Neural network-based preset time robust bipartite swarming control method

Abstract

The invention discloses a neural network-based preset time robust bipartite swarming control method, which comprises the following steps of: firstly, establishing a second-order dynamic model of a multi-robot system with model uncertainty, determining a bipartite swarming control problem with preset time convergence performance, and defining a speed consistency error; then designing an uncertainty estimator based on the RBF neural network to estimate the uncertainty of the model, designing a preset time robust swarming controller according to the uncertainty estimator, constructing a closed-loop error system, establishing an adaptive updating law of the neural network weight, and finally deploying the controller and the adaptive updating law into a robot group. And the preset time robust bipartite swarming control of the multi-robot system is realized. According to the method, under the condition that composite uncertainty and convergence time limitation exist, bipartite swarming control of the multi-robot system can be achieved, the problem that a dynamic model of the system in practical application is possibly unknown is solved, and the method is suitable for swarming control tasks with convergence time requirements.

Description

Technical Field

[0001] The present invention belongs to the technical field of cooperative control of multi-robot systems, and in particular relates to a neural network-based preset time robust binary swarming control method. Background Art

[0002] With the continuous development of modern science and technology, the collaborative control of multiple robots has attracted the attention of many scholars. Due to its advantages of low cost, strong autonomy, and high flexibility, it is widely used in many fields such as industrial manufacturing, disaster relief, intelligent logistics, agricultural planting, and medical health. However, in practical applications, due to the uncertainty of the multi-robot system model and the complex requirements of different tasks, it is very important to study more efficient and accurate collaborative control methods.

[0003] Inspired by the swarming phenomenon exhibited by fish, birds and other organisms during migration and predation, researchers have conducted in-depth research on the swarming behavior of multi-robot systems and proposed a large number of control methods. However, it is worth noting that most of the research work considers that there is only a cooperative relationship between robots, while in actual applications, the system often has both cooperative and competitive relationships. On the other hand, most of the early collaborative control research focused on asymptotic consistency, and in order to improve control performance and pursue rapid convergence, scholars proposed finite time, fixed time, and preset time control algorithms, but there is little research on their application to swarming control. In addition, most of the existing research on swarming focuses on the system's dynamic model that can be predicted in advance, and there is less research on systems with model uncertainty. Therefore, it is of great practical value to study the preset time robust swarming control method based on neural networks. Summary of the invention

[0004] In order to solve the above technical problems, the present invention provides a preset time robust swarming control method based on a neural network, which is used to solve the swarming control problem when the system model is uncertain, and at the same time has preset time convergence performance, thereby realizing preset time robust binary swarming control of multiple robots.

[0005] The technical solution adopted by the present invention is: a preset time robust binary swarming control method based on neural network, and the specific steps are as follows:

[0006] S1. Establish a second-order dynamic model of a multi-robot system with model uncertainty, clarify the bisection swarming control problem with a preset time convergence performance, and define the speed consistency error;

[0007] S2, design uncertainty estimator based on RBF neural network to estimate model uncertainty;

[0008] S3, designing a preset time robust swarming controller based on the uncertainty estimator in step S2;

[0009] S4, based on step S1, construct a closed-loop error system and establish an adaptive update law for the neural network weights;

[0010] S5. Deploy the controller designed in step S3 and the adaptive update law established in step S4 to the robot group, and realize the preset time robust binary swarming control of the multi-robot system in the presence of compound uncertainties and convergence time constraints.

[0011] Furthermore, the step S1 is specifically as follows:

[0012] S11. Establish a second-order dynamics model of a multi-robot system with model uncertainty;

[0013] Assume that the multi-robot system has N robots in total, then the communication topology of the N robots is represented by a weighted graph To express.

[0014] in, A node set representing N robots; Represents communication between robots; represents the weighted adjacency matrix, represents a set of N×N dimensional real number matrices, a ij represents the jth element of the i-th row of the matrix, and if (v i ,v j )∈ε, then a ij ≠0, otherwise a ij =0.

[0015] The degree matrix is ​​set to be expressed as and picture The Laplace matrix of Defined as

[0016] If there is a bipartite set of vertices and For There is a ij ≥0; for There is a ij ≤0, we can see that The structure is balanced.

[0017] Then set the diagonal elements δ of the diagonal matrix δ i =±1.

