Integrated game method for multi-aircraft task allocation, trajectory planning and formation control

Abstract

The present invention discloses an integrated game method for multi-aircraft task allocation, track planning and formation control, including: (1) establishing a dynamic model of a single drone, drone partitions, individual preferences of drones and an information interaction topology diagram of the entire drone cluster; (2) establishing an integrated game framework for task allocation, track planning and formation control and designing mutually coupled performance indicators for the three links of task allocation, track planning and formation control under the framework; (3) designing a reverse strategy mechanism, following the reverse operation sequence, optimizing the performance indicators of each link by using feedback information and designing an optimal game control strategy model for each link, solving the optimal control strategy for each link; (4) based on the optimal control strategy of the three links, following the forward sequence operation to obtain optimized drone task allocation, track planning and formation control. The present invention can realize the two-way adjustment of the strategy of each link of the aircraft and achieve the Nash equilibrium of the integrated game.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-aircraft control, and in particular to an integrated game method for multi-aircraft task allocation, track planning and formation control. Background Art

[0002] As a type of network system coupled by communication, swarm aircraft plays an important role in both military and civilian fields, such as forest fire prevention and enemy monitoring. Game theory is widely used in the three core links of task allocation, trajectory planning and formation control of swarm aircraft to seek better system performance. For example: in the task allocation link, the existing technology studies drones with social inhibition characteristics by establishing anonymous hedonic games, implements alliance switching criteria while minimizing the number of cooperative members, and forms Nash stable drone partitions that match the task. In the trajectory planning link, the existing technology realizes the planning of the expected flight trajectory of drones under obstacle avoidance constraints based on non-zero-sum games. In the formation control link, based on non-cooperative games, leader-follower mode cluster formation control can be realized.

[0003] In some existing game frameworks, the strategies for the three links of task allocation, trajectory planning and formation control of cluster aircraft are usually designed separately and independently. This independent design mainly positively adjusts the performance of each link in the direction of task allocation → path planning → formation control, which can be called an open-loop design. However, this open-loop design ignores the two-way interaction between each link, fails to establish a feedback mechanism, and is difficult to adjust the strategy in a timely manner according to the actual situation. Therefore, it is urgent to establish an integrated game mechanism for the three links so that the performance of each link can be adjusted in both directions. Summary of the invention

[0004] Purpose of the invention: In view of the above shortcomings, the present invention provides an integrated game method for multi-aircraft task allocation, trajectory planning and formation control. By establishing an integrated game framework and associating and coupling the indicators between the three links under the integrated game framework, and combining the feedback information of each link to realize the closed-loop design of the three links, the two-way adjustment of the strategy of each link is realized, and finally the Nash equilibrium of the integrated game is achieved.

[0005] Technical solution: To solve the above problems, the present invention discloses an integrated game method for multi-aircraft task allocation, trajectory planning and formation control, which specifically includes the following steps:

[0006] (1) For multi-aircraft systems, a dynamic model of a single UAV, UAV partitioning, individual preferences of UAVs, and the information interaction topology of the entire UAV cluster are established;

[0007] (2) Establishing an integrated game framework of task allocation, trajectory planning and formation control; Based on the model of each UAV, the UAV partition and the individual preference of the UAV established in step (1), the performance indicators of the three links of task allocation, trajectory planning and formation control are designed for each UAV under the integrated game framework, and the performance indicators of task allocation, trajectory planning and formation control are coupled with each other;

[0008] (3) Designing a reverse strategy mechanism, following the operating sequence of formation control, trajectory planning, and task allocation, optimizing the performance indicators of each link by using feedback information, designing the optimal game control strategy model for each UAV in each link, and calculating and obtaining the optimal control strategy for each UAV in each link; the feedback information includes the state error output of the formation control link, the optimal control input of the formation control link, and the optimal control input of the trajectory planning link;

[0009] (4) Based on the obtained optimal control strategy for each UAV in the three links, the UAV task allocation, trajectory planning, and formation control are carried out in sequence to obtain the optimized task allocation, trajectory planning, and formation control for each UAV.

[0010] Furthermore, step (1) specifically includes: (1.1) constructing a cluster of S drones and defining A collection of drones; i.e. a single drone The dynamic model is:

[0011]

[0012]

[0013] In the formula, represents the position of UAV i at time t; v i (t) represents the speed of UAV i at time t; u i (t) represents the control input of UAV i at time t;

[0014] make:

[0015]

[0016] In the formula, p i is the position of the drone; v i is the speed of the drone;

[0017] Single drone The dynamic model is rewritten as:

[0018]

[0019] In the formula, q is a positive integer; xi (t) represents x at time t i ; For x i (t) dynamic characterization;

[0020] (1.2) (1.2) The tasks are partitioned according to the different geographical areas to which the actual expected location belongs. Each task partition is expressed as: k is the task partition number, is a set of task partitions, is the number of task partitions; since drones and tasks are matched one by one, the drone partitions obtained according to the task partitions are expressed as: And the following conditions are met:

