Adaptive neural network flexible joint robot arm tracking control method and device

Abstract

The application provides a flexible joint robot arm tracking control method and device based on an adaptive neural network, and relates to the technical field of robot intelligent control. The method comprises the following steps: establishing a robot kinematics model, defining a trajectory tracking error, and designing a control input based on the robot kinematics model; adopting a neural network compensation model to compensate for model uncertainty, and adopting a disturbance observer to estimate unknown disturbance, so as to obtain an adaptive bounded neural network control based on state feedback; building a robot system platform to verify the feasibility and effectiveness of the method, and defining a Lyapunov function to prove the stability of the closed-loop system. The application constructs an adaptive bounded neural network controller, which can estimate the uncertainty in the model parameters and adjust the controller gain to adapt to the actuator limit, so as to ensure the effective trajectory tracking of the system. Subsequently, in order to further enhance the stability and robustness of the system, the application also designs a disturbance observer to estimate and compensate for unknown external disturbance.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of robot intelligent control, in particular to a flexible joint robot arm tracking control method and device based on self-adaptive neural network. BACKGROUND

[0002] In the field of robot research, trajectory tracking has always been one of the core topics of robotic arm research, and its application is widely covered in medical care, precision manufacturing, education research, home service, and aerospace and other important fields. Traditional rigid robotic arms have excellent repeatability and high precision, and play an important role in industrial production tasks, especially in production environments with extremely high precision requirements. These robotic arms are structurally robust, and the installation and maintenance process is relatively simple, so they are widely used in high-repetition work scenarios. However, the rigidity of rigid robotic arms is insufficient, and once a collision occurs with a person, it may cause serious injury to the person. In contrast, flexible joint robotic arms, with their excellent flexibility and adaptability, can work efficiently in complex or unpredictable environments, flexibly adapting to different task requirements and environmental changes. Its design allows effective absorption and dispersion of impact force during task execution, thereby significantly reducing the risk of injury to personnel and equipment. In addition, the lightweight design of flexible joint robotic arms not only reduces energy consumption, but also improves operating speed and response capability. However, the control of flexible joint robotic arms is more difficult, with complex dynamic characteristics, nonlinearity and strong coupling characteristics, which brings great challenges to the design of the controller. Therefore, it is particularly important to design an effective control algorithm for flexible joint robotic arms. In this context, self-adaptive neural networks provide a new solution for robotic arm trajectory tracking. Many researchers at home and abroad widely use control algorithms based on self-adaptive neural networks in the study of robotic arm trajectory tracking, enabling robotic arms to achieve accurate trajectory tracking in various complex environments. This method greatly improves the trajectory tracking performance of robotic arms in complex environments, providing a wider space for the application of robotic arms in more fields.

[0003] Under ideal conditions, traditional control methods, due to their simple structure, ease of implementation and low computational cost, are suitable for scenarios with low precision requirements and small environmental changes, and can provide high stability. However, these methods are strongly dependent on the system model, making it difficult to adapt to system parameter changes and external disturbances, resulting in limited precision and flexibility in complex, nonlinear systems, making it difficult to meet the needs of high-precision trajectory tracking and dynamic environmental adaptation. Self-adaptive neural network control methods, through their powerful learning ability and adaptability, can automatically optimize control strategies to adapt to system parameter changes and external disturbances, thereby achieving high-precision trajectory tracking. It not only improves stability and reliability, but also can learn and adjust control strategies in real time in dynamic environments, exhibiting stronger flexibility and robustness, and is particularly suitable for complex tasks and high-precision application scenarios. SUMMARY

[0004] In order to solve the technical problems that the prior art has strong dependence on system model, it is difficult to adapt to system parameter changes and external disturbances, resulting in limited precision and flexibility in complex and nonlinear systems, and it is difficult to meet the needs of high-precision trajectory tracking and dynamic environment adaptation, the embodiments of the present application provide a flexible joint robot arm tracking control method and device based on adaptive neural network. The technical solution is as follows:

[0005] In one aspect, a flexible joint robot arm tracking control method based on adaptive neural network is provided, the method is realized by a flexible joint robot arm tracking control device, and the method comprises:

[0006] S1, a robot kinematics model is established.

