CN115292928A - Unmanned aerial vehicle vertical take-off and landing field capacity assessment method and device - Google Patents
Unmanned aerial vehicle vertical take-off and landing field capacity assessment method and device Download PDFInfo
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Abstract
The invention discloses a method and a device for evaluating the capacity of a vertical take-off and landing field of an unmanned aerial vehicle, wherein the method abstracts the operation flow of the unmanned aerial vehicle and determines a queuing system in the operation flow of the unmanned aerial vehicle according to the topological structure of the vertical take-off and landing field of the unmanned aerial vehicle; respectively establishing a queuing theory model of each queuing system in the unmanned aerial vehicle operation flow according to the operation mode of the vertical take-off and landing field; determining the average service speed of each queuing system according to the set parameters and the field operation parameters of the vertical take-off and landing field of the unmanned aerial vehicle in the vertical take-off and landing process, and obtaining a relation curve between the average queuing time of each queuing system in a stable state and the average arrival speed of the unmanned aerial vehicle; determining the operation capacity of each queuing system according to the maximum unmanned aerial vehicle queuing time accepted by each queuing system and the relation curve; and according to a network flow theory, taking the node with the minimum operation capacity of each queuing system in the operation flow of the unmanned aerial vehicle as a blocking flow to obtain the whole operation capacity of the vertical take-off and landing field. The method lays a foundation for intelligent flow control of the unmanned aerial vehicle.
Description
Technical Field
The invention belongs to the technical field of unmanned aerial vehicles, and particularly relates to a method and a device for evaluating the capacity of a vertical take-off and landing field of an unmanned aerial vehicle.
Background
Compared with the relatively mature land road, waterway and civil aviation transportation, the urban air traffic is still in the exploration stage, and the future development space is larger. With the further opening of the low-altitude airspace in China, the logistics distribution mode of the last kilometer in a city is changed, and the development of a series of problems of layout, design, capacity evaluation, flow regulation and control and the like of the vertical take-off and landing field of the urban logistics unmanned aerial vehicle is promoted.
At present, the capacity evaluation method of the existing foreign vertical take-off and landing field mainly adopts methods such as linear programming containing time, and the like, and although the capacity evaluation result can be obtained more accurately, the practicability is poor due to the complex mathematical model and overlong time consumption, and the timeliness and convenience of the operation of the urban air traffic unmanned aerial vehicle cannot be met; related research of capacity evaluation of the unmanned aerial vehicle vertical take-off and landing field in China is in a starting stage, and a set of complete and effective capacity evaluation method of the vertical take-off and landing field is not provided.
Disclosure of Invention
The invention aims to provide a method and a device for evaluating the capacity of a vertical take-off and landing field of an unmanned aerial vehicle, wherein a queuing theory model of each queuing system in the operation flow of the unmanned aerial vehicle is respectively established according to the operation mode of the vertical take-off and landing field, and the operation capacity of each queuing system is determined; and according to a network flow theory, taking the node with the minimum operation capacity of each queuing system in the unmanned aerial vehicle operation flow as a blocking flow to obtain the whole operation capacity of the vertical take-off and landing field. The invention solves the problems of immature method, imperfect theory and the like in the exploration stage of the air traffic starting development of the city in China.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
the invention provides a capacity evaluation method for a vertical take-off and landing field of an unmanned aerial vehicle, which comprises the following steps:
abstracting the operation flow of the unmanned aerial vehicle according to the topological structure of the vertical take-off and landing field of the unmanned aerial vehicle, and determining a queuing system in the operation flow of the unmanned aerial vehicle;
respectively establishing a queuing theory model of each queuing system in the unmanned aerial vehicle operation process according to the operation mode of the vertical take-off and landing field; the queuing theory model is expressed as a functional relation between the average queuing time in a stable state of the queuing system and the average arrival flow of the unmanned aerial vehicle and the average service speed of the queuing system; the stable state refers to a state that the average arrival flow of the unmanned aerial vehicle is smaller than the average service speed of the queuing system;
determining the average service speed of each queuing system according to the set parameters and the field operation parameters of the vertical take-off and landing field of the unmanned aerial vehicle in the vertical take-off and landing process, and obtaining a relation curve between the average queuing time and the average arrival flow of the unmanned aerial vehicle in the stable state of each queuing system in combination with a queuing theory model of each queuing system;
determining the operation capacity of each queuing system according to the maximum unmanned aerial vehicle queuing time accepted by each queuing system and the relation curve;
according to the network flow theory, the node with the minimum operation capacity of each queuing system in the unmanned aerial vehicle operation flow is used as blocking flow, and the whole operation capacity of the vertical take-off and landing field is obtained.
Further, according to unmanned aerial vehicle VTOL field topological structure, abstract unmanned aerial vehicle operation flow includes: the unmanned aerial vehicle descends to a vertical take-off and landing field terminal area from a nearby airspace, descends to a landing platform through vertical take-off and landing operation, and slides to an apron; after the operation of the parking apron, applying for taking off, moving to a taking-off platform through a taxiway, and vertically taking off and leaving the vertical take-off and landing field;
the queuing system for determining the operation process of the unmanned aerial vehicle comprises the following steps: an approach queuing system at the landing platform, a ground queuing system at the apron and an departure queuing system at the takeoff platform.
Further, the respectively establishing a queuing theory model of each queuing system in the operation flow of the unmanned aerial vehicle according to the operation mode of the vertical take-off and landing site includes:
if the vertical take-off and landing field adopts an isolation operation mode, then,
a single service desk queuing model is adopted for the entrance queuing system and is expressed as M/M/1/∞/∞;
for the ground queuing system, a single-queue multi-service desk queuing model is adopted and expressed as M/M/c/∞/∞;
adopting an M/M/1/N/∞queuingmodel for the off-site queuing system;
if the vertical take-off and landing field adopts a hybrid operation mode, then,
the on-site queuing system and the off-site queuing system are in the same queuing system, and an M/M/1/∞/∞ queuing model is adopted;
and adopting an M/M/c/∞/infinity queuing model for the ground queuing system.
