and inbound segment $r$ at time $t$, respectively.

4. Logistics Air Route Optimization Method

In the air route parameters defined in Section 2.2, their physical meaning determines that certain correspondence must exist among the parameters; for instance, if the outbound air route and the inbound air route are at different altitudes, the departure point and the arrival point must also sit at different altitudes. Prior to developing the air route optimization framework, this section first identifies feasible round-trip parameter combinations—termed basic air route configurations. Building on these configurations, we analyze parametric relationships within each configuration type, establish a feasibility rule base, and formalize them as optimization constraints. Finally, optimization algorithms are applied to determine the optimal configuration for specified parameter sets.

4.1. Determining the Basic Configurations

Combining research results with field experience, and starting from key factors such as the orientation and altitude of the outbound air route and the inbound air route, we simplify the departure and arrival air routes into four design schemes, according to whether the outbound segment 3 and the inbound segment 5 overlap, the orientations of the outbound segment 3 and the inbound segment 5, and the existence of the inbound segment 6, as shown in Figure 4. Taking into account whether the outbound and inbound segments 4 overlap, and the altitude difference between the outbound and inbound segments 4, the en route air routes are simplified into three design schemes, as illustrated in Figure 5.

Combining the departure and arrival air routes shown in Figure 4 with en route air routes shown in Figure 5—eliminating infeasible combinations (such as Figure 4a and Figure 5c due to differing cruising altitudes)—yields four fundamental configurations for one-way round-trip air routes, as shown in Figure 6 and

Table 3. Characters of one-way round-trip air routes for urban logistics.

Configuration	Characters
1	UAVs operate inbound and outbound flights along the same air route.
2	En route air routes are at the same altitude, operating in one direction on different routes. Departure and arrival air routes are separated.
3	En route air routes are at the same altitude, operating in one direction on different air routes. Departure and arrival air routes are separated. The speed on inclined departure and arrival air routes is significantly reduced, enhancing safety.
4	En route air routes are at different altitudes, operating in one direction on different air routes. Departure and arrival air routes are separated.

.

4.2. Definition of Feasibility Rule Base

Analysis reveals two primary reasons for infeasibility, as demonstrated in Figure 4c. First, changing the orientation $S_3$ of the segment in Figure 4c to horizontal (Figure 7a) causes misalignment between the origin vertiport and destination vertiport alignment points, violating the collocation requirement defined in Section 2.2. Second, altering the segment orientations of the outbound segment 3 and the inbound segment 5 in Figure 4c to vertical (Figure 7b) converts unidirectional air routes into exclusive bidirectional air routes, contradicting optimization objectives. Therefore, establishing a feasibility rule base becomes essential to ensure feasible air route designs by eliminating non-compliant solutions during optimization.

For outbound air route parameter combinations, feasibility rule bases are formulated as Equations (14)–(20), where “→” denotes logical implication and “^” represents logical conjunction. Similar feasibility rule bases are established for the inbound air routes.

When $H_4\le H_4^{\prime }$ occurs,

$$(H_4=H_4^{\prime }\wedge S_3=1)\to S_5^{\prime }=1$$

(14)

$$(H_4<H_4^{\prime }\wedge S_3=1)\to S_5^{\prime }\ne 1$$

(15)

$$S_3=2\to S_5^{\prime }\ne 1$$

(16)

$$(S_3=3\wedge C_2+C_6^{\prime }=0)\to S_5^{\prime }=2$$

(17)

$$(S_3=3\wedge C_2+C_6^{\prime }\ge 1)\to S_5^{\prime }\ne 1$$

(18)

When $H_4>H_4^{\prime }$ occurs,

$$S_3\ne 1$$

(19)

$$(S_3=3\wedge C_2+C_6^{\prime }=0)\to S_5^{\prime }\ne 3$$

(20)

Equations (14) and (16)–(18) form feasible rule bases for $H_4=H_4^{\prime }$, Equations (15)–(18) for $H_4<H_4^{\prime }$, and Equations (19)–(20) for $H_4>H_4^{\prime }$, with unlisted cases being inherently feasible. An example is given using Equation (18) to illustrate the meaning of the feasible rule base: when $H_4\le H_4^{\prime }$ exists, if at least one exists between the outbound segment $2$ and the inbound segment $6$ with the outbound segment $3$ maintaining vertical orientation, then the inbound segment $5$ cannot adopt horizontal orientation.

