Game-based multi-unmanned aerial vehicle formation control method

Abstract

A game-based multi-unmanned aerial vehicle formation control method comprises the following steps: constructing a game-based multi-unmanned aerial vehicle model framework, dividing unmanned aerial vehicles into following unmanned aerial vehicles and pilot unmanned aerial vehicles, designing a pilot following network topology, and further dividing the following unmanned aerial vehicles into a first type of following unmanned aerial vehicles and a second type of following unmanned aerial vehicles; respectively designing cost functions for different types of unmanned aerial vehicles to obtain unique Nash equilibrium, and realizing an optimal strategy combination at each moment; and according to the relation between the unmanned aerial vehicle states at adjacent game moments in the unmanned aerial vehicle cluster, obtaining conditions for realizing unmanned aerial vehicle cluster formation control, and performing multi-unmanned aerial vehicle formation control. According to the method, the game theory is used for modeling, cost functions are designed for different types of unmanned aerial vehicles, it is proved that the constructed model has unique Nash equilibrium, the matrix theory and the graph theory are used for obtaining conditions for the system to achieve formation control, and finally a theoretical result is verified through a simulation example. And a new method and theoretical support are provided for multi-unmanned aerial vehicle system formation control.

Description

Technical Field

[0001] The present invention belongs to the field of multi - UAV formation control, and particularly relates to a game - based multi - UAV formation control method. Background Art

[0002] Formation control is a classic multi - UAV coordination control. Generally, in a UAV swarm involving formation control problems, there are leader UAVs and follower UAVs. A leader UAV is a UAV with certain specific capabilities (such as carrying important information, performing special tasks, etc.) or stronger capabilities (such as sensing, computing, etc.), while the remaining UAVs in the UAV swarm are called follower UAVs. Formation control means that follower UAVs dynamically enclose all leader UAVs in a convex hull by designing effective control protocols for different UAVs. In the prior art, research on UAV swarm formation control assumes that UAVs change their states according to predetermined dynamics. However, system dynamics may be difficult to obtain, and the environment of UAVs is highly dynamic. Therefore, UAVs should determine their current states in real - time rather than following a preset control protocol. Summary of the Invention

[0003] Based on this, the purpose of the present invention is to provide a game - based multi - UAV formation control method to avoid the defect that the formation control in the prior art highly depends on dynamics and solve the formation control problem of multi - UAVs.

[0004] To achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0005] A game - based multi - UAV formation control method includes the following steps:

[0006] S101, constructing a game - based multi - UAV model framework, in which a UAV swarm consists of n UAVs, n≥2, and all UAVs in the UAV swarm participate in the game;

[0007] S102, dividing the UAVs in the UAV swarm into follower UAVs and leader UAVs, and designing a leader - follower network topology;

[0008] S103, if a neighbor UAV of a follower UAV includes a leader UAV, then it is defined as a first - type follower UAV, otherwise it is defined as a second - type follower UAV; designing cost functions for the first - type follower UAVs, second - type follower UAVs, and leader UAVs respectively to obtain a unique Nash equilibrium and achieve an optimal strategy combination at each moment;

[0009] S104, according to the relationship between the UAV states at adjacent game moments in the UAV swarm, obtaining the conditions for realizing UAV swarm formation control, and performing multi - UAV formation control according to the conditions.

[0010] Compared with the prior art, the present invention designs a cost function according to the mutual game among multiple unmanned aerial vehicles (UAVs) and sets a function for measuring the behavior cost of UAVs with different roles. Moreover, the state of the UAVs is determined by the Nash equilibrium of the game. Secondly, the unique Nash equilibrium of the proposed multi-player game is proved and calculated. In addition, the relationship between the states at two adjacent game moments is established for the multi-UAV system. Through this relationship, the dynamic changes of the system over time can be analyzed. The present invention uses game theory to model, designs cost functions for different types of UAVs, proves that the constructed model has a unique Nash equilibrium, obtains the conditions for the system to achieve formation control by using matrix theory and graph theory, and finally verifies the theoretical results by using simulation examples, providing a new method and theoretical support for the formation control of multi-UAV systems.

