Cooperative control method and system for multi-link robotic arms with time-varying input delay

Abstract

The present invention provides a method and system for collaborative control of multiple single-link robotic arms with time-varying input lag, and relates to the technical field of collaborative control of multiple single-link robotic arms. The method comprises: acquiring state information of multiple single-link robotic arms and communication topological relationships of the multiple single-link robotic arms; establishing a dynamic model of the multiple single-link robotic arms, and using a radial basis function neural network to approximate unknown nonlinear terms in the dynamic model; considering the communication topological relationships of the multiple single-link robotic arms, designing a compensation signal for eliminating time lag, introducing the compensation signal into a collaborative consistency error and an error surface constructed based on a backstepping method, and combining the filter error compensation signal to construct a virtual controller and a corresponding parameter adaptation rate; designing a continuous control law based on the virtual controller and an actual controller triggered by a switching dynamic event, so that the position of a follower robotic arm can be controlled to be synchronized with the desired trajectory of a leading robotic arm under external disturbances and input time-varying lags.

Description

Technical Field

[0001] The present invention belongs to the technical field of coordinated control of multiple single-link robotic arms, and in particular, relates to a coordinated control method and system for multiple single-link robotic arms with time-varying input lag. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute the prior art that has been known to a person skilled in the art.

[0003] A robotic arm refers to a mechanical arm that operates under computer control. It has been widely used in many fields such as transportation and manufacturing. For example, in the field of industrial manufacturing, some repetitive or dangerous tasks are performed by robotic arms, which can reduce labor costs, improve productivity and production safety. Compared with special machines, robotic arms are more flexible.

[0004] A robotic arm consists of links connected by joints in a kinematic chain. The joints are usually rotational or linear (prismatic). However, a robotic manipulator should not be viewed as just a series of mechanical links. The robotic arm is a component of a complete robotic system, such as Figure 1 As shown in the figure, the robot system consists of a robot, an external power supply, a robot end tool, a computer controller and other parts. At present, the control scheme of the robot usually uses a time-triggered method to act on the controlled system through a digital controller, that is, the system will sample at a fixed period and then update the control signal at the same period. Although the sampling method with time as the period is simple, even when the system has achieved the ideal control accuracy and no longer needs to perform any control operations, the control signal will still be updated at a fixed and faster frequency, which greatly increases the waste of system resources. In addition, when the various components of the robot or the robot arms transmit information and control through the network, the network bandwidth will limit the amount of information transmitted. If there is too much information, the bandwidth will be blocked, so that some data will be lost, affecting the control accuracy.

[0005] In addition, position tracking is also a fundamental issue when applying robotic arms in the engineering field. Neural network control methods have been widely used to solve the tracking problem of traditional rigid robotic arms. Due to the limitation of information transmission speed, there is often a control input lag. If the compensation for time-varying lag is ignored in the controller design, the time-varying input lag may lead to deterioration of system performance, especially in positioning applications, which will reduce the tracking accuracy of the actuator. Summary of the invention

[0006] In order to solve the above problems, the present invention provides a collaborative control method and system for multiple single-link robotic arms with time-varying input lag, which utilizes a base neural network to approximate the unknown nonlinear terms in the dynamic model, constructs a compensation signal in the backstepping coordinate transformation, and offsets the influence of the unknown time-varying input lag; and constructs a switching dynamic event trigger mechanism to determine the time point of communication, which greatly reduces the update frequency of the controller and enables the system to obtain good control performance.

[0007] In order to achieve the above object, the present invention mainly includes the following aspects:

[0008] In a first aspect, an embodiment of the present invention provides a method for coordinated control of a multi-link robot arm with time-varying input lag, comprising:

[0009] Obtaining status information of multiple single-link robotic arms and communication topology relationships of multiple single-link robotic arms;

[0010] Under the condition of considering external disturbance and control input time lag, a dynamic model of a multi-link robot arm is established, and the unknown nonlinear terms in the dynamic model are approximated by radial basis function neural network.

[0011] Considering the communication topology of multiple single-link manipulators, a compensation signal for eliminating time delay is designed, and the compensation signal is introduced into the collaborative consistency error and error surface constructed based on the backstepping method. Combined with the filter error compensation signal, a virtual controller and the corresponding parameter adaptation rate are constructed.

[0012] Based on the virtual controller and the actual controller triggered by switching dynamic events, a continuous control law is designed to control the position of the follower robot to keep synchronization with the desired trajectory of the leader robot in the presence of external disturbances and input time-varying delays.