4.3. Optimization Process

The optimization process is illustrated in Figure 8. In Figure 8, a parametric model is first established based on initial air route designs. Variable parameters are then fed as variables into pre-built feasible rule bases to filter feasible design schemes. These schemes are subsequently evaluated using the air route evaluation model, followed by an exhaustive search to identify the optimized solution. This study adopts an exhaustive search as the optimization process.

Optimization problems can typically be classified according to two dimensions: mathematical characteristics and variable characteristics. In terms of mathematical characteristics, complexity increases from linear problems to second-order cone problems, quadratic convex problems, non-convex quadratic problems, and finally to nonlinear problems. In terms of variable characteristics, problems can be divided into continuous optimization, integer optimization, and mixed-integer optimization based on the types of decision variables. The air route evaluation model in the optimization process is a large-scale integer linear programming model with a massive number of decision variables (reaching thousands in this study). This model can be efficiently solved using commercial solvers such as Gurobi, CPLEX, and FICO Xpress. During the exhaustive search process, variable parameters are continuously updated through iterative cycles. The exact solutions obtained from the air route evaluation model by the solver are compared and analyzed against the computational results from other parametric models to ultimately determine the optimal air route solution.

It should be noted that in Configuration 1 where outbound and inbound air routes fully coincide, segment capacity becomes severely constrained. This configuration only permits singular UAV to complete round-trip operations sequentially, forcing subsequent UAVs to await prior mission completion—drastically reducing operational efficiency. Therefore, while Configuration 1 exists in operational reality, this study excludes it from the in-depth analysis, retaining it solely as a control group for evaluation purposes.

5. UAV Logistics Air Route Optimization Case Study

Meituan UAV operates logistics services at Xinghe Square (Longgang District, Shenzhen), as shown in Figure 9. The red pentagram marks the vertiport at Xinghe Square, serving as both take-off and landing platform. Three color-coded air routes connect this platform with three peripheral vertiports. This scenario validates our optimization algorithm, using airspace above Xinghe Square as the operational boundary for departure and arrival air routes.

Figure 9 shows a schematic diagram of actual UAV air routes. The origin vertiports of the three air routes are located within the same area but each air route operates from a different origin vertiport with maintained safety separation. Furthermore, proper horizontal and vertical separation between air routes ensures conflict-free operations across all air routes. Given this independence among the three air routes, we can focus our study on a single, specifically designed air route scenario.

5.1. Parameter Selection

(1)

Operational Airspace Parameters for Departure and Arrival Air Routes

Using OpenStreetMap data [24], we constructed 3D urban models (Figure 10a) with building coordinates, dimensions, and heights following Method [25]. The vertiport appears as a red dot in Figure 10a. The operational airspace (50 m radius, 90 m height) for the vertiport is designed as a cylindrical airspace (pink transparent cylinder in Figure 10b), with calculation methods detailed in Appendix A.

This case focuses on departure/arrival air route optimization, with en route segments simplified as 2100 m direct connections to cover all demand points within the area.

Based on field surveys, Configuration 4 (Figure 6d) exemplifies parametric modeling, with node positions shown in Figure 11.

Table 4. Parametric representation of outbound air routes under different design schemes.