[0011] Furthermore, the present invention classifies UAVs into three categories and analyzes their cost functions and optimal strategies. A game-based multi-UAV model framework consisting of follower UAVs and leader UAVs is established. Within this framework, the conditions required to achieve formation control are proposed by using the knowledge of game theory and matrix theory. Finally, through mathematical derivation, it is proved that the cost functions and optimal control strategies of the proposed individual UAVs can achieve the required formation control conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] The accompanying drawings that form a part of this application are used to provide a further understanding of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation to the present invention. In the drawings:

[0013] Figure 1 is the flowchart of the game-based multi-UAV formation control method of the present invention.

[0014] Figure 2 is the communication network diagram of 9 UAVs in the embodiment of the present invention.

[0015] Figure 3 is the relationship diagram between the coordinates of the UAVs and the game time in Embodiment 1 of the present invention.

[0016] Figure 4 is the state trajectory diagram of the UAVs in Embodiment 1 of the present invention.

[0017] Figure 5 is the UAV v 1 , v 2 , v 5 , v 7 state trajectory diagram.

[0018] Figure 6 is the UAV v 2 、v3 , v 4 , v 8 The state trajectory diagram of

[0019] Figure 7 is the state trajectory diagram of the UAV v in Embodiment 1 of the present invention 3 , v 4 , v 6 , v 9 The state trajectory diagram of

[0020] Figure 8 is the state trajectory diagram of the UAV in Embodiment 2 of the present invention

[0021] Figure 9 is the state trajectory diagram of the UAV in Embodiment 3 of the present invention

[0022] Figure 10 is the state trajectory diagram of the UAV in the embodiments of the present invention

[0023] In the figure, agent represents the agent in the game, that is, a single UAV in the multi-UAV formation Detailed implementation manners

[0024] The following describes the implementation manners of the present invention in detail with reference to the drawings and embodiments

[0025] As Figure 1 shown, the game-based multi-UAV formation control method of the present invention mainly includes the following steps:

[0026] S101. Construct a game-based multi-UAV model framework for solving the formation control problem

[0027] In the present invention, the game-based multi-UAV model framework is represented as G(V, Ω i , J i ). There are n (n≥2) UAVs in the framework, and all the UAVs form a UAV cluster. All the UAVs in the UAV cluster participate in the game

[0028] Among them, V is the set of all UAVs, and Ω i represents the strategy set of the i-th UAV v i . At the same moment, each UAV independently selects a strategy, and J i represents the cost function of v i , which is defined as:

[0029] If the strategies available to the first UAV v 1 are x 1 , x 1 ∈Ω 1 , and Ω 1 is v 1's strategy set; the \(i\)-th drone \(v\) i The available strategy is \(x\) i , \(x\) i \(\in\Omega\) i , \(\Omega\) i is the strategy set of \(v\) i ; similarly, the \(n\)-th drone \(v\) n The available strategy is \(x\) n , \(x\) n \(\in\Omega\) n , \(\Omega\) n is the strategy set of \(v\) n . Then the cost function \(J\) of \(v\) i The \(n\)-tuple is \((x\) i , \(\cdots\), \(x\) 1 , \(\cdots\), \(x\) i , \(\cdots\), \(x\) n ) \(\in\Omega\), \(\Omega=\Omega\) 1 \(\times\cdots\times\Omega\) i \(\times\cdots\times\Omega\) n , \(\Omega\) is the strategy set of all drones in the framework.

