Unmanned aerial vehicle cluster game nash equilibrium search method and system under preset time

Abstract

The application discloses a UAV cluster game Nash equilibrium search method and system under preset time, and belongs to the field of UAV autonomous control; the UAV cluster game Nash equilibrium search method under preset time comprises the following steps: analyzing the dynamic model of a four-rotor UAV, and generalizing to an Euler-Lagrange system; based on the dynamic model of the UAV generalized to the Euler-Lagrange system, a UAV cluster game model with Euler-Lagrange nonlinear dynamics is constructed; based on the Euler-Lagrange system and the UAV cluster game model, by introducing a time base generator, a Nash equilibrium search algorithm under partial information based on preset time convergence is proposed, so that the convergence time can be accurately controlled and is independent of the initial value and parameters of the system.

Description

Technical Field

[0001] This invention belongs to the field of autonomous control of unmanned aerial vehicles (UAVs), specifically relating to a method and system for searching Nash equilibrium in UAV swarm game under a preset time. Background Technology

[0002] With the rapid development of computer and communication technologies, the coordinated control technology and optimization problems of multi-agent systems such as smart grids, sensor networks, and drone swarms have attracted widespread attention. Among them, the non-cooperative game problem of multi-agent systems has become a research hotspot in recent years. In the non-cooperative game problem, each agent strives to maximize its own interests, and its objective function depends on the decisions of other agents.

[0003] In practice, most systems are complex nonlinear systems. Eulerian-Lagrange systems, as a typical nonlinear system, are widely studied. They can describe complex dynamic systems such as unmanned surface vessels, robotic arms, and drones. Quadrotor drones, due to their simple structure, high maneuverability, and ease of operation, are widely used in aerial photography, geological exploration, environmental assessment, and counter-terrorism reconnaissance. By extending the dynamic system of quadrotor drone swarms to a general Eulerian-Lagrange system [Y. Naidoo, R. Stopforth, and G. Bright, “Quad-rotor unmanned aerial vehicle helicopter modelling and control,” Int. J. Adv. Robot. Syst., vol. 8, no. 4, pp. 139-149, 2011.], and designing suitable swarm coordination control algorithms, multiple quadrotor drones can achieve functions such as cooperative flight, task allocation, and rapid decision-making.

[0004] Currently, research on Nash equilibrium search algorithms for UAV swarm games mainly focuses on how to make the agent's state converge asymptotically or exponentially to the Nash equilibrium point, but research on how to precisely control the convergence time is limited. In actual air combat scenarios, the control of convergence time is crucial to the combat outcome, and UAV swarms need to complete their missions within a precise timeframe. To address this issue, a method based on finite or fixed-time theory has been proposed to allow the agent to control the convergence time within a finite range [P. Lin, W. Ren, and JAFarrell, "Distributed continuous-time optimization: Nonuniform gradient gains, finite-time convergence, and convex constraint set," IEEE Trans. Autom. Control, vol. 62, no. 5, pp. 2239-2253, 2017]. However, this method is affected by the agent's initial state and system parameters and cannot be predicted. Therefore, to solve the above problems, this invention proposes a Nash equilibrium search method and system for UAV swarm games based on a preset time. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the present invention aims to provide a method and system for searching Nash equilibrium in unmanned aerial vehicle (UAV) swarm game under a preset time, thereby solving the problems in existing technologies.

[0006] The objective of this invention can be achieved through the following technical solutions:

[0007] A method for searching the Nash equilibrium in a drone swarm game under a preset time period includes the following steps:

[0008] The dynamic model of a quadcopter UAV is analyzed and extended to the Euler-Lagrange system;

[0009] Based on the dynamic model of UAVs generalized to the Euler-Lagrange system, a UAV swarm game model with Euler-Lagrange nonlinear dynamics is constructed.

