CN116090342B - Distributed task allocation method for large-scale unmanned aerial vehicle based on alliance forming game - Google Patents
Distributed task allocation method for large-scale unmanned aerial vehicle based on alliance forming game Download PDFInfo
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Abstract
The invention discloses a distributed task allocation method of a large-scale unmanned aerial vehicle forming games based on alliance, which comprises the following steps: s1, establishing a task allocation optimization model; based on a large-scale unmanned aerial vehicle task allocation scene, considering constraint conditions such as task demands, scale and the like, designing a profit function related to the unmanned aerial vehicle scale, establishing an optimization model, and realizing mathematical expression of the large-scale task allocation problem; s2, building a alliance to form a game model; s3, solving two stages of game formation based on maximum weighted matching and alliance. According to the large-scale unmanned aerial vehicle distributed task allocation method based on the alliance forming game, the unmanned aerial vehicle is used for selecting tasks based on the game in a distributed mode, and the specific unmanned aerial vehicle is used for processing scale conflicts, so that iteration times of task allocation results can be reduced, the real-time performance of task allocation is improved, unmanned aerial vehicle resources are better utilized, and waste of unmanned aerial vehicle resources is reduced.
Description
Technical Field
The invention relates to the technical fields of game theory, task allocation and multiple agents, in particular to a distributed task allocation method for a large-scale unmanned aerial vehicle forming games based on alliances.
Background
Along with the improvement of unmanned aerial vehicle performance and the increasingly complex and diversified tasks to be executed, unmanned aerial vehicle task execution modes are gradually changed from a single machine to a multi-machine cooperation direction, and a multi-unmanned aerial vehicle system plays an increasingly important role in complex task scenes. The reasonable task allocation plays an important role in improving the task execution efficiency of the multi-unmanned aerial vehicle system.
The multi-unmanned aerial vehicle task allocation refers to allocating a proper unmanned aerial vehicle for each task according to task requirements and unmanned aerial vehicle capabilities, so that the tasks can be efficiently and cooperatively completed, and the task income can be maximized. With the development of unmanned aerial vehicles to low cost and light weight, unmanned aerial vehicles cooperatively execute tasks in a large-scale cluster form, and the unmanned aerial vehicles become a hot spot direction for task allocation research. In the research, the number of unmanned aerial vehicles is usually far greater than the number of tasks, a certain number of unmanned aerial vehicles of a specific type are required to be allocated for each task to be executed, and the advantages and disadvantages of the task allocation result directly determine the execution effect of the task. Currently, the main task allocation methods can be divided into two categories: centralized methods and distributed methods.
The centralized task allocation is that a single control center obtains all information about the task, the unmanned aerial vehicle and the environment, and then adopts a related optimization method to solve the task allocation problem and give a task allocation result, so that each unmanned aerial vehicle is guided to complete the task under the specified constraint condition. Aiming at the task distribution of a plurality of unmanned aerial vehicles with smaller scale, the centralized task distribution method can have optimality and real-time performance. However, the control center is used as a single decision main body, the reliability is poor, and along with the increase of the scale of the unmanned aerial vehicle, the solving time is obviously increased, and the real-time requirement of task allocation cannot be met. Furthermore, for task allocation problems with complex constraints, a centralized approach may not give a viable solution in a short time.
Unlike centralized methods, distributed task allocation does not have a central controller, but rather each unmanned aerial vehicle is used as a decision-making body, and the unmanned aerial vehicles interact with information such as the environment, the task target condition, the self state and the like based on communication. On the basis, each unmanned aerial vehicle selects tasks to be executed by the unmanned aerial vehicle, and the task distribution process is completed. The distributed task allocation research is realized by adopting methods based on a market mechanism, game theory and the like, and has better flexibility and survivability because of no central control node. Compared with a centralized method, the distributed method has the advantage that the solving speed is obviously improved for large-scale task distribution. However, with the increase of the number of unmanned aerial vehicles, a method based on a market mechanism can generate larger communication cost, while a method based on game has advantages in solving efficiency, expandability and communication cost, but has higher requirements on the convergence of an algorithm, and meanwhile, the influence of redundancy of unmanned aerial vehicles on task allocation results is less considered.
Therefore, the following problems still exist in the current large-scale unmanned aerial vehicle task allocation research: the traditional centralized method pursues global optimization, so that the solution efficiency is low, and the requirement of task scenes on allocation instantaneity cannot be met; the distributed method, such as the method based on market mechanism such as auction, has larger communication burden and is not suitable for large-scale scenes; the existing game method has the problems of more iteration times, limitation of unmanned aerial vehicle quantity distribution and the like, which are not considered in most researches.
Disclosure of Invention
The invention aims to provide a large-scale unmanned aerial vehicle distributed task allocation method for forming games based on alliance, wherein unmanned aerial vehicles are used for selecting tasks based on the games in a distributed mode, and specific unmanned aerial vehicles are used for processing scale conflicts, so that iteration times of task allocation results can be reduced, the real-time performance of task allocation is improved, unmanned aerial vehicle resources are better utilized, and waste of unmanned aerial vehicle resources is reduced.
In order to achieve the above purpose, the invention provides a distributed task allocation method for large-scale unmanned aerial vehicles forming games based on alliances, which comprises the following steps:
s1, establishing a task allocation optimization model;
based on a large-scale unmanned aerial vehicle task allocation scene, considering constraint conditions such as task demands, scale and the like, designing a profit function related to the unmanned aerial vehicle scale, establishing an optimization model, and realizing mathematical expression of the large-scale task allocation problem;
s2, building a alliance to form a game model;
s3, solving two stages of game formation based on maximum weighted matching and alliance.
