Multi-arm robot neural network adaptive pulse control method and system

Abstract

The application provides a multi-single-arm manipulator neural network adaptive pulse control method and system, which comprises the following steps: S1, a dynamic model of a multi-single-arm manipulator system containing external interference is established, and graph theory knowledge describing the communication relationship between the multi-single-arm manipulator system is obtained; S2, an RBF neural network approximator is designed, a state observer and a disturbance observer are constructed; S3, a neural network adaptive pulse control algorithm is designed by using a backstepping method, and a distributed consistent controller is designed for each single-arm manipulator system; S4, the initial state of the controller is set, the control parameter is adjusted, the adaptive parameter is adjusted, and the control signal output by the controller is calculated; S5, the corresponding single-arm manipulator system is controlled according to the control signal; S6, whether the single-arm manipulator system reaches the control target is judged, if yes, the method is ended, and if not, the method is returned to S4 and is circular. The application can improve the consistency, flexibility and robustness of the multi-single-arm manipulator system.

Description

Technical Field

[0001] This invention relates to the field of artificial intelligence technology, specifically to a neural network adaptive pulse control method and system for multi-arm robotic arms. Background Technology

[0002] With the rapid development of artificial intelligence technology, the demands on the processing speed of intelligent agents in industrial production tasks are constantly increasing. However, single intelligent agents can no longer meet the ever-growing industrial needs, thus giving rise to multi-agent cooperative control technology. Against this backdrop, multi-arm robotic arms, as a powerful and versatile tool, are widely used in various modern manufacturing processes. Multi-arm robotic arms possess strong cooperative operation flexibility and a large load capacity, and can replace manual labor in performing dangerous, intensive, and highly repetitive tasks. Therefore, research on the cooperative control of multi-arm robotic arms is of great significance.

[0003] Currently, the most critical aspect of multi-agent cooperative control is the consistency control problem, which has attracted widespread attention from researchers. Consistency control of multiple single-arm manipulators aims to utilize local information to construct a controller for each "follower" single-arm manipulator, ensuring its output tracks the output signal of the single-arm manipulator identified as the "leader," thereby achieving the control objective of consistent output across multiple agents. Furthermore, consistency cooperative control of multiple single-arm manipulators can overcome the bottleneck problem of centralized control while possessing strong system flexibility and robustness. However, existing consistency cooperative control methods still have the following shortcomings:

[0004] First, during actual operation, robotic arms are frequently affected by external disturbances, leading to changes in the system's kinematic and dynamic parameters. In such cases, the previous control design may be unable to adapt to these changes, potentially resulting in reduced control performance or even system instability.

[0005] Secondly, most existing research on robot control relies on sensors, which not only increases production and maintenance costs but also makes the acquisition of robot status information dependent on the reliability of the sensors. If unmeasurable or unreliable conditions occur, it will affect the acquisition of robot status information and reduce robot stability.

[0006] Finally, in the process of modeling actual systems, accurate system dynamics models are often difficult to obtain. Although adaptive neural network methods can be used to approximate unknown nonlinear functions and solve control problems of uncertain nonlinear systems, there is still little research on how to achieve rapid approximation of unknown nonlinear functions to improve system performance. Summary of the Invention

[0007] This invention provides a neural network adaptive pulse control method for multi-arm manipulators, aiming to solve the problems of external interference, unpredictable state, and uncertain nonlinearity in existing multi-arm manipulator systems.

[0008] In a first aspect, embodiments of the present invention provide a neural network adaptive pulse control method for multiple single-arm manipulators, comprising the following steps:

[0009] S1. Establish a dynamic model of a multi-arm manipulator system with external interference, and obtain graph theory knowledge describing the communication relationship between the multi-arm manipulator systems;

[0010] S2. Design an RBF neural network approximator and construct a state observer and a disturbance observer;

[0011] S3. Use the backstepping method to design a neural network adaptive pulse control algorithm, and design a distributed consensus controller for each single-arm manipulator system.

[0012] S4. Set the initial state of the controller, adjust the control parameters, adjust the adaptive parameters, and calculate the control signal output by the controller;

[0013] S5. Control the corresponding single-arm robotic arm system according to the control signal;

[0014] S6. Determine whether the single-arm robotic arm system has achieved the control target. If yes, end; otherwise, return to S4 for a loop.

[0015] Preferably, step S1 specifically includes the following sub-steps:

[0016] Establish a dynamic model for a multi-single-arm robotic system;

[0017] Using graph theory, describe the information transmission relationships between robotic arms.

[0018] Preferably, the dynamic model of the multi-arm manipulator system is as shown in expression (1):

[0019]

[0020] Where, q i , These represent the angular position, velocity, and acceleration of the joints of a single-arm robotic hand, respectively. The moment of inertia is represented by m. i The mass of a single-arm robotic arm is represented by l. i D represents the distance between the center of mass and the center of rotation of the manipulator's joints. i Ni represents the coefficient of friction, Ni = m i gl i Let g represent the gravitational term, g represent the gravitational acceleration, and τ represent the gravitational term. iIndicates a bounded external disturbance, u i V represents the control input signal of the system, i = 1, 2, ..., n, where n represents the number of nodes;

[0021] Preset x i1 =q i and The state model of the i-th single-arm manipulator system with unknown disturbance is obtained as expression (2):

[0022]

[0023] Where, x i = [x1, x2] T Represents the state vector, y i f represents the angular position state of the i-th single-arm robotic arm. i (x i ) represents an unknown smooth nonlinearity. Indicates unknown interference terms. This indicates a control input.

