Open AccessArticle

Parametric Analysis of Landing Capacity for UAV Fleet Operations with Specific Airspace Structures and Rule-Based Constraints

College of Air Traffic Management, Civil Aviation University of China, Tianjin 300300, China

Author to whom correspondence should be addressed.

Drones 2024, 8(12), 770; https://doi.org/10.3390/drones8120770

Submission received: 24 November 2024 / Revised: 16 December 2024 / Accepted: 16 December 2024 / Published: 19 December 2024

(This article belongs to the Topic Innovation and Inventions in Aerospace and UAV Applications)

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Figure 1
Airspace structure and operation factors influencing vertiport operational capacity and efficiency. "> Figure 2
Sequential stages of UAV movements from entering the airspace until the end of the landing process. "> Figure 3
Definitions and parameters for the UAV operation required in this study, including holding points (or stations) in different layers with respective radii and heights. "> Figure 4
Number of holding points in different layers associated with the respective radius and safe separation: (a) overall representation of layers; (b) assembly layer and upper layer; (c) lower layer. "> Figure 5
Rule-based UAV operation constraints: (a) sequencing constraint; (b) movement constraint; (c) de-conflict constraint; (d) consecutive service constraint. Shaded circles shown in the diagrams represent occupied holding points. "> Figure 6
Time-based algorithms from phase to phase: (a) flowchart of overall fleet operation according to respective constraints and guidelines; (b) details of “Generating no-conflict movement trajectory” in (a). "> Figure 7
Phase-based time slots defined for UAV fleet operations. "> Figure 8
Flowchart of self-derived movement for each individual UAV governed by constraints and guidelines in <a href="#sec4-drones-08-00770" class="html-sec">Section 4</a> and according to time-based algorithms in <a href="#sec5-drones-08-00770" class="html-sec">Section 5</a>. "> Figure 9
Flowchart to auto-generate the resultant capacity of the fleet operation accomplished by the UAVs involved within a given time duration. "> Figure 10
Tabulated cases to be simulated for capacity of fleet operations in different upper-lower layer radii (for given heights). "> Figure 11
Fleet operation capacity with different airspace structures: (a) illustration of the capacity values for different combinations of upper and lower layers when hupr_lwr = 50 m, hlwr_apr = 20 m, hapr_ldn = 20 m; (b) illustration of the capacity values for different combinations of upper and lower layers when hupr_lwr = 40 m, hlwr_apr = 30 m, hapr_ldn = 20 m; (c) illustration of the capacity values for different combinations of upper and lower layers when hupr_lwr = 35 m, hlwr_apr = 35 m, hapr_ldn = 20 m; (d) illustration of the capacity values for different combinations of upper and lower layers when hupr_lwr = 30 m, hlwr_apr = 40 m, hapr_ldn = 20 m; (e) illustration of the capacity values for different combinations of upper and lower layers when hupr_lwr = 20 m, hlwr_apr = 50 m, hapr_ldn = 20 m. "> Figure 11 Cont.
Fleet operation capacity with different airspace structures: (a) illustration of the capacity values for different combinations of upper and lower layers when hupr_lwr = 50 m, hlwr_apr = 20 m, hapr_ldn = 20 m; (b) illustration of the capacity values for different combinations of upper and lower layers when hupr_lwr = 40 m, hlwr_apr = 30 m, hapr_ldn = 20 m; (c) illustration of the capacity values for different combinations of upper and lower layers when hupr_lwr = 35 m, hlwr_apr = 35 m, hapr_ldn = 20 m; (d) illustration of the capacity values for different combinations of upper and lower layers when hupr_lwr = 30 m, hlwr_apr = 40 m, hapr_ldn = 20 m; (e) illustration of the capacity values for different combinations of upper and lower layers when hupr_lwr = 20 m, hlwr_apr = 50 m, hapr_ldn = 20 m. "> Figure 12
Capacity trends of fusiform structure (rlwr > 0, rupr = 0) with radii and height variations. "> Figure 13
Capacity trends of elongated funnel structure (rupr > 0, rlwr = 0) with radii and height variations. "> Figure 14
Capacity trends of straight-line vertical descent structure (rupr = 0, rlwr = 0) with radii and height variations. "> Figure 15
Capacity trends of inverted conical structure (rupr < rlwr, rupr ≠ 0) with radii and height variations. "> Figure 16
Capacity trends of funnel-shaped structure (rupr > rlwr, rlwr ≠ 0) with radii and height variations. "> Figure 17
Capacity trends of cylindrical structure (rupr = rlwr, rlwr ≠ 0) with radii and height variations. ">

Versions Notes

Abstract

As Urban Air Mobility (UAM) moves toward implementation, managing high-density, high-volume flights in urban airspaces becomes increasingly critical. In such environments, the design of vertiport airspace structures plays a key role in determining how many UAVs can operate safely and efficiently within a specific airspace. Existing studies have not fully explored the complex interdependencies between airspace structure parameters and fleet operation capacity, particularly regarding how various structural components and their configurations affect UAV fleet performance. This paper addresses these gaps by proposing a multi-layered funnel-shaped airspace structure for vertiports, along with an adjustable parameter model to assess factors affecting landing capacity. The proposed design includes the assembly layer, upper layer, lower layer, and approach point, forming the basis for fleet operations, divided into three phases: arrival, approach, and landing. By modeling fleet operations with various constraints and time-based algorithms, simulations have been conducted to analyze the impact of changing airspace structure parametric dimensions on UAV fleet operation capacity. The results reveal that fleet capacity is closely influenced by two limitations: the distance traveled in each phase and the availability of holding points at each layer. These findings provide valuable insights and contribute to future airspace design efforts for UAM vertiports.

Keywords:

low attitude airspace; fleet operation capacity; airspace structure; UAV landing process

1. Introduction

As urbanization and the development of mega-cities deepened worldwide in recent years, sustainable transportation has become a pressing challenge. Severe congestion in ground transportation significantly impacts travel efficiency. In an effort to tackle these issues, the National Aeronautics and Space Administration (NASA) introduced the concept of Urban Air Mobility (UAM) [1]. UAM aims to address challenges in traditional transportation by integrating vertical take-off and landing (VTOL) aircraft, such as UAVs, into current transportation systems. These electrically driven unmanned aerial vehicles (UAVs), with their attributes of convenience, efficiency, strong maneuverability, energy efficiency, and environmental friendliness [2], offer new perspectives and possibilities for solving future urban transportation issues for the movements of passengers, cargo, goods, etc. In 2014, NASA proposed its first conceptual framework for the Unmanned Aircraft Systems (UAS) Traffic Management (UTM) [3], which serves as the foundation and developmental guidance for the safe and efficient operation of UAVs. In 2016, the American Institute of Aviation and Aeronautics (AIAA) released an academic report to comprehensively explain the concept of UTM operation [4]. Subsequently, various organizations, including the Federal Aviation Administration (FAA), conducted in-depth research on the establishment and implementation of UTM, encompassing its vision, operational concepts, and development requirements [5]. After years of focused development and iterative enhancements, the operational concepts within the drone management sector have not only significantly advanced but have also made a significant shift towards Advanced Air Mobility (AAM) [6,7,8,9]. This evolution reflects a broader vision within the sector to embrace more sophisticated and wide-ranging use of UAVs in the airspace.

As UAV applications continue to expand and evolve, the International Civil Aviation Organization (ICAO) predicts a trend toward high-volume, high-density operations, particularly represented by UAM [10,11]. Nations worldwide are actively participating in this initiative. Both domestic and international research institutions, UAV manufacturers, and operators have conducted extensive studies on Unmanned Aircraft System Traffic Management (UTM) [12,13,14]. These studies explore various aspects, including operational and management concepts, application missions, collision avoidance, obstacle evasion, route planning, and infrastructure development [15,16,17]. A series of investigations have specifically focused on the overall configuration and management of UAV traffic systems.

In the field of aviation transportation, airports are key hubs connecting airside and landside traffic, as well as a key factor in air traffic carrying capacity and operational efficiency [18]. Similarly, in the domain of UAVs, landing sites, also called “vertiports”, are assuming a pivotal role within urban air traffic systems. Vascik et al. [19] identified eight factors limiting urban air traffic operations, with the availability of landing areas being a major constraint [20]. These vertiports, encompassing various configurations, serve as multifaceted hubs accommodating both the initiation and culmination of UAV operations. Take-off and landing procedures serve as “nerve centers” for the coordination and optimization of UAV operation systems. UAV fleet operation is another crucial issue that should be considered to ensure the safe, efficient, and scalable navigation of UAVs over low-altitude urban airspace. Accordingly, two crucial aspects directly related to UAV vertiport operational capacity are considered in the present work. As illustrated in Figure 1, the two aspects are (1) airspace structure above the vertiport, including designing of flight routes and functional division of airspace, and (2) UAV operation factors, including vehicle performance and sequencing rules, waiting rules, service priorities, safety intervals, etc. A safe and efficient operation of UAVs surrounding and at vertiports is a primary objective for various stakeholders. Extensive works have been documented, and those related to the two above-mentioned aspects are mentioned in detail next.

2. Literature Review

2.1. Works Relevant to Optimized Airspace Structures

Guided by the urban air traffic operation concepts and scenarios proposed by NASA, Uber, and Airbus [21,22,23], scholars worldwide have actively conducted research on UAV airspace design [24], with a particular emphasis on landing site airspace design arrival and departure paths design and UAV fleet operations. In the optimization design of vertiport airspace structures, many researchers [25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41] have explored various approaches while taking the characteristics of vertical take-off and landing (VTOL) aircraft into account.

Zhang et al. [25] proposed a direct descent airspace structure following traditional transport aviation procedures, dividing VTOL procedures into six program modules. Similarly, Pradeep et al. [26] have proposed similar aircraft arrival flight paths for both the emergent and early expanded periods.

Kleinbekman et al. [27] pioneered the study of an inclined descent airspace structure that resembles conventional aircraft continuous descent operations (CDO). They also developed an operation method using energy-efficient trajectory optimization with fixed arrival times. Leveraging NASA’s principles and algorithms for air traffic arrival scheduling [28], the method is based on a multi-stage control optimization model taking account of the energy consumption of UAVs (Pradeep, 2018) [29]. It is worth mentioning that the operation based on airspace structure adhered to traditional transport aviation terminal procedures, resulting in suboptimal airspace utilization. In their subsequent research, they considered the impact of the number of departure and arrival platforms in the airport on operations [30].

Cui et al. [31] designed a grid-type airspace structure and UAV arrival model based on graph theory based on their previous research by Quan [32] and Zeng et al. [33]. The paper analyzes the relationship among the area, quantity, and arrival capacity of single-access VTOL landing sites. Due to numerous route intersections, the model exhibits a complex control process, demanding high precision in UAV control.