[0018] Among them, δ i =1 indicates a node δ i =-1 means Then we can get δi δ j =sign(a ij ).

[0019] A second-order dynamics model of a multi-robot system with model uncertainty is established. The specific expression of the dynamics model is as follows:

[0020]

[0021] in, denote the position and velocity of the ith robot at time t, respectively. represents the n-dimensional real number field, where n is a natural number greater than or equal to 1; denote the first-order derivative of the position and velocity of the ith robot at time t, respectively, and v i (t) Abbreviated as v i ;u i (t) represents the control input at time t, Γ={1,2,...,n}, f i (v i ) is a continuous unknown nonlinear function, which is used to represent the model uncertainty of the system.

[0022] S12, based on the model established in step S11, clarifying a binary swarming control problem with a preset time convergence performance;

[0023] The requirements that the multi-robot system must meet to achieve binary swarming behavior with a preset time convergence performance are as follows:

[0024] (1) For all The robot's speed satisfies the following conditional expression:

[0025]

[0026] Among them, t p Indicates the preset time, t p It is independent of the system's initial conditions and other controller parameters and is pre-designed according to the needs of the control task. The robots in a cluster achieve speed consistency within the specified time; on the contrary, if the robots belong to different clusters, they keep the same speed but move in opposite directions.

[0027] (2) There exists a constant D>0, and the upper bound of the diameter in the same subset satisfies the condition of formula (3), so that the diameter of each cluster remains within the limit. The expression is as follows:

[0028]

[0029] S13, define speed consistency error;

[0030] At the preset time t p The binary swarming between robots is realized, and a small residual error is allowed between the speeds. The initial time of the system is set to t0, and the speed of the robot should meet the following conditions:

[0031]

[0032] Define the speed consistency error e i (t), the expression is as follows:

[0033]

[0034] The speed consistency error can be simplified as follows:

[0035]

[0036] where θ(t)=[e1(t),e2(t),...,e n (t)] T ,v(t)=[v1(t),v2(t),...,v n (t)] T , [] T Represents the transpose of a matrix.

[0037] Furthermore, the step S2 is specifically as follows:

[0038] S21, RBF neural network;

[0039] The RBF network consists of an input layer, a hidden layer, and an output layer. For any continuous function ξ i (v i ), and use RBF neural network to approximate it into the following form:

[0040]

[0041] Among them, ω i represents the ideal weight, ε i (v i ) represents the approximation error. Gaussian function represents the basis function, v i represents the input vector, c and σ represent the center position and width of the Gaussian function.

[0042] S22. Design uncertainty estimator;

[0043] Through the RBF neural network, the model uncertainty term f i (v i ) is expressed as follows:

[0044]

[0045] in, represents an estimate of the ideal weight.

[0046] Furthermore, the step S3 is specifically as follows:

[0047] The function μ(t, t0) represents a time-varying adjustment function of a preset time, which satisfies the following conditions:

[0048] (1)

[0049] (2)

[0050] Among them, various time-varying functions μ1(t,t0) satisfy the above conditions; τ represents the integral variable.

[0051] Then the time-varying function To achieve the weight update and control target within the preset time, r≥2 represents an integer. Then the function μ(t,t0) can be expressed as

[0052] Then, using the uncertainty estimator designed in step S2 and the above-mentioned time-varying function μ1(t, t0), the preset time robust swarming controller is designed as follows:

[0053]

[0054] Among them, ρ 1i It represents the set positive constant, i.e. the controller parameter, and the corresponding item is the proportional gain item.

[0055] Furthermore, the step S4 is specifically as follows:

[0056] S41, build a closed-loop error system;

[0057] Substitute the controller designed in step S3 into the dynamic model of the multi-robot system established in step S1 to obtain a closed-loop error system, which is expressed as follows:

[0058]

[0059] S42, establishing an adaptive update law for the neural network weights;

[0060] For the closed-loop error system, Lyapunov theory is used to analyze the stability conditions of the closed-loop error system, and the adaptive update law of the neural network weights is established as follows:

[0061]

[0062] Among them, φ i (v i) represents the basis function, ρ 2i Indicates the set normal number, that is, the controller parameter.