[0024] Preferably, the description of the information transmission relationship between robotic arms using graph theory specifically involves:

[0025] Consider a multi-arm robotic system consisting of a single leader and n followers;

[0026] The information transmission topology of the multi-arm robotic system is assumed to be an undirected graph, typically represented by G = (V, ε, A), where V = {v1, v2, ... v}. n} represents a set of nodes, v i Let i represent the robotic arm, ε = V × V be the edge set, and A = [a ij [] is an adjacency matrix with non-negative adjacent elements; e ij =(v i v j ) represents an edge of graph G, e ij =(v i v j )∈ε if and only if there is information transfer from robot i to robot j, the element a of the adjacency matrix A ij This indicates the communication quality from robot i to robot j;

[0027] Right now Otherwise a ij =0, when a ii =0, and for an undirected graph, it specifies that a ij =a ji ; For v i The set of neighbors of graph G; define the Laplacian matrix of graph G as L = [l ijIf i ≠ j, then we have and l ij =-a ij Preset B = diag{b1, ..., b} n}, b i >0 represents the communication weight between robot i and the leader if and only if a connection exists between robot i and the leader; otherwise, b i =0, and there exists at least one follower connected to the leader, where j = 1, 2, ..., n, and n represents the number.

[0028] Preferably, in step S2, designing the RBF neural network approximator specifically includes the following steps:

[0029] The nonlinear terms in the multi-arm manipulator system are approximated by a radial basis function neural network, resulting in expression (3):

[0030] f nn (W, x) = W T φ(x)… (3)

[0031] Where x represents the input vector of the input layer, and W = [w1, w2, ..., w n ] T ∈R l Let W be the weight vector of the neural network, T denote the transpose of W, and l represent the number of nodes in the neural network. This represents the basis function vector of the neural network, and a Gaussian function is chosen as the activation function for the RBF hidden layer;

[0032]

[0033] Where, μ i and ω i These are the center and width of the Gaussian function, respectively;

[0034] Define W * To approximate the nonlinearity of the RBF neural network with optimal weights, we have:

[0035] f(x) = W* T φ(x)+∈(x)

[0036] ∈(x) represents the minimum approximation error of the neural network, and satisfies |∈(x)|≤∈ * .

[0037] Preferably, the construction of the state observer and the disturbance observer specifically includes the following sub-steps:

[0038] definition in It is for x iThe estimation is performed using the RBF neural network to determine the unknown nonlinear terms in the multi-arm manipulator system. By approximation, we obtain expression (4):

[0039]

[0040] in, To substitute the estimated value The subsequent nonlinear function, This indicates the application of RBF neural networks to... The approximation error after approximation, parameter λ i These are the adjustable parameters of the RBF neural network;

[0041] Based on expression (4), we obtain the new state model expression (5):

[0042]

[0043] in,

[0044] Then, based on the obtained new state model, a state observer is designed to reconstruct the state of the system, as shown in expression (6):

[0045]

[0046] in, For γ i The estimation is defined by the observation error e. i =[e i1 e i2 ] T ,in,

[0047] Simultaneously considering unknown disturbances in the system Nonlinear term error and neural network estimation error A composite disturbance observer is proposed to estimate the mismatch disturbance γ. i For example, expression (7):

[0048]

[0049] Define the interference estimation error Where s i =γ i -λ i x i2 ;

[0050] Thus, we obtain expression (8):

[0051]

[0052] Preferably, step S3 specifically includes the following sub-steps:

[0053] Using a backstepping recursive method and based on graph theory knowledge describing multi-arm manipulators, the system error surface is defined as expression (9):

[0054]

[0055] Where, α i This indicates a virtual controller with a design, y r For multiple single-arm robotic arms to output a consistent tracking signal, both their first and second derivatives must exist, and the following conditions must be met: C0 is a constant;

[0056] For z i1 The derivative is expressed as (10):

[0057]

[0058] By selecting the Lyapunov function, the corresponding virtual controller α i It can be designed as expression (11):

[0059]

[0060] Where, k i1 c i1 and p i1 As design parameters, taking the derivative of the selected Lyapunov function will introduce unknown nonlinear terms. Approximating it using the RBF neural network, we have expression (12):

[0061]

[0062] Then, for z i2 The derivative is expressed as (13):

[0063]

[0064] By selecting the Lyapunov function, the controller for the corresponding single-arm robot i can be designed as expression (14):

[0065]

[0066] Where, k i2 c i2 and p i2 The adjustable parameters in the controller of the single-arm manipulator i are all real numbers greater than 0; unknown nonlinear terms will be generated when differentiating the selected Lyapunov function. Approximating it using the RBF neural network, we have expression (15):

[0067]

[0068] The norm method is used to process the weight parameters of a neural network, defining... And design the corresponding parameter adaptive law as shown in expression (16):

[0069]

[0070] in, and ∈ i For parameters The adjustable parameters in the designed adaptive law are all real numbers greater than 0; considering the observation rate of the state observer, it is a neural network parameter. A pulse update law was designed to achieve fast adaptation, thereby realizing fast approximation of nonlinear terms and improving the control performance of the system. The specific form is shown in expression (17):