Bertram and Wei [34] introduced a funnel-shaped airspace structure with concentric circles, utilizing fixed-wing UAVs continuously flying to complete the sorting process. Nevertheless, this approach neglects the hovering capability of UAVs, and the redundant approach phase may lead to more potential conflicts. Based on similar airspace structure designing ideas, Qu et al. provided a comprehensive discussion on the design of UAV departure and arrival areas from the perspective of operational rules. They employed the method of planning departure and arrival routes using continuous flying and waiting, proposing various terminal area layout methods [35,36].

Song et al. [37] expanded airspace structure types to a circular multi-layer funnel airspace structure for hovering multi-rotor UAVs, proposing the free path sequence-based approach method (SBA) and constraint path branch queuing approach (BQA). Optimal airspace radius calculation methods were developed for each. Subsequently, they combined these models to introduce the sequence-based approach with moving circles (SBAM) [38]. Further improvements led to the balanced branch queuing approach (BBQA), enhancing UAV navigable paths while ensuring safety with fixed-path airspace structures [39]. Based on the toroidal multilayer funnel-shaped airspace structure, Shao et al. [40] introduced the concept of an adaptive control system (ACS). Multiple functionally diverse intersections on the islands assist aircraft in joining or leaving concentric rings, facilitating multiple climb and descent segments in a free path. This highly structured airspace design offers a new direction for mitigating conflicts in mixed-operation departure and arrival but introduces a higher level of complexity. In line with these developments, the authors of this paper previously proposed a hybrid departure and arrival operation structure. This model was validated through simulation, demonstrating its safety and operational efficiency [41].

2.2. Works Relevant to Factors of UAV Fleet Operations

Operational factors related to vertiport capacity and efficiency have also been widely studied, mainly focusing on two aspects: the performance of the UAV fleet itself and operational rules and restrictions.

Restrictions of UAV fleets typically include UAV performance, aircraft type, and aircraft mix. Regarding UAV fleet performance, FAA [42] issued guidelines for constructing landing facilities tailored to aircraft with vertical takeoff and landing capability and a maximum takeoff weight of under 12,500 pounds, providing guidance on limitations and constructions for certain levels of vertiports. Yilmaz et al. proposed energy conservation and safety through angled approaches [43]. Vicencio et al. [44] discovered that the optimal method of energy-efficient path-planning is attained by flying at lower altitudes and employing a shallower descent. Another study observed a decrease in cruise efficiency with an elevation in cruise altitude [45]. Concerning fleet configuration, Pradeep et al. [26] introduced a set of mixed operational rules for both fixed-wing and multi-rotor heterogeneous drone fleets.

Regarding operational rules and restrictions, part of them lies in operational rules on the airspace side. German Aerospace Center (DLR) [46] presented the approach and departure task profiles of Volocopter 2X, elucidating the necessary airborne rules for these aircraft. Additionally, the sequencing rule is a crucial aspect of the system. Drawing on the concept of First-Come-First-Served (FCFS) in air transport [47], Pradeep et al. [26] implemented an enhanced FCFS scheduling strategy. This strategy ensures that even if the final aircraft in the fleet can arrive ahead of schedule, it contributes to increasing the airport’s throughput. Song et al. [38] integrated flight schedules into the considerations for sorting and sorting decisions, introducing two sorting strategies based on the deviation between actual and planned arrival times: early arrival and on-time arrival. Another part pertains to the limitations on the use of landing sites. Vascik and Hansman [20] analyzed the relationship between the number and layout of landing platforms, taxiways, and airport capacity within landing sites. Byeongseon and Hwang conducted simulation analyses of landing platform utilization and capacity differences under various landing site topologies [48] based on the design requirements for landing sites by the FAA and the European Union Aviation Safety Agency (EASA) [49].

In conclusion, the above-mentioned research teams have proposed various concepts for airspace structure design and its associated operational methods. They have also evaluated performance indicators, such as fleet operation capacity, under the coupling effects of different structures and operational methods. However, the above-cited works have not fully addressed some crucial issues in airspace design, such as determining the appropriate components of airspace structure and specific parameter settings. Furthermore, the understanding of the complex interplay between these parameters and how the parameters would collectively affect fleet operation capacity is worth exploring. The study of such issues is useful for modeling safe UAV fleet operations. The study associated with the capacity of UAV fleet operations is particularly relevant to future complex air traffic environments involving large-scale, high-density flights.

2.3. Contribution and Outline of the Paper

To answer the questions mentioned above, the relationship of each parameter in the airspace structure and their effects on the capacity of UAV fleet operations are investigated in the present work.

The present research contributes to three areas, as listed below:

A concept of adjustable parameters of airspace structure design is proposed for various flying paths;
From the perspective of air traffic management, the approach capacity of fleet operation under different airspace structures is evaluated and analyzed;
Explore how the structural changes in the airspace itself affect the operation of approaching UAVs and identify the key limitations for vertiport inbound capacity.

For the organization of the paper, Section 1 and Section 2 provide an overview of the research background and the relevant literature. In Section 3, the terminal airspace structure and operation concept are described. Section 4 presents the modeling of fleet operations with various constraints. Based on the developed airspace structure and operation constraints, Section 5 constructs a time-based algorithm for fleet operations. Empirical simulation results obtained are analyzed in Section 6. The results of fleet capacity are explained in Section 7, which concludes the work conducted and proposes future works.

3. Methodology for the Proposed Airspace Structure and Fleet Operation Concept

The fleet operation for UAVs is influenced by the configuration of vertiport airspace. The optimal airspace design is a research worth exploring. In this section, a conceptual structure of the airspace is proposed for the planning of the UAV flying in phase and provides applicable segmentation criteria based on operation requirements.

3.1. Proposed Airspace Structure

Due to the potential impact of UAV fleet operation factors on operational capacity, it is imperative to incorporate operational factors into the design of vertiport airspace structures. UAVs feature a vertical descent capability that simplifies a more straightforward approach procedure. However, before descending vertically, the UAV verifies if its position aligns above the landing pad through mechanisms or sensors such as GPS, visual positioning, Real Time Kinematic (RTK), and other technologies that are capable of self-position and position correction [50]. Therefore, the flight paths of UAVs involve several positioning points to ensure path accuracy and minimize the risk of conflicts caused by positional deviation [51]. A concept of UAV holding points (or stations) is then introduced in our airspace design to cover the technical and operational requirements outlined at the beginning of this section. It is worth mentioning that the holding point serves not only for positioning but also as a location for taking advantage of the character of hovering, which is energy efficiency and environmental friendliness [52]. The introduction of the holding point, in turn, addresses the need for safe and orderly movements in high-density fleet operations.

Although several airspace structures can be adopted, as discussed in Section 2.1, the funnel-shape airspace structure is considered in the present research without loss of generality. As illustrated in Figure 2, the overall funnel-shaped airspace structure for UAV fleet operations consists of three layers in concentric circles connecting by holding points, an approach point, and a landing pad. Note that the centers of these circles, the approach point, and the landing pad are all on the same vertical line. The number of UAV holding points in each respective layer can be arranged by changing the diameter of the layer. Such flexibility in positioning holding points is an advantage for the funnel-shaped multi-layer structure.

The layout of the three introduced layers is depicted in Figure 2. The outermost layer with the largest radius for arriving UAVs is referred to as the assembly layer, which acts as the connection between the terminal area and the airways flight path located in different directions. At the same altitude but with a smaller radius, there is a concentric circle referred to as the upper layer. Another layer with a lower altitude than that of the upper layer is introduced. This is the so-called lower layer for the descending UAVs. It is assumed that the holding points are evenly distributed along the circumference of each layer. An approach point (P_apr) below the lower layer is meant to allow a final positional adjustment of the UAV before its landing for touch-down.

3.2. Concept of Fleet Operations

Based on airspace structure, the fleet operation is promoted to direct arriving UAVs in a standard, orderly, and safe manner through sequential stages of movements until they reach the landing pad. According to the previous subsection, the approach procedure is segmented closely depending on the position of holding points, which are determined by the actual physical airspace structure rather than points of fixed locations.

As illustrated in Figure 2, every UAV in the fleet operation enters the airspace through the arrival phase, followed by the initial, intermediate, and final approach phases, before the landing and touchdown phases. It is worth mentioning that the lower layer and the approach point can be considered as a holding (or standby) position for UAV fleet operations, especially when a large number of UAVs are involved. In other words, both the lower layer and the approach point are not needed if there are only a few UAVs involved in the overall operation.

Details of the applicable segmentation criteria for the phases are outlined below:

Arrival phase: the phase starts when the UAV is scheduled to arrive at the terminal area according to the flight plan and ends when it reaches the arrival gates (points) on the assembly layer. The decision to determine arrival gates falls within the routing stage at airways, which is not subjected to vertiport terminal control. (Note that the process for UAVs entering from the terminal (waiting area) to the assembly is not considered in our analysis. Our analysis starts from the first UAV arrived at the assembly layer from the terminal outside.)

Approach phase: the approach phase consists of the Initial approach phase, Intermediate approach phase, and Final approach phase. Additionally, the endpoint of the Arrival phase is the beginning of the approach control process. The division principle of the approach phase is defined based on the position of layers and the procedure of movement characterized from the upper to lower layers.

Initial approach phase: UAVs’ horizontal moving phase at cruise speed starts from the assembly layer to the upper layer. Additionally, it is a fixed point-to-point horizontal connection for each UAV for the same ride.
Intermediate approach phase: UAVs’ descending phase from the upper to lower layer. It is characterized by multiple choices in trajectory selection generated by different starting and targeting holding points. The beginning point of the Intermediate approach phase depends on the selected target holding points of the Initial approach phase. If there are additional layers, UAVs’ movements, excluding those connecting with the first and bottom layers, fall within the Intermediate approach phase.
Final approach phase: UAVs ‘approaching phase from the lower layer to the approach point. During this phase, the process does not involve selecting different target moving points, as there is only one designated approach point. Therefore, there is no safety risk associated with conflicts due to multiple UAV flight paths.

Landing phase: This phase is for a UAV landing vertically from the approach point to the landing pad. Differentiating from other phases, consecutive interval separation between successive front and rear UAVs is expected to ensure time consumed for ground service of UAVs at the landing pad during the Touchdown phase.

3.3. Parameters of Airspace Structure and Operations in Stages

As stated in Section 3.1, the arrival flight path of UAVs relies on the way the airspace is structured. It is up to the layout of layers and holding points to decide how long the total flight time is, considering different ride of flight trajectories and hovering times. Generally speaking, adjusting each element comprising the airspace structure may have a potential influence on the operation capability of UAVs in the terminal area, including fleet operation capacity. Therefore, in this paper, we start from the variable components within the airspace structure as adjustable parameters (Figure 3) and explore the multifaceted effects that they have, individually or in combination, on the operational capacity of the UAV fleet.

The adjustable parameters in airspace structure that may affect the landing fleet operation capacity of the airspace are classified into two aspects: separation rules and structure dimensions.

