Cooperative transportation robust control method of flexible constraint multi-agent system

Abstract

A collaborative transportation robust control method for a flexible constraint multi-agent system comprises the following steps: establishing the multi-agent system, and taking tether tension generated by a load on each agent as an uncertain nonlinear term of the multi-agent system; an RBF neural network is constructed, and approximation prediction is carried out on the uncertain nonlinear term through the RBF neural network; constructing a test data set by using a multi-agent system to obtain an ideal tether tension value as a data label value; according to the data label value, updating parameters in the RBF neural network through a gradient descent method, and deploying the parameters into an uncertain nonlinear term; and designing a non-singular terminal sliding mode adaptive controller based on RBF neural network prediction of supervised learning, and performing control compensation on the uncertain nonlinear term. According to the method, stable transportation of the tethered multi-agent can be ensured, and model calculation is simple.

Description

Technical Field

[0001] The present application belongs to the field of multi-agent control technology, and specifically relates to a collaborative transportation robust control method for a flexible constrained multi-agent system. Background Art

[0002] With the rapid development of the field of aerial robots, drones, as a free-floating manipulator, have received widespread attention, and short-distance drone transportation has also begun to emerge. During transportation, the load of a single drone will swing when it is transported using a rope hoisting method, and when the weight of the load to be transported is large, the mission may be affected. By using multiple drone ropes to coordinate hoisting and transportation, the limitation of insufficient load capacity of a single drone can be overcome. In addition, this configuration can effectively control the posture of the load, solving the problem of swinging loads when transporting a single drone, and even completing the mission requirements when a single drone fails.

[0003] The coordinated lifting of multiple UAVs by rope system has advantages that cannot be matched by a single UAV, such as high feasibility, high efficiency and strong scalability, but it must consider a series of new factors. The entire system is not only affected by the load, but also by the movement of other UAVs. The independent actions of UAVs must be properly coordinated. Some scholars have studied the control technology of the coordinated lifting system of multiple UAVs by rope system. The patent application document with the publication number CN112650269A discloses a load tracking control method of a multi-UAV coordinated transportation system. The system consists of n UAVs, n tethers and a load. The n UAVs are connected to the load through their own tethers to complete the coordinated transportation of the load in a certain formation. The patent application document with the publication number CN113791638A discloses a new distributed control system for lifting and transporting payloads by multiple UAVs. The system includes a response mechanism to external interference, which can identify and compensate for the interference of the system by the outside world, which can not only maintain the stability of the configuration, but also maintain a more accurate tracking effect. However, the above model is relatively complex to calculate and has low energy efficiency. It also has problems such as nonlinearity, complexity, and inaccuracy. Even through state estimation and other methods, it is still impossible to fully obtain the state information of the multi-UAV rope-based collaborative lifting system. Summary of the invention

[0004] In order to overcome the above problems, this application proposes a robust control method for collaborative transportation of a flexible constrained multi-agent system, in which the tether tension generated by the load on each agent is determined as the uncertain nonlinear term of the system, the tether tension is solved through experimental data and used as the data label value, and the parameters are trained and updated through the gradient descent method and deployed to the uncertain nonlinear term. The RBF neural network with nonlinear approximation capability is combined with a sliding mode variable structure control algorithm with good robustness, and control compensation is performed for the uncertain nonlinear term to ensure the stable transportation of the tethered multi-agent.

[0005] In order to achieve the above purpose, the technical solution adopted in this application is as follows:

[0006] A method for robust control of cooperative transportation of a flexible constrained multi-agent system, comprising:

[0007] A multi-agent system is established, and the tether tension generated by the load on each agent is regarded as the uncertain nonlinear term of the multi-agent system;

[0008] Construct RBF neural network and use it to approximate and predict uncertain nonlinear terms;

[0009] Using a multi-agent system, an experimental data set is constructed to obtain the ideal tether tension value as the data label value;

[0010] According to the data label value, the parameters in the RBF neural network are updated by the gradient descent method and deployed to the uncertain nonlinear terms;

[0011] A non-singular terminal sliding mode adaptive controller based on RBF neural network prediction based on supervised learning is designed to control and compensate for uncertain nonlinear terms.