Preferably, in step S1, constraint conditions of the unmanned aerial vehicle when performing task allocation are specifically:
constraint condition one: type matching constraints
Constraint conditions II: task demand constraints
Constraint conditions three: number relationship constraints
Constraint conditions four: scale constraints
Wherein N is an unmanned aerial vehicle set, and N is the number of unmanned aerial vehicles; a, a ij Indicating whether the unmanned aerial vehicle i selects the task t j ；a ij Is a binary decision variable; t (T) i Representing a task set which can be selected by the unmanned plane i, T\T i Indicating the task that unmanned plane i cannot select, t 0 Is an empty task, m is the number of tasks except the empty task; num (num) j Indicating completion of task t j The number of unmanned aerial vehicles required; l (L) j Representing task t j Upper limit value of unmanned aerial vehicle scale, L j ≥num j 。
Preferably, in step S1, the optimization objective of the unmanned aerial vehicle when performing task allocation is specifically:
maximizing global revenue
The method comprises the steps of designing unmanned aerial vehicle individual profit functions by considering task values, the number of unmanned aerial vehicles for selecting tasks and the cost for executing tasks:
wherein ,|Cj I represents the selection task t j Number of unmanned aerial vehicles, c ij Representing the cost of the unmanned aerial vehicle i to perform the task, u j Is task t j Is of value (1);
task value and task raw value v j Task demand number num j Upper limit value of scale L j And selecting the number of unmanned aerial vehicles of the task to be related, and calculating the task value by considering the scale constraint:
wherein ,vj Is the known raw value of the task, the value of which does not change with the task allocation process, epsilon is a constant for avoiding the situation that the value of the task is equal to zero.
Preferably, in step S2, the building of the coalition-forming game model specifically includes the following steps:
s21, converting task allocation into a game process, determining game elements, and establishing a alliance to form a game model;
s22, determining a preference relation of the unmanned aerial vehicle based on alliance benefits, and designing alliance switching rules of the unmanned aerial vehicle according to the preference relation;
s23, determining the form of forming a game stable solution by the coalition, and determining game convergence conditions.
Preferably, in step S22, the coalition switching rule of the unmanned aerial vehicle is specifically:
given the current coalition partition result pi= { C 0 ,C 1 ,...,C m -if and only if it meetsAt this time, unmanned plane i is from alliance C j Leave, join new alliance C j' Updating the alliance partition result into pi' = (pi\ { C) j ,C j' })∪{C j \{i},C j' ∪{i}}；
wherein ,C0 ,C 1 ,...,C m For task t 0 ,t 1 ,...,t m Respectively are provided withCorresponding alliance, preference relationTo consider the preference for alliance total revenue, i.e. for drone i, any two alliances C are given 1 and C2 The method comprises the following steps:
wherein ,representing equivalence relation, C 1 { i } means that drone i leaves federation C 1 ，r k1 (t 1 ,|C 1 I) is alliance C 1 The benefit of unmanned aerial vehicle k.
Preferably, in step S3, the two-stage solution for forming a game based on the maximum weighted matching and the league specifically includes the following steps:
s31, determining a collar machine corresponding to each task based on a maximum weighted matching algorithm;
s32, forming a game algorithm based on alliance, wherein all unmanned aerial vehicles except the collar machine select tasks in a distributed mode according to the designed switching rules, then resolving scale conflict by the collar machine, and iteratively updating task selection results to obtain stable task allocation results.
Preferably, in step S31, the collar machine corresponding to each task is determined based on the maximum weighted matching, and the method specifically includes the following steps:
s311, initializing a task allocation result, and selecting an empty task t by all unmanned aerial vehicles 0 I.e. the result of the alliance partition is
S312, calculating the profits of each unmanned aerial vehicle for executing tasks independently according to the designed unmanned aerial vehicle profits function, establishing a profits matrix M, and initializing a collar machine set LE;
s313, judging whether the LE contains all the collar machines of the tasks, stopping the stage if each task has the corresponding collar machine, entering the unmanned aerial vehicle task selection stage, and otherwise executing the step S314;
s314, for each task t j ∈T u Finding an unmanned aerial vehicle corresponding to a row with the largest profit value in the row, determining an optimal task of the unmanned aerial vehicle, and adding the unmanned aerial vehicle into the LE if the unmanned aerial vehicle and the task are matched with each other;
after the above operations are sequentially performed on each task, unmanned aerial vehicles added into the LE and the corresponding tasks are deleted from the matrix, and the profit matrix M, N is updated u and Tu The method comprises the steps of carrying out a first treatment on the surface of the Then, the process returns to step S313.
Preferably, in step S32, task selection and conflict resolution of the unmanned aerial vehicle specifically includes the following steps:
s321, initializing a alliance partition result: the result of each task collar machine is included, and other unmanned aerial vehicles are added into the empty task alliance C 0 The result of alliance partition isLE[j]For task t j Corresponding to the collar machine;
wherein, tau represents the iteration times, and pi [ tau ] represents the coalition partition result obtained after the tau-th iteration;
task information is stored in the collar machine, and the task information comprises task types, task demands, task positions, and total gains and total costs of the tasks in the subsequent distribution process;
s322, task selection phase: in the iteration of the τ -th round, firstly, for each unmanned aerial vehicle i epsilon N\LE except a collar machine, obtaining a coalition partition result pi [ τ -1] of the previous round of iteration from the collar machine, wherein the method comprises the steps of selecting the number and the number of unmanned aerial vehicles of each task, and obtaining the total income and the cost of the corresponding task;
then, calculating the change condition of the total alliance benefits before and after switching if the unmanned aerial vehicle is switched to any optional alliance from the current alliance, and selecting a task with the maximum value for switching from the tasks based on the preference relation, or keeping the task in the current alliance;
finally, the task selection result is sent to the collar machine of the corresponding task;
s323, conflict resolution stage: for each collar machine i epsilon LE, after obtaining the selection results of all unmanned aerial vehicles, comparing the upper limit value of the requirement with the number of unmanned aerial vehicles for selecting the task in the current wheel;
if the number of unmanned aerial vehicles selecting the mission is greater than the upper limit, i.e. |C j ′|＞L j Sequencing the unmanned aerial vehicles according to the cost of executing the task from small to large, and selecting a corresponding number of unmanned aerial vehicles according to the upper limit value to obtain a alliance C j * The task selection of the unmanned aerial vehicle exceeding the upper limit is changed into an empty task, the conflict resolution process is completed, and the empty task alliance C is adopted 0′ and Cj * Updating to the partition result pi [ tau ] of the alliance]；
If |C j ′|≤L j Then directly connect C j ' update to federation partition result pi [ tau ]]The method comprises the steps of carrying out a first treatment on the surface of the Sharing the processed partition result with other collar machines to obtain a coalition partition result of the round of iteration;
s324, judging whether the algorithm reaches a convergence condition: the coalition partition result is not changed to obtain a stable partition result, the algorithm is considered to be converged, and the algorithm operation is finished; otherwise, the process returns to step S322.