[0071]

[0072] Where, γ i , λ i σ i β i ρ i and r i For parameters The adjustable parameters in the designed adaptive law are all real numbers greater than 0; t k Indicates the pulse moment. Indicates parameters The dynamic changes at each pulse moment are represented in differential form;

[0073] Finally, the selected Lyapunov function is shown in expression (18):

[0074]

[0075] According to the Lyapunov function stability theory, for a multi-arm manipulator system that satisfies the initial condition V(0)≤-CV+D, the design parameter k is adjusted. i1 k i2 c i1 c i2 p i1 p i2 , ∈ i γ i , λ i σ i βi ρ i r i This can make the system uniformly eventually bounded, and limit the uniform tracking error of the system output to a certain range.

[0076] Secondly, the present invention provides a neural network adaptive pulse control system for multiple single-arm manipulators, comprising:

[0077] A dynamics module is established to build a dynamics model of a multi-arm manipulator system with external disturbances and to obtain graph theory knowledge describing the communication relationships between the multi-arm manipulator systems.

[0078] The module is used to design RBF neural network approximators, build state observers and disturbance observers;

[0079] The design module is used to design a neural network adaptive pulse control algorithm using the backstepping method, and to design a distributed consensus controller for each single-arm manipulator system.

[0080] The calculation module is used to set the initial state of the controller, adjust the control parameters, adjust the adaptive parameters, and calculate the control signal output by the controller.

[0081] The control module is used to control the corresponding single-arm robotic arm system according to the control signal;

[0082] The judgment module is used to determine whether the single-arm robotic arm system has achieved the control target. If yes, the process ends; otherwise, it returns to the calculation module for looping.

[0083] Compared with the prior art, the beneficial effects of the present invention are as follows: A dynamic model of a multi-arm manipulator system with external disturbances is established, and graph theory knowledge describing the communication relationships between the multi-arm manipulator systems is obtained; an RBF neural network approximator is designed, and a state observer and disturbance observer are constructed; a neural network adaptive impulse control algorithm is designed using the backstepping method, and a distributed consensus controller is designed for each arm manipulator system; the initial state of the controller is set, control parameters are adjusted, adaptive parameters are adjusted, and the control signal output by the controller is calculated; the corresponding arm manipulator system is controlled according to the control signal; it is determined whether the arm manipulator system has achieved the control target; if yes, the process ends; otherwise, the process returns to the adaptive parameter adjustment step and repeats. By utilizing neural networks to approximate the unknown nonlinearities of the system and adjusting the neural network weights through a designed adaptive pulse update law, the need for a precise dynamic model for the multi-arm manipulator system can be eliminated, and the rapid adaptation of neural network weights can be achieved to improve the system's transient performance. Secondly, a system state observer is designed to reconstruct the system state. Simultaneously, external disturbances are considered, enabling the designed multi-arm manipulator system control method to be applied to various more complex task environments. Furthermore, the proposed composite disturbance observer simultaneously considers neural network approximation errors and nonlinear function estimation errors, resulting in a certain degree of improvement in system performance. An adaptive backstepping recursive method is used to design a distributed controller for each manipulator to consistently track the leader's trajectory. The proposed control method is highly flexible and exhibits good robustness. Attached Figure Description

[0084] The present invention will now be described in detail with reference to the accompanying drawings. The above and other aspects of the present invention will become clearer and more readily understood through the detailed description following the accompanying drawings. In the drawings:

[0085] Figure 1 This is a flowchart of the neural network adaptive pulse control method for multi-arm manipulators provided in the embodiments of the present invention;

[0086] Figure 2 This is a schematic diagram of the consistency controller design provided in an embodiment of the present invention;

[0087] Figure 3 This is a schematic diagram of the topological relationship of the single-arm manipulator provided in an embodiment of the present invention;

[0088] Figure 4 The four outputs of the single-arm robotic arm provided in this embodiment of the invention are... i Tracking the output of the single-arm robotic arm y r Renderings;

[0089] Figure 5This is a schematic diagram of the tracking error of the follower provided in an embodiment of the present invention;

[0090] Figure 6 The observation error e of the single-arm robotic arm system provided in this embodiment of the invention is... i1 A schematic diagram;

[0091] Figure 7 The observation error e of the single-arm robotic arm system provided in this embodiment of the invention is... i2 A schematic diagram;

[0092] Figure 8 The control input u of the follower provided in this embodiment of the invention. i A schematic diagram;

[0093] Figure 9 This is a comparison of the simulation results of the neural network adaptive impulse control method provided in this embodiment of the invention with existing neural network adaptive control methods. Figure 1 ;

[0094] Figure 10 This is a comparison of the simulation results of the neural network adaptive impulse control method provided in this embodiment of the invention with existing neural network adaptive control methods. Figure 2 ;

[0095] Figure 11 This is a block diagram of the neural network adaptive pulse control system for multi-arm robotic arms provided in an embodiment of the present invention. Detailed Implementation

[0096] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0097] Example 1

[0098] Combined with appendix Figures 1-10 As shown, this embodiment of the invention provides a neural network adaptive pulse control method for multiple single-arm manipulators, comprising the following steps:

[0099] S1. Establish a dynamic model of a multi-arm manipulator system with external interference, and obtain graph theory knowledge describing the communication relationships between the multi-arm manipulator systems.