[0013] In a possible implementation, the dynamic model of the multi-link mechanical arm is:

[0014]

[0015]

[0016] Among them, q i , They represent the link position, velocity and acceleration of the single-link robot i, J i , Y i , M i , E i ,Ψ i , K m，i Respectively represent the parameter values ​​of the single-link robot arm i, w i , Respectively represent the motor shaft angle and speed, wd,i represents the torque disturbance, u τ,i is the control input with time lag and is used to represent the motor torque.

[0017] In a possible implementation, the dynamic model of the multi-link robot arm is converted into a state space equation, and the radial basis function neural network is used to identify the unknown uncertain nonlinear dynamics in the single-link robot arm. The state space equation is rewritten as:

[0018]

[0019]

[0020]

[0021] y i =x i,1

[0022] in, x i,1 ,x i,2 ,x i,3 represents the measurable system state, y i represents the measurable system output, They are x i,1 ,x i,2 ,x i,3 The derivative of represents the weight vector, the superscript T represents the transpose, is the basis function vector, ε i,2 , ε i,3 is the approximation error.

[0023] In a possible implementation, a directed graph is used to describe the directed communication topological relationship between multiple single-link manipulators in cooperative tracking control, specifically including: constructing a directed graph G = (V, E, A);

[0024] Where E = {(m,i)∈V×V,m≠i}, V represents a node, E represents a non-empty set of directed edges, (m,i) single-link robot i can receive the information transmitted from the single-link robot m, if the edge (m,i) exists, (m,i)∈E; A = [a i,m ] is the relevant adjacency weight matrix. If the single-link robot i can receive the communication information from the single-link robot m, a i,m =1, otherwise element a i,m =0.

[0025] In a possible implementation, the compensation signal δ generated by the auxiliary system is generated based on a given reference signal i (t) = [δ i,1,δ i,2 ,δ i,3 ] T , construct consistent tracking error, including:

[0026]

[0027]

[0028]

[0029] Among them, z i,1 ,z i,2 ,z i,3 , is the multi-manipulator consistency tracking error, y i is the output of system i, y j represents the output of neighbor robot j, y r represents the preset reference signal. If the follower robot i can receive the information sent from the leader robot, then b i = 0, otherwise b i =0, Represents the output of the dynamic surface, in order to estimate the virtual controller α i,2 ,α i,3 The derivative of , designs the following dynamic surface:

[0030]

[0031] Among them, α i,2 ,α i,3 is the virtual control signal, τ i,2 ,τ i,3 The parameters for design.

[0032] In a possible implementation manner, the adaptive rate of the relevant parameters of the virtual controller is:

[0033]

[0034]

[0035] Among them, r i，2 ,r i，3 ,ξ i，2 ,ξ i，3 , is the correction parameter, is the tracking error signal, The weights are The estimated value of They are The derivative of i (x) is a Gaussian function, They are The estimated value of .

[0036] In one possible implementation, a trigger strategy based on switching dynamic event trigger conditions and triggering dynamic parameter change laws is constructed. The trigger strategy is configured to design dynamic event trigger conditions. When the trigger conditions are met, the strategy is triggered to reduce the number of controller updates and the communication burden.

[0037] In a second aspect, an embodiment of the present invention provides a multi-single-link robotic arm collaborative control system with time-varying input lag, comprising:

[0038] An information acquisition module, used to acquire status information of multiple single-link robotic arms and communication topological relationships of multiple single-link robotic arms;

[0039] A model building module is used to build a dynamic model of a multi-link robot arm under the condition of considering external disturbance and control input time lag, and to approximate unknown nonlinear terms in the dynamic model using a radial basis neural network;

[0040] A signal compensation module is used to consider the communication topology of the multi-link manipulator, design a compensation signal for eliminating time lag, introduce the compensation signal into the collaborative consistency error and error surface constructed based on the backstepping method, and combine the filter error compensation signal to construct a virtual controller and the corresponding parameter adaptation rate;

[0041] A control module is used to design a continuous control law based on the virtual controller and the actual controller triggered by the switching dynamic event, so as to control the position of the follower robot arm to keep synchronization with the desired trajectory of the leader robot arm under the condition of external disturbance and input time-varying delay.

[0042] In a third aspect, an embodiment of the present invention provides a computer device, comprising: a processor, a memory and a bus, wherein the memory stores machine-readable instructions executable by the processor, and when the computer device is running, the processor and the memory communicate through the bus, and when the machine-readable instructions are executed by the processor, the steps of the multi-single-link robotic arm collaborative control method with time-varying input delay as described in the first aspect above are performed.