[0012] Construct an RBF neural network and use it to approximate and predict uncertain nonlinear terms, including:

[0013] For each intelligent agent, a simple system dynamics model without load information is established. The established simple system dynamics model is expressed as:

[0014]

[0015] Where X = [x i ,y i ,z i ,φ i ,θ i ,ψ i ] T is a state variable, is the uncertain nonlinear term, is the control input variable, G(X) is the coefficient matrix of the control input, and D(t) is the coefficient matrix of the time term;

[0016] Construct an RBF neural network and use the adaptive algorithm of the RBF neural network to approximate and predict the uncertain nonlinear terms. The adaptive algorithm of the RBF neural network is expressed by the formula:

[0017]

[0018] Where i represents the i-th hidden layer neuron (i=1,2,3...M), and the output of each neuron is h i (Γ), Γ is the input characteristic state of the RBF neural network, and the radial basis function center point vector of the i-th neuron is c i =[c1 c2 c3 ... c N ] T , N is the dimension of the input vector feature, σ i is the variance, and the output vector of all neurons in the hidden layer is H(Γ)=[h1(Γ) h2(Γ) ... h M (Γ)] T , W * represents the ideal value of the network weight vector, f * is the true value of the uncertain nonlinear term, and ε is the difference between the output layer result and the true value of the objective function.

[0019] The load is connected to the multi-agent through n equal-length tethers. According to the force analysis, we can get:

[0020] m p a p =R p T (3)

[0021] Among them, a p =[a x ,a y ,a z -g] T is the acceleration of the load, the tether angle and the load information are integrated into the tension uncertainty term T caused by the tether constraint, T = [T1 T2 T3] T , exists in the uncertain nonlinear term Medium, m p is the mass test value of the load, R p is the correlation matrix. According to the spatial geometric relationship between multi-agents and loads in dynamic modeling, the specific value of the correlation matrix R can be obtained p ;

[0022] The load acceleration data a in the test data set p With m p , Rp Substituting into equation (3), the ideal tether tension value T for each set of state quantity data is calculated: * , add this value to the experimental data set to obtain the data label value that can be provided to the RBF neural network based on supervised learning.

[0023] The target loss function of the RBF neural network is as follows:

[0024]

[0025] Among them, m, N s are the number of samples and the number of hidden layer neuron nodes, the input characteristic state quantity Γ and the tension uncertainty term T, respectively, which is determined by x i and i Indicates that x (i) represents the i-th sample of the characteristic state quantity in the training set, y (i) represents the i-th sample of the tension uncertainty term in the training set;

[0026] All parameters are supervisedly trained according to the Adam algorithm to obtain the center point c i , variance σ i , network weight value vector W, bias term b i .

[0027] A non-singular terminal sliding mode adaptive controller based on RBF neural network prediction based on supervised learning is designed to control and compensate for uncertain nonlinear terms, including: input characteristic state quantity, mapping relationship between characteristic state quantity and uncertain nonlinear terms:

[0028]

[0029] in, is the corrected weight value, is the corrected bias term, f RBFNN is the estimated value of the RBF neural network regarding the uncertain nonlinear term;

[0030] The estimated value of the uncertain nonlinear term is applied to the non-singular terminal sliding mode control algorithm to obtain a non-singular terminal sliding mode adaptive controller, which is:

[0031]

[0032] Among them, β>0,η>0,p>q>0 and p,q are positive odd numbers, s is the sliding surface, and D is the upper bound of the external disturbance.

[0033] The RBF neural network consists of three layers: input layer, hidden layer and output layer. The input layer is the input feature state quantity Γ, and the output of the i-th hidden layer neuron is h i(Γ), the radial basis function center point vector of the i-th hidden layer neuron is c i =[c1 c2 c3 ... c N ] T , the output vector of all neurons in the hidden layer is H(Γ)=[h1(Γ) h2(Γ) ...h M (Γ)] T .

