CN111552313A - Multi-unmanned aerial vehicle path planning method based on edge calculation dynamic task arrival - Google Patents

Multi-unmanned aerial vehicle path planning method based on edge calculation dynamic task arrival Download PDF

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CN111552313A
CN111552313A CN202010357106.2A CN202010357106A CN111552313A CN 111552313 A CN111552313 A CN 111552313A CN 202010357106 A CN202010357106 A CN 202010357106A CN 111552313 A CN111552313 A CN 111552313A
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unmanned aerial
aerial vehicle
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time slot
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CN111552313B (en
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孙文煜
王霏霏
钱玉文
李骏
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Nanjing University of Science and Technology
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Abstract

The invention discloses a multi-unmanned aerial vehicle path planning method based on edge computing dynamic task arrival, which comprises the following steps: establishing a system model of a plurality of unmanned aerial vehicle cooperative service users; constructing a path planning problem of multiple unmanned aerial vehicles; simplifying the problem into an optimization problem in a single time slot; and decomposing the optimization problem into a user frequency optimization sub-problem and a joint optimization problem of multi-unmanned aerial vehicle path optimization and user association sub-problems. Compared with a single unmanned aerial vehicle scene, the method and the system have the advantages that multiple tasks and energy queues of multiple unmanned aerial vehicles are increased, and scheduling limitation conditions are increased to ensure cooperative communication among the multiple unmanned aerial vehicles. In addition, in order to solve the complex multi-unmanned aerial vehicle path planning and scheduling problem, the Lyapunov queue optimization theory and the block iterative descent algorithm are combined, and the problem complexity is further reduced by utilizing linear relaxation and continuous convex approximation. Simulation results show that compared with a single unmanned aerial vehicle system, the multi-unmanned aerial vehicle service ground user system has the advantages that the energy consumption of the unmanned aerial vehicle is reduced to some extent, and the queue backlog task amount is reduced.

Description

Multi-unmanned aerial vehicle path planning method based on edge calculation dynamic task arrival
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to a multi-unmanned aerial vehicle path planning method based on edge computing dynamic task arrival.
Background
With the development of the times and the demands of users on communication and data processing, the unmanned aerial vehicle is widely applied to providing communication services for ground users in real time by combining with a small base station. Considering the self energy consumption limitation of the unmanned aerial vehicle, in order to maximize the working energy efficiency of the unmanned aerial vehicle, the flight path of the unmanned aerial vehicle needs to be reasonably planned.
Through optimizing its flight path, unmanned aerial vehicle can toward the direction flight of preferred to the user to shorten the distance between the two, improve channel capacity. However, being too close to a user means being further away from other users (assuming that the users are evenly distributed within a certain range), resulting in a poor communication service for the remote users. Meanwhile, frequent movement can cause excessive energy consumption of the unmanned aerial vehicle, and the service time of the unmanned aerial vehicle is shortened. Therefore, a reasonable flight path is set, and the maximum system efficiency is the key point of the research direction of the unmanned aerial vehicle while the requirement of each user is met. The article 1 "Joint traffic and communication Design for UAV-Enabled Multiple Access" uses continuous convex optimization technology to plan the flight path of the drone base station. Under the limitation of the flight speed of the unmanned aerial vehicle, the problem is firstly modeled into a non-convex mixed integer optimization problem, then the problem is decomposed according to different optimization variables through an iterative algorithm, and finally the optimal flight track of the unmanned aerial vehicle is solved by using a continuous convex optimization technology. Therefore, the minimum throughput is maximized, and the system performance is obviously improved while the fairness is ensured. Paper 2 "Joint traffic and Communication Design for Multi-uav affected Networks" assumes a Communication model with multiple drones as base stations on the basis of paper 1. The throughput of the system is further improved by using the multiple unmanned aerial vehicles to cooperatively serve the ground users. Unlike paper 2, which considers multiple drones, paper 3, "Common Throughput visualization in UAV-Enabled OFDMA Systems With delay negotiation", considers the delay constraints proposed by the users for better serving them. And further, on the basis of an OFDM communication mechanism, an optimal unmanned aerial vehicle path is planned by utilizing a continuous convex optimization technology.
In summary, in the current phase, the energy consumption of the unmanned aerial vehicle is not considered in the path planning scheme for the unmanned aerial vehicle, and the waiting delay caused by the limited processing capability of the base station server is ignored in the process of serving the user by the unmanned aerial vehicle. Meanwhile, the single unmanned aerial vehicle path planning has the condition of low communication efficiency in a large-range area due to the limited self capacity.
Disclosure of Invention
The invention aims to provide a multi-unmanned aerial vehicle path planning method based on edge computing dynamic task arrival.
The technical solution for realizing the purpose of the invention is as follows: a multi-unmanned aerial vehicle path planning method based on edge computing dynamic task arrival comprises the following steps:
step 1, establishing a system model of a multi-unmanned aerial vehicle cooperative service ground user;
step 2, constructing a multi-unmanned aerial vehicle path planning problem in the whole period based on a system model;
step 3, simplifying the multi-unmanned aerial vehicle path planning problem in the whole period by utilizing a Lyapunov queue optimization theory, and obtaining an optimization problem in a single time slot;
and 4, sequentially further optimizing the optimization problem in each single time slot according to the time sequence: and decomposing the optimization problem in the single time slot into a user frequency optimization sub-problem and a joint optimization problem of multi-unmanned aerial vehicle path optimization and user association sub-problems, and solving the two sub-problems.