[0043] In a fourth aspect, an embodiment of the present invention provides a computer-readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the steps of the multi-single-link robotic arm collaborative control method with time-varying input delay as described in the first aspect above are executed.

[0044] One or more of the above technical solutions have the following beneficial effects:

[0045] (1) The present invention proposes a collaborative control method for a multi-link robot with time-varying input lag. Under the conditions of external interference and control input lag, a dynamic model of the multi-link robot is established, and a radial basis function neural network is used to approximate the unknown nonlinear terms in the dynamic model. Considering the communication topology of the multi-link robot, a compensation signal for eliminating the lag is designed, and the compensation signal is introduced into the collaborative consistency error and error surface constructed based on the backstepping method. In combination with the filter error compensation signal, a virtual controller and the corresponding parameter adaptation rate are constructed, which can reveal the relationship between the input lag and the consistency tracking error and improve the tracking accuracy of the actuator.

[0046] (2) By constructing a dynamic surface, the "complexity explosion" problem caused by the traditional backstepping method is solved; the dynamic surface error compensation signal is designed to reduce the error impact and improve the tracking control accuracy of the multi-manipulator; at the same time, the series-parallel estimation model is used to design the prediction error and the parameter adaptive law containing the neural network information to obtain a more accurate approximation.

[0047] (3) By constructing a novel switching dynamic event trigger mechanism, the designed dynamic rules can adjust the threshold parameters in real time, greatly reducing the number of messages sent by each single-link robot. In addition, by designing the threshold parameter Ξ i The value of can avoid the high-frequency update behavior caused by excessive controller amplitude. On the other hand, by adjusting γ i,0 ,γ i,1 ,γ i,2 and μ i,1,∞ ,μ i,2,∞ The value of can be used to transform the designed dynamic event triggering mechanism to meet the system requirements in different situations. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0049] Figure 1 It is a diagram of the components of the robotic arm system;

[0050] Figure 2 A schematic flow chart of a method for cooperatively controlling a multi-link mechanical arm with a time-varying input delay provided in the first embodiment of the present invention;

[0051] Figure 3 A schematic diagram of an actual single-link manipulator provided in the first embodiment of the present invention;

[0052] Figure 4 A directed communication topology diagram of five single-link robotic arms provided in the first embodiment of the present invention;

[0053] Figure 5 Output and reference trajectory tracking diagram of five single-link robotic arms provided in Example 1 of the present invention;

[0054] Figure 6 A curve diagram of the second variable of the five single-link robotic arms provided in the first embodiment of the present invention;

[0055] Figure 7 A curve diagram of the third variable of the five single-link robotic arms provided in the first embodiment of the present invention;

[0056] Figure 8 This is a graph showing the consistency tracking error of five single-link robotic arms provided in the first embodiment of the present invention;

[0057] Fig. 9 A control input curve diagram of a multi-link mechanical arm provided in the first embodiment of the present invention;

[0058] Fig.10 The composite neural network solution provided in the first embodiment of the present invention accurately approximates the unknown nonlinear term curve of the system;

[0059] Fig.11 This is a diagram of the triggering times of a multi-single-link robotic arm under the proposed switching dynamic event triggering mechanism provided in the first embodiment of the present invention. DETAILED DESCRIPTION

[0060] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0061] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0062] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0063] Embodiment 1

[0064] like Figure 2 As shown, this embodiment provides a method for coordinated control of multiple single-link robotic arms with time-varying input lag, which specifically includes the following steps:

[0065] S201: Acquire status information of multiple single-link robotic arms and communication topological relationships of the multiple single-link robotic arms;

[0066] S202: Under the condition of considering external disturbance and control input time lag, a dynamic model of the multi-link robot arm is established, and the unknown nonlinear terms in the dynamic model are approximated by using a radial basis function neural network;

[0067] S203: Considering the communication topology relationship of the multi-single-link manipulator, a compensation signal for eliminating time delay is designed, the compensation signal is introduced into the collaborative consistency error and error surface constructed based on the backstepping method, and a virtual controller and a corresponding adaptive rate are constructed in combination with the filter error compensation signal;

[0068] S204: Design a continuous control law based on the virtual controller and the actual controller triggered by the switching dynamic event to control the position of the follower robot arm to keep synchronization with the desired trajectory of the leader robot arm under the condition of external disturbance and input time-varying delay.

