CN113268088A - Unmanned aerial vehicle task allocation method based on minimum cost and maximum flow - Google Patents

Unmanned aerial vehicle task allocation method based on minimum cost and maximum flow Download PDF

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CN113268088A
CN113268088A CN202110649038.1A CN202110649038A CN113268088A CN 113268088 A CN113268088 A CN 113268088A CN 202110649038 A CN202110649038 A CN 202110649038A CN 113268088 A CN113268088 A CN 113268088A
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unmanned aerial
aerial vehicle
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task
vehicle base
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CN113268088B (en
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李白思雨
施晓东
丁阳
韩东
孙镱诚
魏文波
周捷
潘阳
乐意
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CETC 28 Research Institute
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Abstract

The invention discloses an unmanned aerial vehicle task allocation method based on minimum cost and maximum flow, which is mainly applied to planning a flight route of an unmanned aerial vehicle in advance before the unmanned aerial vehicle with limited energy capacity executes a task in a known area. The method is based on the premise that the energy stored by the unmanned aerial vehicle is limited and all tasks in a task area cannot be completed at one time, and mainly considers how to utilize an unmanned aerial vehicle base station in the task area as a supply point to distribute long-distance tasks for the unmanned aerial vehicle, so that the moving range of the unmanned aerial vehicle is enlarged. The method comprises the steps of firstly modeling a problem as a minimum cost maximum flow model, then dividing tasks and unmanned aerial vehicle base stations in a task area into a plurality of combinations of 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' by using the minimum cost maximum flow model, and then connecting the combinations into a flight path which can be sequentially executed by adjusting. The method provided by the invention can be used for planning the flight route of the unmanned aerial vehicle with limited energy before executing the mission.

Description

Unmanned aerial vehicle task allocation method based on minimum cost and maximum flow
Technical Field
The invention belongs to the technical field of task allocation of unmanned aerial vehicles before tasks are executed, and particularly relates to an unmanned aerial vehicle task allocation method based on minimum cost and maximum flow.
Background
Despite the continuous development of drone technology and longer flight times, the energy consumption of drones remains a challenge.
In the task execution process, considering that the energy of the unmanned aerial vehicle is limited and in continuous consumption and recovery problems, the unmanned aerial vehicle needs to frequently return to a supply point to supplement the energy and materials. The existing research mostly enables the unmanned aerial vehicle to return to the starting point for supply after executing the task, so that the range of motion of the unmanned aerial vehicle is limited around the starting point, the unmanned aerial vehicle cannot execute the task at a longer distance, and the utilization rate of the unmanned aerial vehicle is limited. In conclusion, because the energy that unmanned aerial vehicle stored is limited, how to distribute remote task for unmanned aerial vehicle under the prerequisite of considering unmanned aerial vehicle energy restriction, enlarge unmanned aerial vehicle's home range becomes main technical problem.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to solve the technical problem of the prior art, and provides an unmanned aerial vehicle task allocation method based on minimum cost and maximum flow, which can plan the flight path of an unmanned aerial vehicle in a known area in advance on the premise of limited energy, reduce the energy consumption of the unmanned aerial vehicle, complete a long-distance task and prevent the unmanned aerial vehicle from being incapable of completing the task or recovering the task due to insufficient energy.
In order to solve the technical problem, the invention discloses an unmanned aerial vehicle task allocation method based on minimum cost and maximum flow, which comprises the following steps:
step 1, defining a task object configuration set L ═ L which is N different in the task area1,L2,···,LNEach task only needs to be executed once; in a task area, M different unmanned aerial vehicle base stations form a set S ═ S1,S2,···,SMWhere unmanned aerial vehicle base station SmThe unmanned aerial vehicle charging system is defined as a supply point for storing the unmanned aerial vehicle and charging equipment of the unmanned aerial vehicle, and the unmanned aerial vehicle can supply energy in any unmanned aerial vehicle base station; there is an unmanned aerial vehicle U of preparation executive task in the task region (for the simplification, supposing not to consider when unmanned aerial vehicle takes off to land and receive the energy consumption that natural factor influences in the flight, unmanned aerial vehicle's energy consumption can be equivalent to unmanned aerial vehicle's flying distance), and under the prerequisite that the energy was full of, unmanned aerial vehicle U's longest flying distance was for unmanned aerial vehicle U
Figure BDA0003111023850000011
Initializing the initial station of the unmanned aerial vehicle to SU；
Step 2, constructing a corresponding minimum cost maximum flow model according to the tasks in the task area and the unmanned aerial vehicle base station;
step 3, modeling the number of completed tasks as flow, and dividing the tasks and unmanned aerial vehicle base stations in a task area into a plurality of combinations of 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' by using the minimum cost maximum flow model constructed in the step 2;
step 4, constructing a combination of the take-off unmanned aerial vehicle base station, the task set and the landing unmanned aerial vehicle base station which can be sequentially executed in the combination of the take-off unmanned aerial vehicle base station, the task set and the landing unmanned aerial vehicle base station obtained in the step 3 into an initial path I;
step 5, if the initial path I contains all the combinations of the takeoff unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station obtained in the step 3, the initial path I is the final path F of the unmanned aerial vehicle for executing all tasks; otherwise, recording the combination of the take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station which is obtained in the step 3 and is not included by the initial path I as a candidate combination of the take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station to form a setC ═ c1,c2V.. v.. Sequentially combining each candidate 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' in the set CLSjFinding the best insertion point in the initial path I and calculating cjInserted at the optimal insertion point. When the set CLS is empty, the initial path I is the final path F of the drone for the drone to perform all tasks.
As a preferred embodiment of the present invention, the minimum cost maximum flow model in step 2 is constructed as follows:
(1) node for constructing minimum-cost maximum flow model
1) And adding the source node s and the destination node t as auxiliary nodes.
2) And adding an unmanned aerial vehicle base station aggregation node as a primary node.
Each unmanned aerial vehicle base station set node represents an unmanned aerial vehicle base station set, each unmanned aerial vehicle base station set comprises two unmanned aerial vehicle base stations, and the two unmanned aerial vehicle base stations can be the same or different. M different unmanned aerial vehicle base stations can constitute
Figure BDA0003111023850000021
A set of different unmanned aerial vehicle base stations, denoted as
Figure BDA0003111023850000022
Wherein unmanned aerial vehicle base station set SUgCan be expressed as SUg＝{Sk1,Sk2}，g＝1，2，···,
Figure BDA0003111023850000023
Wherein Sk1Denotes the takeoff unmanned aerial vehicle base station, S, of the unmanned aerial vehicle in a flight missionk2Representing the landing unmanned aerial vehicle base station in the primary flight task of the unmanned aerial vehicle.
3) And adding the task set node as a secondary node.
For unmanned aerial vehicle base station set SUgIf S isk1And Sk2In contrast, then Sk1And Sk2And all task points can form a completely undirected connected graph
Figure BDA0003111023850000024
If Sk1And Sk2Same, firstly, Sk1And Sk2Considered as distinct points, but the distance between them is 0, and all task points are to Sk1To Sk2Are the same, and then S isk1And Sk2And all task points can form a completely undirected connected graph
Figure BDA0003111023850000025
Figure BDA0003111023850000026
The weight of each edge is the distance between two points, and can be obtained by using depth-first algorithm
Figure BDA0003111023850000027
Ofk1To Sk2All possible paths, and the total distance to which the paths correspond. Wherein the total distance is greater than
Figure BDA0003111023850000031
Will be culled and only the one with the shortest total distance will be left for all paths that perform the same task but in a different order of task execution. All the tasks in each of the remaining paths form a task set.