Further, the step 1 of establishing a system model of a ground user of the multi-unmanned aerial vehicle cooperative service specifically includes:
step 1-1, defining relevant variables of a ground user, comprising:
defining the number of users as K;
defining the user geographical location:
zk＝(xk,yk),k∈{1,2,…K}
in the formula, zkIs the geographic location of the kth user, (x)k,yk) Geographical location coordinates for the kth user;
step 1-2, defining relevant variables of the unmanned aerial vehicle, including:
defining tasks for drone service usersPeriod of time
Figure BDA0002473838220000021
Figure BDA0002473838220000022
The formula represents a task cycle
Figure BDA0002473838220000023
The time slot comprises T time slots, and the length of each time slot is equal;
defining a set of unmanned aerial vehicle quantities
Figure BDA0002473838220000024
Figure BDA0002473838220000025
The formula represents the number set of unmanned aerial vehicles
Figure BDA0002473838220000026
The unmanned aerial vehicle comprises N unmanned aerial vehicles;
defining the flight altitude of each drone:
Figure BDA0002473838220000027
Hnrepresenting the flight altitude of the nth drone;
defining the horizontal position of each drone in a single timeslot:
Figure BDA0002473838220000028
in the formula, wn(t) horizontal position of nth UAV at t time slot, (x)n(t),yn(t)) is the horizontal position coordinate of the nth drone at the tth time slot,
Figure BDA0002473838220000031
defining the horizontal flight speed of each drone within a single time slot:
Figure BDA0002473838220000032
in the formula, vn(t) represents the horizontal flight speed of the nth unmanned plane in the tth time slot, vmaxSetting the maximum horizontal flying speed which can be reached by the unmanned aerial vehicle in a single time slot in a self-defined manner;
step 1-3, constructing a data transmission model, comprising:
defining binary variables αk,n(t), the variable representing establishment of a communication link between the nth drone and the kth user in the tth time slot; recording the binary variable as a user associated variable;
for the binary variable αk,n(t) conditional constraints are imposed, using the formula:
Figure BDA0002473838220000033
Figure BDA0002473838220000034
defining an upload rate between the nth drone and the kth user in a single time slot:
Figure BDA0002473838220000035
wherein R isk,n(t) represents the upload rate between the nth drone and the kth user in the tth time slot, hk,n(t) represents the channel gain between the kth user and the nth drone, with the formula:
Figure BDA0002473838220000036
in the formula, ρ0Channel gain, σ, in unit distance2For AWGN power, p0Transmitting power for the user;
according to binary variable αk,n(t) and upload Rate Rk,n(t) calculating the size of the amount of data transmitted between the drone and the user in a single time slot:
Figure BDA0002473838220000037
in the formula (I), the compound is shown in the specification,
Figure BDA0002473838220000038
the data size transmitted between the nth unmanned aerial vehicle and the kth user in the t-th time slot is represented, and B is the channel bandwidth;
step 1-4, constructing a task queue model, specifically comprising:
(1) constructing a single time slot user side task queue set:
Figure BDA0002473838220000041
in the formula, Qk(t) denotes a task queue of the kth user at the tth slot, and Q is initialized when t is 0k(t) ═ 0; task queue Q of kth user at t +1 th time slotk(t +1) is:
Figure BDA0002473838220000042
in the formula, ak(t) represents the size of the amount of tasks received by the kth user in the tth time slot,
Figure BDA0002473838220000043
represents the sum of the task amount transmitted to the unmanned aerial vehicle by the kth user in the t-th time slot,
Figure BDA0002473838220000044
the size of the local task amount processed and completed by the kth user at the t-th time slot is represented by the following formula:
Figure BDA0002473838220000045
in the formula, ζkIndicating the number of CPU revolutions required for every 1bit task of the kth user,
Figure BDA0002473838220000046
the CPU calculation frequency of the kth user in the t time slot is shown;
(2) constructing a task queue set at the unmanned aerial vehicle end of a single time slot:
Figure BDA0002473838220000047
in the formula, Mk,n(t) indicates the length of the task queue stored by the nth drone for the kth user at the tth time slot, and when t is equal to 0, M is initializedk,n(t) ═ 0; the length M of a task queue stored by the nth unmanned aerial vehicle for the kth user in the t +1 th time slotk,n(t +1) is:
Figure BDA0002473838220000048
wherein the content of the first and second substances,
Figure BDA0002473838220000049
indicating the size of the task volume processed by the nth drone for the kth user in the tth time slot,
Figure BDA00024738382200000410
indicating the processing frequency allocated by the nth unmanned plane to the kth user in the tth time slot;
step 1-5, constructing an energy queue model, specifically comprising:
(1) and (3) constructing the computing energy consumption of a single time slot user side:
Figure BDA0002473838220000051
wherein the content of the first and second substances,
Figure BDA0002473838220000052
the calculated energy consumption of the kth user in the t-th time slot is represented by the formula:
Figure BDA0002473838220000053
wherein γ is the effective switched capacitance constant;
(2) constructing an energy queue set at the unmanned aerial vehicle end of a single time slot:
Figure BDA0002473838220000054
in the formula, En(t) represents the size of the battery capacity of the nth unmanned aerial vehicle in the tth time slot, and when t is equal to 0, the initialization E is carried outn(t) ═ 0; size E of battery capacity of nth unmanned aerial vehicle in t +1 time slotn(t +1) is:
Figure BDA0002473838220000055
wherein the content of the first and second substances,
Figure BDA0002473838220000056
represents the solar energy absorbed by the nth drone during the t-th timeslot and is 0 when the drone is fully charged with battery;
Figure BDA0002473838220000057
respectively represent the computational energy consumption and the flight energy consumption of the nth unmanned aerial vehicle in the tth time slot, and the expressions are respectively:
Figure BDA0002473838220000058
Figure BDA0002473838220000059
in the formula, k is 0.5M, M is the weight of the drone, and the energy consumption sum of the single slot drone is limited as follows:
Figure BDA00024738382200000510
further, the step 2 of building a multi-UAV path planning problem in the whole period based on the system model specifically includes:
step 2-1, defining a time average function and giving out a limiting condition, wherein the method specifically comprises the following steps:
the sum of the energy consumption of all unmanned aerial vehicles flying in a single time slot is defined as
Figure BDA00024738382200000511
The time-averaged function is:
Figure BDA0002473838220000061
in the formula (I), the compound is shown in the specification,
Figure BDA0002473838220000062
representing a desired value;
the time-averaged function defining the sum of the energy consumptions of all users is:
Figure BDA0002473838220000063
defining time average functions of a task queue at a user side, a task queue at an unmanned aerial vehicle side and an energy queue as follows:
Figure BDA0002473838220000064
Figure BDA0002473838220000065
Figure BDA0002473838220000066
the time-averaged function above is limited as follows:
Figure BDA0002473838220000067
Figure BDA0002473838220000068
step 2-2, defining a problem optimization variable, which specifically comprises the following steps:
defining the CPU frequency F of the user to be optimizedlocal：
Figure BDA0002473838220000069
Defining a user associated variable A:
Figure BDA00024738382200000610
defining the flight path W in the whole period of the multiple unmanned planes:
Figure BDA00024738382200000611
step 2-3, based on step 2-1 and step 2-2, constructing a multi-unmanned aerial vehicle path planning problem in the whole period as follows:
Figure BDA0002473838220000071
Figure BDA0002473838220000072
Figure BDA0002473838220000073
Figure BDA0002473838220000074
Figure BDA0002473838220000075
Figure BDA0002473838220000076
Figure BDA0002473838220000077
Figure BDA0002473838220000078
Figure BDA0002473838220000079
further, in step 3, the Lyapunov queue optimization theory is used to simplify the multi-UAV path planning problem in the whole period, and an optimization problem in a single time slot is obtained, and the specific process includes:
step 3-1, defining a Lyapunov function:
Figure BDA00024738382200000710
step 3-2, defining a Lyapunov drift penalty function:
Figure BDA00024738382200000711
in the formula (I), the compound is shown in the specification,
Figure BDA00024738382200000712
VUAVand VUEDisturbance parameters which are respectively the optimal target of controlling the minimum energy consumption of the user and the unmanned aerial vehicle and account for the weight of the whole problem;
step 3-3, determining the upper bound of the Lyapunov drift penalty function by utilizing a Lyapunov queue optimization theory as follows:
Figure BDA0002473838220000081
wherein, C is a constant, and C is a linear alkyl group,
Figure BDA0002473838220000082
therefore, the multi-unmanned aerial vehicle path planning problem in the whole period is decomposed into the optimization problem in a single time slot.
Further, in step 4, decomposing the optimization problem in the single time slot into a user frequency optimization problem and a multi-drone path optimization and user association joint optimization problem, and solving two sub-problems specifically includes:
step 4-1, decomposing an optimization problem in a single time slot into a user frequency optimization sub-problem and a combined optimization problem of multi-unmanned aerial vehicle path optimization and user association sub-problems according to a user frequency variable, a multi-unmanned aerial vehicle position variable and a user association variable;
step 4-2, solving the extreme value of the user frequency optimization subproblem by utilizing a cubic function to serve as the optimal solution;
4-3, solving a sub-problem of multi-unmanned aerial vehicle path optimization and user association, wherein the specific process comprises the following steps:
4-3-1, decomposing the sub-problem of multi-unmanned aerial vehicle path optimization and user association into a sub-problem of single-unmanned aerial vehicle path optimization and user association;
step 4-3-2, solving a sub-problem of single unmanned aerial vehicle path optimization and user association, wherein the process comprises the following steps:
step 4-3-2-1, initializing the number of iterations r to 0, and setting the initial position w of the unmanned aerial vehicle0(t)；
Step 4-3-2-2, according to the position w of the unmanned aerial vehicler(t) solving for user-associated variables α using a linear relaxation methodr+1(t)；
Step 4-3-2-3, according to the user association variable αr+1(t) optimizing Single drone position wr+1(t), specifically including:
(1) solving convex upper and lower bounds of uploading rate by utilizing Lipschitz continuity and Taylor expansion, and optimizing the position w of the single unmanned aerial vehicler+1(t) questionThe question is converted into a convex question;
(2) solving the convex problem by using a convex optimization tool;
step 4-3-2-4, updating the iteration number r ═ r +1, if r is less than r0And returning to execute the step 4-3-2-2, otherwise, stopping iteration.