Separation rules: safety distance separation among UAVs in the terminal control area, which is implemented jointly at the strategic and tactical levels. It is assumed that the arriving UAVs have a uniform UAV type, and all UAVs adhere to the same separation rules in this paper.

At the strategic level, lateral separation (s_spa) is applied to prevent potential conflict derived from the inadequate position-keeping capability of UAVs, so it is necessary to satisfy the demand for minimum separation in the pre-operational design of the airspace structure. Consequently, the number of holding points that can be laid on each layer has a maximum upper limit due to the lateral separation distance between the centerline of two adjacent holding points at the same layer.
At the tactical level, it is assumed that the UTM controller is subject to maintaining a safety separation (s_saf) from other UAVs to decrease conflict in operation, so the safety separation is applied as a constraint in the generation of an accessible path. Additionally, safety separation should change depending on multiple factors, such as the operating scenario, accuracy of navigation equipment, types and dimensions of UAVs, and performance of the UAVs, etc.

Structure dimensions: parameters regarding the variations in quantity, positioning, and layout of the physical airspace structure, including layers and holding points. To analyze the impact of structural changes on the operational capacity of the terminal area, the following parameters can be defined:

Variation in radius of layers. The radius (r_upr) of the upper layer and radius (r_lwr) of the lower layer. The radius of the layers is not only closely related to the size of the entirely terminal airspace but also serves as the basis of the number and layout of holding points.
Variation in the height of layers and approach point. Height of spacing (h_{upr_lwr}) between the upper and lower layer, height of spacing (h_{lwr_apr}) between the lower layer and approach point, and vertical distance (h_{apr_ldn}) between the approach point and landing pad. Additionally, the height of the assembly layer and upper layer is assumed to be set at a fixed height, as well as the ceiling height of the airspace.

4. Modelling of Fleet Operations with Various Constraints

Based on the presented airspace structure and fleet operation concept. This section introduces a fleet operation model with various constraints involving guidelines for UAV holding-point occupancy in different layers and rule-based UAV movement over different layers.

4.1. Guidelines of UAV Holding-Point Occupancy in Different Layers

Guidelines of UAV holding-point occupancy in different layers serve as fundamental constraints governing the movement of each UAV within and between phases, ensuring the continuity of the phase utilization and approach process.

In this research, once a UAV is assigned to an accessible target holding point, the previously located holding point is released. At almost the same time, the UAV occupies the following target point; thus, the point turns out to be unusable for other UAVs. In other words, although UAVs do not reach target points or enter layers, they are considered to have already procedurally occupied the target points during the heading time scale. This also implies that the current flight paths are exclusive, and subsequent UAVs are not allowed to closely follow the preceding UAV along the same path until the preceding UAV releases the target point.

From the principle of segment control, we can see that the total number of UAVs that can simultaneously stay in the entire terminal area is closely related to the number of holding points available. As illustrated in Figure 4, the number of holding points (p) can be determined as given by

p = \frac{π}{\sin^{- 1} (\frac{s_{spa}}{2 r})}

(1)

which is derived by virtue of Figure 4c, as given by

\sin (\frac{α}{2}) = \frac{s_{spa}}{2 r}

(2)

where r is the radius of each layer, while s_spa is the lateral separation specified according to safe separation guidelines. It is obvious that the total number of holding points according to the specified safe separation (s_spa) is determined by

p = \frac{2 π}{α}

(3)

which yields

\frac{α}{2} = \frac{π}{p}

(4)

It is important to note that the actual value of holding points (p) in the respective layer, defined by Equation (1), must be running down to a lower integer number.

The UAVs within the terminal area occupy multiple holding points at each respective layer. Therefore, holding points can be either available or occupied at different times. If a point has been targeted by a UAV, the point is considered allocated or occupied by the coming UAV. Hence, a holding point occupancy status matrix represents the occupancy usage relationship between holding points and UAVs at a specific moment, as given below.

Q_{asb} = {[\begin{matrix} q_{11} & \dots & q_{1 N} \\ ⋱ \\ ⋮ & q_{k i} & ⋮ \\ ⋱ \\ q_{K 1} & \dots & q_{K N} \end{matrix}]}_{K \times N}, q = \{\begin{cases} 1, occupied \\ 0, available \end{cases}

(5)

in which Q_asb is a matrix of size K rows by N columns, where K is the total number of holding points given at the assembly layer and N is the total number of arrival UAVs covered in the whole fleet operation. Note that the elements of Q_asb are binary variables (0 or 1) in different time instants. At a time instant t (hereafter omitted in the equation), the rows of matrix Q_asb in Equation (5) represent various holding points (arrival gates) in the assembly layer, while the columns represent the UAVs. For example, Q_asb (k,i) denotes the element in the kth row and ith column of the matrix, which signifies the occupancy relationship between the kth arrival gate (or holding point) in the assembly layer and UAV i. If Q_asb (k,i) = 1, it indicates that UAV i occupies arrival gate P_asb,k; otherwise, Q_asb (k,i) = 0 (arrival gate P_asb,k is not occupied).

By the similar representation, the holding point status matrices for other layers, approach point, and landing pad can be represented as Q_upr (L × N), Q_lwr (M × N), Q_apr (1 × N), Q_ldn (1 × N), etc. Thus, Q_upr (l,i), Q_lwr (m,i), Q_apr (1,i), and Q_ldn (1,i) represent, respectively, the occupancy relationships between the UAV i and the upper-layer holding point P_upr,l, the lower-layer holding point P_lwr,m, and the approach point and landing pad. Note that L and M indicate the total number of holding points at the upper and lower layers, respectively.

Next, we consider the UAV holding-point occupancy for different layers in fleet operation by following three basic guidelines. Guideline (i) ensures that the overall number of UAVs assigned to holding points in certain layers should be no less than the total number of UAVs that holding points can accommodate. Guideline (ii) ensures that one point is rigidly restricted to be occupied by only one UAV at a given time. Guideline (iii) ensures that every UAV is expected to occupy only one point at a given time instant.

(i)

For a specific layer

As defined in Equation (5), the total number of UAVs hovering or pre-assigned to each layer at any time instant does not exceed the number of holding points on that layer; the following equations are formulated using segmented functions:

\sum_{i = 1}^{N} \sum_{k = 1}^{K} Q_{asb} (k, i) \leq K (assembly layer)

(6)

\sum_{i = 1}^{N} \sum_{l = 1}^{L} Q_{upr} (l, i) \leq L (upper layer)

(7)

\sum_{i = 1}^{N} \sum_{m = 1}^{M} Q_{lwr} (m, i) \leq M (lower layer)

(8)

(ii)

For a specific holding point

As for every holding point, there can be at most one UAV at a time instant.

\{\begin{cases} \sum_{i = 1}^{N} Q_{asb} (k, i) = 0 or 1, {for arrival gate (point) P}_{asb, k} \\ \sum_{i = 1}^{N} Q_{upr} (l, i) = 0 or 1, {for holding point P}_{upr, l} \\ \sum_{i = 1}^{N} Q_{lwr} (m, i) = 0 or 1, {for holding point P}_{lwr, m} \end{cases}

(9)

(iii)

For a specific UAV

For every specific UAV, it can only occupy one holding point throughout the process. The following equations are the detailed expansion of guideline (iii) and are required to be satisfied:

(a): Arrival phase (UAV entering assembly layer):

$\sum_{k = 1}^{K} Q_{asb} (k, i) = \{\begin{cases} 1, UAV i occupy one arrival gate (or point) in assembly layer \\ 0, otherwise \end{cases}$

(10)

where k represents holding point k at the assembly layer. For UAV i, Q_asb(k,i) indicates the occupancy of the holding point P_asb,k by UAV i at the time instant. K is the total number of arrival points at the assembly layer. The summation in Equation (10) represents adding up every element in the ith column of matrix Q_asb. It implies that UAV i enters the terminal area at a certain time instant by using no more than one point from the arrival gate (or point) on the assembly layer.
If $\sum_{k = 1}^{K} Q_{asb} (k, i)$ equals 1, it signifies that UAV i completes the Arrival phase by occupying one certain gate at the time instant, and the status of other points for UAV i equals 0. Otherwise, value 0 suggests that UAV i either has not reached the terminal area at that time or has already completed the Arrival phase.
(b): Initial approach phase (UAV moving from assembly to upper layer):

$\sum_{l = 1}^{L} Q_{upr} (l, i) = 1, if \sum_{k = 1}^{K} Q_{asb} (k, i) = 0 UAV i occupies one holding point in the upper layer and releases the arrival gate (or point)$

(11)

where l represents holding point l at the upper layer. For UAV i, Q_asb(k,i) indicates the occupancy of the holding point P_asb,k by the UAV i at a specific time, and Q_upr(l,i) indicates the occupancy of the holding point P_upr,l by UAV i at a specific time. Again, L is the total number of holding points at the upper layer. The summation shown in Equation (11) represents adding up every element in the ith column of matrix Q_upr equals 1 when the summation of the element in the ith column of matrix Q_asb equals 0.
If Equation (11) is satisfied, it signifies that UAV i is allocated to the coordinated holding point P_upr,l at the upper layer and starts the Initial approach phase at the time instant. At the same time, the primary occupied arrival gate (or point) P_asb,k can get free. Moreover, Equation (11) is always valid throughout the entire time slot of the Initial approach phase.
(c): Intermediate approach phase (UAV descending from upper to lower layer):

$\sum_{m = 1}^{M} Q_{lwr} (m, i) = 1, if \sum_{l = 1}^{L} Q_{upr} (l, i) = 0 UAV i occupies one holding point in the lower layer and releases the upper layer holding point$

(12)

where m represents the holding point m at the upper layer. For UAV i, Q_upr(l,i) indicates the occupancy of the holding point P_upr,l by the UAV i at the time, and Q_lwr(m,i) indicates the occupancy of the holding point P_lwr,m by UAV i at the time instant. Again, M is the total number of holding points at the lower layer. The summation in Equation (12) represents adding up every element in the ith column of matrix Q_lwr equals 1 when the summation of the element in the ith column of matrix Q_upr equals 0.
If Equation (12) is satisfied, it signifies that UAV i is allocated to the appropriate holding point P_lwr,m of the lower layer and starts the Intermediate approach phase at the time instant. In the meantime, the primary occupied holding point P_upr,l at the upper layer can be released. Moreover, Equation (12) is always valid throughout the entire time slot of the Intermediate approach phase. Additionally, the equation also applies to the airspace structure of more than two layers.
(d): Final approach phase (UAV approaching from lower layer to approach point):

$Q_{apr} (1, i) = 1, if \sum_{m = 1}^{M} Q_{lwr} (m, i) = 0 UAV i occupies the approach point and releases the lower layer holding point$

(13)