[0034] A cooperative transportation robust control system for a flexible constrained multi-agent system, comprising:

[0035] Multi-agent system module: establish a multi-agent system and take the tether tension generated by the load on each agent as the uncertain nonlinear term of the multi-agent system;

[0036] Construct RBF neural network module: construct RBF neural network and use RBF neural network to make approximate predictions for uncertain nonlinear terms;

[0037] Constructing the experimental data module: Using the multi-agent system, construct the experimental data set and obtain the ideal tether tension value as the data label value;

[0038] RBF neural network training module: According to the data label value, the parameters in the RBF neural network are updated through the gradient descent method and deployed to the uncertain nonlinear terms;

[0039] Control compensation module: Design a non-singular terminal sliding mode adaptive controller based on RBF neural network prediction based on supervised learning to perform control compensation for uncertain nonlinear terms.

[0040] An electronic device, comprising:

[0041] at least one processor;

[0042] and, a memory communicatively coupled to the at least one processor;

[0043] The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute a collaborative transportation robust control method for a flexible constrained multi-agent system.

[0044] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements a collaborative transportation robust control method for a flexible constrained multi-agent system.

[0045] Compared with the prior art, the beneficial effects of this application are:

[0046] (1) This application designs a novel RBF neural network control scheme for multi-agent rope-based collaborative lifting. By rationally designing sample data label values, the scheme optimizes the delay and error existing in the passive compensation of uncertain nonlinear terms by online learning.

[0047] (2) This application can ensure the stable and rapid positioning of the intelligent body, introduce the RBF neural network test data set, actively compensate for the uncertainty errors caused by modeling, and improve the robustness of the controller; through the adaptive network parameters of weight update, the neural network can be updated offline, and all hyperparameters can be supervised for learning, with good effective performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 A flow chart of the method of this application;

[0049] Figure 2 This is the structure diagram of the RBF neural network for supervised learning in this application;

[0050] Figure 3 This is the framework diagram of the Adam algorithm for this application;

[0051] Figure 4 This is the control structure diagram of the system for this application;

[0052] Figure 5 This is the flight trajectory of multiple drone tests in the embodiment of the present application;

[0053] Figure 6 This is a drone position trajectory diagram under supervised learning of the RBF neural network in the embodiment of this application;

[0054] Figure 7 This is the attitude angle of the drone under supervised learning of the RBF neural network in the embodiment of the present application. DETAILED DESCRIPTION

[0055] In order to make the purpose, technical solution and advantages of the present application more clear, the present application is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described here are only used to explain the present application and are not used to limit the present application.

[0056] like Figure 1 As shown, a cooperative transportation robust control method for a flexible constrained multi-agent system includes the following steps:

[0057] (1) Establish a multi-agent system and take the tether tension generated by the load on each agent as the uncertain nonlinear term of the multi-agent system;

[0058] (2) Design RBF network to approximate the prediction of tension uncertainty

[0059] The load is connected to the center of mass of the intelligent body through a tether, and the tether tension acts directly on the center of mass of the intelligent body. Its dynamic model can be expressed as follows:

[0060]

[0061] Where X = [x i ,y i ,z i ,φ i ,θ i ,ψ i ] T is a state variable, is the control input variable.