Further, if the vertical take-off and landing field adopts an isolation operation mode, then,
the queuing theory model of the entrance queuing system is as follows:
wherein the content of the first and second substances,
the average queuing time mu of the unmanned aerial vehicles in the approach queuing system 1 Average service speed, λ, for the inbound queuing system 1 Average arrival flow of the unmanned aerial vehicles in the approach queuing system;
the queuing theory model of the ground queuing system is as follows:
wherein the content of the first and second substances,
represents the average queuing time of the unmanned aerial vehicles in the ground queuing system,
represents the average queue length lambda of the unmanned aerial vehicle in the ground queuing system 2 And mu 2 Respectively representing the average arrival flow of the unmanned aerial vehicle in the ground queuing system and the average service speed of the ground queuing system, c 2 Number of tarmac in the vertical take-off and landing park, p 2 The average occupancy of the tarmac is expressed,
indicating the probability of the apron being completely free,
ρ 2 expressed as:
n represents that the parking apron has n unmanned aerial vehicles;
the queuing theory model of the off-site queuing system is as follows:
wherein, the first and the second end of the pipe are connected with each other,
queuing for departureThe average queuing time of the unmanned aerial vehicles in the system,
the average queue length of the unmanned aerial vehicles in the departure queuing system,
λ 3 and mu 3 Respectively representing the average takeoff flow of the unmanned aerial vehicle in the off-site queuing system and the average service speed of the off-site queuing system,
indicating the probability that the takeoff platform is idle,
further, according to the setting parameters of the unmanned aerial vehicle vertical take-off and landing process and the field operation parameters of the vertical take-off and landing field, the average service speed of each queuing system is determined, and the method comprises the following steps:
according to the height H of the last approach point in the vertical take-off and landing program of the unmanned aerial vehicle a Unmanned aerial vehicle descending rate V a Distance L from landing platform to taxiway entrance t And the ground sliding speed v of the unmanned aerial vehicle t Calculating the average landing time of the unmanned aerial vehicle as follows:
wherein, T a Representing the average landing time of the unmanned aerial vehicle;
calculating the average takeoff time of the unmanned aerial vehicle as follows:
wherein, T d Denotes mean takeoff time of unmanned aerial vehicle, H d Height, V, of unmanned aerial vehicle from a site d To take offClimbing speed;
according to the distance L from the taxiway of the vertical take-off and landing field to the parking apron p Ground sliding speed v of unmanned aerial vehicle t Time t for cargo handling and equipment detection p Calculating the average turnover time of the unmanned aerial vehicle as follows:
wherein, T p Representing the average turnover time of the unmanned aerial vehicle;
the average service speed of each queuing system is calculated as follows:
further, the determining the operation capacity of each queuing system according to the maximum unmanned aerial vehicle queuing time accepted by each queuing system and the relationship curve includes:
determining the maximum unmanned aerial vehicle queuing time accepted by each queuing system, finding a point corresponding to the maximum unmanned aerial vehicle queuing time accepted on the relation curve of the queuing system, and taking the average arrival flow of the unmanned aerial vehicles corresponding to the point as the running capacity of the queuing system.
Further, according to the network flow theory, the method for obtaining the overall operation capacity of the vertical take-off and landing field by using the node with the minimum operation capacity of each queuing system in the operation flow of the unmanned aerial vehicle as the blocking flow includes:
and taking the minimum value of the operation capacity of each queuing system as the whole operation capacity of the whole vertical take-off and landing field.
The invention also provides a device for evaluating the capacity of the vertical take-off and landing field of the unmanned aerial vehicle, which comprises:
the system comprises an initial module, a queue management module and a queue management module, wherein the initial module is used for abstracting the operation flow of the unmanned aerial vehicle according to the topological structure of the vertical take-off and landing field of the unmanned aerial vehicle and determining a queue management system in the operation flow of the unmanned aerial vehicle;
the modeling module is used for respectively establishing a queuing theory model of each queuing system in the unmanned aerial vehicle operation process according to the operation mode of the vertical take-off and landing field; the queuing theory model is expressed as a functional relation between the average queuing time length in a stable state of the queuing system and the average arrival flow of the unmanned aerial vehicle and the average service speed of the queuing system; the stable state refers to a state that the average arrival flow of the unmanned aerial vehicle is smaller than the average service speed of the queuing system;
the correlation module is used for determining the average service speed of each queuing system according to the set parameters in the vertical take-off and landing process of the unmanned aerial vehicle and the field operation parameters of a vertical take-off and landing field, and obtaining a relation curve between the average queuing time and the average arrival flow of the unmanned aerial vehicle under the stable state of each queuing system by combining the queuing theory model of each queuing system;
the determining module is used for determining the operation capacity of each queuing system according to the maximum unmanned aerial vehicle queuing time accepted by each queuing system and the relation curve;
and the output module is used for taking the node with the minimum operation capacity of each queuing system in the operation flow of the unmanned aerial vehicle as a blocking flow according to a network flow theory to obtain the whole operation capacity of the vertical take-off and landing field.
Further, the modeling module is specifically configured to,
for the vertical take-off and landing field adopting the isolation operation mode, a queuing theory model of each queuing system is established as follows:
a single service desk queuing model is adopted for the entrance queuing system and is expressed as M/M/1/∞/∞;
for the ground queuing system, a single-queue multi-service desk queuing model is adopted and expressed as M/M/c/∞/∞;
adopting an M/M/1/N/∞queuingmodel for the off-site queuing system;
for a vertical take-off and landing field adopting a hybrid operation mode, a queuing theory model of each queuing system is established as follows:
the on-site queuing system and the off-site queuing system are in the same queuing system, and an M/M/1/∞/∞ queuing model is adopted;
an M/M/c/∞/∞ queuing model is adopted for the ground queuing system.