[0069] In a specific implementation, the multi-link mechanical arm targeted by this embodiment is composed of a rigid link coupled to a DC motor through a gear, and its structure is as follows: Figure 3 Taking 5 multi-link manipulators as an example, according to the Euler-Lagrange equation and Newton's second law, the dynamic model of the multi-link manipulator with external disturbance is obtained, which is expressed as follows:

[0070]

[0071]

[0072] Among them, q i , They represent the link position, velocity and acceleration of the single-link robot i, J i , Y i , M i , E i ,Ψ i , K m，i Respectively represent the parameter values ​​of the single-link robot arm i, w i , Respectively represent the motor shaft angle and speed, w d,i represents the torque disturbance, u τ,i is the control input with time lag and is used to represent the motor torque.

[0073] Let x i,1 =q i , Among them, u i is the actual control input, τ iIf there is a bounded time-varying input delay, the dynamic model can be transformed into a state-space equation in the following form:

[0074]

[0075]

[0076]

[0077] y i =x i,1

[0078] Among them, x i,1 ,x i,2 ,x i,3 Indicates the measurable system status, represents the unknown nonlinear term of the system, y i Represents a measurable system output.

[0079] As an optional implementation, a directed graph is used to describe the directed communication topology relationship between multiple single-link manipulators in cooperative tracking control, specifically:

[0080] The directed communication topology between the five multi-link manipulators can be represented by a directed graph G = (V, E, A), where V = {1, 2, 3, 4, 5} and E = {(m, i) ∈ V × V, m ≠ i} are non-empty sets of nodes and directed edges, respectively. (m, i) represents that the single-link manipulator i can receive the information transmitted from the single-link manipulator m, and if the edge (m, i) exists, that is, (m, i) ∈ E. In the directed graph G, define A = [a i,m ]∈R M×M is the relevant adjacency weight matrix. If the single-link robot arm i can receive the communication information from the single-link robot arm m, a i,m =1, otherwise element a i,m = 0. Definition is the in-degree matrix, where the in-degree of node i is Definition L=EA is the Laplacian matrix.

[0081] by Figure 4 Taking the directed communication topology of the five single-link robotic arms as an example, the virtual leader single-arm Leader is not affected by the following single-link robotic arms Followers, so a 0,i = 0. If the follower single-link robot arm i can receive the information sent from the virtual leader single arm, then a i,0 >0, otherwise a i,0= 0. The connection relationship between the virtual leader single arm and the follower single-link robot arm (hereinafter referred to as the follower single arm) is expressed as a diagonal matrix B = diag{b1, b2, ..., b i ,…,b N}, where b i =a i,0 .

[0082] Using a neural network system to approximate unknown nonlinear terms in multiple single manipulators:

[0083] The actual single-link manipulator has unknown uncertain nonlinear dynamics that are difficult to identify. In order to use less prior knowledge of the single-link manipulator to complete tracking control, a radial basis function neural network is used to identify the unknown uncertain nonlinear dynamics in the single-link manipulator.

[0084] In tight set RBF Neural Network The unknown nonlinear function g(x) can be approximated with arbitrary precision ε*>0 as follows:

[0085]

[0086] in, is the neural network input, l represents the neural network input dimension, ε(x) is the approximation error, θ * ∈R M is an ideal weight vector and can be expressed as θ=[θ1,…,θ M ] T is the weight vector, is the basis function vector, Usually choose the Gaussian function Where l represents the number of nodes in the neural network. represents the receptive domain of the basis function, ζ i Represents the width of the Gaussian function.

[0087] Based on the radial basis neural network, the state space equation of the system can be rewritten as:

[0088]

[0089]

[0090]

[0091] y i =x i,1

[0092] In this way, the approximation accuracy can be improved compared with the traditional neural network approximation method. The main reason is that the prediction error q is designed i,1 ,qi,2 ,q i,3 And the estimation signal is designed by the serial-parallel estimation model method to make full use of the information of the neural network model. The main design steps are as follows:

[0093] The prediction error is constructed as follows:

[0094]

[0095] Among them, the following series-parallel estimation model is defined

[0096]

[0097]

[0098]

[0099] Among them, λ i,1 ,λ i,2 ,λ i,3 represents suitable design parameters. Represents the weights The estimated value of .