[0062] In this dynamic model, the tether angle and load information are integrated into the tension uncertainty term T caused by the tether constraint, which exists in the nonlinear term In the linear term It is also a dynamic time-varying continuous bounded function. RBF neural network has the ability to approximate uncertain nonlinear continuous functions, such as Figure 2 As shown in the figure, according to the motion characteristics of multi-agent collaborative lifting loads in this system, the RBF neural network adaptive algorithm is designed as follows:

[0063]

[0064] Where i represents the i-th hidden layer neuron (i=1,2,3...M), and the output of each neuron is h i (Γ), the radial basis function center point vector of the i-th neuron is c i =[c1 c2 c3 ... c N ] T , where N is the dimension of the input vector feature, σ i is the variance, which determines the smoothness of the basis function. The smaller the value, the steeper the basis function and the more sensitive it is to the data sample. The output vector of all neurons in the hidden layer is H(Γ)=[h1(Γ) h2(Γ) ... h M (Γ)] T , the network weight vector is W, W * represents its ideal value, and the true value of the uncertain nonlinear term is f * , ε represents the difference between the output layer result and the true value of the objective function.

[0065] In the input space, the RBF neural network input vector feature extraction with the tethered agent as the object is as follows:

[0066]

[0067] E=X d -X and is the state error and its first and second order derivatives,

[0068] are the desired position, velocity, and acceleration respectively.

[0069] The RBF neural network establishes the relationship between the state quantity of the input space and the predicted value of the uncertain nonlinear term:

[0070]

[0071] Where b is the bias term. To simplify the form, the dimension of H(Γ) is increased to [h1(Γ) h2(Γ) ... h M (Γ) 1] T .

[0072] According to the design of the RBF neural network mentioned above, the uncertain nonlinear term The predicted value will play a compensating role in the subsequent controller design.

[0073] (3) Designing data label values ​​using experimental data sets

[0074] Taking the coordinated lifting of loads by three UAVs as an example, it is connected to multiple UAVs through three tethers of equal length. The force analysis shows that:

[0075] m p a p =R p T (5)

[0076] where a p =[a x ,a y ,a z -g] T is the acceleration of the load, T = [T1 T2 T3] T Represents the uncertain tether tension, and the specific content of the correlation matrix is:

[0077]

[0078] In the test, the lift of each drone can be obtained by using multiple drones to coordinately lift the load in a hovering state, and thus the mass test value m of the load can be obtained. p . The load acceleration data a in the test data set p With m p , R p Substituting into equation (5), the ideal tether tension value T for each set of state quantity data can be calculated: * , adding this value to the experimental data set, we can get the label value that can be provided to the RBF neural network based on supervised learning.

[0079] (4) Design a gradient descent method to update the parameters in the RBF network

[0080] The center point, variance, weight value, etc. of the RBF neural network parameters are updated and obtained by the gradient descent method of "forward loss and reverse error" in the neural network. The target loss function of the RBF neural network is specifically designed as follows:

[0081]

[0082] Where m, N s are the number of samples and the number of hidden layer neuron nodes respectively. The neural network input feature state quantity Γ and label value T are determined by x i and i express.

[0083] Through the above objective function, the partial derivatives of the hidden layer center point and variance parameter of the RBF neural network can be obtained as follows:

[0084]

[0085] The partial derivative of the weight value connecting the hidden layer and the output layer in the network is:

[0086]

[0087] Furthermore, all parameters are supervisedly trained by offline learning of RBF neural network. The RBF neural network parameters are updated by adaptive moment estimation gradient descent method, namely Adam optimizer. The parameter update algorithm of this optimizer is as follows: Figure 1 As shown in , it designs learning rates for different network parameters by calculating the first-order moment estimate s and the second-order moment estimate r of the gradient, and each learning rate is independent of each other and has adaptive capabilities. It not only calculates the adaptive parameter learning rate based on the first-order moment mean, but also uses the second-order moment mean of the gradient (i.e., biased variance). This method of first calculating the biased moment estimate and then correcting the moment deviation estimate makes the result more accurate. Based on the Adam algorithm, substitute equations (10), (8), and (9) into Figure 3 In the Adam algorithm framework shown, the gradient can be obtained as:

[0088]

[0089] The parameter update rate is:

[0090]

[0091] According to the above algorithm, the center point c is obtained i , variance σ i , weight value W, bias term b iIt will be deployed into the control law to eliminate the control parameter sensitivity and tracking signal deviation in the control system and realize active compensation for the uncertain nonlinear term T.