Therefore, the distributed task allocation method for the large-scale unmanned aerial vehicle based on the alliance game has the following technical effects:
(1) The problem that the unmanned aerial vehicle needs to carry out global communication in methods based on game theory and the like is solved. The unmanned aerial vehicle and the multi-frame collar machine are adopted to communicate to replace global communication among all unmanned aerial vehicles, the task distribution results are updated through communication among the unmanned aerial vehicle and the collar machine, the interaction times among the unmanned aerial vehicles are reduced, the iteration times required by the unmanned aerial vehicle system to reach the consensus results are reduced, the solving time of task distribution is shortened, and the real-time performance of large-scale task distribution is improved.
(2) The problem that the distribution scale limitation of the unmanned aerial vehicle is not considered is solved. Through considering the scale constraint and designing the unmanned aerial vehicle profit function related to the scale with the scale constraint, the result exceeding the scale constraint is processed by the collar machine, so that the redundant unmanned aerial vehicle can be effectively processed, and the waste of unmanned aerial vehicle resources is avoided.
(3) In each iteration of task allocation, the unmanned aerial vehicle calculates benefits according to global information obtained from the lead machine, and simultaneously performs task selection to replace sequential selection according to the sequence, so that the influence of the unmanned aerial vehicle selection sequence on the task allocation result is avoided.
The technical scheme of the invention is further described in detail through the drawings and the embodiments.
Drawings
FIG. 1 is a flowchart of the overall solution algorithm in an embodiment of a distributed task allocation method for a large-scale unmanned aerial vehicle forming games based on coalitions;
FIG. 2 illustrates method convergence under different unmanned aerial vehicle scales in an embodiment of a distributed task allocation method for a large-scale unmanned aerial vehicle forming a game based on coalition in accordance with the present invention;
FIG. 3 illustrates method convergence under different task scales in an embodiment of a distributed task allocation method for a large-scale unmanned aerial vehicle forming a game based on coalition in accordance with the present invention;
FIG. 4 is a graph comparing average gains of GRAPE algorithm and proposed algorithm in an embodiment of a distributed task allocation method for large-scale unmanned aerial vehicle based on coalition game formation in the present invention;
fig. 5 is a comparison diagram of the running time of the MinKP algorithm and the proposed algorithm in the embodiment of the coalition-based game-forming large-scale unmanned aerial vehicle distributed task allocation method of the present invention.
Detailed Description
The technical scheme of the invention is further described below through the attached drawings and the embodiments.
Unless defined otherwise, technical or scientific terms used herein should be given the ordinary meaning as understood by one of ordinary skill in the art to which this invention belongs.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein.
Furthermore, it should be understood that although the present disclosure describes embodiments, not every embodiment is provided with a separate embodiment, and that this description is provided for clarity only, and that the disclosure is not limited to the embodiments described in detail below, and that the embodiments described in the examples may be combined as appropriate to form other embodiments that will be apparent to those skilled in the art. Such other embodiments are also within the scope of the present invention.
It should also be understood that the above-mentioned embodiments are only for explaining the present invention, the protection scope of the present invention is not limited thereto, and any person skilled in the art should be able to cover the protection scope of the present invention by equally replacing or changing the technical scheme and the inventive concept thereof within the scope of the present invention.
Techniques, methods, and apparatus known to one of ordinary skill in the relevant art may not be discussed in detail, but are intended to be considered part of the specification where appropriate.
The disclosures of the prior art documents cited in the present specification are incorporated by reference in their entirety into the present invention and are therefore part of the present disclosure.
Example 1
A distributed task allocation method for large-scale unmanned aerial vehicles forming games based on alliances. Assuming that a large-scale unmanned aerial vehicle cluster cooperatively executes a plurality of tasks in an urban environment, including various tasks such as communication relay, information collection, search and rescue, a certain number of unmanned aerial vehicles of a specific type need to be dispatched for each task to execute, and each unmanned aerial vehicle can execute one of the tasks at most or select standby.
The variables required in the task allocation scenario are defined below. Assuming that there are N heterogeneous drones, denoted as set n= {1, 2..n }, containing multiple types of drones; there are (m+1) tasks, denoted as set t= { T 0 ,t 1 ,t 2 ,...,t m}, wherein t0 Is an empty task, contains a plurality of different task types, and the number of unmanned aerial vehicles is far greater than the number of tasks, namely n > m. Each unmanned plane i epsilon N can use the tuple < i, pu i ,uav_type i Represented by, where i is the unmanned number, pu i Is a unmanned plane position, uav _type i Is of the unmanned aerial vehicle type. Each task in the task set T may use tuples < T j ,Pt j ,task_type j ,num j ,v j Represented by > where t j For task numbering, pt j Task_type is the task location j Is a task type; num (num) j The number requirement of the tasks on the unmanned aerial vehicles is expressed, and each task is required to be completed by a plurality of unmanned aerial vehicles; each task having a different value v j The unmanned aerial vehicle performing the task can obtain a certain benefit. In the allocation process, since the number of unmanned aerial vehicles is sufficient, unnecessary allocation may be generated when the task demands are satisfied, and an upper limit L needs to be set for the number of unmanned aerial vehicles that can be allocated to each task j 。
Aiming at the task scene description and variable definition, the embodiment provides a distributed task allocation method of a large-scale unmanned aerial vehicle forming games based on alliance, which comprises the following specific implementation steps:
1. establishing an optimization model of task allocation problems, and determining constraint conditions and unmanned aerial vehicle profit functions
1. Constraint conditions
Constraints involved in the large-scale task allocation problem include type matching constraints, task demand constraints, number relationship constraints, and scale constraints. The type matching constraint refers to the requirement of a task on the type of the unmanned aerial vehicle; the task demand constraint and the scale constraint refer to the lower limit and the upper limit of the number of unmanned aerial vehicles which are required to be distributed for completing the task; the number relation constraint means that the unmanned aerial vehicle can only select one task at most.