	Parameters	Configuration 1				Configuration 2				Configuration 3				Configuration 4
Segment Index ($\mathit{r}$)		$\mathit{C}$	$\mathit{S}$	$\mathit{H}$	$\mathit{N}$	$\mathit{C}$	$\mathit{S}$	$\mathit{H}$	$\mathit{N}$	$\mathit{C}$	$\mathit{S}$	$\mathit{H}$	$\mathit{N}$	$\mathit{C}$	$\mathit{S}$	$\mathit{H}$	$\mathit{N}$
$1$		1	3	2	1	1	3	2	1	1	3	2	1	1	3	1	1
$2$		0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
$3$		1	1	2	1	1	1	2	1	1	2	2	1	1	1	1	1
$4$		1	1	2	1	1	1	2	10	1	1	2	10	1	1	1	10
$5$		1	1	2	1	1	1	2	1	1	2	2	1	1	2	1	1
$6$		0	0	0	0	0	0	0	0	0	0	0	0	1	1	1	1
$7$		1	3	2	1	1	3	2	1	1	3	2	1	1	3	1	1

details parameter assignments for departure routes across configurations in Figure 6. Parameterization of inbound air routes follows analogous configuration-specific implementations. In Configuration 1, due to complete overlap of all segments, the cruise segment capacity is limited to one UAV.

(2)

Operational Parameters

Based on the investigation of Meituan’s third-generation UAV, for the outbound air route, UAV speeds vary across different segment orientations: 2 m/s in segment 1 and 1 m/s in segment 7; 5 m/s in segment 2 and 6; 20 m/s in segment 5; conditional speeds apply to segments 3: 5 m/s ($S_3$ is 1), 0.5 m/s ($S_3$ is 2), and 2 m/s ($S_3$ is 3); conditional speeds apply to segments 5: 5 m/s ($S_5$ is 1), 0.5 m/s ($S_5$ is 2), and 1 m/s ($S_5$ is 3). The inbound air route uses the same speeds for segments with matching numbers. Speed variations in departure/arrival segments distinguish Configurations 2 and 3.

Peak-hour operations generate intensive delivery tasks (orders) for logistics UAVs. We simulate this using uniform distribution to generate 10–100 random tasks within 30-min windows. Task escalation beyond 1000 decision variables necessitates MATLAB-Gurobi integration for air route evaluation and optimization, with MATLAB R2022b used in this study.

The evaluation results appear in Section 4.2, with the optimization outcomes detailed in Section 4.3.

5.2. Evaluation Model Analysis

5.2.1. Average Delay

Ten task groups (10–100 tasks with 10-unit increments) were tested across configurations in Figure 6, with results shown in Figure 12. “Configurations” are abbreviated as “Cfg” in subsequent figures.

Figure 12 demonstrates configuration rankings by average delay: Configuration 4 > 3 > 2 > 1. Using Configuration 1 as a baseline, at the 10-task level: Configuration 2/3/4 achieve a 88.9%/89.2%/93.3% delay reduction, respectively. At the 100-task level: absolute delays decrease by 12,195.6 s (Configuration 2), 13,274.6 s (Configuration 3), and 16,301.0 s (Configuration 4).

Configuration 1 suffices for low-demand scenarios (<10 tasks). Below 40 tasks, Configuration 2 outperforms 3 despite higher operational risks from increased speeds requiring advanced navigation systems. Configuration 4 with altitude-stratified operations emerges superior under expanded low-altitude airspace access.

Delays consist of ground dwell delays at the origin vertiport $p_0$ and airborne hovering delays at waypoints. We compare the average dwell time at the origin vertiport $p_0$ and the average flight time to the destination vertiport $p_7$ under different configurations. The results are shown in Figure 13 and Figure 14.

Figure 14 shows Configuration 4 minimizes delays via dedicated holding segments, with origin vertiports being primary congestion points. While Configuration 1 achieves the shortest average flight times (Figure 14), it exhibits the worst delays (Figure 13). This demonstrates the necessity for flight time–delay tradeoffs in configuration selection.