[0021]

[0022]

[0023] Where D k Is to perform task d [k] UAV alliance; m is the task partition number that is not k in the task partition set; To perform task d [m] The Drone Alliance;

[0024] For each task partition d [k] Setting k +1 task, i.e. If the task Assigned to drone i, that is, drone i is relabeled as r [k] , Drone Alliance D k It is expressed as:

[0025] (1.3) The performance index of UAV i in the task allocation phase is designed as follows:

[0026]

[0027] In the formula, represents the desired position, Indicates the desired speed; represents the task-coalition pair, that is, with n k Drones to perform missions together

[0028] Establish drone preferences for any drone definition For a preference choice, k≠m, expression Compared to the mission--the alliance Drones prefer to choose missions - Alliance That is, the personal preference expression of the drone is:

[0029]

[0030] (1.4) Using graph theory to describe the information interaction of drones in each alliance, we can obtain the information interaction topology of the entire drone cluster. k The internal information interaction topology is defined as: ε k It is the edge connecting the nodes in the graph, representing the information interaction between the two drones.

[0031] Furthermore, step (2) specifically includes:

[0032] (2.1) In the trajectory planning phase, each UAV is equipped with a virtual agent responsible for generating the desired flight trajectory. Each UAV is designed to have the same system dynamics as the corresponding virtual agent, expressed as:

[0033]

[0034] In the formula, z r (t) represents the state of the virtual agent at time t; represents the control input of the virtual agent at time t;

[0035] (2.2) Establish an integrated game framework for task allocation, trajectory planning and formation control. The integrated game framework is as follows: establish an anonymous hedonic game for drones and tasks to achieve task allocation, so that each drone chooses different tasks according to its own preferences and forms a corresponding drone alliance; establish a Steinberg differential graph game within each drone alliance to achieve trajectory planning and formation control; in which the virtual agent acts as a leader to generate the desired flight trajectory, and the drone acts as a follower to achieve formation flight;

[0036] (2.3) Based on the integrated game framework, a set of coupled performance indicators are designed for the three links of UAV task allocation, trajectory planning and formation control, including:

[0037] For Alliance D who are willing to choose to join k The performance index of the trajectory planning of UAV i is defined as Γ r , the performance index of the formation control link is J r ;in:

[0038]

[0039] In the formula, zr Represents the state of the agent; d r =d [k] Indicates the UAV mission partition; G r 、F r Both represent the performance index Γ r The weight matrix in ; represents the control input of the virtual agent, i.e., the strategy of the trajectory planning link; u r It represents the control input of the UAV, i.e. the strategy of the formation control link;

[0040]

[0041] In the formula, Q r , R r , L r Both represent performance indicators J r The weight matrix in ;

[0042] Design the performance index W of the task allocation link i It is the sum of the performance indicators of the two links of trajectory planning and formation control, specifically:

[0043]

[0044] Furthermore, step (3) specifically includes:

[0045] (3.1) Design a game control strategy model for the formation control link, including:

[0046] (3.1.1) Given any feasible UAV partition Π and any feasible trajectory planning strategy Define the state error vector The performance index of the formation control link optimized according to the state error vector is J r get:

[0047]

[0048] (3.1.2) Targeting the Alliance The game control strategy model of the UAV formation control link is: based on the given Π, and

[0049]

[0050] The constraints are:

[0051]

[0052] In the formula, u -r Represents Alliance The strategy set of other drones except drone r; is the dynamic characterization of the state error vector system;

[0053] (3.1.3) Calculate the optimal UAV formation control strategy, the formula is:

[0054]

[0055] In the formula, is the optimal formation control strategy for UAVs; R r is the weight matrix of the control input in the performance index, B r is the input matrix, P r is the solution of the asymmetric Riccati differential equation;

[0056] (3.2) Design the game control strategy model for the trajectory planning process, including:

[0057] (3.2.1) The dynamic representation of virtual agents in the same alliance is:

[0058] In the formula, is the dynamic representation of z;

[0059] The performance index of trajectory planning is Γ r Re-expressed as:

[0060]

[0061] In the formula,

[0062] (3.2.2) The game control strategy model of the UAV trajectory planning link is:

[0063]

[0064] The constraints are:

[0065]

[0066]

[0067] (3.2.3) Calculate the optimal trajectory planning strategy for the UAV, the formula is:

[0068]

[0069] In the formula, is the oblique variable,

[0070] (3.3) Design a game control strategy model for task allocation, including:

[0071] (3.3.1) The game control strategy model of the task allocation link is:

[0072]

[0073] Constraints:

[0074]

[0075] δ ir ∈{0, 1},

[0076]

[0077]

[0078] In the formula, δ ir is the matching factor between the mission and the UAV;