[0092] (5) Design of a non-singular terminal sliding mode adaptive controller based on RBF network prediction based on supervised learning

[0093] In order to make full use of the flight data generated by the multi-agent under the tether constraint, an 18-dimensional characteristic state quantity is selected for the situation where three UAVs cooperate to lift the load. Input to the RBF neural network for supervised learning of parameters. The structure of the RBF neural network for full supervised learning is as follows: Figure 2 As shown in the figure, the test data set is input into the RBF neural network, and the network parameters are updated through the gradient descent algorithm, and finally the mapping relationship between the input characteristic state quantity and the nonlinear term tether tension is obtained:

[0094]

[0095] Since the control algorithm is universal in each control channel, taking the horizontal position x control channel as an example, the sliding surface is designed as follows:

[0096]

[0097] Where β>0, p>q>0 and p, q are positive odd numbers. The derivative of the above formula is:

[0098]

[0099] The predicted estimated value of the uncertain nonlinear term is applied to the non-singular terminal sliding mode control algorithm, and a sliding mode controller with active compensation capability is obtained:

[0100]

[0101] Where D is the upper bound of external interference: ||d||≤D, the estimated value f of the RBF neural network about the uncertain nonlinear term is obtained RBFNN Applied in the control law, it plays a role in compensating the uncertainty in the model. The system control structure is as follows Figure 4 As shown, the desired trajectory obtained in the upper layer is input into the sliding mode controller with active compensation capability, and the obtained control signal can accurately control the tethered multi-UAV dynamics model.

[0102] Example

[0103] Experimental verification of sliding mode control based on fully supervised learning RBF neural network offline

[0104] Using the network parameters obtained from the above RBF neural network training, the predicted value expression of the uncertain nonlinear term is expressed as Deployed to the controller, the test results are shown in the figure:

[0105] Figure 5 (a) is the flight trajectory of three drones in three-dimensional space. Figure 5 (b) shows the flight trajectory of the three UAVs in the XY plane. The multiple UAVs lift the suspended load to the specified height in 0-50s and are in the preparatory flight stage of the expected trajectory. They start tracking the expected circular trajectory at 50s.

[0106] Figure 6 (a) Figure 6 (b) and Figure 6 (c) is the trajectory diagram of the first aircraft in the x, y and z directions. Figure 6 (d) Figure 6 (e) and Figure 6 (f) is the trajectory diagram of the second aircraft in the x, y and z directions. Figure 6 (g) Figure 6 (h) and Figure 6 (i) is the trajectory diagram of the third aircraft in the x, y and z directions. At the starting point of the circular trajectory flight, the position state of the first and second UAVs in the y direction shows a small oscillation caused by the sudden change of the tether tension. Relying on the network parameters and the set control parameters that have been learned offline, the real-time system state quantity Γ fed back by the system, the tether tension prediction value f of the controller response is RBFNN Actively compensate for the sudden change in the uncertain tether tension, generate a new attitude angle desired command, and then pass the inner loop controller, the attitude angle presents the test results as follows Figure 7 As shown, Figure 7 (a) Figure 7 (b) and Figure 7 (c) are the rotation angle, nutation angle and precession angle of the first aircraft, Figure 7 (d) Figure 7 (e) and Figure 7 (f) are the rotation, nutation and precession angles of the second aircraft, Figure 7 (g) Figure 7 (h) and Figure 7 (i) are the rotation angle, nutation angle and precession angle of the third aircraft, Figure 7 The attitude angle changes of the first and second drones in the new control output u 1,2,3,4 Control multiple drones to fly stably. Figure 6 It can be seen that the trajectory tracking error at the starting point of the multi-UAV flight (50s moment) is eliminated within 10s, and the flight trajectory of the climate multi-UAV is smooth, indicating that the new controller parameters are more accurate, and the control efficiency and precision are higher. The experimental verification results are generally the same as the simulation results.