Under different urban structures, the Maximum Safety Distance (MSD) varies within the range of 20 m to 60 m (based on investigation results). By testing configurations 1 to 4 with MSD intervals of 10 m from 20 to 60 m, the similar air route evaluation results can be obtained, as shown in Figure 15.

As can be seen from Figure 15, with the gradual increase in MSD, the average delay shows an increasing trend for specific configurations. However, regardless of how MSD changes, Figure 15 demonstrates the configuration rankings by average delay: Configuration 4 > 3 > 2 > 1. This indicates that our method yields consistent conclusions under different urban structures.

5.2.2. Sensitivity Analysis

(1)

Segment Speed

Since the UAVs in Configuration 3 have the minimum flight speed in the departure and arrival segments, the analysis of segment speed impact on average delay is more significant; therefore, Configuration 3 is selected for illustration. We test speed variations (50–150%) across segments, with delays shown in Figure 16.

Speed reductions consistently increase delays across all segments (Figure 16). A 50% speed reduction along the outbound and inbound segments 1 and 7 causes a maximum of 301.6% and average of 101.6% delay increases. Conversely, speed enhancements along the outbound and inbound segments 1 and 7 reduce delays proportionally. A 1.5 speed amplification along the outbound and inbound segments 1 and 7 yields a maximum of 28.4% and average of 24.7% delay reductions.

Increasing the UAV speed along the outbound and inbound segments 1 and 7 has the greatest effect in reducing average delay. Adjusting the UAV speed along the outbound and inbound segments 4 has the least impact on delay. Decreasing the UAV operating speed along a segment affects delay more significantly than increasing it.

(2)

Segment Capacity

With other segments fixed at unit capacity, we analyze capacity effects of the outbound and inbound segments 4.

Increasing the capacity of the outbound and inbound segments 4 can help reduce delays. However, a higher number of UAVs reduces the safety interval between them, increasing the risk of collisions. Assuming a safety interval of 5 s, the maximum segment capacity can be set to 20 based on segment length and UAV operating speed of the outbound and inbound segments 4. The relationship between capacity and delay under different design schemes is illustrated in Figure 17.

As shown in Figure 17, the average delay of each design scheme decreases with increasing segment capacity. When segment capacity is set to 20, versus 10, Configurations 2 and 4 achieve the largest average delay reduction, both with a decrease of 11.1%. When the task number reaches 100, each design achieves its maximum average delay reduction, exceeding 1000 s. This indicates that the greater the number of tasks, the more noticeable the delay reduction. However, this improvement does not grow indefinitely, showing a rising then stabilizing trend.

5.3. Air Routes Optimization

After discussing the air route evaluation model in Section 4.2, air route parameters are adjusted to further optimize the configurations in Figure 6.

The variable parameters include four parameters ($S_3$, $S_3^{\prime }$, $S_5$, and $S_5^{\prime }$) that represent the orientation of the segments, with values ranging from 1 to 3 as positive integers. There are also four parameters ($C_2$, $C_2^{\prime }$, $C_6$, and $C_6^{\prime }$) that represent the existence of the segments, with values of either 0 or 1. Additionally, there are two parameters ($H_4$ and $H_4^{\prime }$) that represent the altitude of the segments, with values between 1 and 2 as positive integers. The search space for air route parameter optimization is the product of parameter ranges, totaling 5184 combinations (according to the multiplication principle).

In the optimization process, results are categorized based on the relationship between cruise altitudes $H_4$ and $H_4^{\prime }$. After applying the feasibility rule base, the feasible search space includes 722, 529, and 400 combinations for different cruise altitude cases: $H_4=H_4^{\prime }$, $H_4<H_4^{\prime }$, and $H_4>H_4^{\prime }$. For computational efficiency, a 60-task scenario is used as input to the air route evaluation model, with each scheme solved by the GUROBI solver (Figure 18).