Each task set node represents a task set, and if the total number of the task sets corresponding to all the unmanned aerial vehicle base stations is P, the model has P different task sets in common to form a set LU ═ LU { (LU)1,LU2,···,LUP}, task set LUpMay be expressed as LUp＝{Lp1,Lp2N, P1, 2, P, wherein Lp1，Lp2Equal representation task set LUpThe task involved.
4) And adding the task node as a three-level node. Each task node represents one task in L, and there are N task nodes in total.
(2) Constructing edges of a least cost maximum flow model
1) Adding edges from a source node
There is an edge between the source node s and each drone base station aggregation node. The capacity of the edge between the source node s and the unmanned aerial vehicle base station aggregation node is N, and the cost is 0.
2) Adding edges from unmanned aerial vehicle base station rendezvous points
There is an edge between each unmanned aerial vehicle base station set node and its corresponding task set node, that is, the unmanned aerial vehicle base station set SUgHow many corresponding task sets of nodes have how many edges from unmanned aerial vehicle base station set SUgAnd (5) starting the node. Each edge is connected with an unmanned aerial vehicle base station set and a task set, so that a take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station (SLS) combination can be formed, and a set LS (LS) formed by combining all the take-off unmanned aerial vehicle base stations-task sets-landing unmanned aerial vehicle base stations is { LS ═1,LS2,···,LSPIn which LS is combinedpDenoted LSp＝{SUg,LUp},g＝1,2，···,
Figure BDA0003111023850000032
P is 1,2, P. When combining LSpAs a flight mission, the drone needs to follow the drone base station Sk1Take off, performed LUpAfter all tasks in the system, the unmanned aerial vehicle lands on an unmanned aerial vehicle base station Sk2LS flight task completed by unmanned planekThe flight distance of (D) is obtained by a depth-first algorithm and is denoted as D (LS)p). Thus, the drone base station set SUgAnd task set LUpCapacity of the edge between is | LUpL, cost D (LS)p)。
3) Adding edges from task rendezvous nodes
Each task set node p will only have edges between task nodes corresponding to tasks included in the task set, i.e. a common | LUpI edge slave task aggregation node LUpAnd (5) starting the node. The capacity of the edge between the task set node and the task node is 1, and the cost is 0.
4) Adding edges from task nodes
An edge exists between each task node and the destination node t. The capacity of the edge between the task node and the terminal node t is 1, and the cost is 0.
As a preferable aspect of the present invention, step 3 includes:
(1) and constructing a corresponding minimum cost maximum flow model G ═ (V, E, $, W).
(2) Initializing the initial station of unmanned aerial vehicle U to SU。
(3) Modeling the number of completed tasks as flow, and obtaining a combined set of 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' with the minimum cost in the minimum cost maximum flow model based on the minimum cost maximum flow model, wherein the combined set comprises the following specific steps:
1) the feasible flow f is initialized to zero flow, at which time the cost of the feasible flow f is 0.
2) Initializing CostminFor the combination LS including 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' with minimum flying distanceminFlow f insideminThe total cost of the combined set of "take-off drone base station-task set-landing drone base station" corresponding to the minimum cost
Figure BDA0003111023850000041
Obtaining a feasible flow f comprising a plurality of 'take-off drone base station-task set-landing drone base station' combinations*Cost $ of the set of "take-off drone base station-task set-landing drone base station" combinations that corresponds to the minimum costf*The steps are as follows:
a) easy known feasible flow f*Cost $f*The sum of the cost of all selected 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' combinations is obtained;
b) selecting remaining flow networks Gf*Medium cost minimum augmentation path p*，p*The corresponding combination of take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station is recorded as LSp′。
c) Will expand the path p*Is added to the viable stream f*In the specification, $f*＝$f*+D(LSp'). If in the remaining streaming network GfB) if there is still an amplification path; otherwise, return $f*；。
3) Combining LS for 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' in LS through circulationiExecuting steps d) to f) in the order of the flight distances from small to large so as to obtain a set of the combination 'take-off drone base station-task set-landing drone base station' with the minimum cost in the streaming network G:
d) obtaining 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' LSi。
e) If LSiIs not selected, then LS is selectediAdding a corresponding path from the source node s to the destination node t as an augmented path into the feasible flow f and returning to d); otherwise f) is executed.
f) All of the feasible flows f are compared with LSiWithdrawing the selected task containing the task conflict, withdrawing the selected task set corresponding to the withdrawing task and the unmanned aerial vehicle base station set to obtain a feasible flow ftemp(ii) a Obtaining a viable flow f by steps a) to c)tempCost of the combined set of "take-off drone base station-task set-landing drone base station" corresponding to minimum cost
Figure BDA0003111023850000051
Order to
Figure BDA0003111023850000052
If it is
Figure BDA0003111023850000053
Let f be ftemp，
Figure BDA0003111023850000054
Returning to d); otherwise, directly returning to d).
4) If some tasks are not in f, aiming at the unselected tasks LnIs prepared by mixing LnAnd (3) sequentially inserting each 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' combination selected in the step (3), recalculating the flight distance of the combination after insertion, and subtracting the flight distance before insertion to obtain the flight distance difference delta Cost before and after insertion into the task. L isnAnd inserting the 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' combination with the minimum delta Cost, wherein the flight distance of the combination also becomes the inserted flight distance. If no matter LnThe flying distances obtained by inserting the combination of any 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' are all larger than
Figure BDA0003111023850000055
Then L will benAnd is away from LnThe nearest unmanned aerial vehicle base station constructs a new combination of takeoff unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station.
As a preferred embodiment of the present invention, the initial path I in step 4 is formed as follows:
(1) judging whether a combination exists in the combination of 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' obtained in the step 3, wherein any one of the take-off unmanned aerial vehicle base station or the landing unmanned aerial vehicle base station is the initial stop unmanned aerial vehicle base station S of the unmanned aerial vehicle UU. If such a combination is not present, then S is usedUTo replace from SUThe nearest task is located in a take-off unmanned aerial vehicle base station or a landing unmanned aerial vehicle base station in a take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station combination.
(2) All combinations capable of sequentially executing 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' are constructed into an initial path, and the initial path is recorded as I ═ I1，i2V.. v.. The method comprises the following specific steps:
1) the initial path I is initialized to null.
2) For each LS combination of the selected 'take-off drone base station-task set-landing drone base station' combinationskAnd (4) carrying out circulation judgment:
if Sk1＝Sk2＝SUThen LS is addedkDirectly inserted into I;
if Sk1＝SU，Sk2≠SU(or S)k2＝SU,Sk2≠SU) Then S will bek1(or S)k2) As LSkTake-off unmanned aerial vehicle base station of, with LSkIs inserted into I, let SU＝Sk2(SU＝Sk1)；
If Sk1≠SUAnd Sk2≠SUThen LS is not addedkIs inserted into I.