[0010] Based on the Eulerian-Lagrange system and the UAV swarm game model, a Nash equilibrium search algorithm based on partial information of convergence at a preset time is proposed by introducing a time base generator to control the convergence time.

[0011] Furthermore, the construction of the quadcopter UAV dynamics model needs to meet the following prerequisites:

[0012] 1) The airframe of a drone is a rigid body and is strictly symmetrical;

[0013] 2) The origin of the body coordinate system coincides with the center of mass of the UAV;

[0014] 3) The blades did not make any waving motion.

[0015] Furthermore, the second-order dynamic model of the i-th quadcopter UAV is as follows:

[0016]

[0017]

[0018]

[0019]

[0020]

[0021]

[0022] Where, x i ,y i ,z i These are the x-axis, y-axis, and z-axis position coordinates of the i-th quadrotor UAV in the inertial coordinate system, respectively. θ i ,ψ i These are the roll angle, pitch angle, and yaw angle of the i-th quadcopter UAV in the inertial coordinate system, respectively. These are the moments of inertia of the i-th quadrotor UAV about the x, y, and z axes of the body coordinate system, respectively. Let m represent the disturbances experienced by the i-th quadrotor UAV in the x-axis, y-axis, and z-axis directions, respectively; i Let u be the mass of the i-th quadcopter UAV; i1 ,u i2 ,u i3 ,u i4 These are the four control inputs for the i-th quadcopter UAV; g is the acceleration due to gravity.

[0023] Furthermore, the four control inputs of the quadcopter drone are as follows:

[0024]

[0025] Among them, F i1 ,F i2 ,F i3 ,F i4 p represents the lift generated by the four motors of the i-th quadcopter UAV; i Let be the distance between the rotor of the i-th quadcopter UAV and the center of mass of the UAV.

[0026] Furthermore, considering a swarm of UAVs with Eulerian-Lagrange nonlinear dynamics, the dynamic model of the i-th UAV can be expressed as:

[0027]

[0028] Where, η i , M represents the generalized coordinates, velocity, and acceleration vectors, respectively; i (η i ) represents a positive definite symmetric inertial matrix; G represents the Coriolis-centripetal force matrix; i (η i ) represents the gravity matrix; u i This refers to the controller that acts on the system.

[0029] Furthermore, the drone swarm game model is as follows:

[0030] A drone swarm consists of n drones. Each drone uses local information to adjust its decisions to minimize its cost function, described as follows:

[0031]

[0032] Where f i (η i ,η -i Let η be the objective function of the i-th UAV; i Let η be the decision variable for the i-th drone; -i Let η be the decision variable for all drones except the i-th drone. -i =[η1,…,η i-1 ,η i+1 ,…,η n ];

[0033] In the process of the game, if satisfy:

[0034]

[0035] but This is called the Nash equilibrium solution; where,

[0036] Furthermore, the time base generator is:

[0037] T(t,t f )=(g(t,σ))′,

[0038] Where σ is a sufficiently small parameter; t fThis is a preset time, mainly adjusted according to the algorithm requirements; g is a bivariate function of time t and parameter σ, and must satisfy the following conditions:

[0039] 0 < σ < < 1,

[0040]

[0041] g(t,σ)-g(t f+ ,σ)≥0,t>t f ,

[0042]

[0043] Furthermore, the Nash equilibrium search algorithm is designed as follows:

[0044]

[0045]

[0046]

[0047] In the formula, η i It is the decision variable for the i-th drone; v is the estimated variable for the decision of the i-th drone regarding the j-th drone; i These are auxiliary variables; α, β, γ, ε > 0 are the corresponding algorithm parameters; a ij It is the weight value of the communication connection between the i-th drone and the j-th drone.