(1) Type matching constraints
The task types are assumed to comprise three types of communication relay, information collection and search and rescue, and each task corresponds to one type. Unmanned aerial vehicle types include fixed wing unmanned aerial vehicles and quad-rotor unmanned aerial vehicles, which may perform one or more tasks depending on their own capabilities. For example, a fixed wing drone may perform communication relay and information gathering tasks, while a quad-rotor drone may perform information gathering and search rescue tasks. According to the matching condition of the unmanned plane and the type of the task, T is used i Representing a task set selectable by the unmanned plane i, and then T\T i Indicating tasks that the drone i cannot select. Let a ij Indicating whether the unmanned aerial vehicle i selects the task t j ，a ij Is a binary decision variable, then unmanned plane i and task t j The type constraint of (c) can be expressed as:
wherein ,aij =0 means that the drone i cannot select the set T i Tasks t other than j The scope of unmanned aerial vehicle selection tasks is limited.
(2) Task demand constraints
Considering that each task at least needs a plurality of unmanned aerial vehicles to cooperatively execute, the number of the unmanned aerial vehicles allocated should not be smaller than the number required by the task, and establishing the following task demand constraint:
wherein ,numj Indicating completion of task t j The number of unmanned aerial vehicles required, num j ＜＜n。
(3) Number relationship constraints
Because unmanned aerial vehicle alone accomplishes the limited ability of task, and can not carry out a plurality of tasks simultaneously, so every unmanned aerial vehicle can select a task to carry out at most, satisfies:
(4) Scale constraints
In order to prevent that too many unmanned aerial vehicles select the same task and cause unmanned aerial vehicle resource waste, therefore set up the upper limit value for the unmanned aerial vehicle quantity that each task can be allocated to, namely:
wherein ,Lj Representing task t j Upper limit value of unmanned aerial vehicle scale, L j ≥num j 。
2. Benefit function
The task allocation problem typically uses global task revenue maximization as a performance index. Comprehensively considering the task value, the number of unmanned aerial vehicles for selecting the task and the cost for executing the task, and designing a profit function for the unmanned aerial vehicles to execute the task. Let C j Representing a selection task t j Unmanned aerial vehicle i performs task t j The benefits of (2) are:
wherein ,|Cj I represents the selection task t j Number of unmanned aerial vehicles, c ij Representing the cost of the unmanned aerial vehicle i to perform the task, u j Is task t j Is of value (c). The above equation shows that unmanned aerial vehicles performing tasks share task value, and then unmanned aerial vehicle individual benefits are the average task value obtained minus the cost required to perform the task. Furthermore, the unmanned aerial vehicle can only be assembled from the set T i The task in (c) gets the benefit, and the benefit of the empty task is zero. The task value u is given below j In particular forms of (2).
Task value u j Is the reality in the task allocation processInter-task value, which is equal to the original value v of the task j Task demand number num j Upper limit value of scale L j And selecting a number of unmanned aerial vehicles for the task, defined as:
wherein ,vj Is the known raw value of the task, the value of which does not change with the task allocation process, epsilon is a smaller constant for avoiding the situation that the value of the task is equal to zero.
As can be seen from equation (6), when the number of unmanned aerial vehicles assigned |c j I is less than the upper limit value L j When the number of unmanned aerial vehicles is increased, the value is increased, if |C j The I is smaller than the number num of task demands j The ability of these unmanned aerial vehicles may not be sufficient to complete an overall mission, only to obtain partial value; if |C j The I is between the number of demands and the upper limit value, and the unmanned aerial vehicle can at least obtain the original value v of the task j As the number of unmanned aerial vehicles performing the task increases, the higher the execution efficiency of the task, the actual task value u j Will be greater than the original value v of the task j The method comprises the steps of carrying out a first treatment on the surface of the When the number of unmanned aerial vehicles distributed meets the upper limit value L j When u j The fixed value is not changed along with the increase of the number of unmanned aerial vehicles, which means that even if more unmanned aerial vehicles participate in the task, the task value is not changed any more, and the less the income is allocated to each unmanned aerial vehicle, the more unmanned aerial vehicles can be prevented from selecting the task, and unnecessary allocation is reduced.
3. Optimization model
According to the constraint conditions and the benefit function, an optimization model of the large-scale unmanned aerial vehicle task allocation problem is established, and the optimization model is as follows:
the optimization model aims at distributing proper tasks for each unmanned aerial vehicle under the constraint conditions of meeting task types, requirements, number relations, scale constraints and the like, and maximizing global benefits, wherein the global benefits are the sum of individual benefits of all unmanned aerial vehicles.
2. Building coalition-forming gaming model
The task allocation problem is converted into a multi-unmanned aerial vehicle alliance forming game process, an alliance forming game model is established, a preference relation is given, an alliance switching rule of the unmanned aerial vehicle is designed, and a solution form is determined.
1. Coalition forming gaming model
Firstly, an optimization model of large-scale heterogeneous unmanned aerial vehicle task allocation is converted into a coalition forming game model. Based on the idea of forming games by alliances, unmanned aerial vehicles cooperatively execute tasks by cooperatively forming stable alliances. Assuming that each alliance corresponds to a task, each unmanned aerial vehicle can only select one alliance, the allocation process divides the unmanned aerial vehicle into a plurality of mutually disjoint alliances containing all unmanned aerial vehicles, called alliance partition, denoted pi= { C 0 ,C 1 ,...,C m}, wherein ,C0 Representing a set of drones corresponding to an empty task,representing task t j A corresponding federation. All federations in federation partition n satisfy +.>C j ∩C j′ ＝φ，j≠j′，C j and Cj′ Representing any two tasks t j and tj′ A corresponding federation.
