Multi-agent system control method for manipulating flexible load through mechanical arm

Abstract

The invention discloses a mechanical arm control flexible load multi-agent system control method, and belongs to the field of mechanical arm multi-agent engineering, and the mechanical arm control flexible load multi-agent system control method comprises the steps that a mechanical arm control flexible load multi-agent system is established; establishing a system dynamics model according to the mechanical arm control flexible load multi-agent system; a system error vector is established according to the mechanical arm operation flexible load multi-agent system; and a system master controller is obtained according to the system dynamics model and the system error vector, and the system master controller is applied to control the mechanical arm control flexible load multi-agent system. According to the method, only the controller and the sensor need to be mounted at the joint, so that the cost can be greatly reduced, the energy consumption is reduced, and the problems of low trajectory control precision, slow tracking and the like caused by difficulty in controller design and uncertainty of a model in the prior art of manipulating the flexible load multi-agent system by the mechanical arm are solved; reliable control input is provided for a mechanical arm multi-agent system, a solution is provided for intensive production in a complex environment, and the method can be applied to complex network systems such as spaceflight, medical treatment and industrial sites.

Description

Technical Field

[0001] The invention discloses a control method for a multi-agent system of a mechanical arm manipulating a flexible load, and belongs to the field of mechanical arm multi-agent engineering. Background Art

[0002] Flexible structures appear in many manufacturing industries, including flexible poles, solar panels, and slender beams. These flexible structures often require manipulators to operate, which makes the operation more accurate, faster, and less lossy. In the industrial field, the connection between this kind of manipulator and flexible structure is very common. For example, in automobile manufacturing, manipulators are used to assemble flexible door panels and electronic equipment. In the aerospace field, almost all space missions require space robots to coordinate operations. For example, the assembly and replacement of equipment, the repair of damaged solar panels, etc., all require the use of manipulators to manipulate flexible solar panels. Therefore, the control research of manipulators on flexible load systems has a certain engineering application technology background.

[0003] However, the task of manipulating flexible loads by a robot is usually not completed by a single robot alone, but often requires the coordinated operation of multiple robots. It can be regarded as a multi-agent system. The multi-agent system of a robot integrates multidisciplinary technologies such as control engineering, artificial intelligence, and mechanical engineering. It represents the forefront of the development of high-tech science and technology and has important applications in industry, military and other fields. The research on the coordinated control problem of multi-agents generally includes three aspects: consistency problem, formation control problem and aggregation control problem. Among them, the consistency problem is the most popular research problem in the current research on multi-agent systems. At present, for the multi-agent system of manipulators manipulating flexible loads, each robot can be regarded as an agent. The coordinated control of the multi-intelligent system composed of multiple robots is a problem to be solved.

[0004] Since the robot arm is a kind of strong real-time system, the flexible load will produce local vibration when performing large-scale and rapid movements, affecting the operating accuracy of the system. In order to improve the working stability and control accuracy of the multi-agent system, the reinforcement learning optimal control method is considered to control it. Unlike the supervised learning method, the reinforcement learning method is to train information from the environment, which is an evaluation signal, not an error signal. The actuator is a policy structure and is proposed to be applied to the control input of the actuator. The judge strategy judges the cost caused by the actuator and records the current performance index with a numerical value. The recorded value is fed back to the actuator as feedback information for revision, and finally the cost function converges to the optimal value. For the robot arm manipulating the flexible load system, the load will change with different tasks, and its dynamic model is difficult to accurately model by traditional methods. How to use the measurable state or known model information to design a suitable controller through the system to ensure trajectory tracking while minimizing the load vibration and input torque, and ensuring the stability and working accuracy of the system is a problem to be solved. Therefore, the present invention studies the consistent tracking strategy of a multi-agent system of a robotic arm manipulating a flexible load based on a reinforcement learning method. It not only ensures that each subsystem can complete consistent tracking while minimizing the vibration of the load, but also has important theoretical significance and practical application value in reducing computational redundancy and storage space. Summary of the invention

[0005] The purpose of the present invention is to solve the problems of tracking control of a conventional robot arm manipulating a flexible load system and vibration of the flexible load, and to propose a control method for a robot arm manipulating a flexible load multi-agent system.