[0100] Considering the multi-single robot communication topology, in order to eliminate the adverse effects of time delay, the following auxiliary system is designed to generate the compensation signal δ i (t) = [δ i,1 ,δ i,2 ,δ i,3 ] T :

[0101]

[0102]

[0103] Among them, p i,w >0, w=1,2,3 indicates appropriate design parameters. When the follower arm can receive the reference information transmitted by the leader arm, b i =1, otherwise, b i = 0. According to the bounded input bounded output theorem Δu i is bounded, u i (t) represents the actual design control input. If the input lag is not considered in the control, it may lead to deterioration of system performance, especially in positioning applications, which will reduce the tracking accuracy and precision of the actuator and even endanger the stability of the system.

[0104] Considering the communication topology of multiple single-link robotic arms, the error surface of consistency error and response of multiple single-link robotic arms is defined. Then, based on the backstepping method, an adaptive composite neural network control scheme is designed to reduce the tracking error and finally realize the coordination of multiple single-link robotic arms.

[0105] The consistency error and error surface of the multi-link robot are defined as:

[0106]

[0107]

[0108]

[0109] Among them, y r Represents a preset reference signal. Represents the output of the dynamic surface, in order to estimate the virtual controller α i,2 ,α i,3 The derivative of , designs the following dynamic surface, its expression is:

[0110]

[0111] Among them, α i,2 ,α i,3 For the subsequent designed virtual control signal, τ i,2 ,τ i,3 is the designed parameter. In the backstepping method, the virtual control signal is designed to make the consistency error tend to a relatively small neighborhood near 0. Since the designed control signal does not contain the control input u τ,i , so α i,2 ,α i,3 It is called virtual control signal.

[0112] In addition, in order to improve the estimation accuracy of the dynamic face virtual controller derivative, the filter error To solve this problem, the following filter error compensation signal is designed:

[0113]

[0114]

[0115]

[0116] At the same time, the consistency tracking error is combined with the filter error compensation signal to obtain the following tracking error compensation signal:

[0117]

[0118] In the backstepping framework, virtual control signals and novel neural network adaptive laws are designed:

[0119] Designing a virtual controller α i，2 ,α i，3 ,α i，4 as follows:

[0120]

[0121]

[0122]

[0123] Among them, c i，1 ,c i，2 ,c i，3 is an appropriate design parameter.

[0124] According to the system state space equation, virtual controller, auxiliary system, error surface and tracking error signal, the tracking error signal is analyzed. The derivative is:

[0125]

[0126]

[0127]

[0128] Among them, D i,2 =ε i,2 +d i,2 , D i,3 =ε i,3 , the actual controller u i =u i (t).

[0129] Design adaptive law θ i,2 ,θ i,3 as follows:

[0130]

[0131]

[0132] Among them, r i，2 ,r i，3 ,ξ i，2 ,ξ i，3 , is an appropriate correction parameter.

[0133] In order to reduce the controller update frequency and controller wear between multiple single-link robotic arms, the present invention designs an adaptive collaborative controller based on a switching dynamic event trigger mechanism:

[0134] Construct the actual controller and event triggering conditions as follows:

[0135]

[0136]

[0137]

[0138] Among them, the dynamic change law of the threshold parameter is:

[0139]

[0140]

[0141]

[0142] in, is a transitional continuous control law, and η i (0),μ i,1 (0),μ i,2 (0)∈(0,1],γ i,0 ,γ i,1 ,γ i,2 and μ i,1,∞ ,μ i,2,∞ is a designed positive constant. Definition To input the update time, i >0 is a designed normal number. Defined as the trigger error. If the trigger condition is met, the actual control signal will be updated.

[0143] Furthermore, the transition continuous control law is designed as:

[0144]

[0145] Among them, M i,0 =max{η i (t)|Ξ i |+μ i,1 (t),μ ii,2 (t)}. Further progress is easy to have

[0146] In order to analyze whether the designed virtual controller, actual controller and adaptive law can stabilize the multi-link robot arm, we select the following Lyapunov candidate function V3:

[0147]

[0148] Among them, r i，2 ,r i，3 ,ξ i,1 ,ξi，2 ,ξ i，3 is an appropriate design parameter.

[0149] Then, the actual controller u i =u i (t) can be obtained:

[0150] Derivative the selected Lyapunov candidate function V3, combined with the prediction error derivative Tracking Error Derivative and the adaptation law θ i，2 ,θ i，3 The calculation can be obtained:

[0151]

[0152] Among them, it can be calculated:

[0153]

[0154]

[0155]

[0156]

[0157]

[0158]

[0159]

[0160]

[0161] Further according to the inequality calculate,

[0162]

[0163]

[0164] in,

[0165] Integrate both sides of the equation

[0166]

[0167] in, β is a relatively small parameter. Therefore, if the L2 gain from the disturbance input to the controlled output of the closed-loop system is no greater than β, better anti-disturbance performance can be obtained.