[0100] Specifically, the dynamic model of the multi-arm manipulator is obtained, and based on its physical characteristics, it is transformed into the state dynamic model required for analysis and design. Graph theory knowledge is also established to describe the information transmission relationship between the multi-arm manipulators.

[0101] S2. Design an RBF neural network approximator and construct a state observer and a disturbance observer.

[0102] Specifically, based on the obtained state dynamics model, a neural network is designed to approximate the unknown nonlinearities of the system. Simultaneously, a state observer and a disturbance observer are designed to compensate for and eliminate the effects of unmeasurable state variables and unknown external disturbances.

[0103] S3. Using the backstepping method, design a neural network adaptive pulse control algorithm and design a distributed consistent controller for each single-arm robotic arm system.

[0104] Specifically, an observer-based neural network adaptive impulse control algorithm for a multi-arm manipulator is proposed, and the stability of the entire closed-loop control system is proven using Lyapunov stability theory. A simulation example is then performed using the MATLAB platform (mathematical modeling software) to verify the output consistency of the multi-arm manipulator system.

[0105] S4. Set the initial state of the controller, adjust the control parameters, adjust the adaptive parameters, and calculate the control signal output by the controller.

[0106] S5. Control the corresponding single-arm robotic arm system according to the control signal.

[0107] S6. Determine whether the single-arm robotic arm system has achieved the control target. If yes, end; otherwise, return to S4 for a loop.

[0108] Specifically, a dynamic model of a multi-arm manipulator system with external disturbances is established, and graph theory knowledge describing the communication relationships between the multi-arm manipulator systems is obtained. An RBF neural network approximator is designed, and a state observer and disturbance observer are constructed. A neural network adaptive impulse control algorithm is designed using the backstepping method, and a distributed consensus controller is designed for each arm manipulator system. The initial state of the controller is set, the control parameters are adjusted, the adaptive parameters are adjusted, and the control signal output by the controller is calculated. The corresponding arm manipulator system is controlled according to the control signal. It is determined whether the arm manipulator system has achieved the control target. If yes, the process ends; otherwise, the process returns to the adaptive parameter adjustment step and repeats. By utilizing neural networks to approximate the unknown nonlinearities of the system and adjusting the neural network weights through a designed adaptive pulse update law, the need for a precise dynamic model for the multi-arm manipulator system can be eliminated, and the rapid adaptation of neural network weights can be achieved to improve the system's transient performance. Secondly, a system state observer is designed to reconstruct the system state. Simultaneously, external disturbances are considered, enabling the designed multi-arm manipulator system control method to be applied to various more complex task environments. Furthermore, the proposed composite disturbance observer simultaneously considers neural network approximation errors and nonlinear function estimation errors, resulting in a certain degree of improvement in system performance. An adaptive backstepping recursive method is used to design a distributed controller for each manipulator to consistently track the leader's trajectory. The proposed control method is highly flexible and exhibits good robustness.

[0109] In this embodiment, step S1 specifically includes the following sub-steps:

[0110] Establish a dynamic model for a multi-single-arm robotic system.

[0111] Using graph theory, describe the information transmission relationships between robotic arms.

[0112] In this embodiment, the dynamic model of the multi-arm manipulator system is as shown in expression (1):

[0113]

[0114] Where, q i , These represent the angular position, velocity, and acceleration of the joints of a single-arm robotic hand, respectively. The moment of inertia, m i The mass of a single-arm robotic arm is represented by l. i D represents the distance between the center of mass and the center of rotation of the manipulator's joints. i N represents the coefficient of friction. i =m i gl i Let g represent the gravitational term, g represent the gravitational acceleration, and τ represent the gravitational term.i Indicates a bounded external disturbance, u i V represents the control input signal of the system, i = 1, 2, ..., n, where n represents the number of nodes;

[0115] Preset x i1 =q i and The state model of the i-th single-arm manipulator system with unknown disturbance is obtained as expression (2):

[0116]

[0117] Where, x i = [x1, x2] T Represents the state vector, y i f represents the angular position state of the i-th single-arm robotic arm. i (x i ) represents an unknown smooth nonlinearity. Indicates unknown interference terms. This indicates a control input.

[0118] In this embodiment, the description of information transmission relationships between robotic arms using graph theory specifically involves:

[0119] Consider a multi-arm robotic system consisting of a single leader and n followers;

[0120] The information transmission topology of the multi-arm robotic system is assumed to be an undirected graph, typically represented by G = (V, ε, A), where V = {v1, v2, ... v}. n} represents a set of nodes, v i Let i represent the robotic arm, ε = V × V be the edge set, and A = [a ij [] is an adjacency matrix with non-negative adjacent elements; e ij =(v i v j ) represents an edge of graph G. eij =(v i v j )∈ε if and only if there is information transfer from robot i to robot j, the element a of the adjacency matrix A ij This indicates the communication quality from robot i to robot j;

[0121] Right now Otherwise a ij =0, when a ii =0, and for an undirected graph, it specifies that a ij =a ji ; For v i The set of neighbors of graph G; define the Laplacian matrix of graph G as L = [lij If i ≠ j, then we have and l ij =-a ij Preset B = diag{b1, ..., b} n}, b i >0 represents the communication weight between robot i and the leader if and only if a connection exists between robot i and the leader; otherwise, b i =0, and there exists at least one follower connected to the leader, where j = 1, 2, ..., n, and n represents the number.