Compared with the prior art, the invention has the following remarkable advantages: 1) a plurality of tasks and energy queues of a plurality of unmanned aerial vehicles are added, so that all queues of the system can quickly tend to be stable in a short time; 2) scheduling limitation conditions are added, and cooperative communication among multiple unmanned aerial vehicles is guaranteed; 3) the Lyapunov queue optimization theory and the block iteration descent algorithm are combined, so that the problem solving complexity is effectively reduced; 4) simulation results show that compared with a single unmanned aerial vehicle system, the system energy efficiency of the multi-unmanned aerial vehicle service ground user system is remarkably improved.
The present invention is described in further detail below with reference to the attached drawing figures.
Drawings
Fig. 1 is a flowchart of a multi-drone path planning method based on edge-computed dynamic task arrival in one embodiment.
Fig. 2 is a diagram of a simulation result of a path optimization algorithm of the drone system based on edge-computed dynamic task arrival in one embodiment.
Fig. 3 is a diagram of simulation results of the queue length of a user varying with time in one embodiment, where (a) is a diagram of simulation results of the queue length of a user varying with time, and (b) is a diagram of simulation results of the user varying with time at different lengths of task queues of the unmanned aerial vehicle, respectively.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
In one embodiment, in conjunction with fig. 1, there is provided a method for multi-drone path planning based on edge-computed dynamic task arrival, the method comprising:
step 1, establishing a system model of a multi-unmanned aerial vehicle cooperative service ground user;
step 2, constructing a multi-unmanned aerial vehicle path planning problem in the whole period based on a system model;
step 3, simplifying the multi-unmanned aerial vehicle path planning problem in the whole period by utilizing a Lyapunov queue optimization theory, and obtaining an optimization problem in a single time slot;
and 4, sequentially further optimizing the optimization problem in each single time slot according to the time sequence: and decomposing the optimization problem in the single time slot into a user frequency optimization sub-problem and a joint optimization problem of multi-unmanned aerial vehicle path optimization and user association sub-problems, and solving the two sub-problems.
Further, in one embodiment, the establishing a system model of a ground user of cooperative multi-drone service in step 1 specifically includes:
step 1-1, defining relevant variables of a ground user, comprising:
defining the number of users as K;
defining the user geographical location:
zk＝(xk,yk),k∈{1,2,…K}
in the formula, zkIs the geographic location of the kth user, (x)k,yk) Geographical location coordinates for the kth user;
step 1-2, defining relevant variables of the unmanned aerial vehicle, including:
defining a task period for a drone service user
Figure BDA0002473838220000101
Figure BDA0002473838220000102
The formula represents a task cycle
Figure BDA0002473838220000103
Includes T time slots, eachThe lengths of the time slots are all;
defining a set of unmanned aerial vehicle quantities
Figure BDA0002473838220000104
Figure BDA0002473838220000105
The formula represents the number set of unmanned aerial vehicles
Figure BDA0002473838220000106
The unmanned aerial vehicle comprises N unmanned aerial vehicles;
defining the flight altitude of each drone:
Figure BDA0002473838220000107
Hnrepresenting the flight altitude of the nth drone;
defining the horizontal position of each drone in a single timeslot:
Figure BDA0002473838220000108
in the formula, wn(t) horizontal position of nth UAV at t time slot, (x)n(t),yn(t)) is the horizontal position coordinate of the nth drone at the tth time slot,
Figure BDA0002473838220000109
defining the horizontal flight speed of each drone within a single time slot:
Figure BDA00024738382200001010
in the formula, vn(t) represents the horizontal flight speed of the nth unmanned plane in the tth time slot, vmaxSetting the maximum horizontal flying speed which can be reached by the unmanned aerial vehicle in a single time slot in a self-defined manner;
step 1-3, constructing a data transmission model, comprising:
defining binary variables αk,n(t), the variable representing establishment of a communication link between the nth drone and the kth user in the tth time slot; recording the binary variable as a user associated variable;
for the binary variable αk,n(t) conditional constraints are imposed, using the formula:
Figure BDA0002473838220000111
Figure BDA0002473838220000112
defining an upload rate between the nth drone and the kth user in a single time slot:
Figure BDA0002473838220000113
wherein R isk,n(t) represents the upload rate between the nth drone and the kth user in the tth time slot, hk,n(t) represents the channel gain between the kth user and the nth drone, with the formula:
Figure BDA0002473838220000114
in the formula, ρ0Channel gain, σ, in unit distance2For AWGN power, p0Transmitting power for the user;
according to binary variable αk,n(t) and upload Rate Rk,n(t) calculating the size of the amount of data transmitted between the drone and the user in a single time slot:
Figure BDA0002473838220000115
in the formula (I), the compound is shown in the specification,
Figure BDA0002473838220000116
is shown at the t-thThe size of data volume transmitted between the nth unmanned aerial vehicle and the kth user in the time slot, wherein B is channel bandwidth;
step 1-4, constructing a task queue model, specifically comprising:
(1) constructing a single time slot user side task queue set:
Figure BDA0002473838220000117
in the formula, Qk(t) denotes a task queue of the kth user at the tth slot, and Q is initialized when t is 0k(t) ═ 0; task queue Q of kth user at t +1 th time slotk(t +1) is:
Figure BDA0002473838220000118