[0063] Beneficial effects of the present invention: The method of the present invention first establishes a second-order dynamic model of a multi-robot system with model uncertainty, clarifies a binary swarming control problem with preset time convergence performance, defines a speed consistency error, then designs an uncertainty estimator based on an RBF neural network to estimate model uncertainty, and designs a preset time robust swarming controller based on the uncertainty estimator, then constructs a closed-loop error system and establishes an adaptive update law for neural network weights, and finally deploys the controller and the adaptive update law to a robot group, and realizes the preset time robust binary swarming control of a multi-robot system in the presence of composite uncertainty and convergence time constraints. The preset time robust swarming controller based on a neural network proposed by the method of the present invention enables all robots to realize binary swarming behavior within a preset time when there is uncertainty in the system, and the convergence time can be predetermined and is not affected by system parameters (such as controller gain, robot initial state, and inter-robot communication topology), and by analyzing the stability conditions of the closed-loop error system, an adaptive weight update law is formulated for the neural network estimator, and the update law realizes effective uncertainty estimation by back-propagating the swarming control error. The method of the present invention can realize binary swarming control of a multi-robot system in the presence of composite uncertainties and convergence time constraints, solves the problem that the dynamic model of the system may be unknown in practical applications, and is suitable for swarming control tasks with convergence time requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 The present invention is a flowchart of a neural network-based preset time robust binary swarming control method.

[0065] Figure 2 Schematic diagram of the communication topology relationship between multiple robots given in an embodiment of the present invention.

[0066] Figure 3 Schematic diagram of position trajectory changes of multiple robots given in an embodiment of the present invention.

[0067] Figure 4 Schematic diagram of the change of position trajectory of multiple robots given in an embodiment of the present invention within time t∈[0,20].

[0068] Figure 5 Schematic diagram of the change of position trajectories of multiple robots given in an embodiment of the present invention over time.

[0069] Figure 6 Schematic diagram of the change of velocity trajectory of multiple robots over time in an embodiment of the present invention. DETAILED DESCRIPTION

[0070] The method of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0071] like Figure 1 As shown, a flowchart of a neural network-based preset time robust binary swarming control method of the present invention, the specific steps are as follows:

[0072] S1. Establish a second-order dynamic model of a multi-robot system with model uncertainty, clarify the bisection swarming control problem with a preset time convergence performance, and define the speed consistency error;

[0073] S2, design uncertainty estimator based on RBF neural network to estimate model uncertainty;

[0074] S3, designing a preset time robust swarming controller based on the uncertainty estimator in step S2;

[0075] S4, based on step S1, construct a closed-loop error system and establish an adaptive update law for the neural network weights;

[0076] S5. Deploy the controller designed in step S3 and the adaptive update law established in step S4 to the robot group, and realize the preset time robust binary swarming control of the multi-robot system in the presence of compound uncertainties and convergence time constraints.

[0077] In this embodiment, the step S1 is specifically as follows:

[0078] S11. Considering the situation that the dynamic model of the system in practical applications may be unknown, a second-order dynamic model of the multi-robot system with model uncertainty is established;

[0079] Assume that the multi-robot system has N robots in total, then the communication topology of the N robots is represented by a weighted graph To express.

[0080] in, A node set representing N robots; Represents communication between robots; represents the weighted adjacency matrix, represents a set of N×N dimensional real number matrices, a ij represents the jth element of the i-th row of the matrix, and if (v i ,v j )∈ε, then a ij ≠0, otherwise a ij =0.

[0081] The degree matrix is ​​set to be expressed as and picture The Laplace matrix of Defined as

[0082] If there is a bipartite set of vertices and For There is a ij ≥0; for There is a ij ≤0, we can see that The structure is balanced.

[0083] Then set the diagonal elements δ of the diagonal matrix δ i =±1.

[0084] Among them, δ i =1 indicates a node δ i =-1 means Then we can get δ i δ j =sign(a ij ).

[0085] A second-order dynamics model of a multi-robot system with model uncertainty is established. The specific expression of the dynamics model is as follows:

[0086]

[0087] in, denote the position and velocity of the ith robot at time t, respectively. represents the n-dimensional real number field, where n is a natural number greater than or equal to 1; denote the first-order derivative of the position and velocity of the ith robot at time t, respectively, and v i (t) Abbreviated as v i ;u i (t) represents the control input at time t, Γ={1,2,...,n}, f i (v i ) is a continuous unknown nonlinear function, which is used to represent the model uncertainty of the system.