[0122] In this embodiment, step S2, designing the RBF neural network approximator, specifically includes the following steps:

[0123] The nonlinear terms in the multi-arm manipulator system are approximated by a radial basis function neural network, resulting in expression (3):

[0124] f nn (W, x) = W T φ(x)… (3)

[0125] Where x represents the input vector of the input layer, and W = [w1, w2, ..., w n ] T ∈R l Let W be the weight vector of the neural network, T denote the transpose of W, and l represent the number of nodes in the neural network. This represents the basis function vector of the neural network, and a Gaussian function is chosen as the activation function for the RBF hidden layer;

[0126]

[0127] Where, μ i and ω i These are the center and width of the Gaussian function, respectively;

[0128] Define W * To approximate the nonlinearity of the RBF neural network with optimal weights, we have:

[0129] f(x) = W* T φ(x)+∈(x)

[0130] ∈(x) represents the minimum approximation error of the neural network, and satisfies |∈(x)|≤∈ * .

[0131] In this embodiment, the construction of the state observer and the disturbance observer specifically includes the following sub-steps:

[0132] definition in It is for xi The estimation is performed using the RBF neural network to determine the unknown nonlinear terms in the multi-arm manipulator system. By approximation, we obtain expression (4):

[0133]

[0134] in, To substitute the estimated value The subsequent nonlinear function, This indicates the application of RBF neural networks to... The approximation error after approximation, parameter λ i These are the adjustable parameters of the RBF neural network;

[0135] Based on expression (4), we obtain the new state model expression (5):

[0136]

[0137] in,

[0138] Then, based on the obtained new state model, a state observer is designed to reconstruct the state of the system, as shown in expression (6):

[0139]

[0140] in, For γ i The estimation is defined by the observation error e. i =[e i1 e i2 ] T ,in,

[0141] Simultaneously considering unknown disturbances in the system Nonlinear term error and neural network estimation error A composite disturbance observer is proposed to estimate the mismatch disturbance γ. i For example, expression (7):

[0142]

[0143] Define the interference estimation error Where s i =γ i -λ i x i2 ;

[0144] Thus, we obtain expression (8):

[0145]

[0146] In this embodiment, to achieve consistent tracking of the leader by the follower output in the multi-arm robotic system, a distributed consensus controller based on a neural network needs to be designed for each single-arm robotic arm. A schematic diagram of the overall controller is shown below. Figure 2 As shown. Step S3 specifically includes the following sub-steps:

[0147] Using a backstepping recursive method and based on graph theory knowledge describing multi-arm manipulators, the system error surface is defined as expression (9):

[0148]

[0149] Where, α i This indicates a virtual controller with a design, y r For multiple single-arm robotic arms to output a consistent tracking signal, both their first and second derivatives must exist, and the following conditions must be met: C0 is a constant;

[0150] For z i1 The derivative is expressed as (10):

[0151]

[0152] By selecting the Lyapunov function, the corresponding virtual controller α i It can be designed as expression (11):

[0153]

[0154] Where, k i1 c i1 and p i1 As design parameters, taking the derivative of the selected Lyapunov function will introduce unknown nonlinear terms. Approximating it using the RBF neural network, we have expression (12):

[0155]

[0156] Then, for z i2 The derivative is expressed as (13):

[0157]

[0158] By selecting the Lyapunov function, the controller for the corresponding single-arm robot i can be designed as expression (14):

[0159]

[0160] Where, k i2 ci2 and p i2 The adjustable parameters in the controller of the single-arm manipulator i are all real numbers greater than 0; unknown nonlinear terms will be generated when differentiating the selected Lyapunov function. Approximating it using the RBF neural network, we have expression (15):

[0161]

[0162] The norm method is used to process the weight parameters of a neural network, defining... And design the corresponding parameter adaptive law as shown in expression (16):

[0163]

[0164] in, and ∈ i For parameters The adjustable parameters in the designed adaptive law are all real numbers greater than 0; considering the observation rate of the state observer, it is a neural network parameter. A pulse update law was designed to achieve fast adaptation, thereby realizing fast approximation of nonlinear terms and improving the control performance of the system. The specific form is shown in expression (17):

[0165]

[0166] Where, γ i , λ i σ i β i ρ i and r i For parameters The adjustable parameters in the designed adaptive law are all real numbers greater than 0; t k Indicates the pulse moment. Indicates parameters The dynamic changes at each pulse moment are represented in differential form;

[0167] Finally, the selected Lyapunov function is shown in expression (18):

[0168]

[0169] According to the Lyapunov function stability theory, for a multi-arm manipulator system that satisfies the initial condition V(0)≤-CV+D, the design parameter k is adjusted. i1 k i2 c i1 c i2 p i1 pi2 , ∈ i γ i , λ i σ i β i ρ i r i This can make the system uniformly eventually bounded, and limit the uniform tracking error of the system output to a certain range.