[0030] Define the optimal strategy combination in the game where are the optimal strategies to be selected by \(v\) 1 , \(v\) i , \(v\) n respectively. The optimal strategy of each drone minimizes its cost given the strategies of the remaining drones, expressed as: for any \(x\) i \(\in\Omega\) i , always holds, where \(J\) i (x\) * ) is the cost required for drone \(v\) i to select its optimal strategy based on the strategies of the remaining drones. ; is the cost required for drone \(v\) i to select its available strategy \(x\) i given the strategies of the remaining drones. denotes the optimal strategy combination of all the remaining drones except \(v\) i . Call \(x\) * a Nash equilibrium of the game. In this Nash equilibrium, the strategies of the drones are interdependent. That is to say, the optimal strategy i of drone \(v\) is made on the basis of considering the optimal strategies of the remaining drones. Therefore, under the Nash equilibrium condition, the optimal strategies of each drone and the optimal strategies of all the remaining drones will form a stable optimal strategy combination.

[0031] Due to the drone v i selects strategy x at the game time t i (t) means that the drone v in the drone swarm based on the game is at time t i in the state of x i (t). Then at the game time t + 1, the drone v i interacts with its neighbor drones and selects the optimal strategy to minimize its cost at time t + 1 where Specifically:

[0032]

[0033] In the formula, is the optimal strategy that can minimize its cost made by v at time t + 1 i on the basis of considering the optimal strategies of the remaining drones and is the best response to the combination of the strategies of the remaining drones; x (t + 1) is the strategy that v can choose at the game time t + 1 i ; i is the optimal strategy combination made by all the remaining drones except v itself at time t + 1 itself i at time t + 1

[0034] S102. Divide the drones in the drone swarm into follower drones and leader drones, and design a leader - follower network topology.

[0035] The drone swarm of the present invention adopts a leader - follower network topology. The leader drones and follower drones are specified during the drone formation stage, and the communication topology of the drone swarm remains fixed and connected during the formation control process. Each drone is a node in the leader - follower network topology. The edges of the leader - follower network topology represent the communication connections between drones. The existence of an edge means that the drones can exchange and transmit information through wireless communication. There is a directed edge from each leader drone to its follower drone, indicating that the leader drone provides information to its follower drone. The drones can communicate and exchange information through the communication module, and the communication and information exchange are synchronous.

[0036] Furthermore, the present invention represents the leader - follower network topology with L=(V, ε, W). The vertex set of the graph is also the set V of all drones. The edge set of the graph is ε, and ε contains all the connections between adjacent drones. If the set of neighbor drones of the drone v i is represented as N i ={v j ∈V∣(v j , vi ) ∈ ε}, then each edge (v j , v i ) represents a relationship of some kind of communication or interaction between the drones v j and v i . W = (a ij ) ∈ R n×n is the weighted adjacency matrix, representing the intensity of the mutual influence between the drones. The element a i，j in the matrix represents the connection strength or weight between v i and v j . Exemplarily, if (v j， v i ) ∈ ε, then a i，j > 0, otherwise a i，j = 0, where i ≠ j.

[0037] S103. Further divide the following drones into the first - type following drones and the second - type following drones. Design cost functions for the first - type following drones, the second - type following drones, and the leading drone respectively. In the case where each drone makes an independent strategy simultaneously, obtain the unique Nash equilibrium to achieve the optimal strategy combination at each moment.

[0038] Specifically, if a following drone has a leading drone among its neighbor drones, then it is defined as a first - type following drone; otherwise, it is defined as a second - type following drone. Further define the set of the first - type following drones as F 1 , the set of the second - type following drones as F 2 , the set of following drones as F, and the set of leading drones as R. There is F 1 ∪ F 2 = F and F 1 has p first - type following drones, F 2 has n - m - p second - type following drones, F has n - m following drones, and R has m leading drones. The leading drone will keep its own state unchanged to minimize its cost function. The cost function of the following drone is related to both itself and its neighbors.

[0039] (1) If the drone v i is a first - type following drone, that is, v i ∈ F 1 , then at the game time t +, its cost is constructed as:

[0040]

[0041] In the formula, α is the first - cost coefficient, This means that F1 The first type of follower drones in [ ] tend to stay away from their follower drone neighbors to minimize costs, because follower drones tend to surround the leader drone within a sufficiently wide surrounding area. However, an overly large surrounding area will result in cost waste, so the parameter α is bounded.