[0107] from Figure 7According to the test results of multi-UAV attitude angle, obvious flutter occurs when switching flight states. Since the tether is directly connected to the center of mass of the UAV, it can also be seen from the dynamic modeling that the tether tension does not produce uncertain nonlinear terms on the attitude channel of the UAV. Instead, it affects the state of the position channel, thereby changing the expected value of the attitude channel and destroying the stability of the UAV attitude. Since the position loop is quickly affected by the controller in a short period of time, the attitude angle is also controlled and stabilized synchronously, tending to a stable value of 0°.

[0108] A cooperative transportation robust control system for a flexible constrained multi-agent system, comprising:

[0109] Multi-agent system module: establish a multi-agent system and take the tether tension generated by the load on each agent as the uncertain nonlinear term of the multi-agent system;

[0110] Construct RBF neural network module: construct RBF neural network and use RBF neural network to make approximate predictions for uncertain nonlinear terms;

[0111] Constructing the experimental data module: Using the multi-agent system, construct the experimental data set and obtain the ideal tether tension value as the data label value;

[0112] RBF neural network training module: According to the data label value, the parameters in the RBF neural network are updated through the gradient descent method and deployed to the uncertain nonlinear terms;

[0113] Control compensation module: Design a non-singular terminal sliding mode adaptive controller based on RBF neural network prediction based on supervised learning to perform control compensation for uncertain nonlinear terms.

[0114] An electronic device, comprising:

[0115] at least one processor;

[0116] and, a memory communicatively coupled to the at least one processor;

[0117] The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute a collaborative transportation robust control method for a flexible constrained multi-agent system.

[0118] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements a collaborative transportation robust control method for a flexible constrained multi-agent system.

[0119] Those skilled in the art will appreciate that the above embodiments are specific embodiments for implementing the present application, and in actual applications, various changes may be made thereto in form and detail without departing from the spirit and scope of the present application.

Claims

1. A method for robust control of cooperative transportation of flexible constrained multi-agent systems, characterized in that: include: A multi-agent system is established, and the tether tension generated by the load on each agent is regarded as the uncertain nonlinear term of the multi-agent system; Construct RBF neural network and use it to approximate and predict uncertain nonlinear terms; Using a multi-agent system, an experimental data set is constructed to obtain the ideal tether tension value as the data label value; According to the data label value, the parameters in the RBF neural network are updated by the gradient descent method and deployed to the uncertain nonlinear terms; A non-singular terminal sliding mode adaptive controller based on RBF neural network prediction based on supervised learning is designed to control and compensate for uncertain nonlinear terms.

2. According to claim 1, a method for robust control of cooperative transportation of a flexible constrained multi-agent system is characterized in that: Construct an RBF neural network and use it to approximate and predict uncertain nonlinear terms, including: For each intelligent agent, a simple system dynamics model without load information is established. The established simple system dynamics model is expressed as: Where X = [x i ,y i ,z i ,φ i ,θ i ,ψ i ] T is a state variable, is the uncertain nonlinear term, is the control input variable, G(X) is the coefficient matrix of the control input, and D(t) is the coefficient matrix of the time term; Construct an RBF neural network and use the adaptive algorithm of the RBF neural network to approximate and predict the uncertain nonlinear terms. The adaptive algorithm of the RBF neural network is expressed by the formula: Where i represents the i-th hidden layer neuron (i=1,2,3...M), and the output of each neuron is h i (Γ), Γ is the input characteristic state of the RBF neural network, and the radial basis function center point vector of the i-th neuron is c i =[c1 c2c3...c N ] T , N is the dimension of the input vector feature, σ i is the variance, and the output vector of all neurons in the hidden layer is H(Γ)=[h1(Γ)h2(Γ)...h M (Γ)] T , W / represents the ideal value of the network weight vector, f / is the true value of the uncertain nonlinear term, and ε is the difference between the output layer result and the true value of the objective function.