In Figure 18, blue circles represent initial parameter configurations, and red circles represent optimized results, all of which outperform the original configurations. In Figure 18a, the first 361 feasible cases are 70 m same-altitude air routes, followed by 90 m ones; the former has lower average delays. As shown in Figure 18b, the first 529 cases in the feasible search space are $H_4<H_4^{\prime }$ samples (with outbound cruise altitude lower than inbound), followed by $H_4<H_4^{\prime }$ samples. The maximum and minimum average delays of the former are both smaller than those of the latter, indicating that lower outbound and higher inbound cruise altitudes minimize overall delay.

According to the optimization flow in Figure 8, air route configurations before and after optimization are shown in Figure 19, and the average delay and flight time in Figure 20.

As shown in Figure 19 and Figure 20, whether the outbound and inbound flights share the same cruise altitude or differ in altitudes, the optimized configurations consistently outperform the original ones. Designing waiting segments during the departure and arrival stages (i.e., horizontal segments connected to the departure holding point $p_2$ and arrival holding point $p_5$ in Figure 19) can reduce take-off delays and average air route delays across all configurations. This also explains why existing studies commonly focus on arrival air routes with holding patterns. Considering the waiting demands of both outbound and inbound air routes, adding waiting segments to the outbound air route is more effective than adding them to the inbound air route. In terms of average flight time, when the number of missions ranges from 20 to 70 per 30 min, the optimized configuration is inferior to Configuration 3 in Figure 6. This indicates that designing inclined departure and arrival segments can reduce flight time. Meituan’s UAV has also adopted this design in its departure and arrival air routes scheme under favorable airspace clearance conditions, which is supported by the above analysis.

6. Conclusions

With the rapid growth of UAV-based urban logistics, designing efficient air routes tailored to local conditions while balancing traffic flow and capacity constraints has become an urgent research priority. This study builds upon a review of theoretical advancements and field operations to achieve the following breakthroughs:

1. A parametric model for UAV air routes in urban logistics is proposed. Drawing from the four departure and arrival air route configurations identified in current theory and the practical designs used by operators such as Meituan, Antwork, and Fengyi, this study defines a parametric model for one-way round-trip logistics air routes, providing a complete representation of urban UAV logistics air routes. This lays the foundation for future integrated design optimization.

2. An air route evaluation model and an optimization design method for UAV routes are developed. Leveraging the parametric model, this study abstracts higher-level air route parameters from the current UAV path-planning literature. These are integrated with classical operational scheduling models, emphasizing safety and capacity constraints, and refining the interrelations between parameters. An air route evaluation model with appropriate granularity and a design-phase-oriented optimization method is proposed. This supports both air route design optimization and further research in scheduling optimization.

3. This study identifies feasible basic air route configurations and further improves them through optimization. Through analysis of parameter representation and interdependencies, four basic configurations of one-way round-trip logistics air routes are revealed. Companies like Meituan, Antwork, and Fengyi have all coincidentally adopted one or more of these configurations in practice. Using Meituan’s real-world operations as a case, two more balanced optimized configurations are identified through further improvement of the basic forms. These can provide valuable guidance for optimizing UAV logistics air route design.

Despite these achievements, several simplifications were adopted in this study: only horizontal, vertical, and inclined shapes are considered for the departure and arrival segments; cruise segments are limited to two altitude levels (70 m and 90 m), and cruise segment lengths are not considered; and only one UAV type (from Meituan) is used in simulation scenarios. These factors further limit deeper insights into the underlying laws of routing patterns and the discovery of more optimal configurations. These limitations point to important directions for future research. In addition, UAV path planning remains a prominent research focus. Efficient planning algorithms can yield more precise air route positioning. The question of how to integrate the macro-level configuration insights from this study with detailed path-planning algorithms to generate more scientifically sound and practical routing solutions is another challenge that requires further investigation. A single efficiency indicator is insufficient for comprehensively evaluating air route structure performance. Therefore, safety-related assessment indicators will be incorporated in future work to achieve a comprehensive assessment of air routes.