[0042] β is the second cost coefficient. The term β∑ j∈R a i，j (x i (t k+1 ) - x j (t k+1 )) 2 ensures that the drones in F 1 surround the leader drone, where the parameter β is positive.

[0043] x i (t) is the state of v i at the game time t, and x j (t + 1) is the state of v j at the game time t + 1. J i (t + 1) is composed of the cost of changing its own state (x i (t + 1) - x i (t)) 2 and the cost required to cooperate with neighbor drones to form an encirclement (x i (t + 1) - x j (t + 1)) 2 jointly.

[0044] (2) If the drone v i is a second - type follower drone, that is, v i ∈F 2 , then at the game time t +, its cost is constructed as:

[0045]

[0046] In the formula, γ is the third cost coefficient, representing the cost weight of the state difference between a second - type follower drone and other follower drones, γ > 0. The second - type follower drones in F 2 will approach their own follower drone neighbors because they cannot receive information from the leader drone. If they blindly expand the surrounding area, they may deviate from the mission.

[0047] (3) If the drone v i is a leader drone, that is, v i ∈R, then at the game time t + 1, its cost is constructed as:

[0048] J i(t + 1) = (x i (t + 1) - x i (t)) 2

[0049] Each unmanned aerial vehicle in G(V, Ω i , J i ) independently selects a strategy to minimize its cost at J i (t + 1) at time t + 1. Therefore, G(V, Ω i , J i ) is a static game.

[0050] If the unmanned aerial vehicle selects state x i (t + 1) at time t + 1, it will reach state x i (t + 1) before time t + 2. Assuming that each unmanned aerial vehicle is rational and its state is determined by the Nash equilibrium of the game, the present invention can obtain a unique Nash equilibrium based on the game.

[0051] (1) If the unmanned aerial vehicle v i is the first type of follower unmanned aerial vehicle, that is, v i ∈F 1 , it can be concluded that:

[0052]

[0053] Therefore is unique.

[0054] (2) Similarly, for the unmanned aerial vehicle v i ∈F 2 , all its neighbors are follower unmanned aerial vehicles, and it can be obtained that:

[0055]

[0056] Therefore is also unique

[0057] (3) For the unmanned aerial vehicle v i ∈R, the cost is only determined by itself, and it will follow to minimize the cost.

[0058] Therefore, is unique for all unmanned aerial vehicles in V.

[0059] S104 represents the connection between the states of unmanned aerial vehicles at adjacent game moments in the unmanned aerial vehicle cluster.

[0060] First, according to the definition of the Nash equilibrium and the Nash equilibrium strategy obtained above, it can be known that:

[0061]

[0062] Has a compact form: Bx(t + 1) = x(t).

[0063] Since B is a strongly diagonally dominant matrix, the relationship between the states of the UAVs at adjacent game moments in the UAV swarm can be expressed as: x(t + 1) = B -1 x(t).

[0064] Where x(t + 1) is the overall state vector of the UAV swarm at time t + 1, and x(t) is the overall state vector of the UAV swarm at time t. To simplify the expression parameters, B is analyzed in blocks and can be expressed as follows:

[0065]

[0066] Where 0 m×(n-m) is an m×(n - m) all - zero matrix, and I m is an m×m identity matrix. B 11 and B 12 are parameters adopted to simplify the expression and can be expressed respectively as:

[0067]

[0068] and are parameters adopted to simplify the expression and are expressed respectively as:

[0069]

[0070] Where m is the number of leader UAVs, n - m is the number of follower UAVs, p is the number of the first - type follower UAVs, and n - m - p is the number of the second - type follower UAVs;

[0071] The elements a 12 in B 1，n-m+1 ,..., a 1，n ;...; a p，n-m+1 ,..., a p，n represent the connection strength or weight between the first - type follower UAVs and the leader UAV;