[0170] In this embodiment, to verify the effectiveness of the proposed multi-arm manipulator consistency control algorithm, the following simulation verification is performed:

[0171] First, consider a multi-arm robotic system with 4 followers (denoted as 1, 2, 3, 4) and 1 leader (denoted as 0). The topological relationship between the single-arm robotic arms is as follows: Figure 3 As shown.

[0172] Wherein, the communication weight matrix between the leader and followers is B = diag{1, 0, 0, 0}, and the adjacency matrix is...

[0173]

[0174] In the simulation experiment, it is assumed that the follower manipulator's joint angle position tracks the ideal trajectory y of the leader. r = sin 2t + 0.2sint. Based on the actual system, the physical parameters of the single-arm manipulator used in this simulation are: m i =1.5kg, l i =0.5m, D i =2, g=9.8m / s 2 τ1=τ2=sin(x 11 x 12 ) and τ3=τ4=1.2sin(x 11 x 12 The external disturbance to the system is x1(0) = [1, 0]. The initial state of the system is x1(0) = [1, 0]. T x2(0) = [2, 1] T x3(0) = [1, 1] T x4(0) = [0, -1] T The initial state of the designed observer is set to... The initial state of the adaptive parameters is set to The pulse time sequence is t k =0.01k (k = 1, 2, 3…). k in the observer i1 =10, k i2 =300, λ i =2, c in the controlleri1 =100, c i2 =100, p in the adaptive law i1 =1, p i2 =1、 ∈ i =0.1, γ i =160, σ i =0.06, β i =8、ρ i =1, r i =0.8.

[0175] Relying on m a tl a Platform b, using the consistency control algorithm proposed in this invention, simulates the above-mentioned multi-arm robotic system, obtaining simulation results. Figure 4-10 .in, Figure 4 For the output y of 4 following single-arm robotic arms i Tracking the output of the single-arm robotic arm y r The diagram shows that i = 1, 2, 3, 4, indicating that the follower output can consistently track the leader's output trajectory. Figure 5 This diagram illustrates the tracking error of the follower, showing that the tracking error can be controlled within a certain range. Figure 6 and Figure 7 The observation errors e of the single-arm robotic arm system are respectively represented by e. i1 and e i2 It can be seen that the state observer designed in this invention has good observation performance; Figure 8 control input u for the follower i The schematic diagram ensures that each system achieves its control objectives; Figure 9 and Figure 10 The simulation results of the proposed neural network adaptive pulse control method are compared with those of existing neural network adaptive control methods. The results show that the adaptive pulse update law proposed in this invention has a fast adaptability and can achieve rapid estimation of neural network weight parameters, thereby improving the system's state observation rate and further improving the system's control performance.

[0176] Example 2

[0177] like Figure 11 As shown, the present invention provides a neural network adaptive pulse control system 200 for multiple single-arm robotic arms, comprising:

[0178] A dynamics module 201 is established to build a dynamics model of a multi-arm manipulator system with external disturbances and to obtain graph theory knowledge describing the communication relationships between the multi-arm manipulator systems.

[0179] Module 202 is used to design an RBF neural network approximator and build a state observer and a disturbance observer.

[0180] Design module 203 is used to design a neural network adaptive pulse control algorithm using the backstepping method, and to design a distributed consensus controller for each single-arm manipulator system.

[0181] The calculation module 204 is used to set the initial state of the controller, adjust the control parameters, adjust the adaptive parameters, and calculate the control signal output by the controller.

[0182] Control module 205 is used to control the corresponding single-arm robotic arm system according to the control signal;

[0183] The judgment module 206 is used to determine whether the single-arm robotic arm system has achieved the control target. If yes, the process ends; otherwise, it returns to the calculation module for looping.

[0184] Specifically, by using a neural network to approximate the unknown nonlinearity of the system and adjusting the neural network weights through a designed adaptive pulse update law, the need for a precise dynamic model for the multi-arm manipulator system can be eliminated, and the rapid adaptation of the neural network weights can be achieved to improve the transient performance of the system. Secondly, a system state observer is designed to reconstruct the system state. Simultaneously, external disturbances are considered, enabling the designed multi-arm manipulator system control method to be applied to various more complex task environments. Furthermore, the proposed composite disturbance observer considers both the neural network approximation error and the nonlinear function estimation error, resulting in a certain degree of improvement in system performance. Through an adaptive backstepping recursive method, a distributed controller is designed for each manipulator to consistently track the leader's trajectory. The proposed control method is highly flexible and has good robustness.

[0185] The multi-arm manipulator neural network adaptive pulse control system 200 can implement the steps in the multi-arm manipulator neural network adaptive pulse control method in the above embodiments, and can achieve the same technical effect. Refer to the description in the above embodiments, which will not be repeated here.

[0186] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0187] The embodiments of the present invention have been described above with reference to the accompanying drawings. The disclosed embodiments are merely preferred embodiments of the present invention. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many equivalent changes in form without departing from the spirit and scope of the claims of the present invention, and all such changes are within the protection scope of the present invention.

