CN113259835B - Unmanned aerial vehicle cluster deployment method based on ground cellular system - Google Patents

Unmanned aerial vehicle cluster deployment method based on ground cellular system Download PDF

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CN113259835B
CN113259835B CN202110314495.5A CN202110314495A CN113259835B CN 113259835 B CN113259835 B CN 113259835B CN 202110314495 A CN202110314495 A CN 202110314495A CN 113259835 B CN113259835 B CN 113259835B
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CN113259835A (en
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沈超
谈思颖
张登涛
艾渤
张纵辉
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Beijing Jiaotong University
Shenzhen Research Institute of Big Data SRIBD
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Shenzhen Research Institute of Big Data SRIBD
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/02—Services making use of location information
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W16/00—Network planning, e.g. coverage or traffic planning tools; Network deployment, e.g. resource partitioning or cells structures
    • H04W16/18—Network planning tools
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W84/00—Network topologies
    • H04W84/02—Hierarchically pre-organised networks, e.g. paging networks, cellular networks, WLAN [Wireless Local Area Network] or WLL [Wireless Local Loop]
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Abstract

The invention provides an unmanned aerial vehicle cluster deployment method based on a ground cellular system, which comprises the following steps: determining the position and height of a user, the position of a base station, the initial number and flight height of unmanned aerial vehicles and the road position of a tethered unmanned aerial vehicle in a region to be deployed, and taking the position constraint of the tethered unmanned aerial vehicle, the maximum communication radius constraint between the tethered unmanned aerial vehicle and the base station, the maximum communication radius constraint between the tethered unmanned aerial vehicle and a non-tethered unmanned aerial vehicle and the maximum communication radius constraint between the unmanned aerial vehicle and the user as constraint conditions; taking the maximum number of the coverable users as a first objective function, and adopting a continuous convex approximation algorithm, a linear relaxation algorithm and a weight l1Solving the maximum number of users which can be covered by the algorithm; the minimum number of unmanned aerial vehicles required by the maximum number of covered users is used as a second objective function, the minimum number and positions of the unmanned aerial vehicles required to be deployed for covering the maximum user are obtained by adopting a continuous convex approximation algorithm and a bisection method, and large-range coverage under the condition of high system capacity can be achieved.

Description

Unmanned aerial vehicle cluster deployment method based on ground cellular system
Technical Field
The invention relates to the technical field of unmanned aerial vehicle communication and resource management, in particular to an unmanned aerial vehicle cluster deployment method based on a ground cellular system.
Background
In recent years, with the advancement of the information-oriented era, the traffic of the terrestrial mobile network increases at a high speed, and particularly in some highly populated areas, the terrestrial base station equipment needs to bear a very large load, and a network blocking phenomenon often occurs, so that terrestrial users cannot obtain normal network services. In addition, the ground base station is often directly damaged due to irresistible factors such as natural disasters, and the base station cannot be reused in a short time, which may also affect normal communication of ground users to a certain extent.
In view of the above problems, it is a good solution to use Unmanned Aerial Vehicle (UAV) as relay. The unmanned aerial vehicle is an unmanned aerial vehicle operated by a radio remote control device or a self program control device, uses aerodynamic force to navigate and execute expected functions, and has the advantages of wide application, low cost, strong viability, good maneuvering performance and convenient use. Unmanned aerial vehicle has all obtained wide application in fields such as military affairs, civilian, has greatly reduced the cost of casualties, has improved the security and the adaptivity of operation system platform. In recent years, with the continuous reduction of production costs and the features of miniaturization, high mobility and flexible deployment, unmanned aerial vehicles are increasingly used in civil and commercial fields, such as: flow control, cargo transportation, precision agriculture, aerial inspection, environment monitoring, emergency search and rescue, emergency communication and the like. Especially for some boring, messy and dangerous tasks, the unmanned aerial vehicle is more advantageous than a manned aircraft, so the demand of the unmanned aerial vehicle is more and more increased.
Along with breakthroughs of an unmanned aerial vehicle vision technology, a fixed-point hovering technology, a tracking shooting technology, an automatic obstacle avoidance technology, a wireless communication technology, an ultra-remote control technology and the like, the load capacity, the endurance time and the flying height of the unmanned aerial vehicle are greatly improved, and therefore the unmanned aerial vehicle can be applied to a wireless communication system to improve the performance.