Furthermore, the association module is specifically configured to,
according to the height H of the last approach point in the vertical take-off and landing program of the unmanned aerial vehicle a Descending rate V of unmanned aerial vehicle a Distance L from landing platform to taxiway entrance t And the ground sliding speed v of the unmanned aerial vehicle t Calculating the average landing time of the unmanned aerial vehicle as follows:
wherein, T a Representing the average landing time of the unmanned aerial vehicle;
calculating the average takeoff time of the unmanned aerial vehicle as follows:
wherein, T d Denotes mean takeoff time of unmanned aerial vehicle, H d For the height of the unmanned aerial vehicle from the field point, V d Is the takeoff climb speed;
according to the distance L from the taxiway of the vertical take-off and landing place to the apron p Ground sliding speed v of unmanned aerial vehicle t Time t for cargo handling and equipment detection p Calculating the average turnover time of the unmanned aerial vehicle as follows:
wherein, T p Representing the average turnover time of the unmanned aerial vehicle;
the average service speed of each queuing system is calculated as follows:
and substituting the obtained average service speed of each queuing system into a queuing theory model of each queuing system to obtain a relation curve between the average queuing time and the average arrival flow of the unmanned aerial vehicle under the stable state of each queuing system.
The invention has the beneficial effects that:
the invention provides a capacity assessment method for a vertical take-off and landing field of an unmanned aerial vehicle, which comprises the steps of respectively establishing a queuing theory model of each queuing system in the operation flow of the unmanned aerial vehicle according to the operation mode of the vertical take-off and landing field, and determining the operation capacity of each queuing system; according to the network flow theory, the node with the minimum operation capacity of each queuing system in the unmanned aerial vehicle operation process is used as a blocking flow, and the whole operation capacity of the vertical take-off and landing field is obtained. The method solves the problems of immature methods, imperfect theories and the like in the initial development and exploration phases of urban air traffic in China, is beneficial to constructing a complete urban air traffic system, improves the urban operation efficiency of the unmanned aerial vehicle, ensures the safety of the unmanned aerial vehicle, and lays a foundation for intelligent regulation and control of unmanned aerial vehicle flow.
Drawings
Fig. 1 is a flowchart of a method for evaluating the capacity of a vertical take-off and landing field of an unmanned aerial vehicle according to an embodiment of the present invention;
FIG. 2 is a schematic view of an operation flow of a vertical take-off and landing field of an unmanned aerial vehicle according to an embodiment of the present invention;
FIG. 3 is a state transition diagram of a queuing system in accordance with an embodiment of the present invention;
FIG. 4 is a relation curve of the average queuing time of the queuing system varying with the arrival traffic of the unmanned aerial vehicle in the embodiment of the present invention;
fig. 5 is a schematic diagram of connection of a queuing system of an unmanned aerial vehicle according to an embodiment of the present invention;
fig. 6 is a schematic diagram of an unmanned aerial vehicle operation network flow model provided in an embodiment of the present invention.
Detailed Description
The embodiments of the present invention will be described more fully hereinafter with reference to the accompanying drawings, in which some, but not all embodiments of the invention are shown. All other embodiments, which can be obtained by a person skilled in the art without making innovations based on the embodiments of the present invention, belong to the protection scope of the present invention.
Example 1
The embodiment provides an unmanned aerial vehicle VTOL field capacity assessment method, refer to fig. 1, including:
step S1: establishing a vertical take-off and landing field topological structure, abstracting the operation flow of the unmanned aerial vehicle, analyzing the quantity and operation mode of each ground facility, and extracting the capacity influence factors of the take-off and landing field;
step S2: respectively establishing a queuing theory model of each queuing system in the unmanned aerial vehicle operation process according to the operation mode of the vertical take-off and landing field; the queuing theory model is expressed as a function relation between the average queuing time length in a stable state of the queuing system and the average arrival speed of the unmanned aerial vehicle and the average service speed of the queuing system;
and step S3: determining the average service speed of each queuing system according to the set parameters and the field operation parameters of the vertical take-off and landing field of the unmanned aerial vehicle in the vertical take-off and landing process, and obtaining a relation curve between the average queuing time of each queuing system and the average arrival speed of the unmanned aerial vehicle by combining with a queuing theory model of each queuing system; obtaining the operation capacity of each queuing system according to the queuing time of the unmanned aerial vehicle acceptable by each queuing system, the average queuing time of each queuing system and the relation curve of the average arrival speed of the unmanned aerial vehicle;
and step S4: according to the network flow theory, the node with the minimum capacity in the unmanned aerial vehicle operation flow is used as blocking flow, and the whole operation capacity of the vertical take-off and landing field is obtained.
It should be noted that, the vertical take-off and landing field of the unmanned aerial vehicle is: the unmanned aerial vehicle landing, taking-off and taxiing area is used for unmanned aerial vehicles with vertical take-off and landing capability.
In this embodiment, a vertical take-off and landing field topology is established, and the operation flow of the unmanned aerial vehicle is abstracted, which is specifically as follows:
the vertical take-off and landing field comprises: the take-off and landing platform, taxiways, parking ramps, hangars and the like abstract the operation flow of the unmanned aerial vehicle in the vertical take-off and landing field, see figure 2,
the unmanned aerial vehicle descends to a vertical take-off and landing field terminal area from a nearby airspace, descends to a platform through vertical take-off and landing operation, and selects autonomous sliding or is carried to an apron by a scooter according to self performance (whether the unmanned aerial vehicle has a sliding function); the operation such as cargo loading and unloading, equipment detection and the like is realized by workers or automatic equipment in the turnover area of the parking apron, and if special operation such as charging, repair and the like is needed, the operation is carried to the hangar for completion; after the unmanned aerial vehicle completes the turnover of the parking apron, the unmanned aerial vehicle applies for taking off, moves to a taking-off platform through a taxiway, vertically takes off and leaves a landing field, and completes the next section of task.
In this embodiment, according to above-mentioned unmanned aerial vehicle operation flow, each ground facility quantity and operational mode are analyzed, draw the influence factor of take-off and landing field capacity, specifically as follows:
the operation mode of the vertical take-off and landing field influences the capacity of the vertical take-off and landing field, and the operation mode of the take-off and landing platform can be divided into an isolation operation mode and a hybrid operation mode according to the multi-runway operation mode of a civil aviation airport. The isolation operation mode is to divide the take-off and landing platform into two parts, wherein one part is used for bearing the landing task, and the other part is used for bearing the take-off task; the hybrid operation mode means that all the take-off and landing platforms can take on the take-off and landing tasks.
When the take-off and landing number of the unmanned aerial vehicles is unbalanced, the hybrid operation mode can more fully utilize the take-off and landing platform resources; conversely, if the unmanned aerial vehicle flow is greater and balanced, the isolation operation mode will appear more efficient.