[0088] S12, based on the model established in step S11, clarifying a binary swarming control problem with a preset time convergence performance;

[0089] The requirements that the multi-robot system must meet to achieve binary swarming behavior with a preset time convergence performance are as follows:

[0090] (1) For all The robot's speed satisfies the following conditional expression:

[0091]

[0092] Among them, t p Indicates the preset time, t p It is independent of the system's initial conditions and other controller parameters and is pre-designed according to the needs of the control task. The robots in a cluster achieve speed consistency within the specified time; on the contrary, if the robots belong to different clusters, they keep the same speed but move in opposite directions.

[0093] (2) There exists a constant D>0, and the upper bound of the diameter in the same subset satisfies the condition of formula (3), so that the diameter of each cluster remains within the limit. The expression is as follows:

[0094]

[0095] S13, define speed consistency error;

[0096] At the preset time t p The binary swarming between robots is realized, and a small residual error is allowed between the speeds. The initial time of the system is set to t0, and the speed of the robot should meet the following conditions:

[0097]

[0098] Define the speed consistency error e i (t), the expression is as follows:

[0099]

[0100] To simplify the analysis, the speed consistency error can be simplified as follows:

[0101]

[0102] where θ(t)=[e1(t),e2(t),...,e n (t)] T ,v(t)=[v1(t),v2(t),...,v n (t)] T , [] T Represents the transpose of a matrix.

[0103] In this embodiment, step S2 is specifically as follows:

[0104] S21, RBF (Radial Basis Function) neural network;

[0105] RBF (Radial Basis Function) neural network is an artificial neural network that processes input data through radial basis function as activation function. RBF neural network belongs to the type of feedforward neural network. The structure of the network is similar to that of multi-layer feedforward network. The basic idea is to use RBF as the "basis" of hidden units to form the hidden layer space. The hidden layer transforms the input vector and transforms the low-dimensional pattern input data into high-dimensional space, so that the linear inseparable problem in low-dimensional space can be linearly separable in high-dimensional space. RBF neural network has a simple structure, concise training and fast learning convergence speed, and can approximate any nonlinear function.

[0106] The RBF network consists of an input layer, a hidden layer (RBF layer), and an output layer. Each neuron in the hidden layer corresponds to a radial basis function, which is usually in the form of a Gaussian function and is used to calculate the distance between the input and the center point. The output layer converts the output of the hidden layer into the final prediction result through linear or nonlinear combination. RBF networks are widely used in pattern recognition, classification, and function approximation.

[0107] For any continuous function ξ i (v i ), and use RBF neural network to approximate it into the following form:

[0108]

[0109] Among them, ω i represents the ideal weight, ε i (v i ) represents the approximation error. Gaussian function represents the basis function, v i represents the input vector, c and σ represent the center position and width of the Gaussian function.

[0110] S22. Design uncertainty estimator;

[0111] Through the RBF neural network, the model uncertainty term f i (v i ) is expressed as follows:

[0112]

[0113] in, represents an estimate of the ideal weight.

[0114] In this embodiment, step S3 is specifically as follows:

[0115] The function μ(t, t0) represents a time-varying adjustment function of a preset time, which satisfies the following conditions:

[0116] (1)

[0117] (2)

[0118] Among them, various time-varying functions μ1(t,t0) satisfy the above conditions, and τ represents the integral variable.

[0119] Then the time-varying function To achieve the weight update and control target within the preset time, r≥2 represents an integer. Then the function μ(t,t0) can be expressed as

[0120] Then, using the uncertainty estimator designed in step S2 and the above-mentioned time-varying function μ1(t, t0), the preset time robust swarming controller is designed as follows:

[0121]

[0122] Among them, ρ 1i It represents the set positive constant, i.e. the controller parameter, and the corresponding item is the proportional gain item.

[0123] The preset time robust swarming controller consists of three parts. The first two parts are crucial to promote the preset time convergence of the system. Used to estimate the uncertainty of the system. The proportional gain term ρ 1i The larger the design, the faster the system converges, but it will also make the transient response of the closed-loop system too large. The control input of the actual physical system has an upper limit, such as the upper limit of the speed of the robot motor. Therefore, when selecting controller parameters, the control performance and system capabilities should be properly balanced.