The unmanned aerial vehicle platform mainly selects a large and medium-sized fixed wing unmanned aerial vehicle and an unmanned helicopter as high-altitude base station platforms in the early stage, and the platforms have the advantages of strong load capacity, large flying height, long flying distance and the like, but also have the limitations of large volume, high cost, complex system, insufficient operation flexibility, short fixed point command dead time and the like, and the limitations cause that the unmanned aerial vehicle platform is difficult to be widely applied in emergency communication scenes. In recent years, a multi-rotor mooring unmanned aerial vehicle system is provided, which mainly comprises a multi-rotor unmanned aerial vehicle, a mooring cable and a ground take-off and landing platform. Many rotor unmanned aerial vehicle passes through ground power supply, can hang for a long time and stagnate sky, simultaneously, through the built-in optic fibre of mooring cable, the data that airborne equipment gathered can pass back to ground. Compared with a large and medium-sized fixed wing unmanned aerial vehicle and an unmanned helicopter, the multi-rotor mooring unmanned aerial vehicle has the advantages of small size, light weight, long-time stable hovering, simplicity in operation, low requirements on the take-off and landing environment, large data transmission bandwidth and the like, and is more suitable for being applied to emergency communication scenes.
In practical application, for different use scenarios, the tethered and non-tethered drones are often required to be used alternately or cooperatively. Because the cost of the unmanned aerial vehicle is high, and the energy of the battery is limited, in order to improve the resource utilization rate and save the cost, the deployment number of the unmanned aerial vehicle base stations needs to be reduced as much as possible to reduce the deployment cost on the premise that the communication service covers all users in the target area. The prior art scheme can provide a communication mode for a user through an unmanned aerial vehicle coverage user, but the shortcoming is that the utilization rate of the unmanned aerial vehicle is low, and the deployment process of the unmanned aerial vehicle is difficult and complicated.
Therefore, there is a need for a method for deploying a cluster of drones to achieve a large coverage area under high system capacity conditions.
Disclosure of Invention
The invention provides an unmanned aerial vehicle cluster deployment method based on a ground cellular system, which aims to solve the problem of deployment of an unmanned aerial vehicle cluster under the conditions of large ground base station load, limited coverage and unmanned aerial vehicle energy limitation.
In order to achieve the purpose, the invention adopts the following technical scheme.
An unmanned aerial vehicle cluster deployment method based on a ground cellular system comprises the following steps:
determining the position and height of a user, the position of a base station, the initial number and flight height of unmanned aerial vehicles and the road position of a tethered unmanned aerial vehicle in a region to be deployed, wherein the position constraint of the tethered unmanned aerial vehicle, the maximum communication radius constraint between the tethered unmanned aerial vehicle and the base station, the maximum communication radius constraint between the tethered unmanned aerial vehicle and a non-tethered unmanned aerial vehicle and the maximum communication radius constraint between the unmanned aerial vehicle and the user are taken as constraint conditions;
taking the maximum number of the coverable users as a first objective function, and adopting a continuous convex approximation algorithm, a linear relaxation algorithm and a weight l1Solving by an algorithm to obtain the maximum number of users which can be covered;
and taking the minimum number of the unmanned aerial vehicles required by covering the maximum number of users as a second objective function, and obtaining the minimum number of the unmanned aerial vehicles required to be deployed and the corresponding deployment positions by adopting a continuous convex approximation algorithm and a bisection method.
Preferably, the first objective function is shown in the following formula (1):
Figure BDA0002990577720000031
Figure BDA0002990577720000032
||q0-qB||≤R1， (1b)
Figure BDA0002990577720000033
Figure BDA0002990577720000034
Figure BDA0002990577720000035
wherein x is the number of users covered, | ·| non-woven phosphorOIs zero norm, qnAs coordinate vector of the nth drone, Ai，biAn ith polygon area parameter matrix for dividing the road into a plurality of polygons, wherein I is 1kPosition coordinates, x, representing the k-th user on the groundkE {0, 1} represents the connection state of the user, when the connection state is 0, the user can communicate with the unmanned aerial vehicle, when the connection state is 1, the user cannot communicate with the unmanned aerial vehicle, and q is0Is a coordinate vector of the mooring type unmanned aerial vehicle, N is the number of the non-mooring type unmanned aerial vehicles, the total number of the unmanned aerial vehicles is (N +1), qBThe maximum communication radius between the tethered unmanned aerial vehicle and the base station is R for the position coordinate of the base station1The maximum communication radius between the tethered unmanned aerial vehicle and the non-tethered unmanned aerial vehicle is R2The maximum communication radius between the unmanned aerial vehicle and the user is R3K is the number of ground users, and K is equal to {1, 2, …, K }.
Preferably, the second objective function is shown in the following equation (2):
Figure BDA0002990577720000041
Figure BDA0002990577720000042
||q0-qB||≤R1， (2b)
Figure BDA0002990577720000043
Figure BDA0002990577720000044
wherein N is the number of non-tethered unmanned aerial vehicles, qnAs coordinate vector of the nth drone, Ai，biA polygonal area parameter matrix, s, for partitioning a road into a plurality of polygonskRepresenting the location coordinates of the kth user on the ground, q0Coordinate vector of the captive drones, N is the number of non-captive drones, qBThe maximum communication radius between the tethered unmanned aerial vehicle and the base station is R for the position coordinate of the base station1The maximum communication radius between the tethered unmanned aerial vehicle and the non-tethered unmanned aerial vehicle is R2The maximum communication radius between the unmanned aerial vehicle and the user is R3，
Figure BDA0002990577720000045
Indicating the connection state of the user under the second objective function when
Figure BDA0002990577720000046
A value of 0 indicates that the user can communicate with the drone when
Figure BDA0002990577720000047
A time of 1 indicates that the user is unable to communicate with the drone.