For UAV i, Q_lwr(m,i) indicates the occupancy of the holding point P_lwr,m by the UAV i at the time, and Q_apr(1,i) indicates the occupancy of the approach point P_apr by UAV i at the time. Since there is only one approach point as the end node of the Final approach phase, Equation (13) represents the element in the ith column of matrix Q_apr equals 1 when the summation of the element in the ith column of matrix Q_lwr equals 0.
If Equation (13) is satisfied, it signifies that UAV i is allocated to the approach point P_apr and starts the Final approach phase at the time instant. In the meantime, the primary occupied holding point P_lwr,m at the lower layer is released. Moreover, Equation (13) is always valid throughout the entire time slot of the Final approach phase.
(e): Landing phase (UAV landing from approach point to landing pad)

$Q_{ldn} (1, i) = 1, if Q_{apr} (1, i) = 0 UAV i occupies the landing pad and releases the approach point$

(14)

For UAV i, Q_apr(1,i) indicates the occupancy of the approach point P_apr by the UAV i at the time, and Q_ldn(1,i) indicates the occupancy of the landing pad P_ldn by UAV i at the time. Since there is only one approach point and landing pad, there is a one-to-one correspondence between the approach point and the landing point. Equation (14) represents the element in the ith column of matrix Q_ldn equals 1 when the element in the ith column of matrix Q_apr equals 0.
If Equation (14) is satisfied, it signifies that UAV i is allocated to the landing pad P_ldn and starts the Landing phase at the time instant. In the meantime, the primary occupied approach point P_apr is released. Moreover, Equation (14) is always valid throughout the entire time slot throughout the Landing phase when the UAV vertically lands at a constant speed (normally less than cruise speed).
(f): Touchdown phase (UAV removed from landing pad)

$\sum_{k = 1}^{K} Q_{asb} (k, i) = 0, \sum_{l = 1}^{L} Q_{upr} (l, i) = 0, \sum_{m = 1}^{M} Q_{lwr} (m, i), Q_{ldn} (1, i) = 0, Q_{apr} (1, i) = 0$

(15)

These guidelines ensure that UAVs always move from top to bottom through holding points between neighboring altitudes, preventing abrupt altitude transitions. It is worth mentioning that these guidelines also restrict movements within the same layer.

4.2. Rule-Based Sequential UAV Movement over Different Layers

Further to the guidelines of UAV holding-point occupancy in different layers (stated in Section 4.1), this section introduces rule-based UAV movements for safe fleet operations.

Firstly, when multiple UAVs are positioned at the beginning of the same phase, standard sorting is required to ensure their safety and orderly operation. Secondly, UAVs should follow specific rules in the selection of movement paths for higher efficiency in the Intermediate approach phase. Additionally, maintaining a valid safety distance among multiple UAVs is crucial. Therefore, collision avoidance restrictions are incorporated into path planning for operation safety, with safety prioritized over efficiency in path selection. Lastly, a certain minimum time interval must be maintained between two UAVs landing successively on the landing pad for ground service.

As a consequence, four constraints depicted in Figure 5 were imposed in our analysis: sequencing constraint, movement constraint, de-conflict constraint, and consecutive service constraint. Details of these constraints are described as follows:

(i): Sequencing constraint (Figure 5a):

Considering the situation where more than one UAV needs to wait to enter the next position, the model advocates a sequencing strategy that prioritizes scheduling the UAV with the highest priority first, following a predetermined order. To this end, a sequencing constraint is proposed by combining FCFS with the initial flight plan (priority for UAV arriving at the terminal earlier in the flight plan). The constraint is designed to ensure an orderly sequential UAV fleet movement. It is worth mentioning that the sequencing requirements are to ensure operational order and minimize individual UAV waiting time during the phase, thereby improving operational capacity in the terminal area.

(ii): Movement constraint (Figure 5b):

When a UAV arrives at the holding point of the upper layer, the terminal traffic controller should make an assignment for its path to the lower layer. We propose a movement constraint to select an accessible target holding point for UAVs descending at the beginning of the Intermediate approach phase. The selection of a target lower holding point involves addressing a multiple-to-multiple choices problem.

To illustrate the spatial relationship between UAVs and holding points, a three-dimensional coordinate system is established with the landing pad as the origin. If the UAV i arrives at the holding point P_upr,l (x_upr,l, y_upr,l, z_upr,l) in the upper layer, the movement constraint determines that the UAV always selects the target point following the rule of distance from close to far. It is worth mentioning that all holding points listed as movement targets must be in an available and allowable state.

As shown in Figure 5b, the UAV at the holding point P_upr,l of the upper layer will fly towards the lower layer. The distance of the descent path from the holding point P_upr,l of the upper layer to the selected holding point P_lwr,m (x_lwr,m, y_lwr,m, z_lwr,m) of the lower layer is given by

\begin{array}{l} s_{l_m} = ‖(x_{upr, l}, y_{upr, l}, z_{upr, l}) - (x_{lwr, m}, y_{lwr, m}, z_{lwr, m})‖ \\ = \sqrt{{(x_{upr, l} - x_{lwr, m})}^{2} + {(y_{upr, l} - y_{lwr, m})}^{2} + {(z_{upr, l} - z_{lwr, m})}^{2}} \end{array}

(16)

where (x, y, z) represents the coordinates of the respective holding points.

The movement constraint ensures that the UAV always selects the nearest allowable holding point while prioritizing safety conditions, aiming to minimize the value of s_l_{_m}.

(iii): De-conflict constraint (Figure 5c):

According to the preceding discussion, when selecting a descent path, UAVs always prioritize unoccupied or untargeted holding points in the lower layer. Additionally, these points are sorted as potential targets based on their distance from near to far in the flight path. However, given the safety requirement of the minimum separation among multiple simultaneous descent UAVs in a structure without fixed paths, it is crucial to ensure the absence of conflicts with other UAVs when planning descent routes.

The UAV already assigned downward to the lower layer is assumed to keep the allocated movement trajectory, while the following UAVs are responsible for searching for a target holding point, at once maintaining separation from other UAVs before movement. At every moment, it is essential to ensure that the distance between any two UAVs is greater than the safety separation distance, which can be represented in a mathematical model using an inequality. For example: s_{i_j}(t) ≥ s_saf in the mathematics model.

\begin{array}{l} s_{i_j} (t) = ‖(x_{i} (t), y_{i} (t), z_{i} (t)) - (x_{j} (t), y_{j} (t), z_{j} (t))‖ \\ = \sqrt{{(x_{i} (t) - x_{j} (t))}^{2} + {(y_{i} (t) - y_{j} (t))}^{2} + {(z_{i} (t) - z_{j} (t))}^{2}} \end{array}

(17)

Here, distance s_{i_j}(t) represents the actual distance between UAVs i and j ({i, j}∈{1, ⋯, N_u}, i ≠ j) at time t. The inequality ensures that this distance is always greater than or equal to the specified safety separation distance. Moreover, the limitation should be adhered to by any pair of UAVs.

Therefore, under the de-conflict constraint, UAVs may not choose the nearest holding point during path planning, with safety always taking precedence, especially in the Intermediate approach phase. Thus, the rerouting required for conflict avoidance results in additional flight time to reach the next layer, meaning a longer trajectory rather than choosing the point of least distance. If none of the lower holding points can satisfy the de-conflict requirements, the UAV is left with no option but to continue hovering and waiting for the next opportunity.

(iv): Consecutive service constraint (Figure 5d)

Consecutive service constraint is mainly a Landing phase limitation, informed by operational experience, causing consecutive service separation of two UAVs arriving in succession, transitioning from the approach point to the landing pad, emphasizing ground service time. UAVs that arrive successively are expected to slide out of the pad range after landing, with a specific constraint related to pad separation serving as a critical element of ground service time t_g.

Looking forward, there is ongoing consideration for the potential future implementation of turbine spacing. This involves evaluating how the spatial arrangement and separation requirements for the turbines of UAVs during Landing phase operations can be optimized to enhance overall operational efficiency and safety in the terminal area.

5. Time-Based Algorithms for Fleet Operations over Proposed Airspace

This section develops algorithms in time functions for UAV fleet operation according to the constraints and guidelines presented in Section 4. The time-based algorithms are developed, from phase to phase, throughout the fleet operations, as implemented according to the flowchart outlined in Figure 6.

5.1. Required UAV Flying Time in Different Stages

The required UAV flying time is advanced to capture the chronological flying time details of the UAV’s journey through arrival terminal airspace, encompassing phases such as the Arrival phase, Initial approach phase, Intermediate approach phase, Final approach phase, Landing phase, and Touchdown phase. This definition of flying time slots serves as inputs for calculating both time and trajectory information as UAVs descend from the top to the bottom, which is further calculated in the operation execution model, as illustrated in Figure 7.

(i): Arrival phase:

Once an available arrival gate (point) appears in the assembly layer, any UAV waiting on the route is considered to access the assembly layer immediately and occupy the arrival gate (or point). Therefore, the time (t_arr,asb,i) for UAV i to reach the assembly layer is calculated by adding the waiting time on the route due to the busy terminal to the scheduled arrival time (t_str,i) according to the flight plan. It is worth mentioning that UAVs entering the terminal area are expected to directly access the assembly layer unless all arrival gates are occupied, thus leading to potential deviations from the planned and actual arrival times.

(ii): Initial approach phase:

The arrival gates correspond one-to-one with the holding points of the upper layer. Therefore, when the corresponding holding point of the upper layer is occupied, UAV i should hover and wait for a while at the arrival gate until it receives a movement permit and releases the arrival gate. The Initial approach phase demands the UAV to maintain a constant speed of horizontal flight path at the cruise altitude for a duration (t_{fly,asb_upr}) to the upper layer holding points.

(iii): Intermediate approach phase:

Unlike in other phases, there is no fixed correspondence between upper and lower holding points during the Intermediate approach phase. When planning its path, each UAV faces the decision of choosing a target lower holding point, which is a manifestation of the movement constraint. Therefore, there are differences in the journey of each UAV during the Intermediate approach phase. The path ride (s_{upr_lwr,i}) of UAV i during the Intermediate approach phase, from the upper to lower layer, is not fixed. The UAV travels for a time slot (t_{fly,upr_lwr,i}) at a constant speed vc before reaching the lower holding point.

(iv): Final approach phase:

In the Final approach phase, only one approach holding point is designated, resulting in a many-to-one correspondence in terms of target point selection. Multiple hovering UAVs waiting at holding points of the lower layer need to hover and queue to ensure that they fly toward the approach point sequentially according to the sequencing constraint. UAV i departs from the lower holding point and follows the same path ride (s_{lwr_apr}) for a duration (t_{fly,lwr_apr}) to reach the approach point.

(v): Landing phase:

The landing phase, set based on the vertical landing characteristic of UAVs, is restricted to a one-to-one matching relationship during landing. Vertical landing flight travels for a duration (t_{fly,apr_ldn}) after obtaining clearance. Considering the necessary ground service time (t_g) after the UAV lands, the landing pad will continue to be occupied until the UAV taxis out or leaves the landing area. This period is referred to as the ground service occupation time, regulated by the consecutive service constraint.