3. According to claim 1, a method for robust control of cooperative transportation of a flexible constrained multi-agent system is characterized in that: The load is connected to the multi-agent through n equal-length tethers. According to the force analysis, we can get: m p a p =R p T (3) Among them, a p =[a x ,a y ,a z -g] T is the acceleration of the load, the tether angle and the load information are integrated into the tension uncertainty term T caused by the tether constraint, T = [T1 T2 T3] T , exists in the uncertain nonlinear term Medium, m p is the mass test value of the load, R p is the correlation matrix. According to the spatial geometric relationship between multi-agents and loads in dynamic modeling, the specific value of the correlation matrix R can be obtained p ; The load acceleration data a in the test data set p With m p , R p Substituting into equation (3), the ideal tether tension value T for each set of state quantity data is calculated: * , add this value to the experimental data set to obtain the data label value that can be provided to the RBF neural network based on supervised learning.

4. The method for coordinated transportation robust control of a flexible constrained multi-agent system according to claim 1, characterized in that: The target loss function of the RBF neural network is as follows: Among them, m, N s are the number of samples and the number of hidden layer neuron nodes, the input characteristic state quantity Γ and the tension uncertainty term T, respectively, which is determined by x i and i Indicates that x (i) represents the i-th sample of the characteristic state quantity in the training set, y (i) represents the i-th sample of the tension uncertainty term in the training set; All parameters are supervisedly trained according to the Adam algorithm to obtain the center point c i , variance σ i , network weight value vector W, bias term b i .

5. The method for coordinated transportation robust control of a flexible constrained multi-agent system according to claim 1, characterized in that: A non-singular terminal sliding mode adaptive controller based on RBF neural network prediction based on supervised learning is designed to control and compensate for uncertain nonlinear terms, including: input characteristic state quantity, mapping relationship between characteristic state quantity and uncertain nonlinear terms: in, is the corrected weight value, is the corrected bias term, f RBFNN is the estimated value of the RBF neural network regarding the uncertain nonlinear term; The estimated value of the uncertain nonlinear term is applied to the non-singular terminal sliding mode control algorithm to obtain a non-singular terminal sliding mode adaptive controller, which is: Among them, β>0,η>0,p>q>0 and p,q are positive odd numbers, s is the sliding surface, and D is the upper bound of the external disturbance.

6. The method for coordinated transportation robust control of a flexible constrained multi-agent system according to claim 2 is characterized in that: The RBF neural network consists of three layers: input layer, hidden layer and output layer. The input layer is the input feature state quantity Γ, and the output of the i-th hidden layer neuron is h i (Γ), the radial basis function center point vector of the i-th hidden layer neuron is c i =[c1 c2 c3...c N ] T , the output vector of all neurons in the hidden layer is H(Γ)=[h1(Γ)h2(Γ)...h M (Γ)] T .

7. A flexible constrained multi-agent system cooperative transportation robust control system, characterized in that: include: Multi-agent system module: establish a multi-agent system and take the tether tension generated by the load on each agent as the uncertain nonlinear term of the multi-agent system; Construct RBF neural network module: construct RBF neural network and use RBF neural network to make approximate predictions for uncertain nonlinear terms; Constructing the experimental data module: Using the multi-agent system, construct the experimental data set and obtain the ideal tether tension value as the data label value; RBF neural network training module: According to the data label value, the parameters in the RBF neural network are updated through the gradient descent method and deployed to the uncertain nonlinear terms; Control compensation module: Design a non-singular terminal sliding mode adaptive controller based on RBF neural network prediction based on supervised learning to perform control compensation for uncertain nonlinear terms.

8. An electronic device, characterized in that: include: at least one processor; and, a memory communicatively coupled to the at least one processor; In which, the memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the collaborative transportation robust control method of the flexible constrained multi-agent system as described in any one of claims 1 to 6.

9. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the method for robust control of cooperative transportation of a flexible constrained multi-agent system as described in any one of claims 1 to 6 is implemented.

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