Claims

1. A neural network adaptive pulse control method for multi-arm robotic arms, characterized in that, Includes the following steps: S1. Establish a dynamic model of a multi-arm manipulator system with external interference, and obtain graph theory knowledge describing the communication relationship between the multi-arm manipulator systems; S1 specifically includes the following sub-steps: Establish a dynamic model for a multi-single-arm robotic system; Using graph theory to describe the information transmission relationships between robotic arms; S2. Design an RBF neural network approximator and construct a state observer and a disturbance observer; S3. Use the backstepping method to design a neural network adaptive pulse control algorithm, and design a distributed consensus controller for each single-arm manipulator system. S4. Set the initial state of the controller, adjust the control parameters, adjust the adaptive parameters, and calculate the control signal output by the controller; S5. Control the corresponding single-arm robotic arm system according to the control signal; S6. Determine whether the single-arm robotic arm system has achieved the control target. If yes, end; otherwise, return to S4 and loop. The specific method of using graph theory to describe the information transmission relationships between robotic arms is as follows: Consider a system with a single leader and A multi-arm robotic arm system with one follower; The information transmission topology of the presupposed multi-arm robotic system is an undirected graph, typically using... It means that among them } represents a set of nodes. Indicates robotic arm , It is an edge set, and It is an adjacency matrix with non-negative adjacent elements; Representation diagram The edge, If and only if there exists a source from the robotic arm To robotic arm Information transmission, adjacency matrix elements Indicates from the robotic arm To robotic arm Communication quality; Right now ,otherwise ,when And for undirected graphs, it stipulates ; for Neighbor set; Define graph The Laplace matrix is ,if Then there is and Preset , It is a robotic arm The communication weight between the leader and the robotic arm is determined if and only if the robotic arm... There must be a connection between the leader and the leader, otherwise And there exists at least one follower connected to the leader, where j = 1, 2, ..., n, and n represents the number; S3 specifically includes the following sub-steps: Using a backstepping recursive method and based on graph theory knowledge describing multi-arm manipulators, the system error surface is defined as expression (9): …（9） in, This indicates a virtual controller with a design. For multiple single-arm robotic arms to output a consistent tracking signal, both their first and second derivatives must exist, and the following conditions must be met: , It is a constant; right The derivative has the expression (10): …（10）； in, Indicates observation error; By selecting the Lyapunov function, the corresponding virtual controller It can be designed as expression (11): … （11） in, , and As design parameters, taking the derivative of the selected Lyapunov function will introduce unknown nonlinear terms. If we approximate it using the RBF neural network, we have expression (12): …（12） Then, to The derivative has the expression (13): …（13） in, Represents the parameters of the neural network. Represents the moment of inertia. This indicates the mass of a single-arm robotic arm. This represents the distance between the center of mass and the center of rotation of the robot's joints. This indicates a bounded external disturbance. Indicates the system's control input signal. i =1,2,…n, where n represents the number; Indicates unknown interference terms. This represents the control input; by selecting a Lyapunov function, the corresponding single-arm robotic arm... The controller can be designed as expression (14): … （14） in, , and For single-arm robotic arm The adjustable parameters in the controller are all real numbers greater than 0; an unknown nonlinear term will be generated when differentiating the selected Lyapunov function. If we approximate it using the RBF neural network, we have expression (15): …（15） The norm method is used to process the weight parameters of a neural network, defining... And design the corresponding parameter adaptive law as shown in expression (16): …（16） in, and For parameters The adjustable parameters in the designed adaptive law are all real numbers greater than 0; considering the observation rate of the state observer, it is a neural network parameter. A pulse update law was designed to achieve fast adaptation, thereby realizing fast approximation of nonlinear terms and improving the control performance of the system. The specific form is shown in expression (17): …（17） in, , , , , and For neural networks ; Indicates the pulse moment. , Representing neural network parameters The dynamic changes at the pulse moment are represented in the form of differences. Finally, the selected Lyapunov function is shown in expression (18): …（18） According to Lyapunov function stability theory, for functions that satisfy the initial conditions... Multi-arm robotic system, adjusting design parameters , , , , , , , , , , , , , , This can make the system uniformly eventually bounded, and limit the uniform tracking error of the system output to a certain range.

2. The neural network adaptive pulse control method for multi-arm robotic arms as described in claim 1, characterized in that, The dynamic model of the multi-single-arm manipulator system is shown in expression (1): …（1） in, , , These represent the angular position, velocity, and acceleration of the joints of a single-arm robotic hand, respectively. Indicates the coefficient of friction. Represents the gravity term. Represents gravitational acceleration. V Represents a set of nodes; Preset and , obtained the The state model of a single-arm robotic arm system with unknown disturbances is expressed as expression (2): …（2） in, Represents the state vector. Indicates the first The angular position of a single-arm robotic arm Then, this represents the state vector of the i-th single-arm robotic arm; It represents an unknown smooth nonlinearity.

3. The neural network adaptive pulse control method for multi-arm robotic arms as described in claim 1, characterized in that, In step S2, the design of the RBF neural network approximator specifically includes the following steps: The nonlinear terms in the multi-arm manipulator system are approximated by a radial basis function neural network, resulting in expression (3): …（3） in, This represents the input vector of the input layer. For the neural network weight vector, T express W transpose, This represents the number of nodes in the neural network. This represents the basis function vector of the neural network, and a Gaussian function is chosen as the activation function for the RBF hidden layer; in, and These are the center and width of the Gaussian function, respectively; definition To approximate the nonlinearity of the RBF neural network with optimal weights, we have: This represents the minimum approximation error of the neural network, and satisfies... .