The coalition forming game model is defined as G= (N, u), wherein N is a game participant set, namely N unmanned aerial vehicles which participate in task allocation; u is the alliance revenue for quantitatively describing alliance quality, the sum of individual revenue for all drones selecting the mission, expressed as:
wherein ,rkj (t j ,|C j I) is alliance C j The benefit of unmanned aerial vehicle k. The final solution goal of the coalition-forming game is to form a stable coalition structure to maximize the total revenue of all coalitions, expressed mathematically as:
from the above formula, the solving target of the coalition game is consistent with the optimizing target of the task allocation problem, and the final coalition partition result is the task allocation result.
2. Switching rules
During the game, the policy of each drone is to decide which coalition to select. The initial strategies of the unmanned aerial vehicle are all to select empty tasks, and the alliance structure at the moment is used as an initial alliance partition. After the initial alliance partition is obtained, the unmanned aerial vehicle joins a new alliance by leaving the current alliance, and simultaneously changes the individual benefits and alliance benefits of the unmanned aerial vehicle, and the behavior of the unmanned aerial vehicle for changing the alliance is called switching operation. The unmanned aerial vehicle follows certain switching rules when executing switching operation, wherein the rules are formulated based on the preference of the unmanned aerial vehicle to the alliance, namely the unmanned aerial vehicle selects to join in the willingness of a certain alliance, and the unmanned aerial vehicle passes throughTo represent. For unmanned plane i, two alliances C are given 1 and C2 If the preference relation for the two alliances is +.>Representing unmanned plane i as compared to alliance C 2 More prone to join federation C 1 Or at least have the same willingness to join two federations. />Representing unmanned plane i to C 1 Is (1)Lattice preference.
According to the unmanned aerial vehicle gain function, taking the total gain of alliances as a preference relation, namely, for unmanned aerial vehicle i, giving any two alliances C 1 and C2 The method comprises the following steps:
wherein ,representing equivalence relation, C 1 { i } means that drone i leaves federation C 1 . The above preference relationship indicates that the unmanned aerial vehicle considers not only itself but also the overall benefits of its coalition members when selecting coalitions. Based on the preference relation, the switching rule of the unmanned aerial vehicle in the process of forming games by the alliance is given: given the current coalition partition result pi= { C 0 ,C 1 ,...,C m -if and only if +.>At this time, unmanned plane i is from alliance C j Leave, join new alliance C j' . At this time, the coalition partition result is updated to pi' = (pi\ { C) j ,C j' })∪{C j \{i},C j' ∪{i}}。
The above-mentioned switching rules indicate that, according to the defined preference relationship, if there is a possibility of switching, no one has the opportunity to leave from the old federation, join the new federation, and increase the sum of the total incomes of both federations before and after switching.
3. Stabilizing federated partitions
The aim of forming games by the alliances is to form a stable alliance structure, so that unmanned opportunities can be continuously switched among the alliances to achieve a final stable state, and the overall benefit of the system is improved. Based on the definition of the preference relationship, the definition of the nash-stable coalition partition in the coalition formation game is given below. Let pi represent alliance partition result, pi (i) represent number of task selected by unmanned plane i, C Π ( i ) Representing the current unmanned plane iThe alliance is located. When all unmanned aerial vehicles i epsilon N prefer to the current alliance, the alliance selection cannot be changed unilaterally to improve the income, namely the satisfaction is metThen the coalition partition pi is Nash stable, and the coalition partition is a stable coalition structure pi obtained by the coalition forming game stable I.e. the solution of the game. Nash stable alliance partition means that the unmanned aerial vehicle can not increase the total income of all alliances through switching operation any more, and the stable state is achieved. Because the target of the game formed by the alliance is consistent with the target of the task allocation problem, the obtained stable alliance partition is the solution of the task allocation problem.
3. Two-stage solution for forming games based on maximum weighted matching and coalition
To obtain stable federated partitions, the solution algorithm is split into two phases: firstly, determining a collar machine corresponding to each task based on maximum weighted matching; then, the unmanned aerial vehicle except the collar machine selects tasks to be executed according to the preference relation and the switching rule defined in the previous step, then each collar machine carries out conflict resolution, the task selection result exceeding the scale limit is processed, the stage is iterated until convergence is carried out, and finally, the Nash stable alliance partition is obtained and is used as a solution of the large-scale task allocation problem. Fig. 1 is an overall flowchart of a solution algorithm.
1. Collar machine determination based on maximum weighted matching
Firstly, all unmanned aerial vehicles select empty tasks, initialization of task allocation results is completed, and then corresponding collar machines are determined for each task based on a maximum weighted matching algorithm. The function of the collar machine is to store task information including task position, type, requirement and the like, and to store unmanned aerial vehicle number, income and cost for selecting the task in each iteration, and to perform conflict resolution operation in the next stage. Each unmanned aerial vehicle can interact with the collar machine to obtain the information, and task selection is performed. Task allocation results stored by other collar machines can be obtained through interaction among the collar machines. The specific algorithm comprises the following steps:
(1) Initialization ofTask allocation result, all unmanned aerial vehicles select empty task t 0 I.e. the result of the alliance partition is
(2) According to the designed unmanned aerial vehicle profit function, calculating the profit of each unmanned aerial vehicle to independently execute the task, and establishing a profit matrix M (unmanned aerial vehicle number N with unmatched behaviors u Listed as unmatched task number T u The elements in the matrix are benefit values), initializing a collar machine set LE;
(3) Judging whether the LE contains all the collar machines of the tasks, stopping the stage if each task has the corresponding collar machine, entering the unmanned aerial vehicle task selection stage, and executing the step (3) if not;
(4) For each task t j ∈T u And (i.e. each column in M), finding the unmanned aerial vehicle corresponding to the row with the biggest profit value in the column, and simultaneously determining the optimal task of the unmanned aerial vehicle, and if the unmanned aerial vehicle and the task are matched with each other, adding the unmanned aerial vehicle into the LE. After the above operations are sequentially performed on each task, unmanned aerial vehicles added into the LE and the corresponding tasks are deleted from the matrix, and the profit matrix M, N is updated u and Tu . Then, the step (3) is returned.