As a preferred scheme of the invention, the combination c of the 'candidate takeoff unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' in the step 5jThe specific method of inserting the initial path I is as follows:
candidate 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' combination cjWhen the initial path I is inserted, three different conditions exist, and the insertion point can be the beginning and the end of the initial path I and the middle of two adjacent combinations of 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station'. c. CjTake-off unmanned aerial vehicle base station recorded as Sj1，cjDescending unmanned aerial vehicle base station record Sj2. The specific explanation is as follows:
(1) the beginning of the initial path I is inserted.
With SzFirst "take-off drone base station-task set-landing drone base station" combination I representing initial path I1Take-off drone base station, i.e. Sz＝Si11。
If Sj1＝Sj2＝SzThen cjMust already be in the initial path I.
If Sj1＝SzAnd Sj1≠Sj2Then will Sj1As c isjStarting base station of cjInsert it at the beginning of the initial path I and add I1Take-off unmanned aerial vehicle base station replacement Sj2. Insertion cjThe total flight distance of the subsequent initial path I can be expressed as:
Figure BDA0003111023850000061
wherein D (I V-V)pcj) Means to convert cjTotal flight distance of I after insertion into designated insertion position p of I, D (C)j) And D (i)1) Each represents cjAnd i1The total flying distance of the aircraft is,
Figure BDA0003111023850000062
represents that i is1Unmanned aerial vehicle basic station S inzReplacement is unmanned aerial vehicle basic station Sj2After i1The flight distance. If Sj2＝SzAnd Sj1≠Sj2When it is, will Sj2Will be as cjStarting unmanned aerial vehicle base station, Sj1Will be as cjLanding unmanned aerial vehicle base station insert initial path I, cjThe order of execution of all tasks in (a) needs to be reversed. Insertion cjThe calculation of the total flight distance of the subsequent initial path I is the same as the calculation of (1).
If Sj1≠SzAnd Sj2≠SzWhen S is presentj1And Sj2May be the same or different. S for calculation by the formulae (2) and (3), respectivelyzSubstitution of Sj1And with SzSubstitution of Sj2Then c is addedjTotal flight distance after insertion into the initial path I, and I1Take-off unmanned aerial vehicle base station is replaced by cjAnd (4) the unmanned aerial vehicle base station which is not replaced. And then selecting the minimum flight distance as a final insertion scheme by using the formula (4).
Figure BDA0003111023850000063
Figure BDA0003111023850000064
Figure BDA0003111023850000065
Wherein
Figure BDA0003111023850000066
And
Figure BDA0003111023850000067
means to convert cjThe total flight distance I after insertion into the initial path I specifies the insertion position p, superscript Sj1And Sj2Respectively represent cjQuilt SZAlternative drone base station.
(2) The end of the initial path I is inserted.
With SzThe last "take-off drone base station-task set-landing drone base station" combination I representing the initial path IendLanding drone base station, i.e. Sz＝Siend。
If Sj1＝SzAnd Sj1≠Sj2Then Sj1Will be as cjStarting unmanned aerial vehicle base station, Sj2Will be as cjDescending unmanned aerial vehicle base station, cjInserted to the end of the initial path I. Insertion cjThe total flight distance of the subsequent initial path I can be expressed as:
D(I∨pcj)＝D(I)+D(cj) (5)
if Sj2＝SzAnd Sj1≠Sj2When it is, will Sj2Will be as cjStarting unmanned aerial vehicle base station, Sj1Will be as cjC, inserting the base station of the landing unmanned aerial vehicle into the tail of the initial path IjThe order of execution of all tasks in (a) needs to be reversed. Calculating the insertion c by equation (5)jThe latter initial path I total flight distance.
If Sj1≠SzAnd Sj2≠SzWhen S is presentj1And Sj2May be the same or different. S for calculation by the equations (6) and (7), respectivelyzSubstitution of Sj1And with SzSubstitution of Sj2Then againC is tojThe total flight distance after the end of the initial path I is inserted. And then selecting the minimum flight distance as a final insertion scheme by using the formula (8).
Figure BDA0003111023850000071
Figure BDA0003111023850000072
Figure BDA0003111023850000073
(3) And inserting the two adjacent combinations of the take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station in the initial path I.
With SzDenotes a combination i of a take-off drone base station, a task set and a landing drone base station before an insertion point(γ-1)The landing unmanned aerial vehicle base station and the next combination i of take-off unmanned aerial vehicle base station, task set and landing unmanned aerial vehicle base stationγTake-off drone base station, i.e. Sz＝Si(γ-1)2＝Siγ1。
If Sj1＝Sj2＝SzThen cjDirectly inserted into a specified position, and the insertion c is expressed by the formula (5)jTotal flight distance of the following initial path I.
If Sj1＝SzAnd Sj1≠Sj2Then Sj1Will be as cjStarting unmanned aerial vehicle base station, Sj2Will be as cjDescending unmanned aerial vehicle base station, cjInserted into the insertion point, and iγThe take-off unmanned aerial vehicle base station is replaced by Sj2. Insertion cjThe total flight distance of the subsequent initial path I can be expressed as:
Figure BDA0003111023850000074
if Sj2＝SzAnd Sj1≠Sj2Will Sj2Will be as cjStarting unmanned aerial vehicle base station, Sj1Will be as cjThe base station of the landing drone is inserted into the insertion point, cjThe order of execution of all tasks in (a) needs to be reversed, and (i)γThe take-off unmanned aerial vehicle base station is replaced by Sj1. Insertion cjAnd (4) calculating the total flight distance of the subsequent initial path I in the same way as the step (9).
If Sj1≠SzAnd Sj2≠SzWhen S is presentj1And Sj2May be the same or different. S for calculation by the formulae (2) and (3), respectivelyzSubstitution of Sj1And with SzSubstitution of Sj2Then c is addedjTotal flying distance after insertion into the insertion point, and iγTake-off drone base station should be replaced with cjAnd (4) the unmanned aerial vehicle base station which is not replaced. And then selecting the minimum flight distance as a final insertion scheme by using the formula (4).
Has the advantages that:
a task allocation method for unmanned aerial vehicles based on minimum cost and maximum flow is provided. Make unmanned aerial vehicle can plan unmanned aerial vehicle's flight path in advance in known area under the prerequisite of limited energy to effectively reduce the consumption of the unmanned aerial vehicle energy, the long-range task of better completion prevents that unmanned aerial vehicle can't accomplish the task or can't retrieve because the energy is not enough the problem. The task distance of the unmanned aerial vehicle is expanded, and the range of motion of the unmanned aerial vehicle is expanded.
Drawings
The foregoing and/or other advantages of the invention will become further apparent from the following detailed description of the invention when taken in conjunction with the accompanying drawings.
Fig. 1 is a minimum cost maximum flow model for dividing tasks and drone base stations in a task area into a plurality of sets of drone base stations-task sets-drone base stations.
Fig. 2 is a schematic flowchart of a method for allocating tasks of an unmanned aerial vehicle based on minimum cost and maximum flow according to an embodiment of the present invention.
Fig. 3 is a first case when a candidate "take-off drone base station-task set-landing drone base station" combination is inserted into the initial path.