[0072] The elements a 1，2 ,..., a 1，p ; a 2，1 ,..., a 2，p ;...; a p，1 ,..., a p，p-1 represent the connection strength or weight between the first - type follower UAVs; a 1，j ,..., a p，jIndicates the connection strength or weight between the first type of follower UAV and its neighbor UAVs;

[0073] Element a in 1，p+1 、…、a 1，n-m ;a 2，p+1 、…、a 2，n-m ;…、;a p，p+1 、…、a p，n-m Indicates the connection strength or weight between the first type of follower UAV and the second type of follower UAV;

[0074] Element a in p+1，1 、…、a p+1，p ;a p+2，1 、…、a p+2，p ;…、;a n-m，1 、…、a n-m，p Indicates the connection strength or weight between the second type of follower UAV and the first type of follower UAV;

[0075] Element a in p+1，j 、…、a n-m，j Indicates the connection strength or weight between the second type of follower UAV and its neighbor UAVs; a p+1，p+2 、…、a p+1，n-m ;…、;a n-m，p+1 、…、a n-m，n-m+1 Indicates the connection strength or weight between the second type of follower UAV and the remaining second type of follower UAVs.

[0076] S105, obtain the conditions for realizing the formation control of the UAV swarm, and perform multi-UAV formation control according to the conditions.

[0077] Such that:

[0078] x(t) = [x 1 (t), x 2 (t), …, x n (t + 1)] T

[0079] x f (t) = [x 1 (t), x 2 (t), …, x n-m (t)] T

[0080] x R (t) = [x n-m+1 (t), x n-m+2 (t), …, x n (t)] T

[0081] Since B11 is invertible, we can obtain

[0082]

[0083] Furthermore, from the above equation and the relationship between the states of UAVs at adjacent game times in the UAV swarm x(t + 1) = B -1 x(t), we can see that

[0084]

[0085] Obviously,[[]]

[0086]

[0087] Since

[0088] and So

[0089]

[0090] This means

[0091]

[0092] And

[0093]

[0094] Let We can see that

[0095]

[0096] Suppose where indicates that among the neighbor UAVs, there is a leader UAV v s and the first type of follower UAV v i . Then we have

[0097]

[0098] where

[0099]

[0100] And

[0101]

[0102] From this, we can know that the leader UAV v s finally locates at v i ∪{Ni / v s} Among the convex hulls formed, N i denotes the UAV v i The set of neighbor UAVs. Since v s is the only leading UAV in the set N i Therefore, the set Ni / v s denotes all the neighbor following UAVs except v s . Therefore, if the following UAVs can generate a convex hull and enclose all the leading UAVs within it, the multi-UAV system is considered to have achieved formation control.

[0103] S105, obtain the conditions for realizing the formation control of the UAV cluster, and perform multi-UAV formation control according to the said conditions.

[0104] According to the foregoing steps, it can be known that the conditions for achieving multi-UAV formation control are as follows:

[0105] Assume that the communication network among the following UAVs is strongly connected. If And At this time, all the following UAVs enclose the leading UAVs within a convex hull, and the multi-UAVs achieve formation control. Among them, Allocate weights to different cost items.

[0106] Among them, the UAV denotes the leading UAV v s is the set of neighbor UAVs N i ={v j ∈V∣(v j , v i )∈ε} The only leading UAV.

[0107] If there is a time delay τ = 1, the cost functions of the first type of following UAVs and the second type of following UAVs can be modified as:

[0108]

[0109] Among them, α < 0, β > 0, and

[0110]

[0111] Among them, γ > 0. At this time, the cost function of the leading UAV is still J i (t k+1 )=(x i (t k+1 )-x i (t k )) 2 .

[0112] Referring to the previous analysis, it can be obtained that

[0113]

[0114] When β = γ = 1, the closed-loop control problem of multiple UAVs can be regarded as a special case of the present invention.