[0079] (3.3.2) Based on the optimal formation control strategy and optimal trajectory planning strategy obtained in step (3.1) and step (3.2), the optimal UAV partition Π corresponding to each UAV is searched according to the switching criteria. * ; The switching criteria are: for a partition of a drone Drone i chooses to leave its alliance Join another alliance k≠m if and only if there exists a task d r , So that:

[0080]

[0081] Then the newly formed drone partition can be expressed as

[0082] Furthermore, step (4) specifically includes:

[0083] (4.1) Initialize the set of drones, the set of tasks, the initial partitions of drones, and the initial weights;

[0084] (4.2) For the current drone partition, determine whether the current drone partition meets the individual preference of the drone, that is, determine whether the following formula is true:

[0085]

[0086] In the formula, represents the optimal formation control strategy of UAV l in the alliance; represents the optimal trajectory planning strategy of UAV l in the alliance; n Π(i) is the number of drones in the current partition Π;

[0087] If true, the drone leaves the current alliance and joins the new alliance and updates the partition, and goes to step (4.3); if not true, the drone partition is output and goes to step (4.4); the formula is:

[0088] (4.3) Repeat step (4.2) until the formula in step (4.2) holds true, then output the drone partition, which is the optimal partition;

[0089] (4.4) Based on the output drone partition, the optimal drone trajectory planning strategy is adopted Minimize the performance index Γ r Get the trajectory plan;

[0090] (4.5) Based on the obtained UAV partitioning and trajectory planning, the optimal UAV formation control strategy is adopted Minimize performance index J r Gain formation control.

[0091] In addition, the present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of any of the above methods when executing the computer program. A computer-readable storage medium stores a computer program thereon, wherein the computer program implements the steps of any of the above methods when executed by the processor.

[0092] Beneficial effects: Compared with the prior art, the integrated game method for multi-aircraft task allocation, trajectory planning and formation control described in the present invention has the following significant advantages: by establishing an integrated game framework and designing a set of mutually coupled performance indicators to associate the three links under the framework; then based on the designed performance indicators, a reverse strategy design mechanism is designed, that is, following the order of formation control → trajectory planning → task allocation, three game strategy models are designed according to the feedback information generated under this operation sequence, and the optimal strategy of each link under reverse operation is calculated; finally, the forward operation strategy is adjusted according to the optimal strategy obtained. This method overcomes the limitation that the three links of traditional cluster aircraft can only be adjusted forward, and effectively realizes the two-way adjustment of the strategy of each link and the two-way regulation of the performance of each link. The designed game strategy can not only achieve the stability and optimal performance of each link, but also achieve the Gestalt Nash equilibrium of the integrated game. BRIEF DESCRIPTION OF THE DRAWINGS

[0093] Figure 1 The figure shows a game framework diagram integrating the three links of task allocation, track planning and formation control according to the present invention;

[0094] Figure 2 The figure shows the overall closed-loop design framework in the integrated game framework of the present invention;

[0095] Figure 3 Shown is a cost graph of the drone of the present invention performing different tasks;

[0096] Figure 4 Shown is a trajectory error curve diagram between the reference flight trajectory and the actual flight trajectory of the present invention;

[0097] Figure 5 The figure shows the formation flight trajectory diagram of UAVs 1-5 in an embodiment of the present invention;

[0098] Figure 6 In the embodiment of the present invention, the alliance The formation flight trajectory diagram of UAVs 1-3;

[0099] Figure 7 In the embodiment of the present invention, the alliance The formation flight trajectory diagram of UAVs 4-5;

[0100] Figure 8 In the embodiment of the present invention, the alliance Speed ​​variation curve of UAV 1-3;

[0101] Fig. 9 In the embodiment of the present invention, the alliance Speed ​​variation curve of UAV 4-5. DETAILED DESCRIPTION

[0102] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0103] like Figure 1 and Figure 2 As shown, the present invention provides an integrated game method for multi-aircraft task allocation, trajectory planning and formation control, which specifically includes the following steps:

[0104] Step 1: Establish a dynamic model of a single drone, drone partitions, individual preferences of drones, and the information interaction topology of the entire drone cluster; specifically:

[0105] (1) Build a cluster of S drones and define A collection of drones; i.e. a single drone The dynamic model is:

[0106]

[0107]

[0108] In the formula, represents the position of drone i at time t; represents the speed of drone i at time t; represents the control input of UAV i at time t;

[0109] By building:

[0110]

[0111] The dynamic model of the drone is further rewritten as follows:

[0112]

[0113] In the formula, q is a positive integer.

[0114] (2) The tasks are partitioned according to the different geographical areas to which the actual expected location belongs. Each task partition is represented as: k is the task partition number, is the set of task partitions. Since drones and tasks match one by one, the partition of drones according to the task partition is expressed as: And the following conditions are met:

[0115]

[0116]

[0117] Where D k Is to perform task d [k] The Drone Alliance;

[0118] For each task partition d [k] Setting k +1 task, i.e. If the task Assigned to drone i, that is, drone i is relabeled as r [k] In this way, the UAV Alliance D k It is expressed as: Since there is a one-to-one correspondence between the drones and tasks studied in this invention, the present invention will use It also represents the set of indices that represent the tasks and the set of indices that represent the drones in the alliance.