Fig. 4 is a second case when a candidate "take-off drone base station-task set-landing drone base station" combination is inserted into the initial path.
Fig. 5 is a third scenario when a candidate "take-off drone base station-task set-landing drone base station" combination is inserted into the initial path.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings. 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.
Fig. 1 is a minimum cost maximum flow model for dividing tasks and drone base stations in a task area into a plurality of sets of drone base stations-task sets-drone base stations. The flow network formed by the minimum cost maximum flow model is a directed graph G ═ (V, E, $, W), where V denotes nodes in the graph, E denotes edges in the graph, $ denotes the cost of the edge, and W denotes the capacity of the edge. Each edge in the directed graph G has three attributes, capacity, traffic and cost. The specific steps of constructing the flow network G ═ (V, E, $, W) corresponding to the minimum cost maximum flow model are as follows:
(1) building a system model
1) N different task target forming sets L ═ L in the task area1,L2,···,LNEach target need only be executed once.
2) In the task area, M different unmanned aerial vehicle base stations form a set S ═ S1,S2,···,SMWhere unmanned aerial vehicle base station SmThe unmanned aerial vehicle can supplement energy in any unmanned aerial vehicle base station.
3) Within the mission area there is a drone U ready to perform the mission (for simplicity, it is assumed that nothing is consideredWhen unmanned aerial vehicle takes off and lands and receives the energy consumption that natural factor influences in the flight, unmanned aerial vehicle's energy consumption can be equivalent to unmanned aerial vehicle's flying distance), under the prerequisite that the energy was full of, unmanned aerial vehicle U's the longest flying distance is for unmanned aerial vehicle U
Figure BDA0003111023850000091
(1) Node for constructing minimum-cost maximum flow model
1) And adding the source node s and the destination node t as auxiliary nodes.
2) And adding an unmanned aerial vehicle base station aggregation node as a primary node.
Each unmanned aerial vehicle base station set node represents an unmanned aerial vehicle base station set, each unmanned aerial vehicle base station set comprises two unmanned aerial vehicle base stations, and the two unmanned aerial vehicle base stations can be the same or different. M different unmanned aerial vehicle base stations can constitute
Figure BDA0003111023850000092
A set of different unmanned aerial vehicle base stations, denoted as
Figure BDA0003111023850000093
Wherein unmanned aerial vehicle base station set SUgCan be expressed as SUg＝{Sk1,Sk2},g＝1,2,···,
Figure BDA0003111023850000094
Wherein Sk1Denotes the takeoff unmanned aerial vehicle base station, S, of the unmanned aerial vehicle in a flight missionk2Representing the landing unmanned aerial vehicle base station in the primary flight task of the unmanned aerial vehicle.
3) And adding the task set node as a secondary node. .
For unmanned aerial vehicle base station set SUgIf S isk1And Sk2In contrast, then Sk1And Sk2And all task points can form a completely undirected connected graph
Figure BDA0003111023850000095
If Sk1And Sk2In the same way, the first and second,then S is firstly addedk1And Sk2Consider different points, but the distance between them is 0, and all task points are to Sk1To Sk2Are the same, and then S isk1And Sk2And all task points can form a completely undirected connected graph
Figure BDA0003111023850000096
Figure BDA0003111023850000097
The weight of each edge is the distance between two points, and can be obtained by using depth-first algorithm
Figure BDA0003111023850000098
Ofk1To Sk2All possible paths, and the total distance to which the paths correspond. Wherein the total distance is greater than
Figure BDA0003111023850000099
Will be culled and only the one with the shortest total distance will be left for all paths that perform the same task but in a different order of task execution. All the tasks in each of the remaining paths form a task set.
Each task set node represents a task set, and if the total number of the task sets corresponding to all the unmanned aerial vehicle base stations is P, the model has P different task sets in common to form a set LU ═ LU { (LU)1,LU2,···,LUP}, task set LUpMay be expressed as LUp＝{Lp1,Lp2N, P1, 2, P, wherein Lp1，Lp2Equal representation task set LUpThe task involved.
4) And adding the task node as a three-level node. Each task node represents one task in L, and there are N task nodes in total.
(2) Constructing edges of a least cost maximum flow model
1) Adding edges from a source node
There is an edge between the source node s and each drone base station aggregation node. The capacity of the edge between the source node s and the unmanned aerial vehicle base station aggregation node is N, and the cost is 0.
2) Adding edges from unmanned aerial vehicle base station rendezvous points
There is an edge between each unmanned aerial vehicle base station set node and its corresponding task set node, that is, the unmanned aerial vehicle base station set SUgHow many corresponding task sets of nodes have how many edges from unmanned aerial vehicle base station set SUgAnd (5) starting the node. Each edge is connected with an unmanned aerial vehicle base station set and a task set, so that a take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station (SLS) combination can be formed, and a set LS (LS) formed by combining all the take-off unmanned aerial vehicle base stations-task sets-landing unmanned aerial vehicle base stations is { LS ═1,LS2,···,LSPIn which LS is combinedpDenoted LSp＝{SUg,LUp},g＝1,2,···,
Figure BDA0003111023850000101
P is 1,2, P. When the LU is combinedpAs a flight mission, the drone needs to follow the drone base station Sk1Take off, performed LUpAfter all tasks in the system, the unmanned aerial vehicle lands on an unmanned aerial vehicle base station Sk2LS flight task completed by unmanned planekThe flight distance of (D) is obtained by a depth-first algorithm and is denoted as D (LS)p). Thus, the drone base station set SUgAnd task set LUpCapacity of the edge between is | LUpL, cost D (LS)p)。
3) Adding edges from task rendezvous nodes
Each task set node p will only have edges between task nodes corresponding to tasks included in the task set, i.e. a common | LUpI edge slave task aggregation node LUpAnd (5) starting the node. The capacity of the edge between the task set node and the task node is 1, and the cost is 0.
4) Adding edges from task nodes
An edge exists between each task node and the destination node t. The capacity of the edge between the task node and the terminal node t is 1, and the cost is 0.
As shown in fig. 2, the present invention provides a method for allocating tasks of an unmanned aerial vehicle based on minimum cost and maximum flow, which comprises the following specific steps:
(1) initial docking unmanned aerial vehicle base station S for initializing unmanned aerial vehicle UU。
(2) And constructing a corresponding minimum cost maximum flow model.
(3) Modeling the number of completed tasks as flow, and dividing the tasks and unmanned aerial vehicle base stations in a task area into a plurality of combinations of 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' based on a minimum cost maximum flow model, and the specific steps are as follows:
(1) and constructing a corresponding minimum cost maximum flow model G ═ (V, E, $, W).
(2) Initializing the initial station of unmanned aerial vehicle U to SU。
(3) Modeling the number of completed tasks as flow, and obtaining a combined set of 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' with the minimum cost in the minimum cost maximum flow model based on the minimum cost maximum flow model, wherein the combined set comprises the following specific steps:
1) the feasible flow f is initialized to zero flow, at which time the cost of the feasible flow f is 0.