Each UAV’s journey from arrival outside the terminal area to waiting for arrival and executing six phases until leaving the landing pad is depicted in the self-derived operational process, as illustrated in Figure 8. It is worth noting that the movement of each individual UAV is governed by constraints and guidelines, following time-based algorithms.

5.2. Fleet Operations Incorporating Various Constraints

The fleet operations, incorporating various constraints, continue to be built upon the phased approach characteristics of UAVs. At each stage of the approach, UAVs execute commands such as hover and movement, all guided by fleet operations incorporating various constraints. This section utilizes a temporal framework to articulate the operational process of UAVs. Based on required UAV flying time in different stages, fleet operations incorporating various constraints capture the intricacies of UAVs throughout different phases, providing a detailed depiction of how they navigate through the predefined operational stages and how they interact with other UAVs.

The conditions of the UAV occupancy situation at a holding point at every time instant are listed below:

Q_{asb} (k, i) = \{\begin{cases} 1, if UAV i {is assigned to arrival gate P}_{asb, k} in assembly layer at time t (t = t_{arr, asb, i}) \\ 0, otherwise \end{cases}

(18)

Q_{upr} (l, i) = \{\begin{cases} 1, if UAV i {is assigned to holding point P}_{upr, l} in upper waiting layer at time t (t = t_{arr, upr, i}) \\ 0, otherwise \end{cases}

(19)

Q_{lwr} (m, i) = \{\begin{cases} 1, if UAV i {is assigned to holding point P}_{lwr, m} in lower waiting layer at time t (t = t_{arr, lwr, i}) \\ 0, otherwise \end{cases}

(20)

Q_{apr} (1, i) = \{\begin{cases} 1, if UAV i {is assigned to approach point P}_{apr} at time t (t = t_{arr, apr, i}) \\ 0, otherwise \end{cases}

(21)

Q_{ldn} (1, i) = \{\begin{cases} 1, if UAV i {is assigned to landing pad P}_{ldn} at time t (t = t_{arr, ldn, i}) \\ 0, otherwise \end{cases}

(22)

As far as time is concerned, Q_asb(k,i) (t = t_arr,asb,i), Q_upr(l,i) (t = t_arr,upr,i), Q_lwr(m,i) (t = t_arr,lwr,i), Q_apr(1,i) (t = t_arr,apr,i) and Q_ldn(1,i) (t = t_arr,ldn,i), respectively, signify the actually occupies point when UAV reaches each phase, the time in parentheses are omitted in subsequent sections.

The time node of the UAV in each phase mainly consists of the following four parts: arrival time, hover time, departure time, and flying time. Moreover, both the hover time and flying time are closely related to various constraints in fleet operation.

(i): Arrival phase:

For the arrival of UAV i, the initial flight plan informs the planned arrival time of the terminal area, which is the expected arrival time to reach the boundary of the assembly layer. However, some UAVs will be rejected from entering the terminal region since flow control is required until moving clearance is received from the air traffic controller of the vertiport, so we obtained an adjusted time of actual arrival. Thus, the actual arrival time (t_arr,asb,i) at the assembly layer of UAV i can be calculated by adding the deviation time (t_wtn,str,i) caused by overload to its scheduled time (t_str,i) of arrival in the flight plan, as given by

t_{arr, asb, i} = t_{str, i} + λ_{i j} t_{wtn, str, i}

(23)

in which

λ_{i j} = \{\begin{cases} 1, & Q_{asb} (k, j) = 1, t = t_{arr, asb, j} \\ 0, & e l s e \end{cases}, i, j \in {1, \dots, N}

(24)

t_{wtn, str, i} = t_{dpt, asb, j} - t_{str, i}

(25)

where t_str,i in Equation (23) represents the cumulative waiting duration for UAV i outside the terminal region, and λ_ij in Equation (24) is a decision index indicating the priority relationship between two UAVs when sequencing outside the terminal. t_wtn,str,i in Equation (25) represents the waiting time of UAV i outside the terminal, resulting from the sequencing constraint as it occurs subsequent to UAV j. t_dpt,asb,j also means the time when UAV j departures the assembly layer.

It is worthwhile to note that if all arrival gates (or points) at the assembly layer are occupied and the arrival gate P_asb,k, which is the closest to being released, is currently occupied by UAV j, UAV i needs to wait until it is released for usage. If there is an available arrival gate (or point) for UAV i to occupy, no more waiting time exists during the phase, which is also applicable to other phases.

(ii): Initial approach phase:

Similarly, UAVs will also experience increased waiting times due to full loads in the next layer, as well as the approach point and landing pad. Thus, the actual departure time (t_dpt,asb,i) at the upper layer of UAV i can be calculated by adding the waiting time (t_wtn,asb,i) at the arrival gate to the arrival time (t_arr,asb,i) of assembly layer, as given by following equations:

t_{dpt, asb, i} = t_{arr, asb, i} + η_{i j} t_{wtn, asb, i}

(26)

in which

η_{i j} = \{\begin{cases} 1, & Q_{upr} (l, j) = 1, t = t_{arr, asb, i} \\ 0, & e l s e \end{cases}, i, j \in {1, \dots, N}

(27)

t_{wtn, asb, i} = t_{dpt, upr, j} - t_{arr, asb, i}

(28)

(iii): Intermediate approach phase:

Where t_wtn,asb,i in Equation (26) represents the cumulative waiting duration for UAV i at the assembly layer, and η_ij in Equation (27) is a decision index indicating the priority relationship between two UAVs when sequencing at the assembly layer. As for t_wtn,asb,i in Equation (28) represents the waiting time of UAV i at the assembly layer, resulting from the sequencing constraint as it occurs subsequent to UAV j. Also, t_dpt,upr,j means the time when UAV j departures the upper layer.

The actual departure time (t_dpt,upr,i) at the lower layer of UAV i can be calculated by adding the hovering time (t_wtn,lwr,i) at the upper layer to the actual arrival time (t_arr,upr,i) of the upper layer, as given by following equations:

t_{dpt, upr, i} = t_{arr, upr, i} + δ_{i j} t_{wtn, upr, i}

(29)

in which

δ_{i j} = \{\begin{cases} 1, & Q_{lwr} (m, j) = 1, t = t_{arr, lwr, i} \\ 0, & e l s e \end{cases}, i, j \in {1, \dots, N}

(30)

t_{wtn, upr, i} = t_{dpt, upr, j} - t_{arr, upr, i}

(31)

where t_wtn,lwr,i in Equation (29) represents the cumulative waiting duration for UAV i at the upper layer, and δ_ij in Equation (30) is a decision index indicating the priority relationship between two UAVs when sequencing at the upper layer. t_wtn,upr,i in Equation (31) represents the waiting time of UAV i at the upper layer, resulting from the sequencing constraint as it occurs subsequent to UAV j. t_dpt,lwr,i is also the time when UAV j departures the lower layer.

(iv): Final approach phase:

The actual departure time (t_dpt,apr,i) at the approach point of UAV i can be calculated by adding the hovering time (t_wtn,apr,i) at the lower layer to the actual arrival time (t_arr,lwr,i) of the lower layer, as given by following equations:

t_{dpt, apr, i} = t_{arr, lwr, i} + φ_{i j} t_{wtn, apr, i}

(32)

φ_{i j} = \{\begin{cases} 1, & Q_{apr} (1, i) = 1, t = t_{arr, lwr, i} \\ 0, & e l s e \end{cases}, i, j \in {1, \dots, N}

(33)

t_{wtn, apr, i} = t_{dpt, apr, j} - t_{arr, lwr, i}

(34)

where t_wtn,apr,i in Equation (32) represents the cumulative waiting duration for UAV i at the lower layer, and φ_ij in Equation (33) is a decision index indicating the priority relationship between two UAVs when sequencing at the lower layer. t_wtn,apr,i in Equation (34) represents the waiting time of UAV i at the lower layer, resulting from the sequencing constraint as it occurs subsequent to UAV j. t_dpt,apr,j also means the time when UAV j departures the approach point.

(v): Landing phase:

The actual departure time (t_dpt,apr,i) at the landing pad of UAV i can be calculated by adding the ground service time (t_g) at approach time to the actual arrival time (t_arr,ldn,i) of the approach point, as given by following equations:

t_{dpt, apr, i} = t_{arr, ldn, i} + t_{g}

(35)

By inputting various parameters related to the airspace structure of the vertiport, we can obtain the fleet operation capacity for different airspace structures. Specifically, Figure 9 illustrates the input (parameter of airspace), output (capacity in given time duration), and process of the fleet operation accomplished by numerous UAVs. This illustration provides a holistic understanding and analysis of how various airspace structure parameters affect operation capacity.

6. Simulation and Analysis of Results with Different Dimensions

With the introduction of airspace structure and fleet operation concept in Section 3, the guidelines and constraints specified in Section 4, on the scheme with time-based algorithms presented in Section 5, we can now investigate the effects of airspace structure dimensions (i.e., radius and height) on the capacity of UAV fleet operations.

6.1. Set-Up for Case Simulation

Ranges of the required airspace structure dimensions used in the following simulation are listed in Table 1. The 90 m flight altitude of UAVs is assumed to follow airspace usage guidelines and available communication ranges of 4G networks. In addition, the vertical and horizontal safe separation are assumed to be 10 m and 20 m, respectively. Furthermore, the vertical height between the approach point and the landing pad is fixed at 20 m.

Next, the values of the velocities (v_c and v_v) defined in Figure 7 are required for the simulation. The cruise velocity (v_c) is assumed to be 3 m/s, whereas the vertical velocity (v_v) is set to be 2 m/s. To better focus on analyzing the impact of airspace structures, the ground service time (t_g) is simplified to 1 s.

A capacity chart illustrated in Figure 10 is used to present the results of UAV fleet capacity with different airspace structure dimensions (i.e., radii and heights). For clarity, the simulation results are presented in grouping to provide insight into how the variations in structure dimensions will affect the fleet capacity. The legend of the grouping with respect to given heights is listed next to the chart in Figure 10.

6.1.1. Variation in Radii (with Fixed Heights)

Simulated cases with different pairs of layer radii are systematically categorized into two main groups: cases with one holding point for at least one layer and cases with multiple holding points.

(i)

Cases with r_lwr = 0 or r_upr = 0 (one holding point for at least one layer).

(a): Cases with r_lwr > 0, r_upr = 0 (one holding point at the upper layer).
When the radius of the upper layer is set to 0 m, the airspace structure adopts a spindle-shaped configuration characterized by a single holding point on the upper layer and evenly spaced holding points along the outer boundary of the lower layer.
(b): Cases with r_upr > 0, r_lwr = 0 (one holding point at the lower layer).
When the radius of the lower layer is set to 0 m, the airspace structure adopts an elongated funnel-shaped configuration characterized by a single holding point on the lower layer and evenly spaced holding points along the outer boundary of the upper layer. However, the higher starting altitude for vertical descent imposes relatively higher precision requirements on operation.
(c): Cases with r_upr = 0, r_lwr = 0 (one holding point at both upper and lower layers).
When there is only one holding point for both the upper and lower layers, the arrival flight trajectory of the UAV follows a straight-line vertical descent pattern. This airspace structure imposes higher demands on airspace clearance conditions, particularly at the upper layer, making it suitable for temporary vertiports with fewer ground obstacles.