Executing the algorithm, a unmanned aerial vehicle can be accurately matched for each task to serve as a collar machine, and benefits are equivalent to weights in the matching process, and the algorithm is also called a maximum weighted matching algorithm.
2. Task selection and conflict resolution for forming games based on coalition
After the collar machine of each task is found based on maximum weighted matching, the result containing the collar machine is used as an initial task distribution result, all unmanned aerial vehicles except the collar machine are initialized to select empty tasks, then coalition switching operation is carried out based on a preference relation, and coalition benefits are continuously optimized until a stable task distribution result is obtained. Because the unmanned aerial vehicle makes decisions at the same time, a situation may be caused in which certain tasks are selected centrally. In order to solve the problem, a conflict resolution stage is introduced, the task selection result of the unmanned aerial vehicle is processed through the collar machine, and the adaptation of the number of the selected unmanned aerial vehicles and the number of the demands is ensured. The specific steps of the algorithm are as follows:
(1) Initializing alliance partition results, namely including results of all task collar machines, and adding the rest unmanned aerial vehicles into an empty task alliance C 0 I.e. the result of the alliance partition isLE[j]For task t j Corresponding to the collar machine. Let τ denote the iteration number, n [ τ ]]And (5) representing the coalition partition result obtained after the tau-th iteration. The lead machine stores task information including task types, task demands, task positions, and total gains and total costs of tasks in a subsequent distribution process.
(2) Task selection: in the iteration of the τ -th round, firstly, for each unmanned aerial vehicle i epsilon N\LE except a collar machine, a coalition partition result pi [ τ -1] of the previous round of iteration is obtained from the collar machine, wherein the method comprises the steps of selecting the number and the number of unmanned aerial vehicles of each task, and obtaining the total income and the cost of the corresponding task; then, calculating the change condition of the total alliance benefits before and after switching if the unmanned aerial vehicle is switched to any optional alliance from the current alliance, and selecting a task with the maximum value for switching from the tasks based on the preference relation, or keeping the task in the current alliance; and finally, sending the task selection result to the collar machine of the corresponding task.
(3) Conflict resolution stage: and comparing the upper limit value of the demand with the number of unmanned aerial vehicles for selecting the task by the current wheel after obtaining the selection results of all unmanned aerial vehicles for each collar machine i epsilon LE. If the number of unmanned aerial vehicles selecting the mission is greater than the upper limit, i.e. |C j ′|＞L j Sequencing the unmanned aerial vehicles according to the cost of executing the task from small to large, and selecting a corresponding number of unmanned aerial vehicles according to the upper limit value to obtain a alliance C j * The task selection of the unmanned aerial vehicle exceeding the upper limit is changed into an empty task, the conflict resolution process is completed, and the empty task alliance C is adopted 0′ and Cj * Updating to the partition result pi [ tau ] of the alliance]The method comprises the steps of carrying out a first treatment on the surface of the If |C j ′|≤L j Then directly connect C j ' update to federation partition result pi [ tau ]]. Between collar machinesAnd sharing the processed partition results to obtain the alliance partition results of the round of iteration.
(4) Judging whether the algorithm reaches a convergence condition, if the alliance partition result is not changed, obtaining a stable partition result, considering the algorithm to converge, and ending the operation of the algorithm; otherwise, returning to the step (4).
The algorithm is iterated continuously in the task selection stage and the conflict resolution stage until the alliance partition converges to a Nash stable partition II stable The method is characterized in that no unmanned aerial vehicle wants to deviate from the current alliance, the overall income of the alliance is increased by unilaterally changing task selection, at the moment, the algorithm converges, the iteration process is stopped, and the obtained alliance partition is the solution of the task allocation problem.
Test
In order to verify the effectiveness of the large-scale unmanned aerial vehicle distributed task allocation method provided by the invention, the simulation environment and parameters used by the invention are firstly provided, then the task allocation result under a typical scene is provided, finally the convergence condition of the method under unmanned aerial vehicles and tasks with different scales is provided, and the effectiveness of the method for large-scale unmanned aerial vehicle task allocation is verified by comparing the method with the existing game method in average income and running time.
1. Simulation environment and parameters
The simulation process is performed in a Windows10 operating platform, and the algorithm is realized by programming in Python language. Assuming that there are 12 known tasks, the task related parameters are shown in Table 1, including task number, task type, task value, and number of unmanned aerial vehicles required by the task, wherein the unmanned aerial vehicle scale upper limit value L of the task is assumed j Number of unmanned racks equal to demand num j . There are 100 unmanned aerial vehicles, and the unmanned aerial vehicle is divided into two types, wherein No. 1-50 is the fixed wing unmanned aerial vehicle, can carry out communication relay and information collection task, and No. 51-100 is four rotor unmanned aerial vehicle, can carry out information collection and search rescue task. The unmanned aerial vehicle autonomously distributes tasks according to task demands, and unmanned aerial vehicles which are not distributed with the tasks select standby. The positions of the unmanned aerial vehicle and the task are randomly generated in a space of 2000m multiplied by 2000 m.
TABLE 1 task parameters
| Task numbering | Task type | Task value v j | Number of unmanned aerial vehicles num needed j |
| 1 | Communication relay 1 | 94 | 7 |
| 2 | Communication relay 2 | 96 | 5 |
| 3 | Communication relay 3 | 88 | 5 |
| 4 | Communication relay 4 | 95 | 7 |
| 5 | Information collection 1 | 92 | 8 |
| 6 | Information collection 2 | 90 | 8 |
| 7 | Information collection 3 | 83 | 10 |
| 8 | Information collection 4 | 86 | 10 |
| 9 | Search rescue 1 | 96 | 5 |
| 10 | Search rescue 2 | 82 | 5 |
| 11 | Search rescue 3 | 86 | 10 |
| 12 | Search rescue 4 | 88 | 10 |
2. Simulation results for a typical scenario
To verify the effectiveness of the proposed task allocation method, the algorithm was run to obtain the task allocation results as shown in table 2 based on the above-described simulation parameter settings. From the allocation result, the type and the number of the unmanned aerial vehicles allocated to each task meet the task requirement, and no unmanned aerial vehicle resource waste exists, namely, except for 10 unmanned aerial vehicles which select standby tasks, the tasks allocated to other unmanned aerial vehicles correspond to the types of the unmanned aerial vehicles, and the requirements of scale constraint are met.