2) Initializing CostminFor the combination LS including 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' with minimum flying distanceminFlow f insideminThe total cost of the combined set of "take-off drone base station-task set-landing drone base station" corresponding to the minimum cost
Figure BDA0003111023850000114
Obtaining a feasible flow f comprising a plurality of 'take-off drone base station-task set-landing drone base station' combinations*Cost $ of the set of "take-off drone base station-task set-landing drone base station" combinations that corresponds to the minimum costf*The steps are as follows:
a) easy known feasible flow f*Cost $f*The sum of the costs of all selected 'take-off drone base station-task set-landing drone base station' combinations.
b) Selecting remaining flow networks Gf*Medium cost minimum augmentation path p*，p*The corresponding combination of take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station is recorded as LSp′。
c) Will expand the path p*Is added to the viable stream f*In the specification, $f*＝$f*+D(LSp'). If in the remaining streaming network GfB) if there is still an amplification path; otherwise, return $f*。
3) Combining LS for 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' in LS through circulationiExecuting steps d) to f) in the order of the flight distances from small to large so as to obtain a set of the combination 'take-off drone base station-task set-landing drone base station' with the minimum cost in the streaming network G:
d) obtaining 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' LSi。
e) If LSiIs not selected, then LS is selectediAdding a corresponding path from the source node s to the destination node t as an augmented path into the feasible flow f and returning to d); otherwise f) is executed.
f) All of the feasible flows f are compared with LSiWithdrawing the selected task containing the task conflict, withdrawing the selected task set corresponding to the withdrawing task and the unmanned aerial vehicle base station set to obtain a feasible flow ftemp(ii) a Obtaining a viable flow f by steps a) to c)tempCost of the combined set of "take-off drone base station-task set-landing drone base station" corresponding to minimum cost
Figure BDA0003111023850000111
Order to
Figure BDA0003111023850000112
If it is
Figure BDA0003111023850000113
Let f be ftemp，
Figure BDA0003111023850000121
Returning to d); otherwise, directly returning to d).
4) If all tasks are in f, executing (4); otherwise for unselected task LnIs prepared by mixing LnAnd (3) sequentially inserting each 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' combination selected in the step (3), recalculating the flight distance of the combination after insertion, and subtracting the flight distance before insertion to obtain the flight distance difference delta Cost before and after insertion into the task. L isnAnd inserting the 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' combination with the minimum delta Cost, wherein the flight distance of the combination also becomes the inserted flight distance. If no matter LnThe flying distances obtained by inserting the combination of any 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' are all larger than
Figure BDA0003111023850000122
Then L will benAnd is away from LnThe nearest unmanned aerial vehicle base station constructs a new combination of takeoff unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station.
(4) Judging whether a combination exists in all the obtained combinations of 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station', wherein any one of the take-off unmanned aerial vehicle base station or the landing unmanned aerial vehicle base station is an initial stop unmanned aerial vehicle base station SU. If such a combination is not present, then S is usedUTo replace from SUThe nearest task is located in a take-off base station or a landing base station in a take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station combination. After the adjustment is completed, all combinations capable of sequentially executing the 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' are constructed into an initial path, and the initial path is recorded as I ═ I1,i2V.. v.. The method comprises the following specific steps:
1) the initial path I is initialized to null.
2) For each selected' take-off noneEach combination LS of the combination of base station-task set-landing unmanned aerial vehicle base stationkAnd (4) carrying out circulation judgment:
if Sk1＝Sk2＝SuThen LS is addedkDirectly inserted into I;
if Sk1＝SU，Sk2≠SU(or S)k2＝SU，Sk2≠SU) Then S will bek1(or S)k2) As LSkTake-off unmanned aerial vehicle base station of, with LSkIs inserted into I, let SU＝Sk2(SU＝Sk1)；
If Sk1≠SUAnd Sk2≠SUThen LS is not addedkIs inserted into I.
(5) If the initial path I contains all the combinations of 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' obtained in the step (3), the initial path I is the final path F of the unmanned aerial vehicle for executing all tasks; otherwise, the combination of the 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' obtained in the step (3) and not included by the initial path I is recorded as a candidate 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' combination, and the formed set CLS ═ c1,c2V.. v.. Sequentially combining c for each candidate 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' in the set CLSjAnd inserting into each insertion point in the initial path I, wherein the insertion points can be the beginning, the end and the middle of two adjacent combinations of the takeoff unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station. By comparing the total flying distance after inserting the candidate 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' into the specified insertion point, selecting the insertion point with the minimum total flying distance as cjAnd c is the optimal insertion point ofjThe optimal insertion point is inserted. When the set CLS is empty, the initial path I is the final path F for the drone to perform all tasks. Each "take-off drone base station-task set-landing drone base station" combination in the final path F is a primary flight task for the drone, which is executed by the drone sequentiallyEach flight task in the final path F can be performed to complete all tasks.
FIG. 3, FIG. 4 and FIG. 5 are combinations c of candidate "takeoff drone base station-task set-landing drone base stationjThree different cases when inserting the initial path I. c. CjTake-off unmanned aerial vehicle base station recorded as Sj1，cjDescending unmanned aerial vehicle base station record Sj2. The specific explanation is as follows:
1) the beginning of the initial path I is inserted.
The insertion position is shown in fig. 3.
With SzFirst "take-off drone base station-task set-landing drone base station" combination I representing initial path I1Take-off drone base station, i.e. Sz＝Si11。
If Sj1＝Sj2＝SzThen cjMust already be in the initial path I.
If Sj1＝SzAnd Sj1≠Sj2Then will Sj1As c isjStarting base station of cjInsert it at the beginning of the initial path I and add I1Take-off unmanned aerial vehicle base station replacement Sj2. Insertion cjThe total flight distance of the subsequent initial path I can be expressed as:
Figure BDA0003111023850000131
wherein D (I V-V)pcj) Means to convert cjTotal flight distance of I after insertion into designated insertion position p of I, D (c)j) And D (i)1) Each represents cjAnd i1The total flying distance of the aircraft is,
Figure BDA0003111023850000132
represents that i is1Unmanned aerial vehicle basic station S inzReplacement is unmanned aerial vehicle basic station Sj2After i1The flight distance. If Sj2＝SzAnd Sj1≠Sj2When it is, will Sj2Will be as cjStarting unmanned aerial vehicle base station, Sj1Will be as cjLanding unmanned aerial vehicle base station insert initial path I, cjThe order of execution of all tasks in (a) needs to be reversed. Insertion cjThe calculation of the total flight distance of the subsequent initial path I is the same as the calculation of (1).
If Sj1≠SzAnd Sj2≠SzWhen S is presentj1And Sj2May be the same or different. S for calculation by the formulae (2) and (3), respectivelyzSubstitution of Sj1And with SzSubstitution of Sj2Then c is addedjTotal flight distance after insertion into the initial path I, and I1Take-off unmanned aerial vehicle base station is replaced by cjAnd (4) the unmanned aerial vehicle base station which is not replaced. And then selecting the minimum flight distance as a final insertion scheme by using the formula (4).
Figure BDA0003111023850000133
Figure BDA0003111023850000134
Figure BDA0003111023850000135
Wherein
Figure BDA0003111023850000136
And
Figure BDA0003111023850000137
means to convert cjThe total flight distance I after insertion into the initial path I specifies the insertion position p, superscript Sj1And Sj2Respectively represent cjQuilt SZAlternative drone base station.