(ii)

Cases with r_lwr ≠ 0 and r_upr ≠ 0 (multiple holding points at both layers).

(a): Cases with r_upr < r_lwr, r_upr ≠ 0.
The inverted conical structures are distinguished by a design where the upper layer’s radius is smaller than the lower layer’s. This type of airspace layout is relatively unusual and not extensively implemented in current practices, but it holds potential for scenarios that might necessitate concurrent inbound and outbound operations in the future.
(b): Cases with r_upr > r_lwr, r_lwr ≠ 0.
The funnel-shaped airspace structure is widely adopted as the prevailing design approach. Within this configuration, particular attention should be given to the maneuverability of UAVs and the range of descent gradients available.
(c): Cases with r_upr = r_lwr, r_lwr ≠ 0.
The cylindrical structure features equal radii for both the upper and lower layers, resembling the terminal zone boundaries in commercial aviation.

6.1.2. Variation in Heights (with Fixed Radii)

According to the size relations between the upper and lower layers, the lower layer and the approach point, the variation in height is hence divided into three scenarios: h_{upr_lwr} > h_{lwr_apr}, h_{upr_lwr} = h_{lwr_apr}, h_{lwr_apr}, h_{upr_lwr} < h_{lwr_apr}. The capacity results for height variations are represented in multiple diagrams in Figure 10.

6.2. Detailed Results and Discussion

Fleet operation capacity is an important indicator when designing the airspace in the terminal area of a vertiport. When the number of UAVs in the fleet exceeds the standard range that the airspace can withstand, these exceeding UAVs will be rejected to land, which in turn causes flight delays and overload in airways with safety hazards. Thus, the fleet operation capacity is undoubtedly an important index for evaluating the structure of the airspace in the terminal area. In this paper, the maximum number of UAV landings within the 1200 s is used to denote the fleet operation capacity.

The operation capacity results are expressed as integer values in Figure 11. It is worth mentioning that due to variations in UAV flying times arising from different airspace structures, there are differences in the time nodes of the last landing UAV before the end of 1200 s. Consequently, the subsequent landing UAV differentiated in phases, as illustrated in Table A1, Appendix A.

For a comprehensive examination of how the airspace structure influences operational capacity, this section utilizes the shortest flying path and time for each phase as examples, as illustrated in the figures below (cases with Figure 11b,d,e), employing arrowed segments for visual representation.

(i)

Cases with r_lwr = 0 or r_upr = 0 (one holding point for at least one layer):

Starting with the scenario where the layer radius of either the upper or lower layer is set to 0 m, the detailed results are analyzed based on cases involving changes in either the radius alone or the combination of heights alone. Additionally, we provide further elucidation on specific results.

(a)

Cases with r_lwr > 0, r_upr = 0:

It can be observed in Figure 12 that the fusiform structure airspace structure exhibits a significantly smaller capacity compared to other types of airspace structures, with a relatively small capacity ranging from 31 to 33 UAVs.

(1): The data from Figure 12 clearly indicate that the flying time for the Initial approach phase from the assembly layer to the upper layer is relatively long, spanning 33.33 s. Therefore, when the preceding UAV leaves the lower layer holding point, the subsequent UAVs have not yet reached the upper layer holding point, resulting in wasted time during the Intermediate approach phase between the upper and lower holding points. Therefore, the Initial approach phase emerges as the primary limitation restricting the capacity of this airspace structure. As shown in Figure 12, there is a slight decreasing trend in the capacity of the airspace structure as the radius of the lower layer increases. As the radius of the lower layer gradually increases, both the flight distances of the Intermediate approach phase and the Final approach phase gradually also increase. Consequently, the total flight time for the first UAV is extended, and the landing time intervals for subsequent UAVs remain limited by the Initial approach phase, resulting in a slight reduction in capacity.
(2): By comparing the three cases illustrated in Figure 12, it becomes evident that an increase in height, resulting in longer flight distances for these phases, leads to a decrease in capacity. Conversely, a decrease in flight distance corresponds to an increase in capacity, consistent with the analysis mentioned above. Additionally, as the height of the lower layer gradually increases, the flight times of the Intermediate approach phase and Final approach phase will also vary.
(3): When both the radius and height of the lower layer change, resulting in the flight distance of either the Intermediate approach phase or the Final approach phase gradually exceeding that of the Initial approach phase, the primary limitation on fleet operation capacity will shift accordingly. In the scenarios corresponding to Figure 12e, when the radius of the lower layer reaches 90 m, the flight distance of the Final approach phase extends to 103 m, with a corresponding flying time of 34.32 s. These values now exceed the horizontal flight distance of 100 m and the flying time of 33.33 s in the Initial approach phase. Consequently, the time interval between consecutive UAVs increases further, becoming a critical limitation on fleet operation capacity. Additionally, considering the combined effect of the increased total flight time of UAVs, the airspace inbound capacity decreases to 31 UAVs.

(b)

Cases with r_upr > 0, r_lwr = 0:

It can be observed in Figure 13 that the elongated funnel structure can achieve a larger capacity compared to the fusiform structure.

It can be observed that when the radius of the upper layer r_upr = 10 m, the fleet operation capacity gradually decreases with the increasing height of the lower holding point. When the radius of the upper layer is 20 m ≤ r_upr ≤ 40 m, the fleet operation capacity first increases and then decreases. When the radius of the upper layer is r_upr ≥ 50 m, the fleet operation capacity continuously increases.

(1): It can be observed from Figure 13b that, with the gradual increase in the radius of the upper layer, the fleet operation capacity significantly decreases. With a larger radius of the upper layer, the duration of the Intermediate approach phase extends. Hence, when the preceding UAV completes the Final approach phase and arrives at the approach point, the UAV moving from the upper holding point to the lower holding point has not yet arrived. Consequently, this situation leads to a wastage of the Final approach phase without any other UAV utilizing it, thus emerging as a critical limitation for capacity improvement. As the radius of the upper layer gradually increases, the flight distance of the Intermediate approach phase also increases. This widening of the flight distance results in longer time intervals between successive approaching UAVs, thereby reducing the overall operation capacity.
(2): When the radius of the upper layer r_upr = 10 m, there are fewer holding points in the upper layer, specifically two points. Thus, the flight distance of the Initial approach phase becomes longer, leading to increased flight time for UAVs’ Initial approach phase. As the two UAVs hovering in the upper layer release lower layer holding points and approach towards the approach point in the sequence, the UAVs descending from the assembly layer to the upper layer have not yet arrived. Hence, this situation becomes a limitation for capacity improvement. As the height of the lower layer gradually increases (with h_{upr_lwr} decreases and h_{lwr_apr} increases), the flight distance of the Final approach phase extends, surpassing that of the Initial approach phase. Consequently, the Final approach phase emerges as the significant limitation, leading to a widening of the time gap between consecutive UAVs during approaching, which subsequently causes the capacity to initially stabilize and then decrease.
(3): When the radius of the upper layer is 20 m ≤ r_upr ≤ 40 m, with the increase in the height of the lower layer, the flight distance of the Intermediate approach phase gradually decreases, while that of the Final approach phase gradually increases. The limitation shifts from the Intermediate approach phase to the Final approach phase. It is noteworthy that when the height (h_{lwr_apr}) between the approach point and lower layer is increased from 40 m to 50 m (with an upper layer radius of 40 m), the flight time of the Intermediate approach phase, as the limitation, is exactly equal to the flight time of Final approach phase when it becomes a limitation. Therefore, the capacity remains the same. However, once the limitation shifts to the Final approach phase, the increase in the height of the lower layer will widen the time interval between successive UAVs during the approach, leading to a decrease in capacity once again.
(4): When r_upr ≥ 50 m, the flight distance of the Intermediate approach phase is the longest among all phases. This elongated distance requires UAVs to spend the longest time transitioning from the upper layer to the lower layer, thereby becoming the primary limitation for capacity improvement. However, as the height of the lower layer increases, the flight distance of the Intermediate approach phase gradually decreases, leading to a reduction in the time interval between successive UAVs during the approach. The reduction in time intervals will increase the capacity of the fleet operation.

(c)

Cases with r_upr = 0, r_lwr = 0:

As shown in Figure 14, when both the upper layer radius and the lower layer radius are 0 m, the airspace structure takes the form of a straight-line vertical descent.

The limitation lies in the 33.33 s flight time of the Initial approach phase, which imposes a significant gap between consecutive UAVs, hampering efficient airspace utilization and limiting the fleet operation capacity to a minimum of 33 UAVs.

(ii)

Cases with r_lwr ≠ 0 and r_upr ≠ 0 (multiple holding points at both layers).

In scenarios where both the upper and lower layer radius are greater than 0 m, the detailed results are analyzed based on cases involving changes in either the radius alone or the combination of heights alone. Additionally, we provide further elucidation on specific results.

(a)

Cases with r_upr < r_lwr, r_upr ≠ 0:

When the radius of the upper and lower layer r_upr < r_lwr, r_upr ≠ 0 m, the airspace structure takes the form of an inverted conical structure. Compared to the fusiform structure and straight-line descent structure, this configuration results in a certain improvement in fleet operation capacity, as shown in Figure 15.

(1): As illustrated in Figure 15b, when the radius of the lower layer is constant, and the radius of the upper layer increases continuously, there is a slight increase in fleet operation capacity.
Specifically, when the upper layer radius r_upr = 10 m, there are fewer upper holding points (only two holding points). In this situation, the trend of capacity is similar to that of the elongated funnel structure. It is primarily caused by the long flight time in the Initial approach phase, resulting in a significantly limited fleet operation capacity.
While the upper layer radius r_upr > 10 m, the upper layer can accommodate multiple UAVs hovering at the same time, and the Initial approach phase is no longer a limitation for fleet operation capacity. However, the extended flight distance from the lower holding points to the approach point imposes a longer flight time in the Final approach phase, which serves as the primary limitation for fleet operation. Thus, as the radius of the upper layer expands, the flight distances in the Initial approach and Intermediate approach phases decrease, thereby reducing the total flight duration of the first UAV in the fleet and leading to a slight increase in capacity.
(2): When the upper layer radius is fixed, and the lower layer radius continuously increases, the fleet operation capacity significantly decreases. In detail, as the radius of the lower layer increases, the flight distance of the Final approach phase also increases, leading to a longer flight time. Therefore, when the preceding UAV leaves the landing pad, the subsequent UAVs have not yet reached the approach point. Since there is only one approach point, it becomes a limitation for capacity improvement. Consequently, the widened time intervals between successive approaching UAVs result in reduced operational capacity.
It is noteworthy that when the lower layer radius r_lwr increases to 90 m, the Final approach phase (same flight time for all UAVs) becomes the limitation, resulting in a capacity similar to the fusiform structure. Additionally, when the upper layer radius r_lwr = 10 m, similar to the structure of an inverted conical funnel, there are fewer upper holding points, and the flight time in the Initial approach phase is greater than that in the Final approach phase. Thus, under the limitation of the Initial approach phase, the capacity is very small. However, when the upper layer radius r_lwr > 10 m and there are more upper layer holding points, the Initial approach phase is no longer a limitation.
(3): By comparing the three cases illustrated in Figure 15, as the height (h_{lwr_apr}) between the approach point and lower layer continuously increases, the flight time in the Final approach phase will also increase. When the Final approach phase is already the limitation before the height increases, raising the height of the lower holding points will widen the time intervals between successive approaching UAVs. However, if the Final approach phase is not the primary limitation before the height increase, raising the height may introduce a new limitation, which manifests as increased flight time in the Final approach phase. Additionally, an overall increase in flight distance under the existing limitation finally leads to a gradual reduction in fleet operation capacity and vice versa.