[0007] S2, based on the robot kinematics model, a trajectory tracking error is defined, and a control input based on the robot kinematics model is designed according to the tracking error.

[0008] S3, a neural network compensation model is used to compensate for model uncertainty, and an interference observer is used to estimate unknown disturbances in the control input, to obtain an adaptive bounded neural network control based on state feedback.

[0009] S4, a robot system platform is built to verify the feasibility and effectiveness of the adaptive bounded neural network control method based on state feedback, and a Lyapunov function is defined to prove the stability of the closed-loop system of the adaptive bounded neural network based on state feedback.

[0010] Optionally, the robot kinematics model in S1 is as shown in the following formula (1):

[0011]

[0012] In the formula, D(γ)∈R n×n represents a positive definite mass inertia matrix, R represents a real number, n represents a dimension, γ∈R n represents a joint position vector, represents the acceleration of the joint position, represents the Coriolis and centrifugal matrix, represents the velocity of the joint position, O(γ)∈R n represents gravity, τ∈R n represents a control input vector, τ d represents unknown disturbances.

[0013] Optionally, the trajectory tracking error in S2 is as shown in the following formula (2):

[0014]

[0015] wherein,

[0016]

[0017] In the formula, e1 represents the first tracking error, γ1 represents the actual joint position vector, and γ d Let represent the ideal joint position vector, e2 represent the second tracking error, γ2 represent the actual joint velocity vector, α represent the virtual controller, and H = [(k1lncosh(e...]. 11 )) / tanh(e 11 )],…[(k n lncosh(e 1n )) / tanh(e 1n ) T ∈R n T denotes matrix transpose, and K = diag[k1, ..., k] n ]∈R n×n R represents a real number, and n represents the dimension. This represents the ideal joint velocity vector.

[0018] Optionally, the control input based on the robot's kinematics model in S2 is as shown in equation (4):

[0019]

[0020] in,

[0021]

[0022]

[0023] In the formula, τ=[τ1,…,τ n ] T ∈R n Let K1 represent the control input vector, R represent real numbers, n represent the dimension, T represent matrix transpose, e1 represent the first tracking error, and K1 = diag[k 11 , ...k 1n ]∈R n×n Let e2 be a positive definite matrix, e2 be the second tracking error, and A be the process variable. τ represents an auxiliary variable. d To represent unknown interference, θ i Represents the switching function. and Let O represent negative and positive constants, P represent the Coriolis and centrifugal matrices, α represent the virtual controller, and D represent the positive definite mass inertia matrix. This represents the derivative of the virtual controller.

[0024] Optionally, the neural network compensation model in S3 is adopted to compensate the uncertainty, as shown in the following equation (7):

[0025]

[0026] where w * represents the desired weight vector, R represents a real number, n represents the dimension, T represents the matrix transpose, e1 represents the first tracking error, γ1 represents the actual joint position vector, γ d represents the ideal joint position vector, e2 represents the second tracking error, γ2 represents the actual joint velocity vector, R(z) represents the radial basis function, represents the auxiliary variable, and ε(z) represents the approximation error.

[0027] Optionally, the state feedback based adaptive bounded neural network control in S3 is as shown in the following equation (8):

[0028]

[0029] where τ = [τ1, …, τ n] T ∈R n represents the control input vector, R represents a real number, n represents the dimension, T represents the matrix transpose, e1 represents the first tracking error, K1 = diag[k 11 , … k 1n ] ∈R n×n represents a positive definite matrix, e2 represents the second tracking error, A represents the process variable, represents the auxiliary variable, represents the disturbance observer, represents the estimated value of the auxiliary variable, represents the estimated value of the weight, R(z) represents the radial basis function, represents the update rate of the estimated value of the weight, Γ i (i = 1, 2, … n) represents a positive definite matrix, e 2i represents the second tracking error of joint i, σ represents a small normal number, represents the estimated value of the weight of joint i.

[0030] Optionally, the definition of Lyapunov function in S4 includes:

[0031] The first Lyapunov function is defined to prove that the trajectory tracking error can converge to a small range, as shown in the following equation (9):

[0032]

[0033] wherein V1 represents a first Lyapunov function, n represents a dimension, e 1i represents a first tracking error of joint i, e2 represents a second tracking error, T represents a matrix transpose, and D represents a positive definite mass inertia matrix.