[0124] In this embodiment, step S4 is specifically as follows:

[0125] S41, build a closed-loop error system;

[0126] Substitute the controller designed in step S3 into the multi-robot dynamics model established in step S1 to obtain a closed-loop error system, which is expressed as follows:

[0127]

[0128] S42, establishing an adaptive update law for the neural network weights;

[0129] For the closed-loop error system, Lyapunov theory is used to analyze the stability conditions of the closed-loop error system, and the adaptive update law of the neural network weights is established as follows:

[0130]

[0131] Among them, φ i (vi ) represents the basis function, ρ 2i Indicates the set normal number, that is, the controller parameter.

[0132] The adaptive update law achieves effective uncertainty estimation by back-propagating the crowding control error.

[0133] In this embodiment, simulation verification is further performed. First, a multi-robot system consisting of 10 robots is set, where the unknown nonlinear function expression of the second-order dynamic model of each robot is as follows:

[0134]

[0135] Where i = 1, 2, 3..., 10, M represents the coupling gain, g i represents the intrinsic parameters of the ith robot.

[0136] Then, the robust controller in step S3 and step S4 and the adaptive update law of the neural network weights are used to perform simulation experiments. The communication topology between the robots is as follows: Figure 2 As shown in the figure, The weighted adjacency matrix expression is as follows:

[0137]

[0138] Then set the parameters: the position and speed states of the robot are defined as x i =[x ix ,x iy ] T and v i =[v ix ,v iy ] T The initial values ​​of position and velocity x i (t0) and v i (t0) is randomly generated in the range [-20, 20] and [-10, 10] respectively. The system coupling gain M = 1, and the robot's intrinsic parameters g = [15, 25, 35, 5, 9, 15, 25, 35, 5, 9]. The controller parameters are set to ρ 1i =1.5 and ρ 2i = 0.05. The convergence time of binary swarming is set to t p =4s. In addition, RBF neural network We use 100 nodes, whose centers c are uniformly distributed in the interval [-10, 10], and whose width σ is set to 2.

[0139] Based on the parameter settings, the preset time binary swarming control of the multi-robot system based on model uncertainty and the co-operation and competition relationship within the system is realized. The final effect is as follows Figure 3-Figure 6 As shown: Figure 3 The figure shows the change of the robot position over time. The arrow indicates the direction of speed. It can be seen that the speed of the robots is consistent, while the speeds of robots in different subsets are opposite. Figure 4 is the change of the position of multiple robots in time t∈[0,20]. The robots continue to converge over time and finally reach the same speed. Finally, Figure 5 and Figure 6 It can be seen that the multi-robot system achieves binary swarming within the preset time. Combining the simulation results with the above analysis, the effectiveness and superiority of the method of the present invention are verified.

[0140] In summary, the preset time robust swarming controller based on neural network proposed by the method of the present invention enables all robots to realize binary swarming behavior within the preset time when there is uncertainty in the system, and the convergence time can be predetermined and is not affected by system parameters (such as controller gain, robot initial state and inter-robot communication topology). By analyzing the stability conditions of the closed-loop error system, an adaptive weight update law is formulated for the neural network estimator, and the update law realizes effective uncertainty estimation by back propagating the swarming control error. The method of the present invention can realize binary swarming control of a multi-robot system in the presence of compound uncertainty and convergence time constraints, solves the problem that the dynamic model of the system may be unknown in practical applications, and is suitable for swarming control tasks with convergence time requirements.

[0141] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A preset time robust binary swarming control method based on neural network, the specific steps are as follows: S1. Establish a second-order dynamic model of a multi-robot system with model uncertainty, clarify the binary swarming control problem with a preset time convergence performance, and define the speed consistency error; S2, design uncertainty estimator based on RBF neural network to estimate model uncertainty; S3, designing a preset time robust swarming controller based on the uncertainty estimator of step S2; S4, based on step S1, construct a closed-loop error system and establish an adaptive update law for the neural network weights; S5. Deploy the controller designed in step S3 and the adaptive update law established in step S4 to the robot group, and realize the preset time robust binary swarming control of the multi-robot system in the presence of compound uncertainties and convergence time constraints.