[0006] The problem to be solved by the present invention is achieved by the following technical solutions:

[0007] A control method for a multi-agent system of a manipulator manipulating a flexible load, comprising:

[0008] Step S10, establishing a multi-agent system for manipulating a flexible load with a robotic arm;

[0009] Step S20, establishing a system dynamics model according to the multi-agent system of manipulating flexible loads by the robot arm;

[0010] Step S30, establishing a system error vector according to the multi-agent system of manipulating a flexible load with a robot arm;

[0011] Step S40, obtaining a system master controller according to the system dynamics model and the system error vector, and applying the system master controller to control the multi-agent system of manipulating flexible loads with a robotic arm.

[0012] Preferably, the step S20 includes:

[0013] The total kinetic energy of the j-th robotic arm system is defined as:

[0014]

[0015] Where: T j is the total kinetic energy of the j-th robotic arm system, m ji is the mass of the robot arm, L jig is the mass center length, θ ji is the joint angle of the connecting rod, I ji is the moment of inertia, where i = 1, 2, 3 represents three connecting rods;

[0016] The total potential energy of the j-th robotic arm system is expressed by formula (2):

[0017]

[0018] Among them: U j is the total potential energy of the j-th robotic arm system, EI j is the stiffness coefficient of the flexible load, u j (t,r j ) represents the flexible load at position r j The elastic deformation at time t;

[0019] According to the total kinetic energy of the j-th robotic arm system and the total potential energy of the j-th robotic arm system, the system PDE-ODE model can be expressed by formula (3) as follows:

[0020]

[0021] Where: τ j is the joint torque;

[0022] The load is assumed to be an Euler beam, and the vibration of the flexible load is separated by the assumed modal method. The dynamic equation of the j-th manipulator system is obtained according to the system PDE-ODE model. The dynamic model of the j-th manipulator system is expressed by formula (4):

[0023]

[0024] Where: Q j =[θ j1 ,θ j2 ,θ j3 ,p j1 ,p j2 ,...,p jN ] T is a column vector consisting of the three joint angles and N modal functions of vibration of the robot j system, H j ∈R (N+3)×(N+3)is the system inertia matrix, P j ∈R (N+3)×(N+3) is the centrifugal force-Coriolis force term, F j ∈R (N+3)×(N+3) is the generalized rigid matrix, H j is a positive definite symmetric matrix that satisfies

[0025] Preferably, the step S30 includes:

[0026] Defining an error vector of the jth agent itself according to the multi-agent system of manipulating flexible loads with a robotic arm;

[0027] Determining a system error between the j-th agent and the k-th agent according to the error vector of the j-th agent itself;

[0028] A system error vector is determined according to the system error between the j-th intelligent agent and the k-th intelligent agent.

[0029] Preferably, the step S40 includes:

[0030] The control target performance index function of the system is established according to the system dynamics formula and is expressed by formula (5):

[0031]

[0032] Among them: A j and O j is a positive definite matrix of order N+3, Y j (t)=(Q j -Q d ) T A j (Q j -Q d )+τ j T O j τ j ≥0 is the effect function, ψ j is a constant, given an initial value of Y j (0) = 0;

[0033] The approximate error obtained by using the judgment neural network to approximate the control target performance index function of the system is:

[0034]

[0035] Define the weight estimation error of the judging neural network and use the gradient descent method to minimize the objective function. To adjust the neural network weight vector The design update rate is:

[0036]

[0037] where σ jc >0 is the learning rate of the neural network, and S jc (Z jc )∈R n is a Gaussian activation function, Z jc =e j is the input of the system;

[0038] The system tracking error is defined as:

[0039]

[0040] in The column vector is composed of is the virtual backstepping control variable, K 1j is a (N+3)×(N+3) positive definite diagonal matrix;

[0041] Define the instantaneous approximation error of the execution neural network, and obtain the system master controller according to the Lyapunov candidate function, Lyapunov function, system tracking error and the dynamic model of the j-th manipulator system:

[0042]

[0043] in: is the instantaneous approximation error of the neural network, N j =K 2j K 4j , K 4j is a (N+3)-dimensional positive definite diagonal matrix;

[0044] The system master controller is used to control the multi-agent system of manipulating flexible loads with a robotic arm.