[0119] (3) The performance indicators of UAV i in the task allocation phase are designed as follows:

[0120]

[0121] In the formula, represents the desired position, Indicates the desired speed; represents the task-coalition pair, that is, with n k Drones to perform missions together Considering the different missions faced by drones - the alliance When , there are individual preferences, so the following preferences of drones are established. For any drone definition is a complete, reflexive, transitive preference choice for a binary relationship. Based on the established preference choice, k≠m, expression Compared to the mission-alliance Drones prefer to choose missions - Alliance That is, the personal preference expression of the drone is:

[0122]

[0123] According to the above formula, there are two determining factors of drone preference: the selected mission and the number of partners n k .

[0124] (4) Graph theory is used to describe the information interaction of drones in each alliance to obtain the information interaction topology of the entire drone cluster. For example, the information interaction topology diagram within the alliance is defined as: in is the edge connecting the nodes in the graph, representing the information interaction between the two drones. In order to simplify the notation, the superscript "[·]" is removed in the unambiguous places to represent the drones and tasks, that is, drone r [k] Let drone r be the mission Let it be task d r Based on simplified notation, drone 0 represents the alliance Select the leader drone for task d0, drone r (r≠0) represents the coalition Select Task d r Follower drone r≠0. Assume that the graph are connected.

[0125] Step 2: Establish an integrated game framework of task allocation, trajectory planning and formation control, and design a set of coupled performance indicators for each drone’s task allocation, trajectory planning and formation control based on this integrated game framework. Specifically:

[0126] (1) Constructing a complete game situation: In the trajectory planning phase, each UAV is equipped with a virtual agent responsible for generating the desired flight trajectory. The UAV and the corresponding virtual agent are designed to have the same system dynamics, expressed as:

[0127]

[0128] In the formula, z r (t) represents the state of the virtual agent at time t; Represents the control input of the virtual agent at time t.

[0129] (2) Establish an integrated game framework of three links: task allocation, trajectory planning, and formation control, in which the players are summarized as follows:

[0130] a) Players of anonymous hedonic games: drones and missions;

[0131] b) Players of the Steinberg differential graph game: virtual agents and drones.

[0132] Specifically, the integrated game framework is as follows: First, an anonymous hedonic game is established for drones and tasks to achieve task allocation, so that each drone chooses different tasks according to its own preferences and forms a corresponding drone alliance. Then, within each drone alliance, a Steinberg differential graph game is established to achieve trajectory planning and formation control. Among them, the virtual agent acts as a leader to generate the desired flight trajectory, and the drone acts as a follower to achieve formation flight;

[0133] (3) Based on the integrated game framework, a set of coupled performance indicators are designed for the three links of task allocation, trajectory planning and formation control, including:

[0134] For Alliance D who are willing to choose to join k The performance index of the trajectory planning of UAV i is defined as Γ r , the performance index of the formation control link is J r ; Design the performance index W of the task allocation link i It is the sum of the performance indicators of the two links of trajectory planning and formation control, specifically:

[0135]

[0136] In the formula, u r represents the control input of the UAV, i.e., the planning strategy of the formation control link; Represents the control input of the virtual agent, i.e., the strategy of the trajectory planning link;

[0137] The advantages of this design are: on the one hand, the performance of task allocation can be improved through the strategies of trajectory planning and formation control. On the other hand, the performance of trajectory planning and formation control can be adjusted by the strategy of task allocation (d r ,n k ) to make adjustments. Therefore, the strategy of each link can be adjusted in both directions, which is conducive to the closed-loop design of the subsequent three links.

[0138] The trajectory planning step Γ is given as follows r , performance indicators of formation control link J r The specific form is:

[0139] Virtual agent-based system dynamics and tasks r The information of the desired destination and the desired speed contained in the virtual agent r is designed as

[0140]

[0141] In the formula, z r Represents the state of the agent; G r 、F r Both represent the performance index Γ r The weight matrix in G r >0、F r >0; This indicator not only takes into account the control energy consumption of the virtual agent itself, but also takes into account the control energy consumption of the UAV, so that the impact of formation control on trajectory planning can be characterized within the framework of the Steinberg differential graph game.

[0142] definition The performance indicators of the leader drone and the follower drone can be uniformly constructed as follows:

[0143]

[0144] In the formula, Q r , R r , L r Both represent performance indicators J r The weight matrix in, L r >0;

[0145] And for r≠0, we have is the weight matrix corresponding to the leader drone; for r≠0, there are:

[0146]

[0147] satisfy Where each submatrix is ​​defined as:

[0148]

[0149]

[0150] In the formula, Indicates follower drone and the weight matrix between the leader drone, and represents the weight matrix between the follower drone r and its neighbor drone l.