2. A neural network-based preset time robust binary swarming control method according to claim 1, characterized in that: The step S1 is specifically as follows: S11. Establish a second-order dynamics model of a multi-robot system with model uncertainty; Assume that the multi-robot system has N robots in total, then the communication topology of the N robots is represented by a weighted graph To express; in, A node set representing N robots; Represents communication between robots; represents the weighted adjacency matrix, represents a set of N×N dimensional real number matrices, a ij represents the jth element of the i-th row of the matrix, and if (v i ,v j )∈ε, then a ij ≠0, otherwise a ij =0; The degree matrix is ​​set to be expressed as and picture The Laplace matrix of Defined as If there is a bipartite set of vertices and For There is a ij ≥0; for There is a ij ≤0, we can see that It is structurally balanced; Then set the diagonal elements δ of the diagonal matrix δ i = ±1; Among them, δ i =1 indicates a node δ i =-1 means Then we can get δ i δ j =sign(a ij ); A second-order dynamics model of a multi-robot system with model uncertainty is established. The specific expression of the dynamics model is as follows: in, denote the position and velocity of the ith robot at time t, respectively. represents the n-dimensional real number field, where n is a natural number greater than or equal to 1; denote the first-order derivative of the position and velocity of the ith robot at time t, respectively, and v i (t) Abbreviated as v i ;u i (t) represents the control input at time t, Γ={1,2,...,n}, f i (v i ) is a continuous unknown nonlinear function, which is used to represent the model uncertainty of the system; S12, based on the model established in step S11, clarifying a binary swarming control problem with a preset time convergence performance; The requirements that the multi-robot system must meet to achieve binary swarming behavior with a preset time convergence performance are as follows: (1) For all The robot's speed satisfies the following conditional expression: Among them, t p Indicates the preset time, t p It is independent of the initial conditions of the system and other controller parameters, and is pre-designed according to the needs of the control task; then the same cluster The robots in a cluster achieve speed consistency within the specified time; on the contrary, if the robots belong to different clusters, they keep the same speed but move in opposite directions; (2) There exists a constant D>0, and the upper bound of the diameter in the same subset satisfies the condition of formula (3), so that the diameter of each cluster remains within the limit. The expression is as follows: S13, define speed consistency error; At the preset time t p The binary swarming between robots is realized, and a small residual error is allowed between the speeds. The initial time of the system is set to t0, and the speed of the robot should meet the following conditions: Define the speed consistency error e i (t), the expression is as follows: The speed consistency error can be simplified as follows: where θ(t)=[e1(t),e2(t),...,e n (t)] T ,v(t)=[v1(t),v2(t),...,v n (t)] T , [ ] T Represents the transpose of a matrix.

3. The neural network-based preset time robust binary swarming control method according to claim 1, characterized in that: The step S2 is specifically as follows: S21, RBF neural network; The RBF network consists of: input layer, hidden layer and output layer; for any continuous function ξ i (v i ), and use RBF neural network to approximate it into the following form: Among them, ω i represents the ideal weight, ε i (v i ) represents the approximation error; Gaussian function represents the basis function, v i represents the input vector, c and σ represent the center position and width of the Gaussian function; S22. Design uncertainty estimator; Through the RBF neural network, the model uncertainty term f i (v i ) is expressed as follows: in, represents an estimate of the ideal weight.

4. The neural network-based preset time robust binary swarming control method according to claim 1, characterized in that: The step S3 is specifically as follows: The function μ(t, t0) represents a time-varying adjustment function of a preset time, which satisfies the following conditions: (1) (2) Among them, various time-varying functions μ1(t,t0) satisfy the above conditions; τ represents the integral variable; Then the time-varying function To achieve the weight update and control target within the preset time, and r ≥ 2 represents an integer; then the function μ(t, t0) can be expressed as Then, using the uncertainty estimator designed in step S2 and the above-mentioned time-varying function μ1(t, t0), the preset time robust swarming controller is designed as follows: Among them, ρ 1i It represents the set positive constant, i.e. the controller parameter, and the corresponding item is the proportional gain item.

5. The neural network-based preset time robust binary swarming control method according to claim 1, characterized in that: The step S4 is specifically as follows: S41, build a closed-loop error system; Substitute the controller designed in step S3 into the dynamic model of the multi-robot system established in step S1 to obtain a closed-loop error system, which is expressed as follows: S42, establishing an adaptive update law for the neural network weights; For the closed-loop error system, the Lyapunov theory is used to analyze the stability conditions of the closed-loop error system, and the adaptive update law of the neural network weights is established as follows: Among them, φ i (v i ) represents the basis function, ρ 2i Indicates the set normal number, that is, the controller parameter.

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