[0168] Therefore, it can be seen that all signals of the multi-link robot system are uniformly ultimately bounded, and the final tracking error can converge to an arbitrarily small neighborhood of zero, and the stability of the system is proved.

[0169] In order to prove the feasibility, effectiveness and correctness of this example, the present invention conducts the following simulation experiments:

[0170] In this simulation experiment, for the multi-link robot system under external disturbance and limited communication bandwidth, an adaptive composite neural network collaborative controller based on the switching dynamic event trigger mechanism is designed to achieve that the operating state of each single-link robot can be consistent with the leading single-link robot, that is, each variable of the multi-link robot tends to be consistent. In addition, while achieving consistency, it not only improves the identification accuracy of unknown nonlinearities in the system, but also greatly reduces the update times and mechanical wear of the single-link robot system controller.

[0171] First, the system model parameters are given: J i =1,Y i =1,M i =0.2,E i =0.05,Ψ i =0.5,K m,i =10; the reference signal of the system is: y r (t) = sin(0.3t). The time-varying input lag function is: τ i (t) = 0.005sin(t) + 0.01; the initial value of the system state is: x 1,1 (0) = -1, x 1,2 (0)=0,x 1,3 (0) = 0, x 2,1 (0) = -0.5, x 2,2 (0)=0,x 2,3 (0) = 0, x 3,1 (0)=0,x 3,2 (0)=0,x 3,3 (0) = 0, x 4,1 (0) = 0.5, x 4,2 (0)=0,x 4,3 (0) = 0, x 5,1 (0) = 1, x 5,2 (0) = 0, x 5,3 (0) = 0; the virtual controller gain is: c i,1 =10, c i,2 =10, c i,3 =10; event triggering mechanism parameters are: η i (0) = 0.7, μ i,1 (0) = 0.8, μ i,2(0) = 0.8, γ i,0 =10,γ i,1 =0.2,γ i,2 =1.2,μ i,1,∞ =μ i,2,∞ =0.01; the parameters of the neural network adaptive law are: r i,2 =r i,3 =0.01, ξ i,2 =ξ i,3 =20,λ i,1 =λ i,2 =λ i,3 =30; dynamic surface parameters are: τ i,2 =τ i,3 =0.008; the time-varying input delay compensation system parameter is p i,1 =0.8, p i,2 =2, p i,3 =0.1.

[0172] The communication topology of the multi-link robot arm is as follows: Figure 4 As shown, the adjacency matrix of the system is obtained as:

[0173]

[0174] Combined with the attached drawings, the effectiveness of this example simulation is further illustrated:

[0175] The simulation results are as follows Figure 5-Figure 11 , Figure 5 The output trajectory and reference trajectory of the five single-link manipulators are described. It can be seen from the figure that after a very short running time, the five single-link manipulators can achieve accurate tracking of the reference signal under external disturbances and time-varying input delays; Figure 6 and Figure 7 The trajectory diagrams of the second and third variables of the five single-link manipulators are depicted, indicating that after a short period of adjustment, all state variables tend to be consistent; Figure 8 The consistent tracking error curves of five single-link manipulators are shown. It can be seen from the figure that the tracking error converges to a region with a relatively small origin, which proves the effectiveness of the strategy proposed in this invention. Fig. 9 The control input curves of the multi-link robot arm are shown; Fig.10 The proposed composite neural network scheme accurately approximates the unknown nonlinear term curve of the system. It can be seen from the figure that the designed composite neural network control scheme can effectively realize the identification of unknown nonlinearity in the multi-link robot arm and accurately describe it. Fig.11 It reflects that the proposed switching dynamic event triggering mechanism can effectively reduce the triggering times of the multi-single-link robotic arm; therefore, the simulation proves the effectiveness of the proposed control scheme.

[0176] In this example, the distributed adaptive tracking control problem is studied for a nonlinear multi-link manipulator system with time-varying input delays, unknown disturbances, and limited communication bandwidth. In order to avoid the "complexity explosion" and the error of the compensation filter, a composite neural network dynamic surface control method is adopted. Different from the compensation strategy with known or constant delay, an auxiliary compensation system is constructed to eliminate the influence of unknown and time-varying delays. In addition, an improved switching dynamic event triggering mechanism is proposed to reduce the number of controller updates and the wear of the controller. Finally, the proposed multi-link manipulator collaborative control method is verified by simulation to ensure the quality of all signals.