Preferably, the unmanned aerial vehicles in the area to be deployed can communicate with the user; the tethered drone is deployed on a road for direct communication with a base station; non-tethered unmanned aerial vehicle passes through tethered unmanned aerial vehicle communicates with the basic station, non-tethered unmanned aerial vehicle can not directly transmit data with the basic station.
Preferably, a successive convex approximation algorithm, a linear relaxation algorithm and a weighting/are used1The maximum number of users which can be covered is obtained by algorithm solution, including approximating non-convex constraints (1a) and (1d) by continuous convex approximation algorithm, performing linear relaxation on integer constraint (1e), and weighting
Figure BDA0002990577720000048
The algorithm constructs a weighted variable for the objective function, and converts the original problem into a convex problem to solve.
Preferably, continuousConvex approximation algorithm, linear relaxation algorithm and weighting l1The method for obtaining the maximum number of the users capable of being covered by the algorithm comprises the following steps:
s61 non-convex objective function using continuous convex approximation algorithm
Figure BDA0002990577720000051
Approximated as a convex function
Figure BDA0002990577720000052
Wherein alpha isnMore than or equal to 0 is the coefficient introduced during the approximation process, when x0＝x1…＝xNOr
Figure BDA0002990577720000053
When the value of the non-convex function is equal to the value of the convex function;
for constraint (1a), the constraint is processed using the algorithm described above
Figure BDA0002990577720000054
Wherein, yi＝max(Aiq0-bi) A convex constraint of the following formula (3) is obtained:
Figure BDA0002990577720000055
wherein x isnIs a variable, αn、αn*And alphaiAll are auxiliary coefficients introduced during approximate processing;
for constraint (1d), let xn＝||qn-sk| |, yielding the following formula (4):
Figure BDA0002990577720000056
the following constraint (5) is obtained by approximation:
Figure BDA0002990577720000057
wherein, betankA coefficient introduced at the time of approximation processing, M → +%, at which point formula (4) is converted into convex constraint;
s62 for integer constraint (1e), the variable x is changed from 0 to 1kRelaxation of xk∈[0，1]，
Figure BDA0002990577720000059
And introducing the following formula (6) as a penalty term on the first objective function:
Figure BDA0002990577720000058
wherein gamma is a penalty coefficient for xk(1-xk) Using Taylor's formula to approximate, neglecting constant terms, and finally approximating as
Figure BDA0002990577720000069
S63 applying weight l1The algorithm constructs a weighted variable w for the objective function as follows (7):
Figure BDA0002990577720000061
wherein, ε → 0, the original non-convex objective function
Figure BDA0002990577720000062
Conversion to convex objective function:
Figure BDA0002990577720000063
s64 updating coefficient alpha by using the result obtained after solvingi，βnkAnd obtaining the maximum number of users which can be covered until the first objective function is converged.
Preferably, the minimum number of unmanned aerial vehicles covering the maximum user to be deployed and the corresponding deployment positions are obtained by adopting a dichotomy and a continuous convex approximation algorithm, the method comprises the steps of approximating non-convex constraints (2a) and (2d) by adopting a continuous convex approximation method, converting an original problem into a convex problem, and solving a second objective function by adopting a dichotomy.
Preferably, the minimum number of unmanned aerial vehicles covering the maximum user to be deployed and the corresponding deployment position are obtained by adopting a continuous convex approximation algorithm and a bisection method, and the method specifically comprises the following steps:
s81 non-convex objective function using continuous convex approximation algorithm
Figure BDA0002990577720000064
Approximated as a convex function
Figure BDA0002990577720000065
Wherein alpha isnMore than or equal to 0 is the coefficient introduced during the approximation process, when x0＝x1…＝xNOr
Figure BDA0002990577720000066
When the value of the non-convex function is equal to the value of the convex function;
for constraint (2a), the constraint is processed using the algorithm described above
Figure BDA0002990577720000067
Wherein, yi＝max(Aiq0-bi) A convex constraint of the following formula (9) is obtained:
Figure BDA0002990577720000068
wherein x isnIs a variable, αn、αn*And alphaiAll are auxiliary coefficients introduced during approximate processing;
for constraint (2d), let xn＝||qn-sk| |, yielding the following formula (10):
Figure BDA0002990577720000071
the following constraint (11) is obtained by approximation:
Figure BDA0002990577720000072
at this time, the formula (10) is convex constraint;
the specific processing steps of the S82 dichotomy are as follows: determining an upper bound N for a required number of dronesmaxAnd a lower bound NmniThen order again
Figure BDA0002990577720000073
Judging whether N is feasible, if N is feasible, making NmaxN, otherwise NminAnd repeating iterative calculation until the algorithm converges to obtain the minimum number of the unmanned aerial vehicles which cover the maximum user and need to be deployed and the corresponding deployment positions.