in the formula, ak(t) represents the size of the amount of tasks received by the kth user in the tth time slot,
Figure BDA0002473838220000119
represents the sum of the task amount transmitted to the unmanned aerial vehicle by the kth user in the t-th time slot,
Figure BDA00024738382200001110
the size of the local task amount processed and completed by the kth user at the t-th time slot is represented by the following formula:
Figure BDA0002473838220000121
in the formula, ζkIndicating the number of CPU revolutions required for every 1bit task of the kth user,
Figure BDA0002473838220000122
the CPU calculation frequency of the kth user in the t time slot is shown;
(2) constructing a task queue set at the unmanned aerial vehicle end of a single time slot:
Figure BDA0002473838220000123
in the formula, Mk,n(t) indicates the length of the task queue stored by the nth drone for the kth user at the tth time slot, and when t is equal to 0, M is initializedk,n(t) ═ 0; the length M of a task queue stored by the nth unmanned aerial vehicle for the kth user in the t +1 th time slotk,n(t +1) is:
Figure BDA0002473838220000124
wherein the content of the first and second substances,
Figure BDA0002473838220000125
indicating the size of the task volume processed by the nth drone for the kth user in the tth time slot,
Figure BDA0002473838220000126
indicating the processing frequency allocated by the nth unmanned plane to the kth user in the tth time slot;
step 1-5, constructing an energy queue model, specifically comprising:
(1) and (3) constructing the computing energy consumption of a single time slot user side:
Figure BDA0002473838220000127
wherein the content of the first and second substances,
Figure BDA0002473838220000128
the calculated energy consumption of the kth user in the t-th time slot is represented by the formula:
Figure BDA0002473838220000129
wherein γ is the effective switched capacitance constant;
(2) constructing an energy queue set at the unmanned aerial vehicle end of a single time slot:
Figure BDA00024738382200001210
in the formula, En(t) represents the size of the battery capacity of the nth unmanned aerial vehicle in the tth time slot, and when t is equal to 0, the initialization E is carried outn(t) ═ 0; size E of battery capacity of nth unmanned aerial vehicle in t +1 time slotn(t +1) is:
Figure BDA0002473838220000131
wherein the content of the first and second substances,
Figure BDA0002473838220000132
represents the solar energy absorbed by the nth drone during the t-th timeslot and is 0 when the drone is fully charged with battery;
Figure BDA0002473838220000133
respectively represent the computational energy consumption and the flight energy consumption of the nth unmanned aerial vehicle in the tth time slot, and the expressions are respectively:
Figure BDA0002473838220000134
Figure BDA0002473838220000135
in the formula, k is 0.5M, M is the weight of the drone, and the energy consumption sum of the single slot drone is limited as follows:
Figure BDA0002473838220000136
further, in one embodiment, the building of the multi-drone path planning problem in the whole period based on the system model in step 2 specifically includes:
step 2-1, defining a time average function and giving out a limiting condition, wherein the method specifically comprises the following steps:
the sum of the energy consumption of all unmanned aerial vehicles flying in a single time slot is defined as
Figure BDA0002473838220000137
The time-averaged function is:
Figure BDA0002473838220000138
in the formula (I), the compound is shown in the specification,
Figure BDA0002473838220000139
representing a desired value;
the time-averaged function defining the sum of the energy consumptions of all users is:
Figure BDA00024738382200001310
defining time average functions of a task queue at a user side, a task queue at an unmanned aerial vehicle side and an energy queue as follows:
Figure BDA00024738382200001311
Figure BDA00024738382200001312
Figure BDA0002473838220000141
the time-averaged function above is limited as follows:
Figure BDA0002473838220000142
Figure BDA0002473838220000143
step 2-2, defining a problem optimization variable, which specifically comprises the following steps:
defining the CPU frequency F of the user to be optimizedlocal：
Figure BDA0002473838220000144
Defining a user associated variable A:
Figure BDA0002473838220000145
defining the flight path W in the whole period of the multiple unmanned planes:
Figure BDA0002473838220000146
step 2-3, based on step 2-1 and step 2-2, constructing a multi-unmanned aerial vehicle path planning problem in the whole period as follows:
Figure BDA0002473838220000147
Figure BDA0002473838220000148
Figure BDA0002473838220000149
Figure BDA00024738382200001410
Figure BDA00024738382200001411
Figure BDA00024738382200001412
Figure BDA00024738382200001413
Figure BDA0002473838220000151
Figure BDA0002473838220000152
further, in one embodiment, the step 3 simplifies the multi-drone path planning problem in the whole period by using the Lyapunov queue optimization theory, and obtains the optimization problem in a single time slot, where the specific process includes:
step 3-1, defining a Lyapunov function:
Figure BDA0002473838220000153
step 3-2, defining a Lyapunov drift penalty function:
Figure BDA0002473838220000154
in the formula (I), the compound is shown in the specification,
Figure BDA0002473838220000155
VUAVand VUEDisturbance parameters which are respectively the optimal target of controlling the minimum energy consumption of the user and the unmanned aerial vehicle and account for the weight of the whole problem;
step 3-3, determining the upper bound of the Lyapunov drift penalty function by utilizing a Lyapunov queue optimization theory as follows:
Figure BDA0002473838220000156
wherein, C is a constant, and C is a linear alkyl group,
Figure BDA0002473838220000157
therefore, the multi-unmanned aerial vehicle path planning problem in the whole period is decomposed into the optimization problem in a single time slot.