[0151] Performance indicators under the integrated game frameworkJ r Added design Used to characterize the impact of prior decisions imposed by trajectory planning on the formation control link.

[0152] Step 3: Propose a reverse strategy design mechanism, follow the order of formation control → trajectory planning → task allocation, use feedback information to optimize the performance indicators of each link and design the optimal game control strategy for each link, and finally calculate and obtain the optimal control strategy for each drone in each link. Specifically include:

[0153] (1) Design a game control strategy model for the formation control link, including:

[0154] (1.1) Given any feasible UAV partition Π and any feasible trajectory planning strategy The drones are used as follower players in the Steinberg differential graph game to realize formation control. Define the state error vector The system dynamics are characterized as follows:

[0155]

[0156] in,

[0157]

[0158] According to the state error vector, the performance index of the formation control link can be obtained as J r Further expressed as:

[0159]

[0160] (1.2) Design Alliance The game control strategy model of the UAV formation control link is proposed. The problem of optimal formation control of UAVs can be described as: given Π, and

[0161]

[0162] The constraints are:

[0163]

[0164] In the formula, Represents Alliance The strategy set of other drones except drone r;

[0165] (1.3) Solve and calculate to obtain the optimal UAV formation control strategy. Specifically, define the Hamiltonian function of UAV r:

[0166]

[0167] Among them, λ r is the covariate variable of UAV r; the optimal control strategy satisfy

[0168]

[0169] Using the minimum principle, we can get

[0170]

[0171] The optimal control strategy of the UAV is

[0172]

[0173] where λ r satisfy:

[0174]

[0175] In order to obtain the optimal control strategy The equivalent state feedback form is

[0176]

[0177] Where P r satisfies the following asymmetric Riccati differential equation:

[0178]

[0179] And g r Satisfies the adjoint equation:

[0180]

[0181] The state feedback form of the optimal control strategy of UAV r can be expressed as

[0182]

[0183] Among them, R ris the weight matrix of the control input in the performance index, B r is the input matrix, P r is the solution of the asymmetric Riccati differential equation.

[0184] According to the designed optimal control strategy You can achieve:

[0185]

[0186]

[0187]

[0188] Alliance Inside the drone k +1 optimal control strategy It constitutes the Nash equilibrium of its graph game.

[0189] (2) Design a game control strategy model for the trajectory planning process.

[0190] The virtual agent is used as the leader player in the Steinberg differential graph game to achieve its optimal trajectory planning under the constraints of formation control.

[0191] (2.1) The dynamic representation of the virtual agent r in the same alliance is:

[0192]

[0193] The performance index of trajectory planning is Γ r Re-expressed as:

[0194]

[0195] In the formula,

[0196] (2.2) Design a game control strategy model for the UAV trajectory planning process. Specifically, in the framework of the Steinberg differential graph game, the optimal trajectory planning problem of the virtual agent r is described as follows: for a given UAV partition,

[0197]

[0198] The constraints are:

[0199]

[0200]

[0201]

[0202] In the framework of Steinberg differential graph game, the optimal response strategy of UAV formation control is considered. and The designed trajectory planning strategy The ability to correct formation errors helps to achieve a closed-loop design between trajectory planning and formation control.

[0203] (2.3) Calculate and obtain the optimal trajectory planning strategy for the UAV. Specifically: Define the Hamiltonian function of the virtual agent r:

[0204]

[0205] in, is a skew variable, β r and r are two Lagrange multipliers. Control strategy for optimal trajectory planning satisfy

[0206]

[0207] Using the minimum principle, we can derive

[0208]

[0209] in and

[0210] Therefore, the optimal control strategy for trajectory planning is designed as

[0211]

[0212] in β r and r Satisfy

[0213]

[0214] Then we get the following three differential equations

[0215]

[0216]

[0217]

[0218] The optimal control strategy is designed below To achieve this goal, define:

[0219]

[0220]

[0221] Based on the above equations, the following differential equation is established

[0222]

[0223]

[0224] in:

[0225]

[0226]

[0227] The submatrices in the design matrix Φ are:

[0228]

[0229] in,

[0230]

[0231]

[0232]

[0233]

[0234]

[0235]

[0236]

[0237] Design Matrix The submatrix in is defined as:

[0238]

[0239]

[0240]

[0241]

[0242] Establish the affine relationship between matrices Ω and Ψ:

[0243]

[0244] in Satisfies the asymmetric Riccati differential equation:

[0245]

[0246] and Satisfies the adjoint equation:

[0247]

[0248] Based on the above formula, the optimal control strategy Expressed as state feedback:

[0249]

[0250] in,

[0251]

[0252]

[0253]

[0254]

[0255] According to the designed optimal aviation planning control strategy accomplish:

[0256]

[0257] And the virtual agent corresponds to (n k +1) optimal control strategy It constitutes the Nash equilibrium of its graph game.