It can be seen from the technical solutions provided by the above-mentioned unmanned aerial vehicle cluster deployment method based on the ground cellular system of the present invention that, under the given arrangement conditions, the method of the present invention takes the radius constraints between unmanned aerial vehicles and unmanned aerial vehicles, between unmanned aerial vehicles and base stations, between unmanned aerial vehicles and users, and the position constraints of tethered unmanned aerial vehicles as constraint conditions, and takes the maximization of the number of coverable users and the minimization of the number of unmanned aerial vehicles required for covering the users as objective functions, first, the maximum number of coverable users is obtained by adopting a continuous convex approximation algorithm, a linear relaxation algorithm, and a weighting algorithm, and then the minimum number of unmanned aerial vehicles covering the users is obtained by using a continuous convex approximation and a bisection method, and the unmanned aerial vehicle cluster is deployed, so that the actual non-convex problem is successfully converted into a convex optimization problem which can be efficiently solved by a CVX convex optimization toolkit, and the large-scale coverage under the condition of high system capacity can be realized, the algorithm operation process is simple, and faster iterative convergence can be realized.
Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
Fig. 1 is a schematic flow chart of a method for deploying an unmanned aerial vehicle cluster based on a ground cellular system;
fig. 2 provides a schematic diagram of a terrestrial-based cellular system scenario for an embodiment;
FIG. 3 is a schematic diagram illustrating a solving process of a maximum number of users that can be covered;
fig. 4 is a schematic diagram of a solving process of the minimum number of drones required to be deployed by the maximum user and the corresponding deployment position.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
As used herein, the singular forms "a", "an", "the" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. It will be understood that when an element is referred to as being "connected" or "coupled" to another element, it can be directly connected or coupled to the other element or intervening elements may also be present. Further, "connected" or "coupled" as used herein may include wirelessly connected or coupled. As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items.
It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
For the convenience of understanding the embodiments of the present invention, the following description will be further explained by taking several specific embodiments as examples in conjunction with the drawings, and the embodiments are not to be construed as limiting the embodiments of the present invention.
Examples
Fig. 1 is a schematic flow chart of a method for deploying an unmanned aerial vehicle cluster based on a ground cellular system, and with reference to fig. 1, the method includes the following steps:
s1, determining the position and height of a user, the position of a base station, the initial number and flight height of unmanned aerial vehicles, and the road position of a tethered unmanned aerial vehicle in a region to be deployed, wherein the position constraint of the tethered unmanned aerial vehicle, the maximum communication radius constraint between the tethered unmanned aerial vehicle and the base station, the maximum communication radius constraint between the tethered unmanned aerial vehicle and a non-tethered unmanned aerial vehicle, and the maximum communication radius constraint between the unmanned aerial vehicle and the user are taken as constraint conditions;
fig. 2 is a schematic view of a scene based on a ground cellular system provided in this embodiment, and referring to fig. 2, K ground users are randomly distributed in an area, a ground base station is disposed in an area to be deployed, and the height of the ground base station is HBSOne tethered drone (Mooring UAV, mvuav) is deployed on a specific road, N non-tethered drones (Flying UAV, fUAV) are deployed around the mvuav, the Flying height of the drones is fixed to H, or the Flying height of the drones can be optimized by using an algorithm, and the Flying height of the drones needs to meet relevant regulations. For the convenience of analysis and solution, a three-dimensional Cartesian coordinate system is established
Figure BDA0002990577720000091
n＝0，1，...N，qnRepresenting the position coordinates of the drone, where q0I.e. n is 0, is the position coordinate of the mUAV, qnN1, N, is the position coordinate of the fUAV, and the position coordinate of the kth user is
Figure BDA0002990577720000092
Wherein K belongs to {1, 2, …, K }, and the base station bit coordinate is qB. And assuming that there are I roads in the scene, I1., I, mhuav can be deployed on any one road. The maximum communication radius between the mUAV and the base station is R1Maximum radius of communication between mUAV and fUAV is R2The maximum communication radius between the unmanned aerial vehicle and the user is R3The dimensions of the ith road are known.