[0048] A Nash equilibrium search system for drone swarm game under a preset time, including:

[0049] Dynamics model building module: Analyzes the dynamics model of a quadcopter UAV and generalizes it to the Euler-Lagrange system;

[0050] Drone swarm game model construction module: Based on the dynamic model of drones generalized to the Eulerian-Lagrange system, construct a drone swarm game model with Eulerian-Lagrange nonlinear dynamics;

[0051] In addition, the search algorithm construction module: based on the Euler-Lagrange system and the UAV swarm game model, a Nash equilibrium search algorithm based on partial information of convergence at a preset time is proposed by introducing a time base generator to control the convergence time.

[0052] A computer storage medium storing a readable program that, when the program is run, can execute the above-described search method.

[0053] The beneficial effects of this invention are:

[0054] This invention enables precise control over the convergence time of drone swarm game algorithms, ensuring that the drone swarm converges to the Nash equilibrium point within a specific time by pre-setting the time basis function. Attached Figure Description

[0055] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0056] Figure 1 This is a flowchart of the search method in this invention;

[0057] Figure 2 This is a structural diagram of a single quadcopter UAV in this invention;

[0058] Figure 3 This is a communication diagram of the four drones in this invention;

[0059] Figure 4 This is a three-dimensional trajectory diagram of four UAVs tracking a time-varying target in this invention;

[0060] Figure 5 This is a schematic diagram showing the convergence of the x-direction coordinates of the game trajectories of four drones in this invention over a preset time.

[0061] Figure 6 This is a schematic diagram showing the convergence of the y-direction coordinates of the four drones' game trajectories over a preset time in this invention;

[0062] Figure 7 This is a schematic diagram showing the convergence of the z-direction coordinates of the game trajectories of four drones in this invention over a preset time.

[0063] Figure 8 This is a communication diagram of the UAV swarm in this invention;

[0064] Figure 9 This is a schematic diagram of the three-dimensional trajectory of the UAV swarm tracking the target in this invention;

[0065] Figure 10 This is a schematic diagram of the preset time convergence of the x-direction coordinate of the UAV swarm game trajectory in this invention;

[0066] Figure 11 This is a schematic diagram of the preset time convergence of the y-direction coordinate of the UAV swarm game trajectory in this invention;

[0067] Figure 12 This is a schematic diagram showing the convergence of the z-direction coordinates of the UAV swarm game trajectory within a preset time in this invention. Detailed Implementation

[0068] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0069] like Figure 1 As shown, the method for searching the Nash equilibrium in a drone swarm game under a preset time includes the following steps:

[0070] S1. Analyze the dynamic model of the quadcopter UAV and generalize it to a general Eulerian-Lagrange system; specific steps include:

[0071] S11, the drone swarm consists entirely of quadcopter drones. To simplify the quadcopter drone dynamics model, some basic assumptions need to be made about the system model: First, the drone's body is a rigid body and strictly symmetrical. Second, the origin of the body coordinate system coincides with the drone's center of mass. Finally, the propellers do not flap. Under these assumptions, the quadcopter drone dynamics model can be divided into two parts: position dynamics and attitude dynamics.

[0072] Assuming a drone swarm consists of n drones, the second-order dynamics model of the i-th quadcopter drone is as follows, where i∈{1,…,n}.

[0073]

[0074]

[0075]

[0076]

[0077]

[0078]

[0079] Where, x i ,y i ,z i These are the x-axis, y-axis, and z-axis position coordinates of the i-th quadrotor UAV in the inertial coordinate system, respectively. θ i ,ψ i These are the roll angle, pitch angle, and yaw angle of the i-th quadcopter UAV in the inertial coordinate system, respectively. These are the moments of inertia of the i-th quadrotor UAV about the x, y, and z axes of the body coordinate system, respectively. Let m represent the disturbances experienced by the i-th quadrotor UAV in the x-axis, y-axis, and z-axis directions, respectively; i Let u be the mass of the i-th quadcopter UAV; i1 ,u i2 ,u i3 ,u i4 These are the four control inputs for the i-th quadcopter UAV; g is the acceleration due to gravity.