(b)

Cases with r_upr > r_lwr, r_lwr ≠ 0:

When r_upr > r_lwr, r_lwr ≠ 0 m, the airspace structure takes on a funnel-shaped structure. Compared to the inverted conical structure, it offers greater capacity, as shown in Figure 16.

(1): As shown in Figure 16b,d,e, when r_lwr is fixed and r_upr increases, the fleet operation capacity remains unchanged for all values except when r_lwr = 10 m, where the capacity gradually decreases. When the lower layer radius r_lwr = 10 m, and there are only two holding points in the lower layer, the capacity trend remains consistent, then increases before decreasing with further changes. In scenarios where the upper layer radius is small, the Final approach phase exhibits the longest flight time among all phases, thus limiting the operation capacity. Even with an increase in the radius of the upper layer, the landing time intervals for each UAV are still influenced by the limitation of the Final approach phase, resulting in no change in capacity trend. However, in scenarios where a larger radius for the upper layer leads to the extended flight time of the Intermediate approach phase, the situation becomes different. Specifically, when the preceding UAV leaves the approach point and moves to land, the UAV at the upper holding point has not yet arrived. Consequently, the Intermediate approach phase becomes the limiting factor affecting capacity. Thus, with the continued expansion of the radius of the upper layer, the interval between the first and subsequent UAVs increases accordingly, resulting in a gradual decrease in capacity. It is worth noting that during the process of increasing the upper layer radius from small to large, a temporary increase in capacity is observed, as shown in Figure 16d. In this figure, the condition corresponding to r_lwr = 10 m and r_upr increasing from 30 m to 40 m illustrates this trend. This occurs because the reduction in the Initial approach phase is greater than the increase in the Intermediate approach phase, and the total flight time of a single UAV decreases, resulting in a brief increase in capacity.
When the lower layer radius r_lwr > 10 m, and the lower layer can accommodate many UAVs for hovering, the Intermediate approach phase is no longer a limitation for capacity enhancement. The limitation for all airspace structures is the Final approach phase. Therefore, with the increase in the upper layer radius, the capacity remains almost unchanged.
(2): When r_upr is fixed (except in the case when r_lwr = 10 m) and r_lwr continuously increases, the fleet operation capacity significantly decreases.
When r_lwr > 10 m, with the increase in the lower radius, the flight time of the Final approach phase, which is the limitation, gradually increases, leading to an expansion of the interval between the preceding and following UAVs during landing. Therefore, the capacity decreases significantly.
When r_lwr = 10 m and 70 m < r_upr < 90 m, the trend is inconsistent with the above, as shown in Figure 16b. The expansion of the upper layer radius triggers a shift in limitation from the Final approach phase to the Intermediate approach phase. It is worth mentioning that when the lower layer holding radius (r_lwr) increases to 20 m, the number of holding points increases, and the Intermediate approach phase no longer serves as the key limiting factor. Moreover, the impact of the expanded Final approach phase, now serving as the key limiting factor, is smaller than the impact of the Intermediate approach phase, which was previously the key limiting factor, on the interval between consecutive UAV landings. As a result, this leads to a temporary increase in fleet operation capacity.
(3): By comparing the three cases illustrated in Figure 16, a gradual reduction in capacity is represented as the height (h_{lwr_apr}) between the lower layer and approach point increases. When the Final approach phase becomes the limitation, as mentioned earlier, the continuous increase in h_{lwr_apr} will result in an expanded time interval between two consecutive UAVs. However, in cases where the Final approach phase is not the limitation, the increase in h_{lwr_apr} may gradually decrease capacity in two ways: firstly, by making the flight time of the Final approach phase the primary limiting factor, and secondly, by increasing the total flight duration for each UAV along the trajectory. In summary, the impact of altitude on capacity is still realized through its influence on the flight distance of each phase and vice versa.

(c)

Cases with r_upr = r_lwr, r_lwr ≠ 0.

When the radii of the upper and lower layers are equal, the airspace structure takes on a cylindrical shape. It is evident that during the Intermediate approach phase, UAVs utilize a vertical descent maneuver. The capacity trend of the cylindrical-shaped structure is shown in Figure 17.

As shown in Figure 17, the fleet operation capacity decreases as the layer radii increase. However, an exception occurs when the radii of both the upper and lower layers are 10 m. This anomaly is primarily attributed to the Initial approach phase becoming the limitation caused by the long duration of the Initial approach phase and the insufficient number of holding points, consequently reducing capacity. However, under typical conditions, as the radii of the layers increase, the overall fleet operation capacity gradually decreases. That is because the extended flight time of the Final approach phase becomes a crucial limitation, influencing the time interval between the front and rear UAVs during landing, thus resulting in a corresponding decrease in capacity. Notably, there is a transient increase in fleet operation capacity, which is due to reasons similar to those discussed earlier.

By comparing the three cases illustrated in Figure 17, the capacity gradually decreases with the continuous increase in the height between the approach point and lower layer. The reason for this is similar to what was described earlier regarding the funnel-shaped structure.

7. Concluding Remarks

In this study, a funnel-shaped multi-layer structure and a phased fleet operational concept have been proposed as a design for vertiport to adapt to future high-density flight demands. For a better adaptive design of vertiport airspace, fleet operation capacity is considered to indicate the compatibility of UAV fleet operation within vertiport airspace. By modeling fleet operations with various constraints and time-based process algorithms for fleet operation, case studies of UAV arrival processes by changing airspace structure dimensions have been simulated to understand the influencing factors on fleet operations from the perspective of airspace structure.

The results of the parametric analysis of the operation capacity under different airspace structure dimensions reveal that the structure dimensions have a great impact on fleet operation capacity. Based on the analysis of cases by different radii and heights, the limitations of the fleet operation capacity have also been studied and discussed. Specifically, different parametric airspace structure not only results in either increases or decreases in traveled distance but also make differences in the total number of available holding points at each layer, both of which will eventually impact the time gap between two consecutive operating UAVs, thus affecting as limitations for the fleet operation capacity improvement. It is hoped that the results presented in this paper will provide an acceptable explanation for the relationship between airspace structure parameters and fleet operation capacity in vertiport. The significance of limitations arising from the incompatible airspace structure parameters mentioned above, which serve as a guiding factor for future vertiport airspace design, is prominently highlighted.

Future research shall continue to explore the impact of alternative airspace structure design on UAV arrival and departure operations, including different layouts and the number of holding points. Energy consumption and the capacity for multi-airport delivery will be key considerations in this exploration [53,54]. Additionally, the research could also explore control strategies for on-demand UAV logistics delivery within vertiport traffic management [55,56], with a keen focus on ensuring fleet operation safety requirements and mitigating ground risk in vertiport [57], thereby improving airspace utilization and safety. Taking into account the operational demands for de-confliction, especially in high-density operations, the implementation of adaptive conflict detection and resolution for multi-UAV routes might be a viable method for optimizing overall capacity and safety [58,59]. Moreover, research topics exploring landing pads on the landside, including their quantity, layout, and operation rules under the setting of logistics [60], will also be worth exploring in the future.

Author Contributions

Conceptualization, P.H., X.Y. and K.H.L.; methodology, P.H., X.Y. and K.H.L.; software, X.Y.; validation, P.H. and X.Y.; resources, Y.Z.; writing—original draft preparation, X.Y.; writing—review and editing, P.H. and K.H.L.; supervision, Y.Z. and K.H.L.; funding acquisition, P.H. and Y.Z. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by the National Natural Science Foundation of China (Grant no.: 52102419); Civil Aviation Safety Capacity Building Project (Civil unmanned aviation development route and key technology verification); Key Laboratory of Flight Techniques and Flight Safety, CAAC (Grant no.: FZ2021KF17).

Data Availability Statement

The data presented in this study are available on request from the corresponding author.