4. The neural network adaptive pulse control method for multi-arm robotic arms as described in claim 3, characterized in that, The construction of the state observer and the disturbance observer specifically includes the following sub-steps: definition ,in Yes The estimation is performed using the RBF neural network to determine the unknown nonlinear terms in the multi-arm manipulator system. By approximation, we obtain expression (4): …（4） in, To substitute the estimated value The subsequent nonlinear function, This indicates the application of RBF neural networks to... Approximation error after approximation, parameters These are the adjustable parameters of the RBF neural network; Based on expression (4), we obtain the new state model expression (5): …（5） in, ; Then, based on the obtained new state model, a state observer is designed to reconstruct the state of the system, as shown in expression (6): …（6） in, for The estimation, defining the observation error in, ; Simultaneously considering unknown disturbances in the system Nonlinear term error and neural network estimation error A composite disturbance observer is proposed to estimate mismatched disturbances. For example, expression (7): …（7） Define the interference estimation error ,in ; Thus, we obtain expression (8): …（8）。 5. A neural network adaptive pulse control system for multiple single-arm robotic arms, characterized in that, include: A dynamics module is established to build a dynamics model of a multi-arm manipulator system with external disturbances and to obtain graph theory knowledge describing the communication relationships between the multi-arm manipulator systems. The aforementioned dynamics module is also used to establish a dynamics model for a multi-arm robotic system. Using graph theory to describe the information transmission relationships between robotic arms; The module is used to design RBF neural network approximators, build state observers and disturbance observers; The design module is used to design a neural network adaptive pulse control algorithm using the backstepping method, and to design a distributed consensus controller for each single-arm manipulator system. The calculation module is used to set the initial state of the controller, adjust the control parameters, adjust the adaptive parameters, and calculate the control signal output by the controller. The control module is used to control the corresponding single-arm robotic arm system according to the control signal; The judgment module is used to determine whether the single-arm robotic arm system has achieved the control target. If yes, the process ends; otherwise, it returns to the calculation module for looping. The specific method of using graph theory to describe the information transmission relationships between robotic arms is as follows: Consider a system with a single leader and A multi-arm robotic arm system with one follower; The information transmission topology of the presupposed multi-arm robotic system is an undirected graph, typically using... It means that among them } represents a set of nodes. Indicates robotic arm , It is an edge set, and It is an adjacency matrix with non-negative adjacent elements; Representation diagram The edge, If and only if there exists a source from the robotic arm To robotic arm Information transmission, adjacency matrix elements Indicates from the robotic arm To robotic arm Communication quality; Right now ,otherwise ,when And for undirected graphs, it stipulates ; for Neighbor set; Define graph The Laplace matrix is ,if Then there is and Preset , It is a robotic arm The communication weight between the leader and the robotic arm is determined if and only if the robotic arm... There must be a connection between the leader and the leader, otherwise And there exists at least one follower connected to the leader, where j = 1, 2, ..., n, and n represents the number; The design module is also used to define the system error surface as expression (9) using a backstepping recursive method and based on graph theory knowledge describing multi-arm manipulators: …（9） in, This indicates a virtual controller with a design. For multiple single-arm robotic arms to output a consistent tracking signal, both their first and second derivatives must exist, and the following conditions must be met: , It is a constant; right The derivative has the expression (10): …（10） in, Indicates observation error; By selecting the Lyapunov function, the corresponding virtual controller It can be designed as expression (11): … （11） in, , and As design parameters, taking the derivative of the selected Lyapunov function will introduce unknown nonlinear terms. If we approximate it using the RBF neural network, we have expression (12): …（12） Then, to The derivative has the expression (13): …（13） in, Representing neural network parameters Represents the moment of inertia. This indicates the mass of a single-arm robotic arm. This represents the distance between the center of mass and the center of rotation of the robot's joints. This indicates a bounded external disturbance. Indicates the system's control input signal. i =1,2,…n, where n represents the number; Indicates unknown interference terms. This represents the control input; by selecting a Lyapunov function, the corresponding single-arm robotic arm... The controller can be designed as expression (14): … （14） in, , and For single-arm robotic arm The adjustable parameters in the controller are all real numbers greater than 0; an unknown nonlinear term will be generated when differentiating the selected Lyapunov function. If we approximate it using the RBF neural network, we have expression (15): …（15） The norm method is used to process the weight parameters of a neural network, defining... And design the corresponding parameter adaptive law as shown in expression (16): …（16） in, and For parameters The adjustable parameters in the designed adaptive law are all real numbers greater than 0; considering the observation rate of the state observer, it is a neural network parameter. A pulse update law was designed to achieve fast adaptation, thereby realizing fast approximation of nonlinear terms and improving the control performance of the system. The specific form is shown in expression (17): …（17） in, , , , , and For neural networks ; Indicates the pulse moment. , Representing neural network parameters The dynamic changes at the pulse moment are represented in differential form; finally, the selected Lyapunov function is shown in expression (18): …（18） According to Lyapunov function stability theory, for functions that satisfy the initial conditions... Multi-arm robotic system, adjusting design parameters , , , , , , , , , , , , , , This can make the system uniformly eventually bounded, and limit the uniform tracking error of the system output to a certain range.

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