Wherein, the UAVs in the area to be deployed can all communicate with users; the mhuav is deployed on the road for direct communication with the base station; the fUAV communicates with the base station through the mUAV, which cannot transmit data directly with the base station. Because any one mhuav can be deployed above an emergency vehicle to solve the problem of continuous power supply, and the emergency vehicle can only stop on a limited road, the location of the mhuav can only be within a limited area. And establishing a coordinate system by taking the position of the base station as a coordinate origin, and dividing the road area into a plurality of polygons. Let q0For coordinate vectors of mUAV, the polygonal area may be represented as Aiq0≤bi，Ai，biThe position constraint for the polygonal area parameter matrix, i.e., the mhuav, is shown as equation (1) below:
Figure BDA0002990577720000101
the following formula (2) can be obtained from the above formula (1):
Figure BDA0002990577720000102
the distance constraint for data transmission between the UAV and the BS is obtained as shown in the following equation (3):
||q0-qB||≤R1 (3)
since the fUAVs are all data-transmitting with the affiliated mUAVs, the distance constraint between the fUAVs and the mUAVs is shown in equation (4) below:
Figure BDA0002990577720000103
since only ground users within the coverage area of the UAV signal can transmit data with the UAV, x is usedkE {0, 1} to represent the connection status of the user, as shown in the following formula (5):
Figure BDA0002990577720000104
when a user is connectable, the user can be covered by at least the signal range of one UAV, i.e., the user is at least within the communication radius of one UAV. By skAnd (3) representing a coordinate vector of the ground user, and obtaining a maximum communication radius constraint between the tethered drone and the base station as shown in the following formula (6):
Figure BDA0002990577720000105
where q isnThe total number of drones is (N +1) for the coordinate vectors of the individual UAVs, including fUAV and mvuav.
The present embodiment divides the final deployment problem into two stages, S2 and S3:
s2 using continuous convex approximation algorithm, linear relaxation algorithm and weighting to maximize the number of coverable users as the first objective function
Figure BDA0002990577720000111
And solving by an algorithm to obtain the maximum number of users which can be covered.
The first objective function is expressed by the following equation (7):
Figure BDA0002990577720000112
Figure BDA0002990577720000113
||q0-qB||≤R1， (1b)
Figure BDA0002990577720000114
Figure BDA0002990577720000115
Figure BDA0002990577720000116
wherein | · | purple sweet0Is zero norm and is used for calculating the number of non-zero elements in the objective function, x is the number of covered users, xkAnd E {0, 1} represents the connection state of the user, wherein the state is 0 to indicate that the user can realize communication with the unmanned aerial vehicle, and the state is 1 to indicate that the user cannot realize communication with the unmanned aerial vehicle.
Approximating the non-convex constraints (7a) and (7d) using a successive convex approximation algorithm and linearly relaxing the integer constraint (7e), using a weighting l1The algorithm constructs a weighted variable for an objective function, converts an original problem into a convex problem and solves the convex problem, and the method comprises the following specific steps:
1) non-convex objective function by adopting continuous convex approximation algorithm
Figure BDA0002990577720000117
Approximated as a convex function
Figure BDA0002990577720000118
Wherein alpha isnMore than or equal to 0 is the coefficient introduced during the approximation process, when x0＝x1…＝xNOr
Figure BDA0002990577720000119
When the value of the non-convex function is equal to the value of the convex function; for constraint (7a), the above algorithm is used to process the constraint, converting the vector inequality to a scalar inequality of the following equation (8):
Figure BDA00029905777200001110
Figure BDA00029905777200001111
wherein, take yi＝max(Aiq0-bi) The constraint can then be processed using a continuous convex approximation algorithm, this time with:
Figure BDA0002990577720000121
wherein x isnIs a variable, αn、αn*And alphaiAll are auxiliary coefficients introduced for the approximation process,
Figure BDA0002990577720000122
αiis more than or equal to 0. When alpha isi*＝1，
Figure BDA0002990577720000123
When the equation is true, when i ≠ i*When is αiWhen the original problem (7) has an optimal solution at 0, it can be deduced that the following equations (10) and (11) are equivalent:
Figure BDA0002990577720000124
Figure BDA0002990577720000125
the non-convex constraint (7a) is converted into a convex constraint form of equation (11).
For the constraints (7b), (7c), the base station coordinates qBAs is known, equations (7b) and (7c) are both convex constraints. For constraint (7d), since only x existskWhen the expression (7d) is satisfied when the value is 0, the right part of the expression (7d) is rewritten to (1-x)k)R3+xkM, at which time formula (7d) is converted to the following formula (12):
Figure BDA0002990577720000126
wherein, M → +. varies.
The left part of the above equation (12) is a form that minimizes the 2 norm, and the known 2 norm form is a convex function when x iskWhen 0, for user sk，
Figure BDA0002990577720000127
The left part of equation (12) satisfies:
Figure BDA0002990577720000128
wherein, betankIn order to approximate the coefficients introduced in the processing,
Figure BDA0002990577720000129
βnkis greater than or equal to 0 when
Figure BDA00029905777200001210
The equation (13) holds. Let the right part of equation (13)
Figure BDA00029905777200001211
The method is equivalent to the method for scaling the formula (12), so that the original constraint is stricter. At this time, the new constraint is in the form of a 2-norm sum, is a convex constraint, and is easier to handle than the original constraint.