[0045] The present invention has the following beneficial effects compared with the prior art:

[0046] The present invention provides a control method for a multi-agent system of a manipulator manipulating a flexible load. In terms of modeling of the multi-agent system of the manipulator, the present invention discretizes the multi-agent system by using a hypothetical modal method, and solves the problem of modeling mechanism caused by the infinite-dimensional characteristics of the flexible load system. In terms of tracking control of the multi-agent system of the manipulator, the present invention designs a strongly connected topological structure according to the structure of each manipulator system so that the entire manipulator system can complete consistent tracking while suppressing the vibration of the load. In terms of the control accuracy of the manipulator, the present invention considers the uncertainty of the system dynamics model caused by the load variability, and uses an execution neural network to perform approximate fitting on it, so that the system can quickly and accurately complete trajectory tracking while achieving load vibration suppression. Compared with the existing flexible structure system control method, the present invention only needs to install a controller and a sensor at the joint, so that the cost and energy consumption can be greatly reduced, and the problems of controller design difficulties and low trajectory control accuracy and slow tracking caused by model uncertainty in the prior art of the multi-agent system of manipulating a flexible load of the manipulator are solved, and reliable control input is provided for the multi-agent system of the manipulator, and solutions are provided for intensive production in complex environments, and the system can be applied to complex network systems, such as aerospace, medical, industrial sites, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a flow chart of the control method of the multi-agent system of manipulating flexible loads by a robot arm of the present invention.

[0048] Figure 2 It is a flow chart of a control method for a multi-agent system of a manipulator clamping a flexible load according to the present invention.

[0049] Figure 3 It is a flow chart of discretization of the control method of the multi-agent system of the manipulator clamping the flexible load of the present invention using the assumed modal method.

[0050] Figure 4 It is a schematic diagram of the mathematical model of the intelligent agent system of an embodiment of the control method of a multi-agent system of a robot arm clamping a flexible load of the present invention.

[0051] Figure 5 It is a three-dimensional diagram of load vibration of an embodiment of the control method of a multi-agent system of a robot arm clamping a flexible load of the present invention.

[0052] Figure 6 It is a three-dimensional diagram of load vibration of an embodiment of the control method of a multi-agent system of a robot arm clamping a flexible load of the present invention.

[0053] Figure 7 It is a three-dimensional diagram of load vibration of an embodiment of the control method of a multi-agent system of a robot arm clamping a flexible load of the present invention.

[0054] Figure 8It is a load end vibration diagram of an embodiment of a control method for a multi-agent system of a robot arm clamping a flexible load according to the present invention.

[0055] Fig. 9 It is a tracking curve diagram of joint errors of an embodiment of a control method for a multi-agent system of a robot arm holding a flexible load according to the present invention.

[0056] Fig.10 It is a tracking curve diagram of joint errors of an embodiment of a control method for a multi-agent system of a robot arm holding a flexible load according to the present invention.

[0057] Fig.11 It is a tracking curve diagram of joint errors of an embodiment of a control method for a multi-agent system of a robot arm holding a flexible load according to the present invention.

[0058] Fig.12 It is a tracking curve diagram of joint errors of an embodiment of a control method for a multi-agent system of a robot arm holding a flexible load according to the present invention.

[0059] Fig.13 It is a tracking curve diagram of joint errors of an embodiment of a control method for a multi-agent system of a robot arm holding a flexible load according to the present invention.

[0060] Fig.14 It is a tracking curve diagram of joint errors of an embodiment of a control method for a multi-agent system of a robot arm holding a flexible load according to the present invention.

[0061] Fig.15 It is a tracking curve diagram of joint errors of an embodiment of a control method for a multi-agent system of a robot arm holding a flexible load according to the present invention.

[0062] Fig.16 It is a tracking curve diagram of joint errors of an embodiment of a control method for a multi-agent system of a robot arm holding a flexible load according to the present invention.

[0063] Fig.17 It is a tracking curve diagram of joint errors of an embodiment of a control method for a multi-agent system of a robot arm holding a flexible load according to the present invention. DETAILED DESCRIPTION

[0064] The following is based on the attached Figure 1-10 The present invention is further described:

[0065] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0066] In the description of the present invention, it should be noted that the terms "center", "up", "down", "left", "right", "vertical", "horizontal", "inside", "outside", etc. indicate directions or positional relationships based on the directions or positional relationships shown in the accompanying drawings. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific direction, be constructed and operated in a specific direction. Therefore, they cannot be understood as limitations on the present invention.