[0080] In addition, the four control inputs for the quadcopter drone are:

[0081]

[0082] Among them, F i1 ,F i2 ,F i3 ,F i4 p represents the lift generated by the four motors of the i-th quadcopter UAV; i Let be the distance between the rotor of the i-th quadcopter UAV and the center of mass of the UAV.

[0083] In the above dynamic model, u i1 The displacement is allocated to the x, y, and z directions, u i2 ,u i3 ,u i4 The inputs are distributed to the three attitude angle channels, so the entire control system can be divided into three parts: ui, uj, ... i1 Composed of position control and by u i2 ,u i3 ,u i4 Composed of attitude control, such as Figure 2 As shown.

[0084] S12, Define variables The above quadcopter UAV dynamics model can then be described as the following Euler-Lagrange system:

[0085]

[0086] M in the system i (η i ), G i (η i ), u i They are respectively

[0087]

[0088]

[0089]

[0090] u i =[u i1 ,u i1 ,u i1 ,u i2 ,u i3 ,u i4 ] T ,

[0091] Among them, O 3×3 It is a 3×3 zero matrix; Matrix A i B 1i B 2i They are represented as follows:

[0092]

[0093]

[0094]

[0095] S13, abstracting the dynamics of a quadcopter UAV into a general Eulerian-Lagrange system, considering a UAV swarm with Eulerian-Lagrange nonlinear dynamics, the dynamic model of the i-th UAV can be expressed as follows:

[0096]

[0097] Where η i , M represents the generalized coordinates, velocity, and acceleration vectors, respectively; i (η i ) represents a positive definite symmetric inertial matrix; G represents the Coriolis-centripetal force matrix; i (η i ) represents the gravity matrix; u i This represents the controller acting on the system. For the convenience of subsequent algorithm design, we assume M to be... i (η i It is reversible. The purpose of this invention is to design a controller u. i The goal is to enable the drone swarm to adjust its decisions based on local information and converge to a Nash equilibrium point within a preset time.

[0098] S2, based on the UAV dynamics model generalized to the Eulerian-Lagrange system in S1, constructs a UAV swarm game model with Eulerian-Lagrange nonlinear dynamics; the specific steps are as follows:

[0099] S21, Construct a game theory model for drone swarms;

[0100] Consider a swarm of n drones, where each drone uses local information to adjust its decisions to minimize its cost function. This problem can be described as follows:

[0101]

[0102] Where f i (η i ,η -i Let η be the objective function of the i-th UAV; i Let η be the decision variable for the i-th drone; -i Let η be the decision variable for all drones except the i-th drone. -i =[η1,…,η i-1 ,η i+1 ,…,η n ].

[0103] In the game, if no drone can unilaterally change its strategy to reduce its own gain, then a Nash equilibrium is reached, that is, if... satisfy:

[0104]

[0105] but This is called the Nash equilibrium solution; where,

[0106] S22. To ensure the convergence of the designed algorithm, some basic assumptions are given below:

[0107] Assumption 1: Communication Topology Diagram It is an undirected connected graph;

[0108] Assumption 2: The objective function of agent i is f i (η) is a twice continuously differentiable function.

[0109] Assumption 3: The gradient of the objective function The global Lipschitz continuity condition must be satisfied, i.e., there exists a constant l. i >0, for have

[0110] Assumption 4: For any There is (η-z) T (F(η)-F(z))≥m||η-z|| 2 Where the constant m > 0,

[0111] Assumption 5: There exists a constant h > 0 such that in

[0112] In the aforementioned non-cooperative game problem, it is assumed that each drone can only obtain information about its neighbors and cannot obtain information about the actions of non-neighbor drones. Therefore, each drone will generate an estimate of the actions of other drones and update its estimate by using information exchange with its neighbors.