[0034] A second Lyapunov function is defined for proving the stability of the closed-loop system of the adaptive bounded neural network based on state feedback, as shown in the following formula (10):

[0035]

[0036] wherein V2 represents a second Lyapunov function, represents an error of weight, and Γ i represents a positive definite matrix, and χ2 represents a constant, represents an error of disturbance.

[0037] On the other hand, an adaptive neural network flexible joint robot arm tracking control device is provided, which is applied to the adaptive neural network flexible joint robot arm tracking control method, and the device comprises:

[0038] A building module is configured to build a robot kinematics model.

[0039] A design module is configured to define a trajectory tracking error based on the robot kinematics model, and to design a control input based on the robot kinematics model according to the tracking error.

[0040] A control module is configured to compensate for the uncertainty of the neural network model, to estimate unknown disturbances in the control input by using a disturbance observer, and to obtain an adaptive bounded neural network control based on state feedback.

[0041] A proof module is configured to build a robot system platform to verify the feasibility and effectiveness of the adaptive bounded neural network control based on state feedback, and to define a Lyapunov function to prove the stability of the closed-loop system of the adaptive bounded neural network based on state feedback.

[0042] Optionally, the robot kinematics model is as shown in the following formula (1):

[0043]

[0044] wherein D(γ)∈R n×n represents a positive definite mass inertia matrix, R represents a real number, n represents a dimension, and γ∈R n represents a joint position vector, represents an acceleration of joint position, represents a Coriolis and centrifugal matrix, The velocity representing the joint position, O(γ)∈R n Represents gravity, τ∈R n τ represents the control input vector. d This indicates unknown interference.

[0045] Optionally, the trajectory tracking error is as shown in equation (2):

[0046]

[0047] in,

[0048]

[0049] In the formula, e1 represents the first tracking error, γ1 represents the actual joint position vector, and γ d Let represent the ideal joint position vector, e2 represent the second tracking error, γ2 represent the actual joint velocity vector, α represent the virtual controller, and H = [(k1lncosh(e...]. 11 )) / tanh(e 11 )],…[(k n lncosh(e 1n )) / tanh(e 1n )] T ∈R n T denotes matrix transpose, and K = diag[k1, ..., k] n ]∈R n×n R represents a real number, and n represents the dimension. This represents the ideal joint velocity vector.

[0050] Optionally, the control input based on the robot's kinematic model is as shown in equation (4):

[0051]

[0052] in,

[0053]

[0054]

[0055] In the formula, τ=[τ1,…,τ n ] T ∈R n Let K1 represent the control input vector, R represent real numbers, n represent the dimension, T represent matrix transpose, e1 represent the first tracking error, and K1 = diag[k 11 , ...k 1n ]∈R n×n Let e2 be a positive definite matrix, e2 be the second tracking error, and A be the process variable. denotes an auxiliary variable, τ d denotes an unknown disturbance, θ i denotes a switching function, and denote negative and positive constants, respectively, O denotes the gravity, P denotes the Coriolis and centrifugal matrices, a denotes a virtual controller, D denotes a positive definite mass inertia matrix, denotes the derivative of the virtual controller.

[0056] Optionally, a neural network compensation model is employed to compensate for model uncertainties, as shown in equation (7) below:

[0057]

[0058] where w * denotes a desired weight vector, R denotes a real number, n denotes a dimension, T denotes a matrix transpose, e1 denotes a first tracking error, γ1 denotes an actual joint position vector, γ d denotes an ideal joint position vector, e2 denotes a second tracking error, γ2 denotes an actual joint velocity vector, R(z) denotes a radial basis function, denotes an auxiliary variable, ε(z) denotes an approximation error.

[0059] Optionally, a state feedback based adaptive bounded neural network control is employed, as shown in equation (8) below:

[0060]

[0061] where τ = [τ1,..., τ n ] T ∈ R n denotes a control input vector, R denotes a real number, n denotes a dimension, T denotes a matrix transpose, e1 denotes a first tracking error, K1 = diag[k 11 ,... k 1n ] ∈ R n×n denotes a positive definite matrix, e2 denotes a second tracking error, A denotes a process variable, denotes an auxiliary variable, denotes a disturbance observer, denotes an estimate of the auxiliary variable, denotes an estimate of the weight, R(z) denotes a radial basis function, denotes an update rate of the estimate of the weight, Γ i (i = 1, 2,... n) denotes a positive definite matrix, e 2i denotes a second tracking error of joint i, σ denotes a small positive number, denotes an estimate of the weight of joint i.