TABLE 2 task assignment results
3. Algorithm performance verification
In order to verify the convergence of the proposed algorithm under unmanned aerial vehicles and tasks of different scales, the simulation parameters are fixed to the task number m=15, the unmanned aerial vehicle takes n e {80,100,120,140,160,180,200}, and the fixed unmanned aerial vehicle number n=100, the task number takes m e {4,8,12,16,20}.
Fig. 2 and 3 show statistics using box graphs, where the polyline is the average number of iterations required to achieve convergence. With the increase of the number of unmanned aerial vehicles and the number of tasks, the provided algorithm can still achieve convergence in limited iteration times, task distribution is completed, and the effectiveness and expandability of the algorithm are verified.
To further verify the performance of the proposed algorithm, the mission allocation method Group Agent Partitioning and Placing Event (GRAPE) based on the enjoyment game concept was compared to compare the average drone revenues of the two methods, where the number of drones n e {80,85,90,95,100} with a fixed total demand number of 80.
The simulation result is shown in fig. 4, wherein the dotted line and the solid line in the figure are average gains of the unmanned aerial vehicle of the GRAPE algorithm and the proposed algorithm respectively. When the total number of unmanned aerial vehicles is equal to the required number, the gains of the unmanned aerial vehicles in the two methods are basically equal, and when the number of unmanned aerial vehicles is redundant, the GRAPE method requires all unmanned aerial vehicles to execute tasks, so that unnecessary allocation exists, and the average gain of the unmanned aerial vehicles is smaller than that of the proposed method. The gain of the unmanned aerial vehicle of the method is basically kept unchanged, and the more the number of unmanned aerial vehicles is redundant, the larger the difference value between the unmanned aerial vehicles is.
On the basis of considering the coalition scale limitation as well, the method provided by the invention is compared with a MinKP algorithm [3] based on distributed game for running time, wherein the task number m=15, the unmanned plane number n is {80,100,120,140,160,180,200}, and 10% of unmanned opportunities are available for selecting idle tasks for standby.
Fig. 5 shows statistics of the running times of the two algorithms, the solid line is the average running time of the proposed algorithm and the dotted line is the average running time of the MinKP algorithm. Simulation results show that as the scale of the unmanned aerial vehicle is enlarged, the running time of the two methods is linearly increased, and longer time convergence is needed. For task allocation of unmanned aerial vehicles with different numbers, the solving time of the method is smaller than MinKP algorithm, and the real-time requirement of task allocation is met.
The simulation shows that the task allocation method has faster solving efficiency, can obtain higher average gain of the unmanned aerial vehicle, and verifies the effectiveness of the method on the task allocation of the large-scale unmanned aerial vehicle.
Therefore, by adopting the large-scale unmanned aerial vehicle distributed task allocation method based on the alliance forming game, the unmanned aerial vehicle is used for selecting tasks based on the game distributed mode, and the specific unmanned aerial vehicle is used for processing scale conflicts, so that iteration times of task allocation results can be reduced, the real-time performance of task allocation is improved, unmanned aerial vehicle resources are better utilized, and waste of unmanned aerial vehicle resources is reduced.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention and not for limiting it, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that: the technical scheme of the invention can be modified or replaced by the same, and the modified technical scheme cannot deviate from the spirit and scope of the technical scheme of the invention.
Claims (6)
1. A distributed task allocation method for a large-scale unmanned aerial vehicle forming games based on alliance is characterized by comprising the following steps: the method comprises the following steps:
s1, establishing a task allocation optimization model;
based on a large-scale unmanned aerial vehicle task allocation scene, considering type matching constraint, task demand constraint, number relation constraint and scale constraint conditions, designing a benefit function related to the unmanned aerial vehicle scale and establishing an optimization model to realize mathematical expression of large-scale task allocation problems;
in step S1, constraint conditions of the unmanned aerial vehicle when performing task allocation are specifically:
constraint condition one: type matching constraints
Constraint conditions II: task demand constraints
Constraint conditions three: number relationship constraints
Constraint conditions four: scale constraints
Wherein N is an unmanned aerial vehicle set, and N is the number of unmanned aerial vehicles; a, a ij Indicating whether the unmanned aerial vehicle i selects the task t j ；a ij Is a binary decision variable; t (T) i Representation of unmanned plane i canWith a selected set of tasks T\T i Indicating the task that unmanned plane i cannot select, t 0 Is an empty task, m is the number of tasks except the empty task; num (num) j Indicating completion of task t j The number of unmanned aerial vehicles required; l (L) j Representing task t j Upper limit value of unmanned aerial vehicle scale, L j ≥num j ；T\{t 0 The task set T represents a nulling task T 0 Other tasks;
in step S1, the optimization objective of the unmanned aerial vehicle when performing task allocation is specifically:
maximizing global revenue
The method comprises the steps of designing unmanned aerial vehicle individual profit functions by considering task values, the number of unmanned aerial vehicles for selecting tasks and the cost for executing tasks:
wherein ,|Cj I represents the selection task t j Number of unmanned aerial vehicles, c ij Representing the cost of the unmanned aerial vehicle i to perform the task, u j Is task t j Is of value (1);
task value and task raw value v j Task demand number num j Upper limit value of scale L j And selecting the number of unmanned aerial vehicles of the task to be related, and calculating the task value by considering the scale constraint:
wherein ,vj The method is a known original value of the task, the value of the original value does not change along with the task allocation process, epsilon is a constant, and the situation that the value of the task is equal to zero is avoided;
s2, building a alliance to form a game model;
s3, solving two stages of game formation based on maximum weighted matching and alliance.