[0115] Specifically considering the UAV swarm, let the weighted adjacency matrix be configured as W, then Set x(0) and y(0). In Embodiments 1-4, UAV swarms with different α, β, and γ are considered. In addition, the UAVs in each embodiment adopt the same initial state.

[0116] As Figure 2 shown depicts the communication network of all 9 UAVs {v 1 , v 2 ,..., v 9}. These 9 UAVs are respectively placed into the following three different sets, where the first type of follower UAVs F 1 = {v 1 , v 2 , v 3 , v 4}, the second type of follower UAVs F 2 = {v 5 , v 6}, and the leader UAV R = {v 7 , v 8 , v 9}

[0117] The weighted adjacency matrix is configured as

[0118]

[0119] Then Describe the interaction between UAVs as a game, that is, the aforementioned framework G(V, Ω i , J i ) of the present invention.

[0120] Let x(0) = [-15, -15, -20, 3, 5, 10, 12, 15, 12] T , y(0) = [20, 2, 10, 3, 2, 2, 6, 8, 8] T ,

[0121] Embodiment 1: Let α = -0.5, β = 1.1, γ = 1. Figure 3 Shows the relationship between the UAV coordinates and the game time. The method of multi-UAV formation control based on the game is obtained Figure 4 supported by Figure 4 showing that the follower UAVs generate a convex hull surrounding all the leader UAVs.

[0122] Example 2: Let α = -0.5, β = 1.1, γ = 1. The state trajectories of each UAV are as Figure 8 shown, and the follower UAVs generate a convex hull surrounding all the leader UAVs. It is verified that the method of multi-UAV formation control based on game theory is feasible.

[0123] Example 3: Let α = -0.1. β = 1.1, γ = 1. The state trajectories of all UAVs are as Figure 9 shown, where the follower UAVs generate a convex hull surrounding all the leaders. It is verified that the method of multi-UAV formation control based on game theory is feasible.

[0124] Example 4: Let α = -0.1. Since β = 2, γ = 2. The state trajectories of all UAVs are as Figure 10 shown, where the follower UAVs generate a convex hull surrounding all the leader UAVs. It is verified that the method of multi-UAV formation control based on game theory is feasible.

[0125] Figure 3 It shows that the follower UAVs v 1 , v 2 ,..., v 6 do not move their positions after surrounding the leader UAVs. Therefore, once the closed-loop control problem is solved, the UAV swarm can maintain the closed-loop control all the time.

[0126] Figure 5 It shows that the leader UAV v 7 finally locates in the convex hull formed by the follower UAV v 1 and its adjacent UAVs except the leader UAV v itself.

[0127] Figure 6 The shown leader UAV v 8 finally locates in the convex hull formed by the follower UAV v 3 and its adjacent UAVs except the leader UAV v 8 itself.

[0128] Figure 7 It shows that the leader UAV v 9 finally locates in the convex hull formed by the follower UAV v 4 and its adjacent UAVs except the leader UAV v itself. Generally speaking, Figures 5 - 7 It shows that the leader UAV v s finally locates in the convex hull formed by v r ∪{N r / v s}. This is consistent with the result of the multi-UAV formation control based on game theory

[0129] .

[0130] Examples 1 and 2 show that the larger the parameter β, the smaller the convex hull finally generated by the following UAV. The parameter β represents the willingness of the following UAV to approach the leading UAV. Therefore, a larger parameter β results in a smaller final convex hull. Thus, the larger the parameter β, the smaller the final convex hull. Examples 1 and 3 show that the larger the parameter α, the smaller the convex hull finally generated by the following UAV. Examples 1 and 4 show that the larger the parameter γ, the smaller the convex hull finally generated by the following UAV. This is because the parameter γ represents the willingness of the following UAV to approach other following UAVs among its neighbors. The larger the parameter γ, the closer the following UAV approaches other following UAVs among its neighbors, and the smaller the final convex hull.