[0113] S3, based on the Eulerian-Lagrange system in S1 and the UAV swarm game model in S2, proposes a Nash equilibrium search algorithm based on partial information of convergence at a preset time by introducing a time base generator, thereby achieving precise control of the convergence time;

[0114] The specific steps are as follows:

[0115] S31, In order to achieve convergence of the algorithm within the preset time and ensure the continuity or smoothness of the control behavior, we introduce a time base generator, which is specifically represented as follows:

[0116] T(t,t f )=(g(t,σ))′,

[0117] Where σ is a sufficiently small parameter; t f This is a preset time, mainly adjusted according to the algorithm requirements; g is a bivariate function of time t and parameter σ. Furthermore, g(t,σ) must satisfy the following conditions:

[0118] 0 < σ < < 1,

[0119]

[0120] g(t,σ)-g(t f+ ,σ)≥0,t>t f ,

[0121]

[0122] S23, under the action of the time base generator in S31, an algorithm can be designed to enable a system to achieve convergence within a preset time. The following introduces a definition for achieving convergence within a preset time. For any initial state η(0), there exists 0 < δ = δ(η(0)) << 1 satisfying the following three conditions:

[0123]

[0124]

[0125]

[0126] The system is said to be at time t f The point converged within the preset time.

[0127] S33, utilizing the gradient information and consensus protocol of the UAV, the control input design for the i-th quadcopter UAV is as follows:

[0128]

[0129] Where η i It is the decision variable for the i-th drone; α, β, γ, ε>0 are the estimated variables for the decision of the i-th UAV on the j-th UAV; α, β, γ, ε>0 are the corresponding algorithm parameters; a ij T(t,t) is the weight of the communication connection between the i-th drone and the j-th drone; f () indicates that the time base generator satisfies the condition in S31.

[0130] Substituting the above control inputs into the Euler-Lagrange system of S13, the overall algorithm design is as follows:

[0131]

[0132]

[0133]

[0134] In the formula, v i It is an auxiliary variable.

[0135] S4. The convergence of the above algorithm is proven using Lyapunov stability theory; the specific steps include:

[0136] S41, Let τ = εt, then the above algorithm can be converted into the following compact form:

[0137]

[0138] Where L is the graph The corresponding Laplace matrix; I nm×nm It is an identity matrix of nm × nm dimensions; due to the limitations of quadcopter UAV dynamics, m = 6 here;

[0139]

[0140] S42, using Lyapunov stability theory, proves that the above Euler-Lagrange system can converge to the Nash equilibrium point within a preset time under the action of control input, specifically stated as the following theorem:

[0141] If all the assumptions in S22 are true, then there exists a positive number ε. * Make the when At that time, the Euler-Lagrange system in S13, under the control input of S33, can achieve the desired result within a preset time t. f It converges to the neighborhood of the Nash equilibrium solution, that is:

[0142]

[0143] in And 0 < σ < < 1.

[0144] Proof: Let ε = 0, then according to assumption one in S22, Established, for At this point, the algorithm in S41 can be transformed into the following form:

[0145]

[0146] Let θ = η - η * φ=F(η)+v, where η * It is a Nash equilibrium solution, and a Lyapunov function is defined as follows:

[0147]

[0148] Differentiating the Lyapunov function with respect to time t, we get:

[0149]

[0150] From the Lipschitz continuity of F guaranteed by assumption two in S22, we know that ||F(η)-F(η) * )||≤L||θ||, where Furthermore, based on the assumption that four have θ T F(η)≥m||θ|| 2 Furthermore, Assumption 5 states that ||H(η)||≤h.

[0151] In conclusion,

[0152]

[0153] Matrix A is defined as follows:

[0154]

[0155] Obviously, when When A is a positive definite matrix, therefore we have

[0156]

[0157] Integrating both sides of the above equation from 0 to τ, we get:

[0158] When τ→t f Sometimes, in Due to ||η-η * || 2 ≤2V, therefore Similarly, utilizing the properties of the time base generator in S31, for ||η(τ)-η * ||≤δ and This is clearly true.