2) For constraint (7e), xkE {0, 1} is not a convex set. To eliminate the integer constraint, the original problem is linearly relaxed. A variable x is changed from 0 to 1kRelaxation of xk∈[0，1]，
Figure BDA0002990577720000131
And introducing the following formula (14) as a penalty term on the first objective function:
Figure BDA0002990577720000132
wherein gamma is a penalty coefficient for xk(1-xk) Using Taylor's formula to approximate, neglecting constant terms, and finally approximating as
Figure BDA0002990577720000133
3) Using weighting l1The algorithm constructs a weighted variable ω for the objective function as follows (15):
Figure BDA0002990577720000134
wherein, ε → 0, the original non-convex objective function
Figure BDA0002990577720000135
Conversion to convex objective function:
Figure BDA0002990577720000136
therefore, the original problem (7) is finally transformed into the following convex optimization problem:
Figure BDA0002990577720000137
Figure BDA0002990577720000138
||q0-qB||≤R1， (17b)
Figure BDA0002990577720000139
Figure BDA00029905777200001310
Figure BDA00029905777200001311
in particular, αiThe updating method comprises the following two steps:
the first scheme is as follows:
Figure BDA0002990577720000141
scheme II:
Figure BDA0002990577720000149
wherein the content of the first and second substances,
Figure BDA0002990577720000142
ρ is the step size, which is set to 0.2 in this embodiment, let
Figure BDA0002990577720000143
And is
Figure BDA0002990577720000144
βnkThe update method (2) is shown in the following equation (20):
Figure BDA0002990577720000145
4) updating the coefficient alpha by using the result obtained after solvingi，βnkUntil the first objective function converges, obtaining the maximum number of users K which can be covered*. The specific solving process is shown in FIG. 3
S3 to cover the maximum number K of users*And minimizing the number of the required unmanned aerial vehicles as a second objective function, and obtaining the minimum number of the unmanned aerial vehicles which cover the maximum user and need to be deployed and the corresponding deployment positions by adopting a continuous convex approximation algorithm and a dichotomy.
K found*The position of each user is fixed, at the moment
Figure BDA0002990577720000146
And (3) approximating the non-convex constraints (2a) and (2d) by adopting a continuous convex approximation method, converting the original problem into a convex problem, and solving the second objective function by adopting a dichotomy.
The second objective function is expressed by the following equation (21):
Figure BDA0002990577720000147
Figure BDA0002990577720000148
||q0-qB||≤R1， (21b)
Figure BDA0002990577720000151
Figure BDA0002990577720000152
Figure BDA0002990577720000153
indicating the connection state of the user under the second objective function when
Figure BDA0002990577720000154
A value of 0 indicates that the user can communicate with the drone when
Figure BDA0002990577720000155
A time of 1 indicates that the user is unable to communicate with the drone.
The processing methods S2 of the constraints (21a), (21b), and (21c) are the same, and are not described again here. The constraint (21d) is processed in a similar manner as in stage one. First, scaling the left part of equation (21d) yields equation (22):
Figure BDA0002990577720000156
so that in the first iteration
Figure BDA0002990577720000157
If it is true, a variable D is added to the right part of the equation, and D is satisfied when D is infinite
Figure BDA0002990577720000158
When D is less than or equal to 0, the original constraint is established.
Thus, each iteration solves the following problem:
Figure BDA0002990577720000159
Figure BDA00029905777200001510
||q0-qB||≤R1， (23b)
Figure BDA00029905777200001511
Figure BDA00029905777200001512
when the problem (23d) gets the best optimization variable
Figure BDA00029905777200001513
When the temperature of the water is higher than the set temperature,
Figure BDA00029905777200001514
namely s.t.
Figure BDA00029905777200001515
I obtains equal sign, and the equal sign is satisfied to satisfy the requirement of any k, | | q1-sk||＝||q2-sk||＝...＝||qn-skI or
Figure BDA00029905777200001516
When | | | q1-sk||＝||q2-sk||＝...＝||qn-skWhen | l, the drones are all deployed with user skThe circle as the center of the circle obviously does not meet the practical situation, so the circle must meet the requirement
Figure BDA0002990577720000162
The concrete steps of solving by adopting the dichotomy in the calculation process of the continuous convex approximation algorithm are as follows:
determining an upper bound N for a required number of dronesmaxAnd a lower bound NminThen order again
Figure BDA0002990577720000163
Judging whether N is feasible, if N is feasible, making NmaxN, otherwise NminAnd repeating the iterative calculation until the algorithm converges to obtain the coverage. The specific solving process is shown in fig. 4.
Tables 1 and 2 below are specific solving algorithms of S1 and S2, respectively.