[0177] Embodiment 2

[0178] The embodiment of the present invention further provides a multi-single-link mechanical arm cooperative control system with time-varying input delay, comprising:

[0179] An information acquisition module, used to acquire status information of multiple single-link robotic arms and communication topological relationships of multiple single-link robotic arms;

[0180] A model building module is used to build a dynamic model of a multi-link robot arm under the condition of considering external disturbance and control input time lag, and to approximate unknown nonlinear terms in the dynamic model using a radial basis neural network;

[0181] A signal compensation module is used to consider the communication topology of the multi-link manipulator, design a compensation signal for eliminating time lag, introduce the compensation signal into the collaborative consistency error and error surface constructed based on the backstepping method, and combine the filter error compensation signal to construct a virtual controller and the corresponding parameter adaptation rate;

[0182] A control module is used to design a continuous control law based on the virtual controller and the actual controller triggered by the switching dynamic event, so as to control the position of the follower robot arm to keep synchronization with the desired trajectory of the leader robot arm under the condition of external disturbance and input time-varying delay.

[0183] The multi-single-link robotic arm collaborative control system with time-varying input lag provided in this embodiment is used to implement the aforementioned multi-single-link robotic arm collaborative control method with time-varying input lag. Therefore, the specific implementation method of the multi-single-link robotic arm collaborative control system with time-varying input lag can be seen in the embodiment section of the multi-single-link robotic arm collaborative control method with time-varying input lag in the previous text, and will not be repeated here.

[0184] Embodiment 3

[0185] The embodiment of the present invention further provides a computer device, the computer device comprising a processor, a memory and a bus. The memory stores machine-readable instructions executable by the processor. When the computer device is running, the processor communicates with the memory via the bus. When the machine-readable instructions are executed by the processor, the above-mentioned Figure 2 The steps of the method for collaborative control of multiple single-link robotic arms with time-varying input delay in the method embodiment shown in the figure, and the specific implementation method can be found in the method embodiment, which will not be repeated here.

[0186] Embodiment 4

[0187] An embodiment of the present invention also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of the multi-single-link robotic arm collaborative control method with time-varying input delay described in the above method embodiment are executed.

[0188] A person skilled in the art can understand that all or part of the processes in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a computer program, and the program can be stored in a computer-readable storage medium, and when the program is executed, it can include the processes of the embodiments of the above-mentioned methods. The storage medium can be a disk, an optical disk, a read-only memory (ROM) or a random access memory (RAM), etc.

[0189] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for cooperative control of multiple single-link manipulators with time-varying input delay, characterized in that: include: Obtaining status information of multiple single-link robotic arms and communication topology relationships of multiple single-link robotic arms; Under the condition of considering external disturbance and control input time lag, a dynamic model of a multi-link robot arm is established, and the unknown nonlinear terms in the dynamic model are approximated by radial basis function neural network. Considering the communication topology of multiple single-link manipulators, a compensation signal for eliminating time delay is designed. The compensation signal is introduced into the collaborative consistency error and error surface constructed based on the backstepping method, and combined with the filter error compensation signal, a virtual controller and the corresponding parameter adaptive law are constructed. The compensation signal for eliminating time delay is specifically: Design auxiliary systems to generate compensation signals, : in, Indicates appropriate design parameters; when the follower arm can receive the reference information transmitted by the leader arm, ,otherwise, ; According to the bounded input bounded output theorem is bounded, represents the actual design control input; Designing a continuous control law based on the virtual controller and the actual controller triggered by the switching dynamic event to control the position of the follower robot arm to keep synchronization with the desired trajectory of the leader robot arm under the condition of external disturbance and input time-varying time delay; Construct a trigger strategy based on the switching dynamic event triggering conditions and the triggering dynamic parameter change law. The trigger strategy is configured to design dynamic event triggering conditions. When the triggering conditions are met, the strategy is triggered to reduce the number of controller updates and the communication burden. Specifically: Among them, the dynamic change law of the threshold parameter is: in, is a transitional continuous control law, and , and is a designed positive constant, and is defined as To enter the update time, is a designed normal number; Defined as the trigger error, if the trigger condition is met, the actual control signal will be updated; where the transition continuous control law for: in, , .