[0159] Numerical simulations were performed on the UAV swarm game problem in an air combat context to further verify the effectiveness of the algorithm; the search method of this invention was also verified through simulation.

[0160] This paper considers the problem of tracking a swarm of drones in airspace and uses Python simulation to verify the effectiveness of the proposed control strategy. The simulation object is a Hummingbird drone manufactured by ASCTEC. The drone swarm parameters and controller parameters are as follows:

[0161] Table 1. Parameter Settings for UAV Clusters and Controllers

[0162]

[0163] The objective function for each drone can be expressed in the following form:

[0164]

[0165] Clearly, since a swarm of drones cannot fly along the same trajectory simultaneously, the individual objectives of the drones conflict with each other. The purpose of this experiment is to control the drone swarm to reach a Nash equilibrium position within a preset time, in order to balance the group objective and the individual objectives of the drones. The time base generator selected for this experiment is as follows:

[0166]

[0167] in,

[0168]

[0169] The following two examples demonstrate that the proposed algorithm can converge to the Nash equilibrium solution within 0.2s using the aforementioned time base generator.

[0170] Example 1

[0171] Considering the case where n=4, the communication diagram between the four drones is as follows: Figure 3 As shown. Furthermore, the time-varying target being tracked by the drone is set as η0 = [20(sint-1), 20(cost-1), 40 + 20sint, 0, 0, 0] T To ensure that the drones maintain a relative distance, the desired displacement between each drone and its neighbor is d. 12 =[10,0,0,0,0,0] T d 24 =[-10,0,0,0,0,0] T d 31 =[0,10,0,0,0,0] T d 43 =[0,-10,0,0,0,0] T Under the proposed control input, the three-dimensional trajectories of the four UAVs are as follows: Figure 4 As shown, the four drones tracked the time-varying Nash equilibrium solution while maintaining a relative distance, effectively balancing the group target and the individual target. To clearly observe the convergence of the drone trajectories, η0 is set as a fixed target η0 = [-20, -20, 40, 0, 0, 0]. T The trajectories of the drone swarm in the x, y, and z axes over time are as follows: Figure 5 As shown in Figures 6 and 7, it is clear that the positions of the four drones converged to the Nash equilibrium point within 0.2 seconds.

[0172] Example 2

[0173] To further verify the effectiveness of the algorithm, the number of drones was increased.

[0174] Considering the case where n=52, the communication graph between drone swarms is designed as an ER random network with an edge connection probability of 0.4, as follows: Figure 8 As shown, the drone swarm is divided into four clusters, and their tracking target is η0 = [-30, -50, 80, 0, 0, 0]. T The expected displacements between each drone and its neighbor are: d 1+4n,j =[30,0,0,0,0,0] T d 2+4n,j =[-30,0,0,0,0,0] T d 3+4n,j =[0,30,0,0,0,0] T d 4+4n,j =[0,-30,0,0,0,0] T Where n∈{0,…,12}, j∈{1,…,52}. Under the influence of control input, the three-dimensional trajectory of the UAV swarm is as follows: Figure 9As shown, the trajectories of the x, y, and z axes as a function of time are respectively as follows: Figure 10 As shown in Figures 11 and 12, it is clear that the drone swarm converged to the Nash equilibrium point within 0.2 seconds. Furthermore, by adjusting the time base generator, convergence to the Nash equilibrium point can be achieved within any specified time period.

[0175] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0176] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention.