The number of the take-off and landing platforms and the number of the parking aprons play a decisive role in the capacity of the vertical take-off and landing field, and the more the number of the take-off and landing platforms is, the more the unmanned aerial vehicles can take off and land in unit time; likewise, the greater the number of ramps, the more drone turnaround service may be provided.
The capacity of the vertical take-off and landing field is also influenced by the number of the unmanned aerial vehicles capable of being accommodated in the hangar, and the more the unmanned aerial vehicles capable of being accommodated in the hangar, the more unmanned aerial vehicles can be charged and repaired in the hangar; on the contrary, if the hangar can accommodate a small number of unmanned aerial vehicles, the situation that the unmanned aerial vehicles needing to be charged occupy the parking apron may occur.
The height of the last approach point in the vertical take-off and landing procedure of the unmanned aerial vehicle, the landing descent rate of the unmanned aerial vehicle, the distance from the take-off and landing platform of the vertical take-off and landing field to the entrance of the taxiway, the ground sliding speed of the unmanned aerial vehicle and other parameters jointly determine the average take-off/landing time of the unmanned aerial vehicle. The unmanned aerial vehicle operation model is analyzed, so that the unmanned aerial vehicle entering and leaving behavior is a discrete event and has uncertainty; meanwhile, for each unmanned aerial vehicle, the landing time and the takeoff time are random models and are mutually independent, and negative index distribution is obeyed, namely the arrival flow and the departure flow of the unmanned aerial vehicle are both poisson flows.
In this embodiment, according to the operation mode of the vertical take-off and landing site, the queuing theory models of the queuing systems are respectively established for different ground facilities, and the indexes of the queuing systems in the stable state are respectively solved, which is specifically implemented as follows:
it should be noted that the queuing systems of the vertical take-off and landing field include an entrance queuing system, a ground queuing system and an exit queuing system, and refer to fig. 5 in detail.
A. If the vertical take-off and landing field adopts an isolation operation mode, the following steps are performed:
for landing platforms (the approach queuing system numbered (1) in figure 5),
the arrival flow of the unmanned aerial vehicle can be regarded as infinite, namely, the unmanned aerial vehicle is enough in the airspace to be ready to land, the arrival number of the unmanned aerial vehicle in unit time is defined, namely, the arrival flow is lambda 1 Defining the average landing time of the unmanned plane as
I.e. average landing platform service speed is mu 1 。
If λ 1 ＞μ 1 If the average arrival flow is larger than the average service speed, the queuing system can never reach a stable state, the number of the arriving unmanned aerial vehicles in unit time is more than that of the unmanned aerial vehicles which finish landing and leave the landing platform, and the longer the queue is; on the contrary, if λ 1 ＜μ 1 The inbound queuing system can reach a steady state.
In both cases, λ 1 ＞μ 1 In time, will cause a large amount of delays, be not conform to unmanned aerial vehicle operation requirement, consequently, main analysis lambda 1 ＜μ 1 The capacity of the platform at a certain waiting (delay) level is then lowered.
The unmanned aerial vehicle admission queuing system of the single landing platform serves according to a first-come-first-serve rule, when the unmanned aerial vehicle reaches a terminal area of a take-off and landing field, if the take-off and landing platform is occupied, the unmanned aerial vehicle enters into the queue to wait, and the waiting airspace is considered to be unlimited. The system conforms to a single service desk queuing model in queuing theory and can be expressed as M/M/1/∞/∞ (abbreviated as M/M/1), and the transition relation of each state is shown in FIG. 3.
When the queuing state of the unmanned aerial vehicles in the terminal area is analyzed, the probability that the state of the entrance queuing system at any time t under the stable state is required to be n (indicating that n unmanned aerial vehicles exist in the system) is
Wherein the probability at steady state is independent of time, the probability of system state n is
For a stable system, the input rate of each state should be equal to the output rate, as shown in fig. 3, and the transfer rate λ for the number of drones from 0 to 1 1 P 0 Conversely, the transfer rate at which the number of drones is transferred from 1 to 0 is μ 1 P 1 Thus, for state 0, there is a balance equation:
likewise, for system states n > 0, there is a balance equation:
the formula (1) and (2) can be used for obtaining:
according to the normalization of the probability under each state, have
Namely, it is
Thus:
in the formula (5)
Namely the ratio of the average arrival flow of the unmanned aerial vehicle to the average service speed of the landing platform. When n =0, the number of the bits is set to n =0,
the system is in an idle state, namely the landing platform is not occupied by the unmanned aerial vehicle; on the contrary, the first step is to take the reverse,
indicating that at least one drone is in the queuing system and the landing platform is busy, therefore rho 1 Also representing the average utilization of the landing platform.
According to equation (5), the average number of drones in the approach queuing system can be further derived as:
therefore, the average approach time of the unmanned aerial vehicle can be calculated
Wherein the content of the first and second substances,
for the average approach time length of the unmanned aerial vehicle in the approach queuing system,
the average number (average queue length) of the unmanned planes in the approach queuing system is lambda 1 And averaging the arrival flow of the unmanned aerial vehicle in the entrance queuing system.
The approach time of the unmanned aerial vehicle can be divided into two parts of queuing time and landing time, so that the average queuing (delay) duration of the unmanned aerial vehicle can be expressed as follows:
in the formula (I), the compound is shown in the specification,
for the average queuing (delay) duration of the unmanned aerial vehicles in the approach queuing system,
the average landing time of the unmanned aerial vehicle in the entrance queuing system is obtained.
For a vertical take-off and landing floor apron (the ground queuing system with serial number (2) in figure 5),
the unmanned aerial vehicle is still in Poisson flow on the taxiway, the landed unmanned aerial vehicle moves to each parking apron from the taxiway, an idle parking apron is searched and slides in, turnover tasks such as loading and unloading are completed, if all parking aprons are occupied, the unmanned aerial vehicle needs to wait in line and follows the first-come-first-serve rule. Therefore, the vertical take-off and landing apron conforms to the characteristics of a single-row multi-service-desk queuing system in a queuing theory, can be represented by M/M/c/∞/∞, and can deduce the state probability according to the equilibrium state:
in the formula, λ 2 And mu 2 Mean arrival flow of drones and mean service speed of tarmac, c, representing ground queuing system 2 The number of tarps in the vertical take-off and landing site,
the probability that the apron is completely free is represented, i.e. all the aprons are available;
the probability of n unmanned aerial vehicles in the parking apron system is shown, and when n is less than c 2 When n is more than or equal to c, the parking apron system is not saturated, the idle parking apron still exists for use 2 In time, the apron system is saturated, and the unmanned aerial vehicles need to queue up for entry, resulting in delays.