2. The coalition-based gaming large-scale unmanned aerial vehicle distributed task allocation method of claim 1, wherein: in step S2, the building of the coalition-forming game model specifically includes the following steps:
s21, converting task allocation into a game process, determining game elements, and establishing a alliance to form a game model;
s22, determining a preference relation of the unmanned aerial vehicle based on alliance benefits, and designing alliance switching rules of the unmanned aerial vehicle according to the preference relation;
s23, determining the form of forming a game stable solution by the coalition, and determining game convergence conditions.
3. The coalition-based gaming large-scale unmanned aerial vehicle distributed task allocation method of claim 2, wherein: in step S22, the alliance switching rule of the unmanned aerial vehicle specifically includes:
given the current coalition partition result pi= { C 0 ,C 1 ,...,C m -if and only if it meetsAt this time, unmanned plane i is from alliance C j Leave, join new alliance C j' Updating the alliance partition result into pi' = (pi\ { C) j ,C j' })∪{C j \{i},C j' ∪{i}}；
wherein ,C0 ,C 1 ,...,C m For task t 0 ,t 1 ,...,t m Respectively corresponding alliances, preference relationsTo consider the preference for alliance total revenue, i.e. for drone i, any two alliances C are given 1 and C2 The method comprises the following steps:
wherein ,representing equivalence relation, C 1 { i } represents that unmanned plane i leaves federation C 1 ，r k1 (t 1 ,|C 1 I) is alliance C 1 The benefit of unmanned aerial vehicle k.
4. The coalition-based gaming large-scale unmanned aerial vehicle distributed task allocation method of claim 1, wherein: in step S3, the two-stage solution for forming a game based on the maximum weighted matching and the coalition specifically includes the following steps:
s31, determining a collar machine corresponding to each task based on a maximum weighted matching algorithm;
s32, forming a game algorithm based on alliance, wherein all unmanned aerial vehicles except the collar machine select tasks in a distributed mode according to the designed switching rules, then resolving scale conflict by the collar machine, and iteratively updating task selection results to obtain stable task allocation results.
5. The coalition-based gaming large-scale unmanned aerial vehicle distributed task allocation method of claim 4, wherein: in step S31, determining a collar machine corresponding to each task based on the maximum weighted matching, which specifically includes the following steps:
s311, initializing a task allocation result, and selecting an empty task t by all unmanned aerial vehicles 0 I.e. the result of the alliance partition isWherein phi is an empty set;
s312, calculating the profits of each unmanned aerial vehicle for executing tasks independently according to the designed unmanned aerial vehicle profits function, establishing a profits matrix M, and initializing a collar machine set LE;
s313, judging whether the LE contains all the collar machines of the tasks, stopping the stage if each task has the corresponding collar machine, entering the unmanned aerial vehicle task selection stage, and otherwise executing the step S314;
s314, for each task t j ∈T u Finding an unmanned aerial vehicle corresponding to a row with the largest profit value in the row, determining an optimal task of the unmanned aerial vehicle, and adding the unmanned aerial vehicle into the LE if the unmanned aerial vehicle and the task are matched with each other;
after the above operations are sequentially performed on each task, unmanned aerial vehicles added into the LE and the corresponding tasks are deleted from the matrix, and the profit matrix M, N is updated u and Tu The method comprises the steps of carrying out a first treatment on the surface of the Then, the process returns to step S313;
wherein ,Nu Numbering unmatched unmanned aerial vehicles; t (T) u The unmatched tasks are numbered.
6. The coalition-based gaming large-scale unmanned aerial vehicle distributed task allocation method of claim 4, wherein: in step S32, task selection and conflict resolution of the unmanned aerial vehicle specifically includes the following steps:
s321, initializing a alliance partition result: the result of each task collar machine is included, and other unmanned aerial vehicles are added into the empty task alliance C 0 The result of alliance partition isLE[j]For task t j Corresponding to the collar machine;
task information is stored in the collar machine, and the task information comprises task types, task demands, task positions, and total gains and total costs of the tasks in the subsequent distribution process;
s322, task selection phase: in the iteration of the τ -th round, firstly, for each unmanned aerial vehicle i epsilon N\LE except a collar machine, obtaining a coalition partition result pi [ τ -1] of the previous round of iteration from the collar machine, wherein the method comprises the steps of selecting the number and the number of unmanned aerial vehicles of each task, and obtaining the total income and the cost of the corresponding task; wherein τ represents the number of iterations;
then, calculating the change condition of the total alliance benefits before and after switching if the unmanned aerial vehicle is switched to any optional alliance from the current alliance, and selecting a task with the maximum value for switching from the tasks based on the preference relation, or keeping the task in the current alliance;
finally, the task selection result is sent to the collar machine of the corresponding task;
s323, conflict resolution stage: for each collar machine i epsilon LE, after obtaining the selection results of all unmanned aerial vehicles, comparing the upper limit value of the requirement with the number of unmanned aerial vehicles for selecting the task in the current wheel;
if the number of unmanned aerial vehicles selecting the mission is greater than the upper limit, i.e. |C j ′|＞L j Sequencing the unmanned aerial vehicles according to the cost of executing the task from small to large, and selecting a corresponding number of unmanned aerial vehicles according to the upper limit value to obtain a alliance C j * The task selection of the unmanned aerial vehicle exceeding the upper limit is changed into an empty task, the conflict resolution process is completed, and the empty task alliance C is adopted 0′ and Cj * Updating to the partition result pi [ tau ] of the alliance]；Π[τ]Representing a coalition partition result obtained after the tau-th iteration;
if |C j ′|≤L j Then directly connect C j ' update to federation partition result pi [ tau ]]The method comprises the steps of carrying out a first treatment on the surface of the Sharing the processed partition result with other collar machines to obtain a coalition partition result of the round of iteration;
s324, judging whether the algorithm reaches a convergence condition: the coalition partition result is not changed to obtain a stable partition result, the algorithm is considered to be converged, and the algorithm operation is finished; otherwise, the process returns to step S322.
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