Claims

1. A method for searching Nash equilibrium in drone swarm game under a preset time, characterized in that, Includes the following steps: The dynamic model of a quadcopter UAV is analyzed and extended to the Euler-Lagrange system; Based on the dynamic model of UAVs generalized to the Euler-Lagrange system, a UAV swarm game model with Euler-Lagrange nonlinear dynamics is constructed. Based on the Euler-Lagrange system and the UAV swarm game model, a Nash equilibrium search algorithm based on partial information of convergence with a preset time is proposed by introducing a time base generator to control the convergence time. The time base generator is: in, It is a sufficiently small parameter; This is a preset time, which is mainly adjusted according to the algorithm requirements; Regarding time and parameters A bivariate function that satisfies the following conditions: The Nash equilibrium search algorithm is designed as follows: In the formula, It is the first Decision variables for deploying drones; It is the first The drone was used to attack the first Estimated variables for drone deployment decisions; It is an auxiliary variable; These are the corresponding algorithm parameters; It is the first The drone and the first The weight values ​​of the communication links between drones, where n is the total number of drones in the drone swarm. This represents the weight value of the communication connection between the i-th drone and the k-th drone.

2. The method for searching Nash equilibrium in a drone swarm game under a preset time according to claim 1, characterized in that, The construction of the quadcopter UAV dynamics model needs to meet the following prerequisites: 1) The airframe of a drone is a rigid body and is strictly symmetrical; 2) The origin of the body coordinate system coincides with the center of mass of the UAV; 3) The blades did not make any waving motion.

3. The method for searching Nash equilibrium in a drone swarm game under a preset time according to claim 2, characterized in that, No. The second-order dynamic model of the quadcopter UAV is as follows: in, They are the first A quadcopter UAV in an inertial coordinate system Axis position coordinates, Axis position coordinates and Axis position coordinates; They are the first The roll angle, pitch angle, and yaw angle of a quadcopter UAV in an inertial coordinate system; They are the first A quadcopter drone orbiting its body coordinate system Moment of inertia of the shaft; The first The disturbances experienced by a quadcopter UAV in the x-axis, y-axis and z-axis directions; For the first The mass of a quadcopter drone; They are the first The four control inputs for a quadcopter drone; This is the acceleration due to gravity.

4. The method for searching Nash equilibrium in a drone swarm game under a preset time according to claim 3, characterized in that, The four control inputs for the quadcopter drone are: in, The first The lift generated by the four motors of the quadcopter drone; For the first The distance between the rotor of a quadcopter drone and the center of mass of the drone.

5. The method for searching Nash equilibrium in a drone swarm game under a preset time according to claim 3, characterized in that, Consider a swarm of unmanned aerial vehicles with Euler-Lagrange nonlinear dynamics, the first The dynamic model of the drone can be represented as: in, These represent the generalized coordinates, velocity, and acceleration vectors, respectively. Represents a positive definite symmetric inertia matrix; Represents the Coriolis-centripetal force matrix; Represents the gravity matrix; This refers to the controller that acts on the system.

6. The method for searching Nash equilibrium in a drone swarm game under a preset time according to claim 5, characterized in that, The drone swarm game model is as follows: There are a total of drones in the swarm Consider a fleet of drones. Each drone uses local information to adjust its decisions to minimize its cost function, described as follows: in For the first The objective function of the drone; For the first Decision variables for deploying drones; In addition to the first The decision variables of all other drones that are in use, i.e. ; In the process of the game, if satisfy: but This is called the Nash equilibrium solution; among which, .

7. A Nash equilibrium search system for drone swarm game under a preset time, comprising the method described in any one of claims 1-6, characterized in that, include: Dynamics model building module: Analyzes the dynamics model of a quadcopter UAV and generalizes it to the Euler-Lagrange system; Drone swarm game model construction module: Based on the dynamic model of drones generalized to the Eulerian-Lagrange system, construct a drone swarm game model with Eulerian-Lagrange nonlinear dynamics; In addition, the search algorithm construction module: based on the Euler-Lagrange system and the UAV swarm game model, a Nash equilibrium search algorithm based on partial information of convergence at a preset time is proposed by introducing a time base generator to control the convergence time.

8. A computer storage medium storing a readable program that, when the program is run, can execute the search method according to any one of claims 1-6.

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