2) The end of the initial path I is inserted.
The insertion position is shown in fig. 4. With SzRepresents the last of the initial path ICombination i of take-off unmanned aerial vehicle base station, task set and landing unmanned aerial vehicle base stationendLanding drone base station, i.e. Sz＝Siend2。
If Sj1＝SzAnd Sj1≠Sj2Then Sj1Will be as cjStarting unmanned aerial vehicle base station, Sj2Will be as cjDescending unmanned aerial vehicle base station, cjInserted to the end of the initial path I. Insertion cjThe total flight distance of the subsequent initial path I can be expressed as:
D(I∨pcj)＝D(I)+D(cj) (5)
if Sj2＝SzAnd Sj1≠Sj2When it is, will Sj2Will be as cjStarting unmanned aerial vehicle base station, Sj1Will be as cjC, inserting the base station of the landing unmanned aerial vehicle into the tail of the initial path IjThe order of execution of all tasks in (a) needs to be reversed. Calculating the insertion c by equation (5)jThe latter initial path I total flight distance.
If Sj1≠SzAnd Sj2≠SzWhen S is presentj1And Sj2May be the same or different. S for calculation by the equations (6) and (7), respectivelyzSubstitution of Sj1And with SzSubstitution of Sj2Then c is addedjThe total flight distance after the end of the initial path I is inserted. And then selecting the minimum flight distance as a final insertion scheme by using the formula (8).
Figure BDA0003111023850000141
Figure BDA0003111023850000142
Figure BDA0003111023850000143
3) And inserting the two adjacent combinations of the take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station in the initial path I.
The insertion position is shown in fig. 5. With SzDenotes a combination i of a take-off drone base station, a task set and a landing drone base station before an insertion point(γ-1)The landing unmanned aerial vehicle base station and the next combination i of take-off unmanned aerial vehicle base station, task set and landing unmanned aerial vehicle base stationγTake-off drone base station, i.e. Sz＝Si(γ-1)2＝Siγ1。
If Sj1＝Sj2＝SzThen cjDirectly inserted into a specified position, and the insertion c is expressed by the formula (5)jTotal flight distance of the following initial path I.
If Sj1＝SzAnd Sj1≠Sj2Then Sj1Will be as cjStarting unmanned aerial vehicle base station, Sj2Will be as cjDescending unmanned aerial vehicle base station, cjInserted into the insertion point, and iγThe take-off unmanned aerial vehicle base station is replaced by Sj2. Insertion cjThe total flight distance of the subsequent initial path I can be expressed as:
Figure BDA0003111023850000144
if Sj2＝SzAnd Sj1≠Sj2Will Sj2Will be as cjStarting unmanned aerial vehicle base station, Sj1Will be as cjThe base station of the landing drone is inserted into the insertion point, cjThe order of execution of all tasks in (a) needs to be reversed, and (i)γThe take-off unmanned aerial vehicle base station is replaced by Sj1. Insertion cjAnd (4) calculating the total flight distance of the subsequent initial path I in the same way as the step (9).
If Sj1≠SzAnd Sj2≠SzWhen S is presentj1And Sj2May be the same or different. S for calculation by the formulae (2) and (3), respectivelyzSubstitution of Sj1And with SzSubstitution of Sj2Then c is addedjTotal flying distance after insertion into the insertion point, and iγTake-off drone base station should be replaced with cjAnd (4) the unmanned aerial vehicle base station which is not replaced. And then selecting the minimum flight distance as a final insertion scheme by using the formula (4).
The present invention provides a method for allocating tasks of an unmanned aerial vehicle based on minimum cost and maximum flow, and a plurality of methods and ways for implementing the technical scheme are provided, the above description is only a specific embodiment of the present invention, it should be noted that, for those skilled in the art, without departing from the principle of the present invention, several improvements and modifications may be made, and these improvements and modifications should also be regarded as the protection scope of the present invention. All the components not specified in the present embodiment can be realized by the prior art.

Claims (5)

1. An unmanned aerial vehicle task allocation method based on minimum cost and maximum flow comprises the following steps:
step 1, defining a task object configuration set L ═ L which is N different in the task area1，L2，…，LNEach task only needs to be executed once; in a task area, M different unmanned aerial vehicle base stations form a set S ═ S1，S2，…，SMWhere unmanned aerial vehicle base station SmThe unmanned aerial vehicle charging system is defined as a supply point for storing the unmanned aerial vehicle and charging equipment of the unmanned aerial vehicle, and the unmanned aerial vehicle can supply energy in any unmanned aerial vehicle base station; have an unmanned aerial vehicle U who prepares to carry out the task in the task region, for the simplification, when considering unmanned aerial vehicle takes off to land and receive the energy consumption that natural factor influences in the flight, unmanned aerial vehicle's energy consumption equivalence is unmanned aerial vehicle's flying distance, under the prerequisite that the energy was full of, unmanned aerial vehicle U's longest flying distance is for unmanned aerial vehicle U's flying distance
Figure FDA0003111023840000011
Initializing the initial station of the unmanned aerial vehicle to SU；
Step 2, constructing a corresponding minimum cost maximum flow model according to the tasks in the task area and the unmanned aerial vehicle base station;
step 3, modeling the number of completed tasks as flow, and dividing the tasks and unmanned aerial vehicle base stations in a task area into more than two take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station combinations by using the minimum cost maximum flow model constructed in the step 2;
step 4, constructing a combination of the take-off unmanned aerial vehicle base station, the task set and the landing unmanned aerial vehicle base station which can be sequentially executed in the combination of the take-off unmanned aerial vehicle base station, the task set and the landing unmanned aerial vehicle base station obtained in the step 3 into an initial path I;
step 5, if the initial path I contains all the combinations of the takeoff unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station obtained in the step 3, the initial path I is the final path F of the unmanned aerial vehicle for executing all tasks; otherwise, the combination of the takeoff unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station which is obtained in the step 3 and is not included in the initial path I is recorded as a candidate combination of the takeoff unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station, and a set CLS (common line system) is formed as { c ═ c { (c) }1，c2… }; sequentially combining each candidate 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' in the set CLSjFinding the best insertion point in the initial path I and calculating cjInserting the optimal insertion point; when the set CLS is empty, the initial path I is the final path F of the drone for the drone to perform all tasks.