Further, the number of the unmanned aerial vehicles (average queue length) and the average queuing (delay) time of the ground queuing system are as follows:
in the formula (I), the compound is shown in the specification,
represents the average captain of the drones of the ground queuing system,
representing the average occupancy of the ramps, or the number of drones averagely received per ramp,
means of being perpendicularThe average number of the unmanned aerial vehicles parked on the landing site;
mean queuing (delay) time of drones representing a ground queuing system.
For a takeoff platform (off-site queuing system numbered (3) in figure 5),
after the unmanned aerial vehicles complete turnover on the parking apron, the unmanned aerial vehicles randomly apply for taking off and leaving, and the request time obeys independent and same negative exponential distribution, so that the unmanned aerial vehicles leaving the parking apron are also poisson flow. If the takeoff platform is idle, the unmanned aerial vehicle requesting takeoff leaves the parking apron and slides into the platform through the taxiways to execute a takeoff task; on the contrary, if the takeoff platform is occupied, the unmanned aerial vehicle waits in place, delay is generated, the unmanned aerial vehicle sequentially takes off according to the first application first service principle, and the number of the parking aprons is the upper limit of the takeoff captain of the unmanned aerial vehicle.
The takeoff platform is therefore an M/M/1/N/∞queuingsystem, where N = c 2 The probability of each state during stabilization is as follows:
in the formula, λ 3 And mu 3 The average takeoff flow of the unmanned aerial vehicle of the off-site queuing system and the average service speed of a takeoff platform are shown,
representing the probability of the number of unmanned aerial vehicle stands being n in the off-site queuing system,
which represents the probability of the takeoff platform being free,
the superscript n of (a) denotes p 3 To the n power of; due to limited queuing space, at this time
And does not represent the average take-off platform utilization.
Further, the number of unmanned aerial vehicles (average queue length) and the average queuing (delay) time in the off-site queuing system are as follows:
in the formula (I), the compound is shown in the specification,
for the number of drones in the departure queuing system (average queue length),
the average queuing (delay) time in the off-line queuing system is long.
B. If the vertical take-off and landing field adopts a hybrid operation mode, the following steps are performed:
the take-off and landing platform is used in a mixed mode, the unmanned aerial vehicles requesting landing and taking-off are located in the same queuing system, and when other queuing properties are unchanged, the take-off and landing platform can be regarded as an M/M/1/∞/infinity queuing system; the operation characteristics of the air park are unchanged, and the air park is still an M/M/N/∞/infinity queuing system.
In this embodiment, the average service speed of each queuing system is determined according to the set parameters during the vertical take-off and landing process of the unmanned aerial vehicle and the field operation parameters of the vertical take-off and landing field, and the specific steps are as follows:
according to the height H of the last approach point in the vertical take-off and landing program of the unmanned aerial vehicle a Descending rate V of unmanned aerial vehicle a Distance L from landing platform to taxiway entrance t And the ground sliding speed v of the unmanned aerial vehicle t And calculating the average landing time of the unmanned aerial vehicle, namely the average service time of a landing platform:
wherein, T a Representing the average landing time of the unmanned aerial vehicle;
similarly, the average takeoff time of the unmanned aerial vehicle, namely the average service time of a takeoff platform, can be calculated as follows:
in the formula, H d Height, V, of unmanned aerial vehicle from a site d Is the takeoff climb speed.
According to the distance L from the taxiway of the vertical take-off and landing place to the apron p Ground sliding speed v of unmanned aerial vehicle t Time t for cargo handling and equipment detection p Calculating the average turnover time of the unmanned aerial vehicle, namely the average service time of the parking apron:
further, using the average service duration, calculating the average service speed of each queuing system in step S2:
determining the number of service desks in the parking apron queuing system according to the number of the parking aprons:
c 2 ＝N p (20)
in the formula, c 2 Number of service desks, N, in a system for queuing multiple service desks at an aircraft park p The number of the air ramps contained in the vertical take-off and landing site.
In this embodiment, a relation curve between the average queuing time of each queuing system and the average arrival speed of the unmanned aerial vehicle is obtained by combining the queuing theory models of each queuing system, which is specifically as follows:
substituting the calculated parameters into the queuing theory model of each queuing system in the step S2 to obtain each queuing systemThe average queuing (delay) duration of the queuing system varies with the arrival traffic of the drone, as shown in fig. 4, where W q The average queuing (delay) time length of a certain queuing system is shown, and lambda is the arrival flow of the unmanned aerial vehicle of the queuing system.
In this embodiment, the operation capacity of each queuing system is obtained according to the queuing time of the unmanned aerial vehicle that can be accepted by each queuing system and the relationship curve between the average queuing time of each queuing system and the average arrival speed of the unmanned aerial vehicle, and the operation capacity is specifically as follows:
determining an acceptable queuing (delay) time T according to the unmanned aerial vehicle performance limit and the operation requirement max And obtaining corresponding unmanned aerial vehicle arrival flow lambda according to the relation curve max I.e. the operating capacity of the queuing system.
In this embodiment, according to the network flow theory, the node with the minimum capacity in the operation flow of the unmanned aerial vehicle is used as the blocking flow to obtain the overall operation capacity of the vertical take-off and landing field, and the specific implementation process is as follows:
in conjunction with each queuing theory model, the operation process of the drone can be abstracted as three queuing systems connected in sequence, as shown in fig. 5, where the operation capacity of each queuing system has been found in step S3.
According to the flow, the abstract unmanned aerial vehicle operation key node comprises an unmanned aerial vehicle last approach point, an unmanned aerial vehicle sliding-in waiting point, an unmanned aerial vehicle sliding-out waiting point and an unmanned aerial vehicle flying off site point, and the path connecting the key node is the three queuing systems.