[0067] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0068] like Figure 1 and 2 As shown, the first embodiment of the present invention provides a control method for a multi-agent system of a robot arm holding a flexible load based on the prior art, and the specific steps are as follows:

[0069] Step S10, establishing a multi-agent system for manipulating flexible loads with a robotic arm, the specific contents are as follows:

[0070] In order to solve the consensus tracking problem of multi-agent system, multiple robotic arms are regarded as a multi-agent system. In this invention, Θ = {Λ, G, X} is used to represent M∈Z + The communication topology between agents, where Λ={1,...M} is a set of nodes, is an edge set, X=[x jk ]∈R M×M is the adjacency matrix of multiple agents, and the edge set (k,j)∈G indicates that the jth agent can receive information from the kth agent, and j,k∈Λ. For an element in the adjacency matrix, if (k,j)∈G, then x jk =1, otherwise 0. Since it has no self-adjacency, x jj = 0. The adjacent set of the jth agent is represented by Λ j ={k|(k,j)∈G} means that the degree of the jth agent is defined as Ξ=diag[Ξ1,Ξ2,......Ξ N ], the Laplace matrix is ​​defined as Π=Ξ-X.

[0071] Assumption 1. The communication topology of the multi-agent is represented by an undirected connected graph Θ.

[0072] Assumption 2. Expected signal Q d At least one agent is available.

[0073] Define the matrix ο=diag{ο1,......ο M} to indicate whether each agent can obtain the expected signal, where j =1 indicates that the jth agent can receive the expected signal; otherwise j =0.

[0074] Assumption 1 shows that the Laplacian matrix is ​​symmetric. Assumption 2 means that the matrix ο has at least one non-zero element. Therefore, there is at least one path between the desired signal and the agent.

[0075] Step S20, a system dynamics model is established according to the multi-agent system of manipulating flexible loads by the robot arm, and the specific contents are as follows:

[0076] like Figure 3-8 As shown in the figure, each robot system consists of three rigid links and a flexible load structure. The jth (j = 1, 2, .. M) robot system is analyzed, and the dynamic equation of the system is established using the assumed modal method and Lagrange equation. The total kinetic energy T of the jth robot system j It is expressed as:

[0077]

[0078] Where m ji is the mass of the robot arm, L jig is the mass center length, θ ji is the joint angle of the connecting rod, I ji is the moment of inertia. Where i=1,2,3 represents three connecting rods. ρ j is the mass density per unit length of the flexible load, let and They represent the x-axis and y-axis positions of the second link, the third link and the center of mass of the flexible load in the reference coordinate system, respectively. j is the length of the load. The superscript “.” indicates the derivative of the variable with respect to time t. Then the total potential energy U of the j-th robot system is j It is expressed as:

[0079]

[0080] EI j is the stiffness coefficient of the flexible load, u j (t,r j ) represents the flexible load at position r j The elastic deformation at time t, hereinafter referred to as u j The superscript "'" indicates the position rj Derivative.

[0081] Using Hamilton's principle, the system PDE-ODE model can be obtained as follows:

[0082]

[0083] Where τj is the joint torque. The load is assumed to be an Euler beam, and its vibration equation is:

[0084]

[0085] The superscript “(4)” indicates u j For position variable r j Find the fourth-order partial derivative, where y j for:

[0086]

[0087] The boundary conditions are:

[0088] u j0 =0,u j0 ′=0,u jE ″=0,u jE ″′=0 (6)

[0090] where u j0 =u j (t,0),u jE =u j (t,l j ).

[0091] The assumed modal method is used to separate the variables of the vibration of the flexible load as follows:

[0092]

[0093] in is the vth-order position-dependent mode function, p jv (t) represents the v-th order time-dependent function. Since the first few low-frequency modes in elastic deformation are dominant, the first N orders are taken to discretize the infinite-dimensional mode into a finite-dimensional model. Combined with the assumed modal method and the Lagrange equation method, the dynamic equation of the j-th robotic arm system is derived as follows:

[0094]

[0095] Where Q j =[θ j1 ,θ j2 ,θ j3 ,p j1 ,p j2,...,p jN ] T is a column vector consisting of the three joint angles and N modal functions of vibration of the robot j system, H j ∈R (N+3)×(N+3) is the inertia matrix, P j ∈R (N+3)×(N+3) is the centrifugal force-Coriolis force matrix, F j ∈R (N+3)×(N+3) is a generalized rigid matrix. j is a positive definite symmetric matrix that satisfies

[0096] like Figure 5 is the three-dimensional diagram of the flexible load vibration of agent 1, Figure 6 is the three-dimensional diagram of the flexible load vibration of agent 2, Figure 7 is the three-dimensional diagram of the flexible load vibration of agent 3, Figure 8 The load end vibration curves of agents 1, 2, and 3.