[0258] (3) Design a game control strategy model for the task allocation process, including:

[0259] (3.1) Game control strategy model for task allocation. Specifically, under the influence of trajectory planning and formation control strategy, an anonymous hedonic game is established to realize the task allocation of UAVs. The problem of task allocation can be described as:

[0260]

[0261] Constraints:

[0262]

[0263] δ ir ∈{0, 1},

[0264]

[0265]

[0266] Among them, δir is the matching factor between the task and the drone. r Assigned to drone i, then δ ir =1; otherwise δ ir =0.

[0267] (3.2) Based on the individual selection preferences of the established drones, establish switching criteria for whether the drones join or leave a certain alliance.

[0268] The switching criteria are: for a partition of a drone Drone i chooses to leave its alliance Join another alliance k≠m if and only if there exists a task d r , So that:

[0269]

[0270] Then the newly formed drone partition can be expressed as

[0271] By using the above switching criteria, the drones spontaneously evolve into different partitioning configurations, where a stable configuration is defined as the Nash stable partitioning. is the partition to which drone i belongs, If for each drone There are inequalities If true, then partition Π is a Nash stable partition.

[0272] For any possible tasks r , If the drone i, The corresponding virtual agent i uses the designed control strategy and Then, under the action of the switching criterion, any initial UAV partition Π0 can converge to a final UAV partition Π * . And, this final drone partition Π * Is a Nash stable partition.

[0273] Step 4: According to the optimal control strategy of the three links, the task allocation, trajectory planning, and formation control are carried out in the order of forward operation to obtain multi-aircraft task allocation, trajectory planning, and formation control. The specific steps include:

[0274] (1) Initialize the collection of drones A collection of tasks Initial partitioning of the drone Initial weight G r 、F r , Q r , R r , L r ;

[0275] (2) Establish an anonymous hedonic game to achieve task allocation. For the current drone partition Π (at the first iteration, Π = Π0), determine whether the following formula is valid;

[0276]

[0277] If true, perform a switching operation: specifically:

[0278] (2.1) Leave the current alliance:

[0279] (2.2) Join a new alliance:

[0280] (2.3) Update partition Π: Use the alliance separately and Alternative Alliance and

[0281] Repeat steps (2.1)-(2.3) until partition Π converges to the final Nash stable partition Π.

[0282] (3) Establish the Steinberg differential graph game: obtain trajectory planning and formation control.

[0283] Under the Nash stable partition Π, the drones in the alliance are re-labeled according to the assigned tasks and equipped with virtual agents to perform the following operations:

[0284] (3.1) According to the output UAV partition Π, the optimal UAV trajectory planning strategy is adopted Minimize the performance index Γ r Get the route plan

[0285] (3.2) Based on the obtained drone partition Π and trajectory planning Adopting the optimal formation control strategy of UAVs Minimize performance index J r Get formation control r .

[0286] Repeat steps (2)-(3) until the strategy converges to the Gestalt Nash equilibrium point.

[0287] In the embodiment of the present invention, a cluster consisting of 5 drones is used to verify the effectiveness of the proposed integrated game method.

[0288] First, initialize the position and speed of the drone. Set the initial position of each drone to:

[0289] p1(0)=[0.480.62] T ,p2(0)=[1.520.65] T ,

[0290] p3(0) = [2.560.60] T ,p4(0)=[5.006.00] T ,

[0291] p5(0) = [7.009.00] T .

[0292] The initial speed of each drone is set as:

[0293] v1(0)=[0.550.81] T ,v2(0)=[0.520.86] T ,

[0294] v3(0) = [0.470.86] T ,v4(0)=[0.270.11] T ,

[0295] v5(0) = [0.220.26] T .

[0296] The virtual agent and the drone are set to have the same initial conditions. The expected position and expected velocity of each drone in the task are set as:

[0297]

[0298]

[0299]

[0300] The weight matrix in the design performance index is

[0301]

[0302]

[0303] By using the control strategy designed by the present invention, the cost required for the drone to perform each task is obtained, such as Figure 3As shown. Furthermore, by minimizing the global performance index, the result of the task allocation of each drone is obtained as follows:

[0304]

[0305]

[0306]

[0307]

[0308]

[0309] Combination Figure 3 The results of task allocation are analyzed from the perspective of individual drones and the overall cluster. First, from the perspective of individual drones: each drone may be more inclined to choose tasks with lower consumption costs. Figure 3 It can be seen that UAV 1-UAV 3 tend to choose to join the alliance Let's complete the task together [1] , while UAV 4 and UAV 5 tend to join the alliance To perform task d [2] Among them, UAV 4 performs the mission and tasks The cost is the same. However, due to the influence of social inhibition, drone 4 tends to choose to join the alliance. Not an alliance Secondly, from the perspective of the entire cluster: the overall goal of task allocation is to minimize the global performance index. Although UAV 4 and UAV 5 are also assigned to perform tasks The cost of UAV 5 is higher than that of UAV 4, but from the perspective of minimizing the global performance index, the task It will still be assigned to UAV 5. At the same time, the assignment result conforms to the individual preferences of UAV 4 and UAV 5.