As shown in fig. 6, a network flow model N = (V, S, T, a, C) is established, S is a source point set of the network, T is a sink point set of the network, and V and a are a vertex set and an arc set, respectively. The source point and the sink point correspond to an inlet and an outlet of a network in an actual network, namely a last approach point and a takeoff and departure point of the unmanned aerial vehicle, and vertexes except the source point and the sink point in the network are called transfer points, namely an unmanned aerial vehicle slides in a waiting point and slides out of the waiting point. C is the capacity function of the network, which is a non-negative function defined on arc set a, and corresponds to the transport capacity on the corresponding route, i.e. the operating capacity of the above-mentioned queuing systems.
In network flow, drones enter from a source point, pass through a transit point, reach a sink point, form a real flow, and satisfy antisymmetry, capacity limitations, and flow conservation.
According to the maximum flow theory, the maximum flow has a capacity equal to the minimum cut (cut-set), i.e. the traffic bottleneck in the network determines the capacity of the overall network flow model. Therefore, the minimum value of the operation capacity of each queuing system in the step S3 is regarded as the operation capacity of the whole vertical take-off and landing field:
example 2
This embodiment still provides an unmanned aerial vehicle VTOL field capacity evaluation device, includes:
the system comprises an initial module, a queue management module and a queue management module, wherein the initial module is used for abstracting the operation flow of the unmanned aerial vehicle according to the topological structure of the vertical take-off and landing field of the unmanned aerial vehicle and determining a queue management system in the operation flow of the unmanned aerial vehicle;
the modeling module is used for respectively establishing a queuing theory model of each queuing system in the operation flow of the unmanned aerial vehicle according to the operation mode of the vertical take-off and landing field; the queuing theory model is expressed as a functional relation between the average queuing time in a stable state of the queuing system and the average arrival flow of the unmanned aerial vehicle and the average service speed of the queuing system; the stable state refers to a state that the average arrival flow of the unmanned aerial vehicle is smaller than the average service speed of the queuing system;
the correlation module is used for determining the average service speed of each queuing system according to the set parameters in the vertical take-off and landing process of the unmanned aerial vehicle and the field operation parameters of a vertical take-off and landing field, and obtaining a relation curve between the average queuing time and the average arrival flow of the unmanned aerial vehicle under the stable state of each queuing system by combining the queuing theory model of each queuing system;
the determining module is used for determining the operation capacity of each queuing system according to the maximum unmanned aerial vehicle queuing time accepted by each queuing system and the relation curve;
and the output module is used for taking the node with the minimum operation capacity of each queuing system in the operation flow of the unmanned aerial vehicle as a blocking flow according to a network flow theory to obtain the whole operation capacity of the vertical take-off and landing field.
In this embodiment, the initial module is specifically configured to,
according to the topological structure of the vertical take-off and landing field of the unmanned aerial vehicle, the operation flow of the abstract unmanned aerial vehicle is as follows: the unmanned aerial vehicle descends to a terminal area of a vertical take-off and landing field from a nearby airspace, descends to a landing platform through vertical take-off and landing operation and slides to an apron; after the operation of the parking apron, applying for taking off, moving to a taking-off platform through a taxiway, and vertically taking off and leaving the vertical landing field;
the queuing system for determining the operation process of the unmanned aerial vehicle comprises the following steps: an entrance queuing system at a landing platform, a ground queuing system at an apron and an exit queuing system at a flying platform.
In this embodiment, the modeling module is specifically configured to,
for the vertical take-off and landing field adopting the isolation operation mode, a queuing theory model of each queuing system is established as follows:
a single service desk queuing model is adopted for the entrance queuing system and is expressed as M/M/1/∞/∞;
for the ground queuing system, a single-queue multi-service desk queuing model is adopted and expressed as M/M/c/∞/∞;
adopting an M/M/1/N/∞queuingmodel for the off-site queuing system;
for a vertical take-off and landing field adopting a hybrid operation mode, a queuing theory model of each queuing system is established as follows:
the on-site queuing system and the off-site queuing system are in the same queuing system, and an M/M/1/∞/∞ queuing model is adopted;
an M/M/c/∞/∞ queuing model is adopted for the ground queuing system.
In this embodiment, for a vertical take-off and landing field that employs an isolated mode of operation,
the queuing theory model of the approach queuing system is as follows:
wherein the content of the first and second substances,
average queuing time mu of unmanned aerial vehicles in the approach queuing system 1 Average service speed, lambda, for an inbound queuing system 1 Average arrival flow of the unmanned aerial vehicles in the approach queuing system;
the queuing theory model of the ground queuing system is as follows:
wherein, the first and the second end of the pipe are connected with each other,
the average queuing time of the unmanned aerial vehicles in the ground queuing system is shown,
represents the average queue length lambda of the unmanned aerial vehicle in the ground queuing system 2 And mu 2 Respectively representing the average arrival flow of the unmanned aerial vehicle in the ground queuing system and the average service speed of the ground queuing system, c 2 Number of tarmac in the vertical take-off and landing park, p 2 The average occupancy of the tarmac is represented,
indicating the probability of the apron being completely free,
ρ 2 expressed as:
n represents that the parking apron has n unmanned aerial vehicles;
the queuing theory model of the off-site queuing system is as follows:
wherein the content of the first and second substances,
for the average queuing time of the unmanned aerial vehicles in the departure queuing system,
the average queue length of the unmanned aerial vehicles in the departure queuing system,
λ 3 and mu 3 Respectively representing the average takeoff flow of the unmanned aerial vehicle in the off-site queuing system and the average service speed of the off-site queuing system,
indicating the probability that the takeoff platform is idle,
in this embodiment, the association module is specifically configured to,
according to the height H of the last approach point in the vertical take-off and landing program of the unmanned aerial vehicle a Unmanned aerial vehicle descending rate V a Distance L from landing platform to taxiway entrance t And ground sliding speed v of unmanned aerial vehicle t Calculating the average landing time of the unmanned aerial vehicle as follows:
wherein, T a Representing the average landing time of the unmanned aerial vehicle;
calculating the average takeoff time of the unmanned aerial vehicle as follows:
wherein, T d Denotes mean takeoff time of unmanned aerial vehicle, H d For the height of the unmanned aerial vehicle from the field point, V d Is the takeoff climb speed;
according to the distance L from the taxiway of the vertical take-off and landing field to the parking apron p Ground sliding speed v of unmanned aerial vehicle t Time t for cargo and equipment loading and unloading detection p Calculating the average turnover time of the unmanned aerial vehicle as follows:
wherein, T p Representing the average turnaround time of the drone;
the average service speed of each queuing system is calculated as follows:
in this embodiment, the determining module is specifically configured to,
determining the maximum unmanned aerial vehicle queuing time accepted by each queuing system, finding a point corresponding to the maximum unmanned aerial vehicle queuing time accepted on the relation curve of the queuing system, and taking the average arrival flow of the unmanned aerial vehicles corresponding to the point as the running capacity of the queuing system.