[0097] Step S30, establishing a system error vector according to the multi-agent system of manipulating flexible loads by the robot arm, the specific contents are as follows:

[0098] In order to facilitate the design of the consistency tracking controller later, the error vector of the jth agent itself is defined according to the multi-agent system of the manipulator manipulating the flexible load, and the error term of the system is defined as e j =Q j -Q d represents the error vector of the jth agent itself, where Q d Represents the expected value of the robot arm.

[0099] And there is

[0100] The system error between the jth agent and the kth agent is determined according to the error vector of the jth agent itself, and the system error between the jth agent and the kth agent is defined as e jk =Q j -Q k , so far the control goal is to design a control scheme so that when t→∞, e j →0, e jk →0.

[0101] Introduce additional variables as follows:

[0102]

[0103] where matrix ο=diag{ο1,......ο M}Whether each agent can obtain the expected signal. j =1 means that the jth agent can receive the expected signal, otherwise j = 0. Definition And define E N+3 represents the N+3-order unit matrix. By defining Π, Ξ and o, we get:

[0104]

[0105] Since Φ is a positive definite symmetric matrix,

[0106] like Fig. 9 is the tracking error e of joint angle 1 of agents 1, 2, and 3 j (1) Curve, Fig.10 is the velocity error of joint angle 1 of agents 1, 2, and 3 curve, Fig.11 is the tracking error e of joint angle 2 of agents 1, 2, and 3 j (2) Curve, Fig.12 is the velocity error of joint angle 2 of agents 1, 2, and 3 curve, Fig.13 is the tracking error e of joint angle 3 of agents 1, 2, and 3 j (3) Curve, Fig.14 is the velocity error of joint angle 3 of agent 1, 2, and 3 curve, Figure 15-17 The joint errors e between agents 1, 2, and 3 are the three joint angles. 12 (i)e 23 (i), (i=1,2,3) curve.

[0107] Step S40, obtaining a system master controller according to the system dynamics model and the system error vector, and applying the system master controller to control the multi-agent system of manipulating flexible loads by a robot arm, the specific contents are as follows:

[0108] The control target performance index function of the system is established according to the system dynamics formula as follows:

[0109]

[0110] Among them A j and O j is a positive definite matrix of order N+3, Y j (t)=(Q j -Q d ) T A j (Q j-Q d )+τ j T O j τ j ≥0 is the effect function, ψ j is a constant, given an initial value of Y j (0)=0.

[0111] In order to calculate the established target performance index function, the cost function I is evaluated by using the judgment neural network. j (t) is approximated by:

[0112]

[0113] in is the ideal weight of the neural network, n is the number of neurons in the hidden layer, S jc (Z jc )∈R n is a Gaussian activation function, Z jc =e j is the input of the system, is the approximate residual of the evaluation neural network.

[0114] Since the ideal weights of the neural network are Unknown, the estimate of the cost function can be written as:

[0115]

[0116] At this point, the approximate error of the cost function is:

[0117]

[0118] Define the weight estimation error of the judging neural network as In order to judge the weights of the neural network Tracking expected weight The objective function is minimized using the gradient descent method. To adjust the neural network weight vector The design update rate is:

[0119]

[0120] where σ jc >0 is the learning rate of the neural network, and

[0121] The system tracking error is defined as:

[0122]

[0123] in The column vector is composed of is the virtual backstepping control variable, K 1j is a (N+3)×(N+3) positive definite diagonal matrix.

[0124] Selecting Lyapunov candidate functions Taking its time derivative we get:

[0125]

[0126] Where K2 = diag[K 21 ,K 22 ,...K 2M ],K 2j is a (N+3)×(N+3) positive definite diagonal matrix.

[0127] Select the Lyapunov function Where H∈R M(N+3)×M(N+3) is the inertia term H in the dynamic equation of each intelligent agent j The matrix composed of . Taking its derivative, we get:

[0128]

[0129] Substituting the kinetic model (8) and formula (16) into formula (31), we can obtain:

[0130]

[0131] Consider the dynamic model (8) where the system model parameter H is variable due to the changing operation tasks. j ,P j ,F j Unknown, so use the execution neural network to estimate the unknown information:

[0132]

[0133] Taking into account Therefore, formula (20) can be written as

[0134]

[0135] in is the actual value of the neural weight, and

[0136] The instantaneous approximation error of executing the neural network is defined as And design the function in represents the expected cost, and K 3j is a positive number. Using the function Adjust the weight vector of the neural network Therefore, the update rate of the neural network is defined as And the overall controller of the system is obtained as:

[0137]

[0138] in: is the instantaneous approximation error of the neural network, N j =K 2j K 4j , K 4j is a (N+3)-dimensional positive definite diagonal matrix;

[0139] The application system master controller controls the multi-agent system of the robotic arm manipulating the flexible load.