[0310] Combining the two perspectives, it can be seen that when the scheme described in the present invention is used in the task allocation link, the final allocation result meets the preferences of each individual drone and ensures that the cluster aircraft achieves the global optimal performance.

[0311] Based on the results of the above task allocation, a Steinberg differential graph game between UAVs and virtual agents is established to achieve trajectory planning and formation control. Figure 4The curve of the trajectory error between the actual flight trajectory of each UAV and the reference flight trajectory over time is shown. The simulation results in the figure show that the designed formation control strategy can drive the UAV to follow the reference flight trajectory, and during the flight, the trajectory error converges asymptotically to 0. Figure 5 The real-time formation of UAVs 1-5 is demonstrated, and the results show that the designed formation control strategy can enable the UAVs to follow the reference flight trajectory to reach the destination. Figure 6 Showing the Alliance The real-time formation of UAVs 1-3, Figure 7 The Alliance Real-time formation status of UAVs 4 and 5. Figure 8 and Fig. 9 The curves of the speed of UAVs 1-6 changing with time during the formation process are shown. The results show that when the UAVs reach the final destination, the UAVs reach the desired speed. In summary, the trajectory planning and formation control obtained by the present invention meet the expected requirements.

[0312] In summary, the method described in the present invention can not only ensure the two-way adjustment of the performance of each link of multiple aircraft in task allocation, trajectory planning and formation control, but also synchronously achieve the stability and optimal performance of cluster aircraft.