In this embodiment, the output module is specifically configured to,
and taking the minimum value of the operation capacity of each queuing system as the whole operation capacity of the whole vertical take-off and landing field.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims.
Claims (10)
1. A capacity assessment method for a vertical take-off and landing field of an unmanned aerial vehicle is characterized by comprising the following steps:
abstracting the operation flow of the unmanned aerial vehicle according to the topological structure of the vertical take-off and landing field of the unmanned aerial vehicle, and determining a queuing system in the operation flow of the unmanned aerial vehicle;
respectively establishing a queuing theory model of each queuing system in the unmanned aerial vehicle operation flow according to the operation mode of the vertical take-off and landing field; the queuing theory model is expressed as a functional relation between the average queuing time length in a stable state of the queuing system and the average arrival flow of the unmanned aerial vehicle and the average service speed of the queuing system; the stable state refers to a state that the average arrival flow of the unmanned aerial vehicle is smaller than the average service speed of the queuing system;
determining the average service speed of each queuing system according to the set parameters in the vertical take-off and landing process of the unmanned aerial vehicle and the field operation parameters of a vertical take-off and landing field, and obtaining a relation curve between the average queuing time and the average arrival flow of the unmanned aerial vehicle under the stable state of each queuing system by combining the queuing theory model of each queuing system;
determining the operation capacity of each queuing system according to the maximum unmanned aerial vehicle queuing time accepted by each queuing system and the relation curve;
and according to a network flow theory, taking the node with the minimum operation capacity of each queuing system in the operation flow of the unmanned aerial vehicle as a blocking flow to obtain the whole operation capacity of the vertical take-off and landing field.
2. The method for assessing the capacity of the VTOL of the UAV according to claim 1,
according to unmanned aerial vehicle VTOL field topological structure, abstract unmanned aerial vehicle operation flow includes: the unmanned aerial vehicle descends to a vertical take-off and landing field terminal area from a nearby airspace, descends to a landing platform through vertical take-off and landing operation, and slides to an apron; after the operation of the parking apron, applying for taking off, moving to a taking-off platform through a taxiway, and vertically taking off and leaving the vertical take-off and landing field;
the queuing system for determining the operation process of the unmanned aerial vehicle comprises the following steps: an entrance queuing system at a landing platform, a ground queuing system at an apron and an exit queuing system at a take-off platform.
3. The method for evaluating the capacity of the vertical take-off and landing site of the unmanned aerial vehicle according to claim 2, wherein the step of respectively establishing a queuing theory model of each queuing system in the operation process of the unmanned aerial vehicle according to the operation mode of the vertical take-off and landing site comprises the following steps:
if the vertical take-off and landing field adopts an isolation operation mode, then,
a single service desk queuing model is adopted for the entrance queuing system and is expressed as M/M/1/∞/∞;
a single-queue multi-service desk queuing model is adopted for the ground queuing system and is expressed as M/M/c/∞/∞;
adopting an M/M/1/N/∞queuingmodel for the off-site queuing system;
if the vertical take-off and landing field adopts a hybrid operation mode, then,
the entrance queuing system and the departure queuing system are positioned in the same queuing system, and an M/M/1/∞ queuing model is adopted;
and adopting an M/M/c/∞/infinity queuing model for the ground queuing system.
4. The method for assessing the capacity of the VTOL of the UAV according to claim 3,
if the vertical take-off and landing field adopts an isolation operation mode, then,
the queuing theory model of the entrance queuing system is as follows:
wherein the content of the first and second substances,
the average queuing time mu of the unmanned aerial vehicles in the approach queuing system 1 Average service speed, lambda, for an inbound queuing system 1 Average arrival flow of the unmanned aerial vehicles in the entrance queuing system;
the queuing theory model of the ground queuing system is as follows:
wherein the content of the first and second substances,
the average queuing time of the unmanned aerial vehicles in the ground queuing system is shown,
represents the average queue length lambda of the unmanned aerial vehicle in the ground queuing system 2 And mu 2 Respectively representing the average arrival flow of the unmanned aerial vehicle in the ground queuing system and the average service speed of the ground queuing system, c 2 Number of tarps in the vertical take-off and landing site, p 2 The average occupancy of the tarmac is represented,
indicating the probability of the apron being completely free,
ρ 2 expressed as:
n represents that the parking apron has n unmanned aerial vehicles;
the queuing theory model of the off-site queuing system is as follows:
wherein the content of the first and second substances,
for the average queuing time of the unmanned aerial vehicles in the departure queuing system,
the average queue length of the unmanned aerial vehicles in the departure queuing system,
λ 3 and mu 3 Respectively represents the average takeoff flow of the unmanned aerial vehicle in the departure queuing system and the average service speed of the departure queuing system,
indicating the probability that the takeoff platform is idle,
5. the method for evaluating the capacity of the vertical take-off and landing site of the unmanned aerial vehicle according to claim 4, wherein the step of determining the average service speed of each queuing system according to the set parameters of the vertical take-off and landing process of the unmanned aerial vehicle and the field operation parameters of the vertical take-off and landing site comprises the following steps:
according to the height H of the last approach point in the vertical take-off and landing program of the unmanned aerial vehicle a Descending rate V of unmanned aerial vehicle a Distance L from landing platform to taxiway entrance t And the ground sliding speed v of the unmanned aerial vehicle t Calculating the average landing time of the unmanned aerial vehicle as follows:
wherein, T a Representing the average landing time of the unmanned aerial vehicle;
calculating the average takeoff time of the unmanned aerial vehicle as follows:
wherein, T d Indicating mean time to take-off of the drone, H d For the height of the unmanned aerial vehicle from the field point, V d Is the takeoff climb speed;
according to the distance L from the taxiway of the vertical take-off and landing place to the apron p Ground sliding speed v of unmanned aerial vehicle t Time t for cargo handling and equipment detection p Calculating the average turnover time of the unmanned aerial vehicle as follows:
wherein, T p Representing the average turnover time of the unmanned aerial vehicle;
the average service speed of each queuing system is calculated as follows:
6. the method for estimating the capacity of the vertical take-off and landing site of the unmanned aerial vehicle according to claim 4, wherein the determining the operation capacity of each queuing system according to the maximum acceptable queuing time of the unmanned aerial vehicle of each queuing system and the relationship curve comprises:
determining the maximum unmanned aerial vehicle queuing time accepted by each queuing system, finding a point corresponding to the maximum unmanned aerial vehicle queuing time accepted on the relation curve of the queuing system, and taking the average arrival flow of the corresponding unmanned aerial vehicles as the running capacity of the queuing system.