TABLE 1
Figure BDA0002990577720000161
TABLE 2
Figure BDA0002990577720000171
To sum up, in this embodiment, when a certain number of users and a certain number of roads and base station positions are given, the base station signal coverage is expanded through the communication between the auxiliary base station of the unmanned aerial vehicle and the ground user, under the condition of ensuring the maximum communication radius constraint among the unmanned aerial vehicle, the base station and the users, the number of the unmanned aerial vehicles is minimized by optimizing the positions and the number of the unmanned aerial vehicles under the condition of maximizing the number of covered users, the number N of the roads and the number N of the unmanned aerial vehicles deployed by the mhuavs is given first, and the continuous convex approximation and the weighting l are used1The method is used for solving, then the users which can be covered most in the scene are obtained, and then the minimum number N of the unmanned aerial vehicles covering the users can be finally obtained by utilizing a dichotomy and a continuous convex approximation method. The problem that the original problem is difficult to solve is solved.
Those skilled in the art should understand that the above-mentioned application types of the input box are only examples, and other existing or future application types of the input box, such as those applicable to the embodiments of the present invention, should be included in the scope of the present invention and are also included herein by reference.
Those of ordinary skill in the art will understand that: the attached drawings are only schematic diagrams of one embodiment, the scene to be deployed in the attached drawings is not limited to the scene, and the method can be adopted for unmanned aerial vehicle arrangement of emergency communication of a gymnasium, railway slope sensor communication and construction site communication.
From the above description of the embodiments, it is clear to those skilled in the art that the present invention can be implemented by software plus necessary general hardware platform. Based on such understanding, the technical solutions of the present invention may be embodied in the form of a software product, which may be stored in a storage medium, such as ROM/RAM, magnetic disk, optical disk, etc., and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the method according to the embodiments or some parts of the embodiments.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (5)

1. An unmanned aerial vehicle cluster deployment method based on a ground cellular system is characterized by comprising the following steps:
determining the position and height of a user, the position of a base station, the initial number and flight height of unmanned aerial vehicles and the road position of a tethered unmanned aerial vehicle in a region to be deployed, wherein the position constraint of the tethered unmanned aerial vehicle, the maximum communication radius constraint between the tethered unmanned aerial vehicle and the base station, the maximum communication radius constraint between the tethered unmanned aerial vehicle and a non-tethered unmanned aerial vehicle and the maximum communication radius constraint between the unmanned aerial vehicle and the user are taken as constraint conditions;
taking the maximum number of the coverable users as a first objective function, and adopting a continuous convex approximation algorithm, a linear relaxation algorithm and a weight l1Solving by an algorithm to obtain the maximum number of users which can be covered;
the minimum number of unmanned aerial vehicles required by covering the maximum number of users is taken as a second objective function, and the minimum number of unmanned aerial vehicles required to be deployed and corresponding deployment positions for covering the maximum users are obtained by adopting a continuous convex approximation algorithm and a bisection method;
the first objective function is shown in the following formula (1):
Figure FDA0003399775410000011
Figure FDA0003399775410000012
||q0-qB||≤R1， (1b)
Figure FDA0003399775410000013
Figure FDA0003399775410000014
Figure FDA0003399775410000015
wherein x is the number of users covered, | ·| non-woven phosphor0Is zero norm, qnAs coordinate vector of the nth drone, AiAnd biAn ith polygon area parameter matrix for dividing the road into a plurality of polygons, wherein I is 1kPosition coordinates, x, representing the k-th user on the groundkE {0, 1} represents the connection state of the user, when the connection state is 0, the user can communicate with the unmanned aerial vehicle, when the connection state is 1, the user cannot communicate with the unmanned aerial vehicle, and q is0Is a coordinate vector of the mooring type unmanned aerial vehicle, N is the number of the non-mooring type unmanned aerial vehicles, the total number of the unmanned aerial vehicles is (N +1), qBThe maximum communication radius between the tethered unmanned aerial vehicle and the base station is R for the position coordinate of the base station1The maximum communication radius between the tethered unmanned aerial vehicle and the non-tethered unmanned aerial vehicle is R2The maximum communication radius between the unmanned aerial vehicle and the user is R3K is the number of ground users, and K belongs to {1, 2, …, K };
the second objective function is shown in the following formula (2):
Figure FDA0003399775410000021
Figure FDA0003399775410000022
||q0-qB||≤R1， (2b)
Figure FDA0003399775410000023
Figure FDA0003399775410000024
wherein N is the number of non-tethered unmanned aerial vehicles, qnIs the coordinate vector of the nth drone, skRepresenting the location coordinates of the kth user on the ground, q0Coordinate vector of the captive drones, N is the number of non-captive drones, qBThe maximum communication radius between the tethered unmanned aerial vehicle and the base station is R for the position coordinate of the base station1The maximum communication radius between the tethered unmanned aerial vehicle and the non-tethered unmanned aerial vehicle is R2The maximum communication radius between the unmanned aerial vehicle and the user is R3，
Figure FDA0003399775410000025
Indicating the connection state of the user under the second objective function when
Figure FDA0003399775410000026
A value of 0 indicates that the user can communicate with the drone when
Figure FDA0003399775410000027
A 1 indicates that the user cannot communicate with the unmanned aerial vehicle;
the unmanned aerial vehicles in the area to be deployed can communicate with users; the tethered drone is deployed on a road for direct communication with a base station; non-tethered unmanned aerial vehicle passes through tethered unmanned aerial vehicle communicates with the basic station, non-tethered unmanned aerial vehicle can not directly transmit data with the basic station.