2. The method for cooperative control of multiple single-link manipulators with time-varying input delay according to claim 1, characterized in that: The dynamic model of the multi-link mechanical arm is: in, Respectively represent single-link robotic arms i connecting rod position, velocity and acceleration, Respectively represent single-link robotic arms i Parameter value, Represent the motor shaft angle and speed respectively, represents the torque disturbance, is the control input with time lag and is used to represent the motor torque.

3. The method for cooperative control of multiple single-link manipulators with time-varying input delay as claimed in claim 2, characterized in that: The dynamic model of the multi-link manipulator is transformed into a state space equation, and the radial basis function neural network is used to identify the unknown uncertain nonlinear dynamics in the single-link manipulator. The state space equation is rewritten as: in, , Indicates the measurable system status, represents the measurable system output, They are The derivative of represents the weight vector, the superscript T represents the transpose, is the basis function vector, , is the approximation error.

4. The method for cooperative control of multiple single-link manipulators with time-varying input delay as claimed in claim 3, characterized in that: Use directed graphs to describe the directed communication topology between multiple single-link manipulators in cooperative tracking control, including: constructing directed graphs ; in, , V Represents a node, E represents a non-empty set of directed edges, ( m , i )Single-link robotic arm i Can receive from the single-link robotic arm m If the edge exist, ; is the relevant adjacency weight matrix, if the single-link robot i Can receive from the single-link robotic arm Communication information, , otherwise the element .

5. The method for cooperative control of multiple single-link manipulators with time-varying input delay as claimed in claim 4, characterized in that: Based on a given reference signal to assist the system in generating a compensation signal , construct consistent tracking error, including: in, is the multi-manipulator consistency tracking error, It is a system i The output, Representing Neighbor Robotic Arm j The output, Represents a preset reference signal. If you follow the robot i Can receive information sent from the leader robot arm, then ,otherwise , Represents the output of the dynamic surface, in order to estimate the virtual controller The derivative of , designs the following dynamic surface: ； in, is the virtual control signal, The design parameters.

6. The method for cooperative control of multiple single-link manipulators with time-varying input delay according to claim 5, characterized in that: The adaptive rate of the relevant parameters of the virtual controller is: in, is the correction parameter, is the tracking error signal, The weights are The estimated value of They are The derivative of is a Gaussian function, They are The estimated value of .

7. A multi-link robot arm cooperative control system with time-varying input delay, characterized in that: include: An information acquisition module, used to acquire status information of multiple single-link robotic arms and communication topological relationships of multiple single-link robotic arms; A model building module is used to build a dynamic model of a multi-link robot arm under the condition of considering external disturbance and control input time lag, and to approximate unknown nonlinear terms in the dynamic model using a radial basis neural network; The signal compensation module is used to consider the communication topology of the multi-link manipulator, design a compensation signal for eliminating time delay, introduce the compensation signal into the collaborative consistency error and error surface constructed based on the backstepping method, and combine the filter error compensation signal to construct a virtual controller and the corresponding parameter adaptive law. The compensation signal for eliminating time delay is specifically: Design auxiliary systems to generate compensation signals, : in, Indicates appropriate design parameters; when the follower arm can receive the reference information transmitted by the leader arm, ,otherwise, ; According to the bounded input bounded output theorem is bounded, Represents actual design control input; A control module, for designing a continuous control law based on the virtual controller and the actual controller triggered based on the switching dynamic event, so as to control the position of the follower robot arm to be synchronized with the desired trajectory of the leader robot arm under the condition of external disturbance and input time-varying time lag; Construct a trigger strategy based on the switching dynamic event triggering conditions and the triggering dynamic parameter change law. The trigger strategy is configured to design dynamic event triggering conditions. When the triggering conditions are met, the strategy is triggered to reduce the number of controller updates and the communication burden. Specifically: Among them, the dynamic change law of the threshold parameter is: in, is a transitional continuous control law, and , and is a designed positive constant, and is defined as To enter the update time, is a designed normal number; Defined as the trigger error, if the trigger condition is met, the actual control signal will be updated; where the transition continuous control law for: in, , .

8. A computer device, characterized in that: include: A processor, a memory and a bus, wherein the memory stores machine-readable instructions executable by the processor, and when the computer device is running, the processor and the memory communicate via the bus, and when the machine-readable instructions are executed by the processor, the steps of the collaborative control method of multiple single-link robotic arms with time-varying input delay as described in any one of claims 1 to 6 are performed.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the multi-single-link robotic arm collaborative control method with time-varying input delay as described in any one of claims 1 to 6 are executed.

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