Further, in one embodiment, the decomposing of the optimization problem in the single time slot into a user frequency optimization problem and a multi-drone path optimization and user association joint optimization problem in step 4, and solving two sub-problems specifically include:
step 4-1, decomposing an optimization problem in a single time slot into a user frequency optimization sub-problem and a combined optimization problem of multi-unmanned aerial vehicle path optimization and user association sub-problems according to a user frequency variable, a multi-unmanned aerial vehicle position variable and a user association variable;
step 4-2, solving the extreme value of the user frequency optimization subproblem by utilizing a cubic function to serve as the optimal solution;
4-3, solving a sub-problem of multi-unmanned aerial vehicle path optimization and user association, wherein the specific process comprises the following steps:
4-3-1, decomposing the sub-problem of multi-unmanned aerial vehicle path optimization and user association into a sub-problem of single-unmanned aerial vehicle path optimization and user association;
step 4-3-2, solving a sub-problem of single unmanned aerial vehicle path optimization and user association, wherein the process comprises the following steps:
step 4-3-2-1, initializing the number of iterations r to 0, and setting the initial position w of the unmanned aerial vehicle0(t)；
Step 4-3-2-2, according to the position w of the unmanned aerial vehicler(t) solving for user-associated variables α using a linear relaxation methodr+1(t)；
Step 4-3-2-3, according to the user association variable αr+1(t) optimizing Single drone position wr+1(t), specifically including:
(1) solving convex upper and lower bounds of uploading rate by utilizing Lipschitz continuity and Taylor expansion, and optimizing the position w of the single unmanned aerial vehicler+1(t) the problem translates into a convex problem;
(2) solving the convex problem by using a convex optimization tool;
step 4-3-2-4, updating the iteration number r ═ r +1, if r is less than r0And returning to execute the step 4-3-2-2, otherwise, stopping iteration.
As a specific example, the invention is further explained by simulation verification, which comprises the following contents:
setting simulation conditions: is free ofThe human-machine initial flight path is set to be a semi-circle. Task arrival a per user time slotk(t) (Mbits) obedience interval [0,1 ]]And expected value
Figure BDA0002473838220000161
Are independently and equally distributed.
Fig. 2 is a flight path optimization diagram of the dynamic multi-drone under the condition of keeping the queue stable under the above conditions, wherein the initial points of the drones are (1000, 0) and (1000, 500), respectively, and the initial battery charge is 5000J. On the other hand, the star marks in the figure represent the horizontal positions of the users respectively, and the sampling interval of the horizontal flight path of the unmanned aerial vehicle is 50. As can be seen from fig. 2, multiple drones can adjust their flight trajectories in real time according to the state of the user task queue and in consideration of the current position of each drone to serve the user, thereby demonstrating that the present invention has good real-time dynamic performance.
Fig. 3 is a graph showing the change of queue length of a user at the device side and the unmanned side of the user with time under the above conditions. According to the graph, the change trend of the task backlog of the user at each device and the unmanned aerial vehicle end is increased firstly and then stabilized at 60Mbits, and the fact that the multi-unmanned aerial vehicle path planning algorithm provided by the invention can effectively keep the task queue stable is proved.
The foregoing illustrates and describes the principles, general features, and advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (5)

1. A multi-unmanned aerial vehicle path planning method based on edge calculation dynamic task arrival is characterized by comprising the following steps:
step 1, establishing a system model of a multi-unmanned aerial vehicle cooperative service ground user;
step 2, constructing a multi-unmanned aerial vehicle path planning problem in the whole period based on a system model;
step 3, simplifying the multi-unmanned aerial vehicle path planning problem in the whole period by utilizing a Lyapunov queue optimization theory, and obtaining an optimization problem in a single time slot;
and 4, sequentially further optimizing the optimization problem in each single time slot according to the time sequence: and decomposing the optimization problem in the single time slot into a user frequency optimization sub-problem and a joint optimization problem of multi-unmanned aerial vehicle path optimization and user association sub-problems, and solving the two sub-problems.