2. The method for allocating tasks to unmanned aerial vehicle based on minimum cost maximum flow according to claim 1, wherein the minimum cost maximum flow model in step 2 is constructed as follows:
(1) node for constructing minimum-cost maximum flow model
1) Adding a source node s and a destination node t as auxiliary nodes;
2) adding an unmanned aerial vehicle base station set node as a primary node;
each unmanned aerial vehicle base station set node represents an unmanned aerial vehicle base station set, and each unmanned aerial vehicle base station set is composed of two unmanned aerial vehicle base stationsThe two unmanned aerial vehicle base stations can be the same or different; m different unmanned aerial vehicle base stations can constitute
Figure FDA0003111023840000021
A set of different unmanned aerial vehicle base stations, denoted as
Figure FDA0003111023840000022
Wherein unmanned aerial vehicle base station set SUgCan be expressed as
Figure FDA0003111023840000023
Wherein Sk1Denotes the takeoff unmanned aerial vehicle base station, S, of the unmanned aerial vehicle in a flight missionk2Representing a landing unmanned aerial vehicle base station in a primary flight task of the unmanned aerial vehicle;
3) adding a task set node as a secondary node;
for unmanned aerial vehicle base station set SUgIf S isk1And Sk2In contrast, then Sk1And Sk2And all task points can form a completely undirected connected graph
Figure FDA0003111023840000024
If Sk1And Sk2Same, firstly, Sk1And Sk2Considered as distinct points, but the distance between them is 0, and all task points are to Sk1To Sk2Are the same, and then S isk1And Sk2And all task points form a completely undirected connected graph
Figure FDA0003111023840000025
Figure FDA0003111023840000026
The weight of each edge is the distance between two points, and the depth-first algorithm is used to obtain the weight
Figure FDA0003111023840000027
Ofk1To Sk2All possible paths and the total distance corresponding to the paths; wherein the total distance is greater than
Figure FDA0003111023840000028
The paths of (2) are eliminated, and only the path with the shortest total distance is left for all paths which execute the same task but have different task execution sequences; all the tasks in each of the rest paths form a task set;
each task set node represents a task set, and if the total number of the task sets corresponding to all the unmanned aerial vehicle base stations is P, the model has P different task sets in common to form a set LU ═ LU { (LU)1，LU2，…，LUP}, task set LUpMay be expressed as LUp＝{Lp1，Lp2… }, P ═ 1,2, …, P, where L isp1，Lp2Representing a set of tasks LUpThe tasks involved;
4) adding task nodes as three-level nodes; each task node represents one task in the L, and N task nodes are shared;
(2) constructing edges of a least cost maximum flow model
1) Adding edges from a source node
Edges exist between the source node s and each unmanned aerial vehicle base station aggregation node; the capacity of the edge between the source node s and the unmanned aerial vehicle base station aggregation node is N, and the cost is 0;
2) adding edges from unmanned aerial vehicle base station rendezvous points
There is an edge between each unmanned aerial vehicle base station set node and its corresponding task set node, that is, the unmanned aerial vehicle base station set SUgHow many corresponding task sets of nodes have how many edges from unmanned aerial vehicle base station set SUgStarting a node; each edge is connected with an unmanned aerial vehicle base station set and a task set to form a take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station combination, and all the take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station combinations form a set LS (the set LS is the { LS) }1，LS2，…，LSPIn which LS is combinedpIs shown as
Figure FDA0003111023840000029
Figure FDA00031110238400000210
When combining LSpAs a flight mission, the drone needs to follow the drone base station Sk1Take off, performed LUpAfter all tasks in the system, the unmanned aerial vehicle lands on an unmanned aerial vehicle base station Sk2LS flight task completed by unmanned planekThe flight distance of (D) is obtained by a depth-first algorithm and is denoted as D (LS)p) (ii) a Thus, the drone base station set SUgAnd task set LUhCapacity of the edge between is | LUpL, cost D (LS)p)；
3) Adding edges from task rendezvous nodes
Each task set node p will only have edges between task nodes corresponding to tasks included in the task set, i.e. a common | LUpI edge slave task aggregation node LUpStarting a node; the capacity of the edge between the task set node and the task node is 1, and the cost is 0;
4) adding edges from task nodes
Edges exist between each task node and the terminal node t; the capacity of the edge between the task node and the terminal node t is 1, and the cost is 0.
3. The method for task allocation of unmanned aerial vehicles based on minimum cost maximum flow as claimed in claim 1, wherein step 3 comprises:
(1) constructing a corresponding minimum cost maximum flow model G ═ (V, E, $, W);
(2) initializing the initial station of unmanned aerial vehicle U to SU；
(3) Modeling the number of completed tasks as flow, and obtaining a combined set of 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' with the minimum cost in the minimum cost maximum flow model based on the minimum cost maximum flow model, wherein the combined set comprises the following steps:
1) initializing the feasible flow f as a zero flow, wherein the cost of the feasible flow f is 0;
2) initializing CostminFor the combination LS including 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' with minimum flying distanceminFlow f insideminThe total cost of the combined set of "take-off drone base station-task set-landing drone base station" corresponding to the minimum cost
Figure FDA0003111023840000031
Obtaining a feasible flow f comprising a plurality of 'take-off drone base station-task set-landing drone base station' combinations*Cost $ of the set of "take-off drone base station-task set-landing drone base station" combinations that corresponds to the minimum costf*The steps are as follows:
a) easy known feasible flow f*Cost $f*The sum of the cost of all selected 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' combinations is obtained;
b) selecting remaining flow networks Gf*Medium cost minimum augmentation path p*，p*The corresponding combination of take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station is recorded as LSp′；
c) Will expand the path p*Is added to the viable stream f*In the specification, $f*＝$f*+D(LSp') to a host; if in the remaining streaming network GfB) if there is still an amplification path; otherwise, return $f*；
3) Combining LS for 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' in LS through circulationiExecuting steps d) to f) in the order of the flight distances from small to large so as to obtain a set of the combination 'take-off drone base station-task set-landing drone base station' with the minimum cost in the streaming network G:
d) obtaining 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' LSi；
e) If LSiIs not selected, then LS is selectediAdding a corresponding path from the source node s to the destination node t as an augmented path into the feasible flow f and returning to d); otherwise, f) is executed;
f) all of the feasible flows f are compared with LSiWithdrawing the selected task containing the task conflict, withdrawing the selected task set corresponding to the withdrawing task and the unmanned aerial vehicle base station set to obtain a feasible flow ftemp(ii) a Obtaining a viable flow f by steps a) to c)tempCost of the combined set of "take-off drone base station-task set-landing drone base station" corresponding to minimum cost
Figure FDA0003111023840000041
Order to
Figure FDA0003111023840000042
If it is
Figure FDA0003111023840000043
Let f be ftemp，
Figure FDA0003111023840000044
Returning to d); otherwise, directly returning to d);
4) if some tasks are not in f, aiming at the unselected tasks LnIs prepared by mixing LnSequentially inserting each 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' combination selected in the step 3), recalculating the flight distance of the inserted combination, and subtracting the flight distance before insertion to obtain the flight distance difference delta Cost before and after insertion into the task; l isnInserting the minimum delta Cost combination of the take-off unmanned aerial vehicle base station, the task set and the landing unmanned aerial vehicle base station, wherein the flight distance of the combination is also changed into the inserted flight distance; if no matter LnThe flying distances obtained by inserting the combination of any 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' are all larger than
Figure FDA0003111023840000045
Then L will benAnd is away from LnThe nearest unmanned aerial vehicle base station constructs a new combination of takeoff unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station.