2. The method of claim 1, wherein the successive convex approximation algorithm, the linear relaxation algorithm and the weighting/, are used1The maximum number of users which can be covered is obtained by algorithm solution, including approximating non-convex constraints (1a) and (1d) by continuous convex approximation algorithm, performing linear relaxation on integer constraint (1e), and adopting weighting l1The algorithm constructs a weighted variable for the objective function, and converts the original problem into a convex problem to solve.
3. The method of claim 2, wherein the successive convex approximation algorithm, the linear relaxation algorithm and the weighting/, are used1The method for obtaining the maximum number of the users capable of being covered by the algorithm comprises the following steps:
s61 non-convex objective function using continuous convex approximation algorithm
Figure FDA0003399775410000031
Approximated as a convex function
Figure FDA0003399775410000032
Wherein z isnIs a variable, αn> 0 is a coefficient introduced in the approximation process, when z is0＝z1…＝zNOr
Figure FDA0003399775410000033
When the value of the non-convex function is equal to the value of the convex function;
for constraint (1a), the constraint is processed using the algorithm described above
Figure FDA0003399775410000034
Wherein, yi＝max(Aiq0-bi) A convex constraint of the following formula (3) is obtained:
Figure FDA0003399775410000035
wherein alpha isn、αn*And alphaiαiAll auxiliary coefficients are introduced during approximate processing;
for constraint (1d), let zn＝||qn-sk| |, yielding the following formula (4):
Figure FDA0003399775410000036
the following constraint (5) is obtained by approximation:
Figure FDA0003399775410000037
wherein, betankFor coefficients introduced during the approximation process, M → + ∞, at which point equation (4) is converted to a convex constraint;
s62 for integer constraint (1e), the variable x is changed from 0 to 1kIs relaxed to
Figure FDA0003399775410000038
And introducing the following formula (6) as a penalty term on the first objective function:
Figure FDA0003399775410000039
wherein gamma is a penalty coefficient for xk(1-xk) Using Taylor's formula to approximate, neglecting constant terms, and finally approximating as
Figure FDA0003399775410000041
S63 applying weight l1The algorithm constructs a weighting variable omega for the objective function as follows (7):
Figure FDA0003399775410000042
wherein, ε → 0, the original non-convex objective function
Figure FDA0003399775410000043
Conversion to convex objective function:
Figure FDA0003399775410000044
s64 updating coefficient alpha by using the result obtained after solvingi；βnkAnd obtaining the maximum number of users which can be covered until the first objective function is converged.
4. The method according to claim 1, wherein the obtaining the minimum number of drones covering the maximum user to be deployed and the corresponding deployment positions by using the bisection method and the successive convex approximation algorithm comprises approximating non-convex constraints (2a) and (2d) by using the successive convex approximation method, converting an original problem into a convex problem, and solving a second objective function by using the bisection method.
5. The method according to claim 4, wherein the obtaining of the minimum number of drones covering the maximum user to be deployed and the corresponding deployment position by using the successive convex approximation algorithm and the bisection method specifically comprises the following steps:
s81 non-convex objective function using continuous convex approximation algorithm
Figure FDA0003399775410000045
Approximated as a convex function
Figure FDA0003399775410000046
Wherein alpha isn> 0 is a coefficient introduced in the approximation process, when z is0＝z1…＝zNOr
Figure FDA0003399775410000047
When the value of the non-convex function is equal to the value of the convex function;
for constraint (2a), the constraint is processed using the algorithm described above
Figure FDA0003399775410000048
Wherein, yi＝max(Aiq0-bi) A convex constraint of the following formula (9) is obtained:
Figure FDA0003399775410000049
wherein alpha isn、αn*And alphaiAll are auxiliary coefficients introduced during approximate processing;
for constraint (2d), let xn＝||qn-sk| |, yielding the following formula (10):
Figure FDA0003399775410000051
the following constraint (11) is obtained by approximation:
Figure FDA0003399775410000052
at this time, the formula (10) is convex constraint;
the specific processing steps of the S82 dichotomy are as follows: determining an upper bound N for a required number of dronesmaxAnd a lower bound NminThen order again
Figure FDA0003399775410000053
Judging whether N is feasible, if N is feasible, making NmaxN, otherwise NminAnd repeating iterative calculation until the algorithm converges to obtain the minimum number of the unmanned aerial vehicles which cover the maximum user and need to be deployed and the corresponding deployment positions.
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