2. The method for planning paths of multiple unmanned aerial vehicles based on edge-based computation dynamic task arrival according to claim 1, wherein the step 1 of establishing a system model of a multi-unmanned aerial vehicle cooperative service ground user specifically comprises:
step 1-1, defining relevant variables of a ground user, comprising:
defining the number of users as K;
defining the user geographical location:
zk＝(xk,yk),k∈{1,2,…K}
in the formula, zkIs the geographic location of the kth user, (x)k,yk) Geographical location coordinates for the kth user;
step 1-2, defining relevant variables of the unmanned aerial vehicle, including:
defining a task period for a drone service user
Figure FDA0002473838210000011
Figure FDA0002473838210000012
The formula represents a task cycle
Figure FDA0002473838210000013
Includes T time slots, each timeThe length of the gap is equal;
defining a set of unmanned aerial vehicle quantities
Figure FDA0002473838210000014
Figure FDA0002473838210000015
The formula represents the number set of unmanned aerial vehicles
Figure FDA0002473838210000016
The unmanned aerial vehicle comprises N unmanned aerial vehicles;
defining the flight altitude of each drone:
Figure FDA0002473838210000017
Hnrepresenting the flight altitude of the nth drone;
defining the horizontal position of each drone in a single timeslot:
Figure FDA0002473838210000018
in the formula, wn(t) horizontal position of nth UAV at t time slot, (x)n(t),yn(t)) is the horizontal position coordinate of the nth drone at the tth time slot,
Figure FDA0002473838210000021
defining the horizontal flight speed of each drone within a single time slot:
Figure FDA0002473838210000022
in the formula, vn(t) represents the horizontal flight speed of the nth unmanned plane in the tth time slot, vmaxSetting the maximum horizontal flying speed which can be reached by the unmanned aerial vehicle in a single time slot in a self-defined manner;
step 1-3, constructing a data transmission model, comprising:
defining binary variables αk,n(t), the variable representing establishment of a communication link between the nth drone and the kth user in the tth time slot; recording the binary variable as a user associated variable;
for the binary variable αk,n(t) conditional constraints are imposed, using the formula:
Figure FDA0002473838210000023
Figure FDA0002473838210000024
defining an upload rate between the nth drone and the kth user in a single time slot:
Figure FDA0002473838210000025
wherein R isk,n(t) represents the upload rate between the nth drone and the kth user in the tth time slot, hk,n(t) represents the channel gain between the kth user and the nth drone, with the formula:
Figure FDA0002473838210000026
in the formula, ρ0Channel gain, σ, in unit distance2For AWGN power, p0Transmitting power for the user;
according to binary variable αk,n(t) and upload Rate Rk,n(t) calculating the size of the amount of data transmitted between the drone and the user in a single time slot:
Figure FDA0002473838210000027
in the formula (I), the compound is shown in the specification,
Figure FDA0002473838210000031
the data size transmitted between the nth unmanned aerial vehicle and the kth user in the t-th time slot is represented, and B is the channel bandwidth;
step 1-4, constructing a task queue model, specifically comprising:
(1) constructing a single time slot user side task queue set:
Figure FDA0002473838210000032
in the formula, Qk(t) denotes a task queue of the kth user at the tth slot, and Q is initialized when t is 0k(t) ═ 0; task queue Q of kth user at t +1 th time slotk(t +1) is:
Figure FDA0002473838210000033
in the formula, ak(t) represents the size of the amount of tasks received by the kth user in the tth time slot,
Figure FDA0002473838210000034
represents the sum of the task amount transmitted to the unmanned aerial vehicle by the kth user in the t-th time slot,
Figure FDA0002473838210000035
the size of the local task amount processed and completed by the kth user at the t-th time slot is represented by the following formula:
Figure FDA0002473838210000036
in the formula, ζkIndicating the number of CPU revolutions required for every 1bit task of the kth user,
Figure FDA0002473838210000037
the CPU calculation frequency of the kth user in the t time slot is shown;
(2) constructing a task queue set at the unmanned aerial vehicle end of a single time slot:
Figure FDA0002473838210000038
in the formula, Mk,n(t) indicates the length of the task queue stored by the nth drone for the kth user at the tth time slot, and when t is equal to 0, M is initializedk,n(t) ═ 0; the length M of a task queue stored by the nth unmanned aerial vehicle for the kth user in the t +1 th time slotk,n(t +1) is:
Figure FDA0002473838210000039
wherein the content of the first and second substances,
Figure FDA00024738382100000310
indicating the size of the task volume processed by the nth drone for the kth user in the tth time slot,
Figure FDA0002473838210000041
indicating the processing frequency allocated by the nth unmanned plane to the kth user in the tth time slot;
step 1-5, constructing an energy queue model, specifically comprising:
(1) and (3) constructing the computing energy consumption of a single time slot user side:
Figure FDA0002473838210000042
wherein the content of the first and second substances,
Figure FDA0002473838210000043
the calculated energy consumption of the kth user in the t-th time slot is represented by the formula:
Figure FDA0002473838210000044
wherein γ is the effective switched capacitance constant;
(2) constructing an energy queue set at the unmanned aerial vehicle end of a single time slot:
Figure FDA0002473838210000045
in the formula, En(t) represents the size of the battery capacity of the nth unmanned aerial vehicle in the tth time slot, and when t is equal to 0, the initialization E is carried outn(t) ═ 0; size E of battery capacity of nth unmanned aerial vehicle in t +1 time slotn(t +1) is:
Figure FDA0002473838210000046
wherein the content of the first and second substances,
Figure FDA0002473838210000047