7. The method for evaluating the capacity of the vertical take-off and landing field of the unmanned aerial vehicle according to claim 6, wherein the step of obtaining the overall operation capacity of the vertical take-off and landing field by using a node with the minimum operation capacity of each queuing system in the operation flow of the unmanned aerial vehicle as a blocking flow according to a network flow theory comprises the following steps:
and taking the minimum value of the operation capacity of each queuing system as the whole operation capacity of the whole vertical take-off and landing field.
8. The utility model provides an unmanned aerial vehicle VTOL field capacity evaluation device which characterized in that includes:
the initial module is used for abstracting the operation flow of the unmanned aerial vehicle according to the topological structure of the vertical take-off and landing field of the unmanned aerial vehicle and determining a queuing system in the operation flow of the unmanned aerial vehicle;
the modeling module is used for respectively establishing a queuing theory model of each queuing system in the unmanned aerial vehicle operation process according to the operation mode of the vertical take-off and landing field; the queuing theory model is expressed as a functional relation between the average queuing time length in a stable state of the queuing system and the average arrival flow of the unmanned aerial vehicle and the average service speed of the queuing system; the stable state refers to a state that the average arrival flow of the unmanned aerial vehicle is smaller than the average service speed of the queuing system;
the correlation module is used for determining the average service speed of each queuing system according to the set parameters in the vertical take-off and landing process of the unmanned aerial vehicle and the field operation parameters of the vertical take-off and landing field, and obtaining a relation curve between the average queuing time and the average arrival flow of the unmanned aerial vehicle under the stable state of each queuing system by combining with a queuing theory model of each queuing system;
the determining module is used for determining the operation capacity of each queuing system according to the maximum unmanned aerial vehicle queuing time accepted by each queuing system and the relation curve;
and the output module is used for taking the node with the minimum operation capacity of each queuing system in the operation flow of the unmanned aerial vehicle as a blocking flow according to a network flow theory to obtain the whole operation capacity of the vertical take-off and landing field.
9. The device for assessing the vertical take-off and landing field capacity of an unmanned aerial vehicle according to claim 8, wherein the modeling module is specifically configured to,
for the vertical take-off and landing field adopting the isolation operation mode, a queuing theory model of each queuing system is established as follows:
a single service desk queuing model is adopted for the entrance queuing system and is expressed as M/M/1/∞/∞;
for the ground queuing system, a single-queue multi-service desk queuing model is adopted and expressed as M/M/c/∞/∞;
adopting an M/M/1/N/∞queuingmodel for the off-site queuing system;
for a vertical take-off and landing field adopting a hybrid operation mode, a queuing theory model of each queuing system is established as follows:
the entrance queuing system and the departure queuing system are positioned in the same queuing system, and an M/M/1/∞ queuing model is adopted;
an M/M/c/∞/∞ queuing model is adopted for the ground queuing system.
10. The UAV VTOL lot capacity assessment apparatus of claim 9, wherein said correlation module is specifically configured to,
according to the height H of the last approach point in the vertical take-off and landing program of the unmanned aerial vehicle a Descending rate V of unmanned aerial vehicle a Distance L from landing platform to taxiway entrance t And the ground sliding speed v of the unmanned aerial vehicle t Calculating the average landing time of the unmanned aerial vehicle as follows:
wherein, T a Representing the average landing time of the unmanned aerial vehicle;
calculating the average takeoff time of the unmanned aerial vehicle as follows:
wherein, T d Denotes mean takeoff time of unmanned aerial vehicle, H d Height, V, of unmanned aerial vehicle from a site d Is the takeoff climb speed;
according to the distance L from the taxiway of the vertical take-off and landing place to the apron p Ground sliding speed v of unmanned aerial vehicle t Time t for cargo handling and equipment detection p Calculating the average turnover time of the unmanned aerial vehicle as follows:
wherein, T p Representing the average turnaround time of the drone;
the average service speed of each queuing system is calculated as follows:
and substituting the obtained average service speed of each queuing system into a queuing theory model of each queuing system to obtain a relation curve between the average queuing time and the average arrival flow of the unmanned aerial vehicle under the stable state of each queuing system.
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| CN116151590A (en) * | 2023-04-07 | 2023-05-23 | 中国民用航空飞行学院 | Modularized unmanned aerial vehicle airport planning method for urban air traffic |
| CN117746692A (en) * | 2024-02-19 | 2024-03-22 | 中国民用航空飞行学院 | Airport modularization adjustment method based on capacity envelope curve |
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| CN116151590A (en) * | 2023-04-07 | 2023-05-23 | 中国民用航空飞行学院 | Modularized unmanned aerial vehicle airport planning method for urban air traffic |
| CN117746692A (en) * | 2024-02-19 | 2024-03-22 | 中国民用航空飞行学院 | Airport modularization adjustment method based on capacity envelope curve |
| CN117746692B (en) * | 2024-02-19 | 2024-05-10 | 中国民用航空飞行学院 | Airport modularization adjustment method based on capacity envelope curve |
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