[0140] Although the embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and the embodiments. It can be fully applied to various fields suitable for the present invention. For those familiar with the art, additional modifications can be easily realized. Therefore, without departing from the general concept defined by the claims and equivalent scope, the present invention is not limited to the specific details and the illustrations shown and described here.

Claims

1. A control method for a multi-agent system of a manipulator manipulating a flexible load. It is characterized in that include: Step S10, establishing a multi-agent system for manipulating a flexible load with a robotic arm; Step S20, establishing a system dynamics model according to the multi-agent system of manipulating flexible loads by the robot arm; Step S30, establishing a system error vector according to the multi-agent system of manipulating a flexible load with a robot arm; Step S40, obtaining a system master controller according to the system dynamics model and the system error vector, and applying the system master controller to control the multi-agent system of manipulating flexible loads with a robotic arm.

2. According to claim 1, a control method for a multi-agent system for manipulating a flexible load with a robot arm, It is characterized in that The step S20 comprises: The total kinetic energy of the j-th robotic arm system is defined as: Where: T j is the total kinetic energy of the j-th robotic arm system, m ji is the mass of the robot arm, L jig is the mass center length, θ ji is the joint angle of the connecting rod, I ji is the moment of inertia, where i = 1, 2, 3 represents three connecting rods; The total potential energy of the j-th robotic arm system is expressed by formula (2): Among them: U j is the total potential energy of the j-th robotic arm system, EI j is the stiffness coefficient of the flexible load, u j (t,r j ) represents the flexible load at position r j The elastic deformation at time t; According to the total kinetic energy of the j-th robotic arm system and the total potential energy of the j-th robotic arm system, the system PDE-ODE model can be expressed by formula (3) as follows: Where: τ j is the joint torque; The load is assumed to be an Euler beam, and the vibration of the flexible load is separated by the assumed modal method. The dynamic equation of the j-th manipulator system is obtained according to the system PDE-ODE model. The dynamic model of the j-th manipulator system is expressed by formula (4): Where: Q j =[θ j1 ,θ j2 ,θ j3 ,p j1 ,p j2 ,...,p jN ] T is a column vector consisting of the three joint angles and N modal functions of vibration of the robot j system, H j ∈R (N+3)×(N+3) is the system inertia matrix, P j ∈R (N+3)×(N+3) is the centrifugal force-Coriolis force term, F j ∈R (N+3)×(N+3) is the generalized rigid matrix, H j is a positive definite symmetric matrix that satisfies 3. A control method for a multi-agent system for manipulating a flexible load by a robot according to claim 2, It is characterized in that The step S30 includes: Defining an error vector of the jth agent itself according to the multi-agent system of manipulating flexible loads with a robotic arm; Determining a system error between the j-th agent and the k-th agent according to the error vector of the j-th agent itself; A system error vector is determined according to the system error between the j-th intelligent agent and the k-th intelligent agent.

4. A control method for a multi-agent system for manipulating a flexible load with a robot according to claim 3, It is characterized in that The step S40 includes: The control target performance index function of the system is established according to the system dynamics formula and is expressed by formula (5): Among them: A j and O j is a positive definite matrix of order N+3, Y j (t)=(Q j -Q d ) T A j (Q j -Q d )+τ j T O j τ j ≥0 is the effect function, ψ j is a constant, given an initial value of Y j (0) = 0; The approximate error obtained by using the judgment neural network to approximate the control target performance index function of the system is: Define the weight estimation error of the judging neural network and use the gradient descent method to minimize the objective function. To adjust the neural network weight vector The design update rate is: where σ jc >0 is the learning rate of the neural network, and Sjc(Zjc)∈Rn is a Gaussian activation function, Z jc =e j is the input of the system; The system tracking error is defined as: in The column vector is composed of is the virtual backstepping control variable, K 1j is a (N+3)×(N+3) positive definite diagonal matrix; Define the instantaneous approximation error of the execution neural network, and obtain the system master controller according to the Lyapunov candidate function, Lyapunov function, system tracking error and the dynamic model of the j-th manipulator system: in: is the instantaneous approximation error of the neural network, N j =K 2j K 4j , K 4j is a (N+3)-dimensional positive definite diagonal matrix; The system master controller is used to control the multi-agent system of manipulating flexible loads with a robotic arm.

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