represents the solar energy absorbed by the nth drone during the t-th timeslot and is 0 when the drone is fully charged with battery;
Figure FDA0002473838210000048
respectively represent the computational energy consumption and the flight energy consumption of the nth unmanned aerial vehicle in the tth time slot, and the expressions are respectively:
Figure FDA0002473838210000049
Figure FDA00024738382100000410
in the formula, k is 0.5M, M is the weight of the drone, and the energy consumption sum of the single slot drone is limited as follows:
Figure FDA00024738382100000411
3. the method for planning paths of multiple unmanned aerial vehicles based on dynamic task arrival of edge computing according to claim 1, wherein the step 2 of building the path planning problem of multiple unmanned aerial vehicles in the whole period based on the system model specifically comprises:
step 2-1, defining a time average function and giving out a limiting condition, wherein the method specifically comprises the following steps:
the sum of the energy consumption of all unmanned aerial vehicles flying in a single time slot is defined as
Figure FDA0002473838210000051
The time-averaged function is:
Figure FDA0002473838210000052
in the formula (I), the compound is shown in the specification,
Figure FDA0002473838210000053
representing a desired value;
the time-averaged function defining the sum of the energy consumptions of all users is:
Figure FDA0002473838210000054
defining time average functions of a task queue at a user side, a task queue at an unmanned aerial vehicle side and an energy queue as follows:
Figure FDA0002473838210000055
Figure FDA0002473838210000056
Figure FDA0002473838210000057
the time-averaged function above is limited as follows:
Figure FDA0002473838210000058
Figure FDA0002473838210000059
step 2-2, defining a problem optimization variable, which specifically comprises the following steps:
defining the CPU frequency F of the user to be optimizedlocal：
Figure FDA00024738382100000510
Defining a user associated variable A:
Figure FDA00024738382100000511
defining the flight path W in the whole period of the multiple unmanned planes:
Figure FDA0002473838210000061
step 2-3, based on step 2-1 and step 2-2, constructing a multi-unmanned aerial vehicle path planning problem in the whole period as follows:
Figure FDA0002473838210000062
Figure FDA0002473838210000063
Figure FDA0002473838210000064
Figure FDA0002473838210000065
Figure FDA0002473838210000066
Figure FDA0002473838210000067
Figure FDA0002473838210000068
Figure FDA0002473838210000069
Figure FDA00024738382100000610
4. the method for planning paths of multiple unmanned aerial vehicles based on edge-computed dynamic task arrival according to claim 1, wherein the step 3 simplifies the multiple unmanned aerial vehicle path planning problem in the whole period by using a Lyapunov queue optimization theory, and obtains an optimization problem in a single time slot, and the specific process includes:
step 3-1, defining a Lyapunov function:
Figure FDA00024738382100000611
step 3-2, defining a Lyapunov drift penalty function:
Figure FDA00024738382100000612
in the formula (I), the compound is shown in the specification,
Figure FDA00024738382100000613
VUAVand VUERespectively controlling the energy consumption of the user and the unmanned aerial vehicleThe small optimization target is a disturbance parameter occupying weight in the whole problem;
step 3-3, determining the upper bound of the Lyapunov drift penalty function by utilizing a Lyapunov queue optimization theory as follows:
Figure FDA0002473838210000071
wherein, C is a constant, and C is a linear alkyl group,
Figure FDA0002473838210000072
therefore, the multi-unmanned aerial vehicle path planning problem in the whole period is decomposed into the optimization problem in a single time slot.
5. The method for planning paths of multiple unmanned aerial vehicles based on edge-computed dynamic task arrival according to claim 1, wherein the step 4 decomposes the optimization problem in the single time slot into a user frequency optimization problem and a multi-unmanned aerial vehicle path optimization and user association joint optimization problem, and solves two sub-problems, specifically comprising:
step 4-1, decomposing an optimization problem in a single time slot into a user frequency optimization sub-problem and a combined optimization problem of multi-unmanned aerial vehicle path optimization and user association sub-problems according to a user frequency variable, a multi-unmanned aerial vehicle position variable and a user association variable;
step 4-2, solving the extreme value of the user frequency optimization subproblem by utilizing a cubic function to serve as the optimal solution;
4-3, solving a sub-problem of multi-unmanned aerial vehicle path optimization and user association, wherein the specific process comprises the following steps:
4-3-1, decomposing the sub-problem of multi-unmanned aerial vehicle path optimization and user association into a sub-problem of single-unmanned aerial vehicle path optimization and user association;
step 4-3-2, solving a sub-problem of single unmanned aerial vehicle path optimization and user association, wherein the process comprises the following steps:
step 4-3-2-1, initializing the number of iterations r to 0, and setting the initial position w of the unmanned aerial vehicle0(t)；
Step 4-3-2-2, according to the position w of the unmanned aerial vehicler(t) solving for user-associated variables α using a linear relaxation methodr+1(t)；
Step 4-3-2-3, according to the user association variable αr+1(t) optimizing Single drone position wr+1(t), specifically including:
(1) solving convex upper and lower bounds of uploading rate by utilizing Lipschitz continuity and Taylor expansion, and optimizing the position w of the single unmanned aerial vehicler+1(t) the problem translates into a convex problem;
(2) solving the convex problem by using a convex optimization tool;
step 4-3-2-4, updating the iteration number r ═ r +1, if r is less than r0And returning to execute the step 4-3-2-2, otherwise, stopping iteration.
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