Claims

1. An integrated game method for multi-aircraft task allocation, trajectory planning and formation control, characterized in that: The following steps are involved: (1) Establish a dynamic model of a single UAV, UAV partitioning, individual preferences of UAVs, and the information interaction topology of the entire UAV cluster; (2) Establish an integrated game framework for task allocation, trajectory planning, and formation control; Based on each drone model, drone partition, and drone individual preference established in step (1), performance indicators are designed for each drone's task allocation, trajectory planning, and formation control in an integrated game framework, and the performance indicators of task allocation, trajectory planning, and formation control are coupled with each other. (3) Designing a reverse strategy mechanism, following the operating sequence of formation control, trajectory planning, and task allocation, optimizing the performance indicators of each link by using feedback information, designing the optimal game control strategy model for each UAV in each link, and calculating and obtaining the optimal control strategy for each UAV in each link; the feedback information includes the state error output of the formation control link, the optimal control input of the formation control link, and the optimal control input of the trajectory planning link; (4) According to the obtained optimal control strategy of each UAV in the three links, the order of UAV task allocation, trajectory planning, and formation control is followed to obtain the optimized task allocation, trajectory planning, and formation control of each UAV; Step (1) specifically includes: (1.1) Build a cluster of S drones and define A collection of drones; i.e. a single drone The dynamic model is: In the formula, represents the position of UAV i at time t; v i (t) represents the speed of UAV i at time t; u i (t) represents the control input of UAV i at time t; make: In the formula, p i is the position of the drone; v i is the speed of the drone; Single drone The dynamic model is rewritten as: In the formula, q is a positive integer; x i (t) represents x at time t i ; For x i (t) dynamic characterization; (1.2) The tasks are partitioned according to the different geographical areas to which the actual expected location belongs. Each task partition is expressed as: k is the task partition number, is a set of task partitions, is the number of task partitions; since drones and tasks are matched one by one, the drone partitions obtained according to the task partitions are expressed as: And the following conditions are met: Where D k Yes k≠m rows of task d [k] UAV alliance; m is the task partition number that is not k in the task partition set; To perform task d [m] The Drone Alliance; For each task partition d [k] Setting k +1 task, i.e. If the task Assigned to drone i, that is, drone i is relabeled as r [k] , Drone Alliance D k Expressed as: D k ={0 [k] , 1 [k] ,…,n k [k] }, (1.3) The performance index of UAV i in the task allocation phase is designed as follows: In the formula, represents the desired position, Indicates the desired speed; represents the task-coalition pair, that is, with n k Drones to perform missions together Establish drone preferences for any drone Definition> i For a preference choice, k≠m, expression Compared to the mission--the alliance Drones prefer to choose missions - Alliance That is, the personal preference expression of the drone is: (1.4) Using graph theory to describe the information interaction of drones in each alliance, we can obtain the information interaction topology of the entire drone cluster. k The internal information interaction topology is defined as: ε k is the edge connecting the nodes in the graph, representing the information interaction between the two drones; Step (2) specifically includes: (2.1) In the trajectory planning phase, each UAV is equipped with a virtual agent responsible for generating the desired flight trajectory. Each UAV is designed to have the same system dynamics as the corresponding virtual agent, expressed as: In the formula, z r (t) represents the state of the virtual agent at time t; represents the control input of the virtual agent at time t; For z r (t) dynamic characterization; (2.2) Establish an integrated game framework for task allocation, trajectory planning and formation control. The integrated game framework is as follows: establish an anonymous hedonic game for drones and tasks to achieve task allocation, so that each drone chooses different tasks according to its own preferences and forms a corresponding drone alliance; establish a Steinberg differential graph game within each drone alliance to achieve trajectory planning and formation control; in which the virtual agent acts as a leader to generate the desired flight trajectory, and the drone acts as a follower to achieve formation flight; (2.3) Based on the integrated game framework, a set of coupled performance indicators are designed for the three links of UAV task allocation, trajectory planning and formation control, including: For Alliance D who are willing to choose to join k The performance index of the trajectory planning of UAV i is defined as Γ r , the performance index of the formation control link is J r ;in: In the formula, z r Represents the state of the agent; d r =d [k] Indicates the UAV mission partition; G r 、F r Both represent the performance index Γ r The weight matrix in ; represents the control input of the virtual agent, i.e., the strategy of the trajectory planning link; u r It represents the control input of the UAV, i.e. the strategy of the formation control link; In the formula, Q r , R r , L r Both represent performance indicators J r The weight matrix in ; Design the performance index W of the task allocation link i It is the sum of the performance indicators of the two links of trajectory planning and formation control, specifically: Step (3) specifically includes: (3.1) Design a game control strategy model for the formation control link, including: (3.1.1) Given any feasible UAV partition Π and any feasible trajectory planning strategy Define the state error vector The performance index of the formation control link optimized according to the state error vector is J r get: (3.1.2) Targeting the Alliance The game control strategy model of the UAV formation control link is: based on the given Π, and The constraints are: In the formula, u -r Represents Alliance The strategy set of other drones except drone r; is the dynamic characterization of the state error vector system; (3.1.3) Calculate the optimal UAV formation control strategy, the formula is: In the formula, is the optimal formation control strategy for UAVs; R r is the weight matrix of the control input in the performance index, B r is the input matrix, P r is the solution of the asymmetric Riccati differential equation; (3.2) Design the game control strategy model for the trajectory planning process, including: (3.2.1) The dynamic representation of virtual agents in the same alliance is: In the formula, is the dynamic representation of z; The performance index of trajectory planning is Γ r Re-expressed as: In the formula, (3.2.2) The game control strategy model of the UAV trajectory planning link is: The constraints are: (3.2.3) Calculate the optimal trajectory planning strategy for the UAV, the formula is: In the formula, is the oblique variable, (3.3) Design a game control strategy model for task allocation, including: (3.3.1) The game control strategy model of the task allocation link is: Constraints: d ir ∈{0,1}, In the formula, δ ir is the matching factor between the mission and the drone; (3.3.2) Based on the optimal formation control strategy and optimal trajectory planning strategy obtained in step (3.1) and step (3.2), the optimal UAV partition Π corresponding to each UAV is searched according to the switching criteria. * ; The switching criteria are: for a partition of a drone Drone i chooses to leave its alliance Join another alliance k≠m if and only if there exists a task d r , So that: Then the newly formed drone partition can be expressed as 2. The integrated game method for multi-aircraft task allocation, trajectory planning and formation control according to claim 1 is characterized in that: Step (4) specifically includes: (4.1) Initialize the set of drones, the set of tasks, the initial partitions of drones, and the initial weights; (4.2) For the current drone partition, determine whether the current drone partition meets the individual preference of the drone, that is, determine whether the following formula is true: In the formula, represents the optimal formation control strategy of UAV l in the alliance; represents the optimal trajectory planning strategy of UAV l in the alliance; n Π(i) is the number of drones in the current partition Π; If true, the drone leaves the current alliance and joins the new alliance and updates the partition, and goes to step (4.3); if not true, the drone partition is output and goes to step (4.4); the formula is: (4.3) Repeat step (4.2) until the formula in step (4.2) holds true, then output the drone partition, which is the optimal partition; (4.4) Based on the output drone partition, the optimal drone trajectory planning strategy is adopted Minimize the performance index Γ r Get the trajectory plan; (4.5) Based on the obtained UAV partitioning and trajectory planning, the optimal UAV formation control strategy is adopted Minimize performance index J r Gain formation control.

3. A computer-readable storage medium, characterized in that: The computer-readable storage medium includes a stored computer program, wherein when the computer program is executed, the device where the computer-readable storage medium is located is controlled to execute the steps of the method according to any one of claims 1 and 2.

4. A debugging device, characterized in that: A memory, a processor, and a program stored and executable on the memory, wherein the program implements the steps of the method according to any one of claims 1 and 2 when executed by the processor.

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