Conflicts of Interest

The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

Abbreviations

Subscripts
asb	indicates “assembly layer”
upr	indicates “upper layer”
lwr	indicates “lower layer”
apr	indicates “approach point”
ldn	indicates “landing pad”
arr	indicates “arrival”
dpt	indicates “departure”
fly	indicates “flying”
wtn	indicates “waiting”
(p)_(q)	indicating the relationship between (p) and (q); for example, asb_upr indicates the process from the assembly layer (asb) to the upper layer (upr)
Symbols
holding point
P_asb,k	holding point k at the assembly layer
P_upr,l	holding point l at the upper layer
P_lwr,m	holding point m at the lower layer
P_apr	approach point
P_ldn	landing pad
Parameters
radius (m)
r_asb	radius of the assembly layer
r_upr	radius of the upper layer
r_lwr	radius of the lower layer
height (m)
h_asb	height of the assembly layer
h_upr	height of the upper layer
h_lwr	height of the lower layer
h_apr	height of the approach point
h_{upr_lwr}	height between the upper and lower layers
h_{lwr_apr}	height between the lower layer and approach point
h_{apr_ldn}	height between the approach point and landing pad
distance and ride (m)
s_{asb_upr}	path ride from the assembly layer to the upper layer
s_{upr_lwr,i}	path ride from the upper layer to the lower layer of UAV i
s_{lwr_apr}	path ride from the lower layer to the approach point
s_{apr_ldn}	path ride from the approach point to the landing pad
s_saf	safety separation for two UAVs
s_spa	lateral separation for two adjacent holding points
s_l_{_m}	distance from holding point l at the upper layer to holding point m at the lower layer
s_i_{_j}(t)	distance between UAV i and UAV j at time t
(x, y, z)	3D positional coordinates for holding points or UAVs
velocity (m/s)
v_c	cruise velocity of shallow descent
v_v	vertical velocity of landing
Indices
k	numbering of holding point at the assembly layer, k∈{1, …, K}
K	total number of holding points at the assembly layer
l	numbering of holding point at the upper layer, l∈{1, …, L}
L	total number of holding points at the upper layer
m	numbering of holding point at the lower layer, m∈{1, …, M}
M	total number of holding points at the lower layer
i	numbering for a UAV of the fleet, i∈{1, …, N}
N	total UAV fleet number
Matrices
holding point occupancy status matrix
Q_asb(k,i)	indicates the occupancy relationship between UAV i and holding point k at the assembly layer (for the element of the matrix Q_asb)
Q_upr(l,i)	indicates the occupancy relationship between UAV i and holding point l at the upper layer (for the element of the matrix Q_upr)
Q_lwr(m,i)	indicates the occupancy relationship between UAV i and holding point m at the lower layer (for the element of the matrix Q_lwr)
Q_dapr(1,i)	indicates the occupancy relationship between UAV i and the approach point (for the element of the matrix Q_apr)
Q_ldn(1,i)	indicates the occupancy relationship between UAV i and the landing pad (for the element of the matrix Q_ldn)
Indices
time (s)
t_str,i	starting time node for UAV i occurring outside the terminal airspace
t_wtn,str,i	waiting time outside the terminal airspace of UAV i
t_arr,asb,i	arrival time at the assembly layer of UAV i
t_wtn,asb,i	waiting time at the assembly layer of UAV i
t_dpt,asb,i	departure time from the assembly layer of UAV i
t_{fly,asb_upr}	flying time from the assembly layer to the upper layer
t_arr,upr,i	arrival time at the upper layer of UAV i
t_wtn,upr,i	waiting time at the upper layer of UAV i
t_dpt,upr,i	departure time from the upper layer of UAV i
t_{fly,upr_lwr,i}	flying time from the upper layer to the lower layer of UAV i
t_arr,lwr,i	arrival time at the lower layer of UAV i
t_wtn,lwr,i	waiting time at the lower layer of UAV i
t_dpt,lwr,i	departure time from the lower layer of UAV i
t_{fly,lwr_apr}	flying time from the lower layer to the approach point
t_arr,apr,i	arrival time at the approach point of UAV i
t_wtn,apr,i	waiting time at the approach point of UAV i
t_dpt,apr,i	departure time from the approach point of UAV i
t_{fly,apr_ldn}	flying time from the approach point to the landing pad
t_arr,ldn,i	arrival time at the landing pad of UAV i
t_dpt,apr,i	departure time from the landing pad of UAV i
t_g	necessary ground service time
λ, η, δ, φ	decision variables for determining the waiting time of UAVs.

Appendix A

Table A1 illustrates the relationship between the time difference of UAVs that have already landed or are waiting to land with the cutoff time under different combinations of layers radii in case Figure 11a h_{upr_lwr} = 50 m, h_{lwr_apr} = 20 m, h_{apr_ldn} = 20m (Section 6). Table A1 depicts the already landed UAVs and the progress of the succeeding UAV’s landing. This is demonstrated across various combinations of layers radii, as illustrated in case (a) of Section 6.

Table A1. Cutoff time between 1200s and UAVs that have already landed or are waiting to land.

90		32.1	35.3	35.4	35.6	35.8	36	36.1	36.3	36.4	36.5
80		32.3	39	39.2	39.4	39.6	39.8	39.9	40.1	40.2	40.3
70		32.5	43.6	43.8	44	44.2	44.4	44.6	44.7	44.8	44.9
60		32.6	49.4	49.6	49.8	50.1	50.3	50.4	50.6	50.76	50.77
50		32.8	59.9	60.2	60.4	60.7	60.8	61	61.23	61.24	61.3
40		32.9	71.3	71.6	71.8	72.1	72.33	72.36	72.5	72.66	72.67
30		33.1	73.9 *	81.9	82.1	82.3	82.5	82.6	82.7	82.87	82.88
20		33.2 ^{^}	74.3	104.26 ^#	104.57 ^#	104.6 ^#	104.8 ^#	104.9 ^#	105.12	105.14	105.2
10		33.31	74.4	104.27 ^#	104.58 ^#	101.9	90.6	82.9	76.1	69.3	64.8
0		33.32	64.1	60.8	55.2	50.6	46.6	41.8	39.1	35.6	32.8
$r_{lwr}$		0	10	20	30	40	50	60	70	80	90
	$r_{upr}$	0	10	20	30	40	50	60	70	80	90

^ 33.2 indicates that 32 UAVs have landed, and the 34th UAV has not obtained landing clearance for the Landing phase by the end of 1200 s. * 73.9 indicates that 73 UAVs have landed, and the 74th UAV has received landing clearance for the Landing phase and is anticipated to land shortly. ^# 104.26, 104.57, 104.6, 104.8, 104.9, 104.27, and 104.58 have slight differences, but if only considering the Roman numerical values show the integer flight number and ignoring the decimal points in italics, the capacity is the same 104, as shown in the figure in the paper.

These decimal points underscore that, despite certain airspace structures displaying identical values in capacity analysis, operational discrepancies persist and become apparent in an on-demand operational context. For clarity, digits after the decimal point have been ignored in our results presented.

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Figure 1. Airspace structure and operation factors influencing vertiport operational capacity and efficiency.

Figure 2. Sequential stages of UAV movements from entering the airspace until the end of the landing process.

Figure 3. Definitions and parameters for the UAV operation required in this study, including holding points (or stations) in different layers with respective radii and heights.

Figure 4. Number of holding points in different layers associated with the respective radius and safe separation: (a) overall representation of layers; (b) assembly layer and upper layer; (c) lower layer.

Figure 5. Rule-based UAV operation constraints: (a) sequencing constraint; (b) movement constraint; (c) de-conflict constraint; (d) consecutive service constraint. Shaded circles shown in the diagrams represent occupied holding points.

Figure 6. Time-based algorithms from phase to phase: (a) flowchart of overall fleet operation according to respective constraints and guidelines; (b) details of “Generating no-conflict movement trajectory” in (a).

Figure 7. Phase-based time slots defined for UAV fleet operations.

Figure 8. Flowchart of self-derived movement for each individual UAV governed by constraints and guidelines in Section 4 and according to time-based algorithms in Section 5.

Figure 9. Flowchart to auto-generate the resultant capacity of the fleet operation accomplished by the UAVs involved within a given time duration.

Figure 10. Tabulated cases to be simulated for capacity of fleet operations in different upper-lower layer radii (for given heights).

Figure 11. Fleet operation capacity with different airspace structures: (a) illustration of the capacity values for different combinations of upper and lower layers when h_{upr_lwr} = 50 m, h_{lwr_apr} = 20 m, h_{apr_ldn} = 20 m; (b) illustration of the capacity values for different combinations of upper and lower layers when h_{upr_lwr} = 40 m, h_{lwr_apr} = 30 m, h_{apr_ldn} = 20 m; (c) illustration of the capacity values for different combinations of upper and lower layers when h_{upr_lwr} = 35 m, h_{lwr_apr} = 35 m, h_{apr_ldn} = 20 m; (d) illustration of the capacity values for different combinations of upper and lower layers when h_{upr_lwr} = 30 m, h_{lwr_apr} = 40 m, h_{apr_ldn} = 20 m; (e) illustration of the capacity values for different combinations of upper and lower layers when h_{upr_lwr} = 20 m, h_{lwr_apr} = 50 m, h_{apr_ldn} = 20 m.

Figure 12. Capacity trends of fusiform structure (r_lwr > 0, r_upr = 0) with radii and height variations.

Figure 13. Capacity trends of elongated funnel structure (r_upr > 0, r_lwr = 0) with radii and height variations.

Figure 14. Capacity trends of straight-line vertical descent structure (r_upr = 0, r_lwr = 0) with radii and height variations.

Figure 15. Capacity trends of inverted conical structure (r_upr < r_lwr, r_upr ≠ 0) with radii and height variations.

Figure 16. Capacity trends of funnel-shaped structure (r_upr > r_lwr, r_lwr ≠ 0) with radii and height variations.

Figure 17. Capacity trends of cylindrical structure (r_upr = r_lwr, r_lwr ≠ 0) with radii and height variations.

Table 1. Symbol and ranges of parameters assumed (r, h, s illustrated in Figure 3).

Parameter	Symbol	Range (m)
Radius of the upper layer	r_upr	0–90
Radius of the lower layer	r_lwr	0–90
Vertical height between the upper and lower layer	h_upr_{_lwr}	10–70
Vertical height between lower layer and approach point	h_{lwr_apr}	10–70
Vertical height between approach point and landing pad	h_{apr_ldn}	20
Lateral separation of any two adjacent holding points at the same layer	s_spa	20
Safety separation of any two adjacent UAVs	s_saf	10

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Han, P.; Yang, X.; Low, K.H.; Zhao, Y. Parametric Analysis of Landing Capacity for UAV Fleet Operations with Specific Airspace Structures and Rule-Based Constraints. Drones 2024, 8, 770. https://doi.org/10.3390/drones8120770

AMA Style

Han P, Yang X, Low KH, Zhao Y. Parametric Analysis of Landing Capacity for UAV Fleet Operations with Specific Airspace Structures and Rule-Based Constraints. Drones. 2024; 8(12):770. https://doi.org/10.3390/drones8120770

Chicago/Turabian Style

Han, Peng, Xinyue Yang, Kin Huat Low, and Yifei Zhao. 2024. "Parametric Analysis of Landing Capacity for UAV Fleet Operations with Specific Airspace Structures and Rule-Based Constraints" Drones 8, no. 12: 770. https://doi.org/10.3390/drones8120770

APA Style

Han, P., Yang, X., Low, K. H., & Zhao, Y. (2024). Parametric Analysis of Landing Capacity for UAV Fleet Operations with Specific Airspace Structures and Rule-Based Constraints. Drones, 8(12), 770. https://doi.org/10.3390/drones8120770

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Parametric Analysis of Landing Capacity for UAV Fleet Operations with Specific Airspace Structures and Rule-Based Constraints

Abstract

1. Introduction

2. Literature Review

2.1. Works Relevant to Optimized Airspace Structures

2.2. Works Relevant to Factors of UAV Fleet Operations

2.3. Contribution and Outline of the Paper

3. Methodology for the Proposed Airspace Structure and Fleet Operation Concept

3.1. Proposed Airspace Structure

3.2. Concept of Fleet Operations

3.3. Parameters of Airspace Structure and Operations in Stages

4. Modelling of Fleet Operations with Various Constraints

4.1. Guidelines of UAV Holding-Point Occupancy in Different Layers

4.2. Rule-Based Sequential UAV Movement over Different Layers

5. Time-Based Algorithms for Fleet Operations over Proposed Airspace

5.1. Required UAV Flying Time in Different Stages

5.2. Fleet Operations Incorporating Various Constraints

6. Simulation and Analysis of Results with Different Dimensions

6.1. Set-Up for Case Simulation

6.1.1. Variation in Radii (with Fixed Heights)

6.1.2. Variation in Heights (with Fixed Radii)

6.2. Detailed Results and Discussion

7. Concluding Remarks

Author Contributions

Funding

Data Availability Statement

Conflicts of Interest

Abbreviations

Appendix A

References

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