[0131] The present invention also provides a multi-UAV formation device. The multi-UAV group has a leader-follower network topology, including

[0132] Data acquisition module: used to acquire the state information of multiple UAVs; in some embodiments, the data module can be some on-board sensing devices, and its function is to acquire the state information of the UAVs.

[0133] Communication module: used for information exchange between multiple UAVs; in some embodiments, the communication module can be a data transmission device. By using the ad hoc network technology for the UAV cluster in the formation, the UAVs can communicate and transmit data within the ad hoc network.

[0134] Control module: makes an independent policy decision according to the state information of the following UAV and the state information of the leading UAV to minimize its cost. In some embodiments, adopting the idea of a modular control system, the control module can be flight control software, and its function is to execute control instructions and control the flight attitude of the UAV.

[0135] According to the game-based multi-UAV formation control method provided by the present invention, the UAV can determine its current state in real time, and within a certain communication cycle, the UAV cluster can form an expected formation configuration, overcoming the difficulties that the system dynamics may be difficult to obtain and the UAV environment is highly dynamic.

[0136] The above specific embodiments further elaborate on the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above are only specific embodiments of the present invention and are not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A multi-UAV formation control method based on game theory, characterized in that: The following steps are involved: S101, construct a multi-UAV model framework based on game theory, in which a UAV cluster is composed of n UAVs, n ≥ 2, and all UAVs in the UAV cluster participate in the game; S102, dividing the drones in the drone cluster into follower drones and pilot drones, and designing a pilot-follower network topology; S103, if the neighboring drones of a follower drone include a pilot drone, it is defined as a first-category follower drone, otherwise it is defined as a second-category follower drone; cost functions are designed for the first-category follower drones, the second-category follower drones, and the pilot drone, respectively, to obtain a unique Nash equilibrium and achieve the optimal strategy combination at each moment; S104, obtaining conditions for realizing formation control of the drone cluster according to the connection between the states of the drones at adjacent game moments in the drone cluster, and performing formation control of multiple drones according to the conditions.

2. The game-based multi-UAV formation control method according to claim 1 is characterized in that: The game-based multi-UAV model framework is represented as G(V,Ω i , J i ), where V is the set of all drones, Ω i represents the i-th drone v i strategy set, at the same time, each drone independently selects a strategy, J i Indicates v i The cost function is defined as: If the first drone v1 can choose a strategy x1, x1∈Ω1, Ω1 is the strategy set of v1; the i-th drone v i The available strategies are x i , x i ∈Ω i ,Ω i Yes i The strategy set of the nth drone v n The available strategies are x n , x n ∈Ω n ,Ω n Yes n strategy set; then J i The n-tuple of (x1, ..., x i , …, x n )∈Ω,Ω=Ω1×…×Ω i ×…×Ω n ,Ω is the strategy set of all drones; Defining the optimal strategy combination in Yes i The optimal strategy to be selected is that the optimal strategy for each drone minimizes its cost under the known strategies of other drones, expressed as: i ∈Ω i , All of them are established, among which J i (x * ) is v i Given the strategies of other drones, the best strategy to choose is based on itself. the costs required; Yes i Given the strategies of other drones, based on their own selectable strategy x i the costs required; Indicates that except v i The optimal strategy combination of all other drones except * is a Nash equilibrium of the game.

3. The game-based multi-UAV formation control method according to claim 2 is characterized in that: At game time t+1, v i Interact with its neighbor drones and choose the best strategy To minimize its cost at time t+1 in: In the formula, is v at time t+1 i Considering the optimal strategy for the remaining drones The optimal strategy based on the cost minimization is a combination of the remaining UAV strategies. The best strategy for i (t+1) is the game time t+1 v i Alternative strategies; Except for v i The optimal strategy combination made by all other drones except itself at time t+1.