4. The method for task allocation of unmanned aerial vehicles based on minimum cost maximum flow as claimed in claim 1, wherein step 4 comprises:
(1) judging whether a combination exists in the combination of 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' obtained in the step 3, wherein any one of the take-off unmanned aerial vehicle base station or the landing unmanned aerial vehicle base station is the initial stop unmanned aerial vehicle base station S of the unmanned aerial vehicle UU(ii) a If such a combination is not present, then S is usedUTo replace from SUA take-off unmanned aerial vehicle base station or a landing unmanned aerial vehicle base station in a combination of a take-off unmanned aerial vehicle base station, a task set and a landing unmanned aerial vehicle base station where the nearest task is located;
(2) all combinations capable of sequentially executing 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station' are constructed into an initial path, and the initial path is recorded as I ═ I1，i2…, the steps are as follows:
1) initializing an initial path I to be null;
2) for each LS combination of the selected 'take-off drone base station-task set-landing drone base station' combinationskAnd (4) carrying out circulation judgment:
if Sk1＝Sk2＝SUThen LS is addedkDirectly inserted into I;
if Sk1＝SU，Sk2≠SUThen S will bek1As LSkTake-off unmanned aerial vehicle base station of, with LSkIs inserted into I, let SU＝Sk2；
If Sk2＝SU，Sk1≠SUThen S will bek2As LSkTake-off unmanned aerial vehicle base station of, with LSkIs inserted into I, let SU＝Sk1；
If Sk1≠SUAnd Sk2≠SUThen LS is not addedkIs inserted into I.
5. The method as claimed in claim 1, wherein the combination c of "take-off drone base station-task set-landing drone base station" is selected in step 5jThere are three different situations when inserting the initial path I: the insertion points are the beginning and the end of the initial path I and the middle of the combination of two adjacent 'take-off unmanned aerial vehicle base station-task set-landing unmanned aerial vehicle base station'; c. CjTake-off unmanned aerial vehicle base station recorded as Sj1，cjDescending unmanned aerial vehicle base station record Sj2；
(1) Inserting the beginning of the initial path I;
with SzFirst "take-off drone base station-task set-landing drone base station" combination I representing initial path I1Take-off drone base station, i.e. Sz＝Si11；
If Sj1＝Sj2＝SzThen cjMust already be in the initial path I;
if Sj1＝SzAnd Sj1≠Sj2Then will Sj1As c isjStarting base station of cjInsert it at the beginning of the initial path I and add I1Take-off unmanned aerial vehicle base station replacement Sj2(ii) a Insertion cjThe total flight distance of the following initial path I is expressed as:
Figure FDA0003111023840000051
wherein D (IV)pcj) Means to convert cjTotal flight distance of I after insertion into designated insertion position p of I, D (c)j) And D (i)1) Each represents cjAnd i1The total flying distance of the aircraft is,
Figure FDA0003111023840000052
represents that i is1Unmanned aerial vehicle basic station S inzReplacement is unmanned aerial vehicle basic station Sj2After i1A flight distance; if Sj2＝SzAnd Sj1≠Sj2When it is, will Sj2Will be as cjStarting unmanned aerial vehicle base station, Sj1Will be as cjLanding unmanned aerial vehicle base station insert initial path I, cjThe execution sequence of all tasks in the system needs to be reversed; insertion cjThe calculation of the total flying distance of the subsequent initial path I is the same as the calculation of the total flying distance of the subsequent initial path I in the same way as the step (1);
if Sj1≠SzAnd Sj2≠SzWhen S is presentj1And Sj2May be the same or different; s for calculation by the formulae (2) and (3), respectivelyzSubstitution of Sj1And with SzSubstitution of Sj2Then c is addedjTotal flight distance after insertion into the initial path I, and I1Take-off unmanned aerial vehicle base station is replaced by cjThe unmanned aerial vehicle base station which is not replaced; then selecting the minimum flight distance as a final insertion scheme by using a formula (4);
Figure FDA0003111023840000061
Figure FDA0003111023840000062
Figure FDA0003111023840000063
wherein
Figure FDA0003111023840000064
And
Figure FDA0003111023840000065
means to convert cjThe total flight distance of I after inserting into the initial path I and specifying the insertion position pUpper scale Sj1And Sj2Respectively represent cjQuilt SZA replacement drone base station;
(2) inserting the end of the initial path I;
with SzThe last "take-off drone base station-task set-landing drone base station" combination I representing the initial path IendLanding drone base station, i.e. Sz＝Siend2；
If Sj1＝SzAnd Sj1≠Sj2Then Sj1Will be as cjStarting unmanned aerial vehicle base station, Sj2Will be as cjDescending unmanned aerial vehicle base station, cjInserting the path I to the end of the initial path I; insertion cjThe total flight distance of the following initial path I is expressed as:
D(IVpcj)＝D(I)+D(cj) (5)
if Sj2＝SzAnd Sj1≠Sj2When it is, will Sj2Will be as cjStarting unmanned aerial vehicle base station, Sj1Will be as cjC, inserting the base station of the landing unmanned aerial vehicle into the tail of the initial path IjThe execution sequence of all tasks in the system needs to be reversed; calculating the insertion c by equation (5)jThe total flying distance of the subsequent initial path I;
if Sj1≠SzAnd Sj2≠SzWhen S is presentj1And Sj2May be the same or different; s for calculation by the equations (6) and (7), respectivelyzSubstitution of Sj1And with SzSubstitution of Sj2Then c is addedjInserting the total flight distance after the end of the initial path I; then, selecting the minimum flight distance as a final insertion scheme by using a formula (8);
Figure FDA0003111023840000066
Figure FDA0003111023840000067
Figure FDA0003111023840000068
(3) inserting the two adjacent combinations of the take-off unmanned aerial vehicle base station, the task set and the landing unmanned aerial vehicle base station in the initial path I;
with SzDenotes a combination i of a take-off drone base station, a task set and a landing drone base station before an insertion point(γ-1)The landing unmanned aerial vehicle base station and the next combination i of take-off unmanned aerial vehicle base station, task set and landing unmanned aerial vehicle base stationγTake-off drone base station, i.e. Sz＝Si(γ-1)2＝Siγ1；
If Sj1＝Sj2＝SzThen cjDirectly inserted into a specified position, and the insertion c is expressed by the formula (5)jThe total flight distance of the subsequent initial path I;
if Sj1＝SzAnd Sj1≠Sj2Then Sj1Will be as cjStarting unmanned aerial vehicle base station, Sj2Will be as cjDescending unmanned aerial vehicle base station, cjInserted into the insertion point, and iγThe take-off unmanned aerial vehicle base station is replaced by Sj2(ii) a Insertion cjThe total flight distance of the following initial path I is expressed as:
Figure FDA0003111023840000071
if Sj2＝SzAnd Sj1≠Sj2Will Sj2Will be as cjStarting unmanned aerial vehicle base station, Sj1Will be as cjThe base station of the landing drone is inserted into the insertion point, cjThe order of execution of all tasks in (a) needs to be reversed, and (i)γThe take-off unmanned aerial vehicle base station is replaced by Sj1(ii) a Insertion cjThe calculation of the total flight distance of the subsequent initial path I is similar to the method (9)；
If Sj1≠SzAnd Sj2≠SzWhen S is presentj1And Sj2May be the same or different; s for calculation by the formulae (2) and (3), respectivelyzSubstitution of Sj1And with SzSubstitution of Sj2Then c is addedjTotal flying distance after insertion into the insertion point, and iγTake-off drone base station should be replaced with cjThe unmanned aerial vehicle base station which is not replaced; and then selecting the minimum flight distance as a final insertion scheme by using the formula (4).
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