4. The game-based multi-UAV formation control method according to claim 2 or 3 is characterized in that: In S102, the pilot-follower network topology is designed, and the method is as follows: The pilot-follower network topology uses each drone as a node and the communication connection between drones as an edge. There is a directed edge from each pilot drone to its follower drone, indicating that the pilot drone provides information to its follower drone; The pilot-follower network topology is represented by L = (V, ε, W), where the set V of all drones also constitutes the vertex set of the graph, ε is the edge set of the graph, and the drone v i The set of neighboring drones is denoted as N i = {v j ∈V∣(v j , v i )∈ε}, each edge (v j , v i ) indicates drone v j and v i There is some kind of communication or interaction relationship between them, ε includes the connections between all adjacent drones; W = (a ij )∈R n×n is a weighted adjacency matrix, which is used to represent the mutual influence strength between drones. The element a in the matrix is i，j Represents v and v j The connection strength or weight between j , v i )∈ε, then a i，j >0, otherwise a i，j =0, where i≠j.

5. The game-based multi-UAV formation control method according to claim 4 is characterized in that: S103, if the drone v i For the first type of follower drone, at game time t+1, its cost is constructed as: Where α is the first cost coefficient, β is the second cost coefficient, F1 is the set of the first type of follower drones, F is the set of follower drones, and R is the set of pilot drones; x i (t) is v i The state at game time t, x j (t+1) is v j The state at game time t+1; If the drone v i For the second type of follower drone, at game time t+1, its cost is constructed as: Where γ is the third cost coefficient, which represents the cost weight of the state difference between a second-class follower UAV and other follower UAVs, γ>0; If the drone v i is the pilot drone, then at game time t+1, its cost is constructed as: J i (t+1)=(x i (t+1)-x i (t)) 2 In G(V,Ω i , J i ), each drone independently and simultaneously chooses its strategy at game time t+1 to minimize its costs.

6. The game-based multi-UAV formation control method according to claim 5 is characterized in that: In S104, the connection between the states of the drones at adjacent game moments in the drone cluster is expressed as: x(t+1)=B -1 x(t) In the formula, x(t+1) is the overall state vector of the drone cluster at time t+1, x(t) is the overall state vector of the drone cluster at time t, and B is a matrix used to describe the state transition relationship of the drone cluster at different game moments, which is expressed as follows: Where, 0 m×(n-m) is an m×(nm) all-zero matrix, I m is the m×m identity matrix; B 11 and B 12 In order to simplify the expression of the parameters used, they are expressed as: and In order to simplify the expression of the parameters used, they are expressed as: Where m is the number of pilot drones, nm is the number of follower drones, p is the number of first-type follower drones, and nmp is the number of second-type follower drones; B 12 The element a in 1，n-m+1 , …, a 1，n ;…、;a p，n-m+1 , …, a p，n represents the connection strength or weight between the first type of follower drone and the pilot drone; The element a in 1，2 , …, a 1，p ; a 2，1 , …, a 2，p ;…、;a p，1 , …, a p，p-1 represents the connection strength or weight between the first type of following drones; a 1，j , …, a p，j represents the connection strength or weight between the first type of following UAV and its neighboring UAVs; The element a in 1，p+1 , …, a 1，n-m ; a 2，p+1 , …, a 2，n-m ;…、;a p，p+1 , …, a p，n-m represents the connection strength or weight between the first type of following drone and the second type of following drone; The element a in p+1，1 , …, a p+1，p ; a p+2，1 , …, a p+2，p ;…、;a n-m，1 , …, a n-m，p represents the connection strength or weight between the second type of follower drone and the first type of follower drone; The element a in p+1，j , …, a n-m，j represents the connection strength or weight between the second type of following UAV and its neighboring UAVs; a p+1，p+2 , …, a p+1，n-m ;…、;a n-m，p+1 , …, a n-m，n-m+1 ; represents the connection strength or weight between the second-category following UAV and the remaining second-category following UAVs.

7. The game-based multi-UAV formation control method according to claim 6 is characterized in that: The conditions for achieving UAV swarm formation control are: if and Among them, drones Indicates pilot drone v i is the set of neighbor drones N i = {v j ∈V∣(v j , v i )∈ε} the only pilot drone.

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