[0062] Optionally, the proving module is further configured to:

[0063] A first Lyapunov function is defined to prove that the trajectory tracking error can converge to a small range, as shown in the following formula (9):

[0064]

[0065] In the formula, V1 represents the first Lyapunov function, n represents the dimension, e 1i represents the first tracking error of joint i, e2 represents the second tracking error, T represents the matrix transpose, and D represents the positive mass inertia matrix.

[0066] A second Lyapunov function is defined to prove the stability of the closed-loop system of the adaptive bounded neural network based on state feedback, as shown in the following formula (10):

[0067]

[0068] In the formula, V2 represents the second Lyapunov function, represents the error of the weight, and Γ i (i = 1, 2,..., n) represents a positive definite matrix, and χ2 represents a constant, represents the error of the disturbance.

[0069] On the other hand, a flexible joint robot arm tracking control device is provided, which comprises a processor and a memory, wherein the memory stores computer readable instructions, and the computer readable instructions are executed by the processor to implement any one of the adaptive neural network flexible joint robot arm tracking control methods described above.

[0070] On the other hand, a computer readable storage medium is provided, wherein the storage medium stores at least one instruction, and the at least one instruction is loaded and executed by a processor to implement any one of the adaptive neural network flexible joint robot arm tracking control methods described above.

[0071] The technical solutions provided by the embodiments of the present application have at least the following beneficial effects:

[0072] In the present application, an adaptive neural network controller is designed to estimate the uncertainty of the model parameters, the boundary of which is known and can adapt to the constraints of the actuator.

[0073] The present application introduces a hyperbolic tangent function (tanh) to realize a bounded control signal, which avoids the adverse effects of input saturation by designing an auxiliary system to offset the input saturation, thereby simplifying the design process of the controller.

[0074] The present application considers an interference observer to estimate external interference, which significantly improves the robustness and stability of the system.

[0075] The robot system platform based on ROS realizes real-time monitoring and control of the joint state of the robot through efficient communication mechanism and hardware and software integration, has strong perception, decision and execution ability, and can efficiently complete tasks in a complex environment.

[0076] The present application proves the stability of the closed-loop system by defining Lyapunov function, and ensures efficient and stable control of the system by optimizing design parameters. BRIEF DESCRIPTION OF DRAWINGS

[0077] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0078] Figure 1 It is a flow chart of a flexible joint robot arm tracking control method based on an adaptive bounded neural network provided by the embodiment of the present application.

[0079] Figure 2 It is a schematic diagram of the simulation platform connected with the computer IP provided by the embodiment of the present application.

[0080] Figure 3 It is a schematic diagram of the start Gazebo simulation command provided by the embodiment of the present application.

[0081] Figure 4 It is a simulation interface diagram provided by the embodiment of the present application.

[0082] Figure 5 It is a robot enabling command diagram provided by the embodiment of the present application.

[0083] Figure 6 It is a trajectory tracking curve diagram of joint 1 provided by the embodiment of the present application.

[0084] Figure 7 It is an error curve diagram of joint 1 provided by the embodiment of the present application.

[0085] Figure 8 It is a trajectory tracking curve of joint 2 provided by the embodiment of the present application.

[0086] Figure 9 It is an error curve of joint 2 provided by the embodiment of the present application.

[0087] Figure 10A flexible joint robot arm tracking control device block diagram based on an adaptive bounded neural network is provided in the embodiment of the present application.

[0088] Figure 11 A flexible joint robot arm tracking control device structure schematic diagram is provided in the embodiment of the present application. DETAILED DESCRIPTION

[0089] The technical solutions in the present application will be described below with reference to the drawings.

[0090] In the embodiments of the present application, the words such as "example", "for example" and the like are used to represent as an example, illustration or description. Any embodiment or design scheme described as "example" in the present application should not be interpreted as more preferred or more advantageous than other embodiments or design schemes. Rather, the word "example" is intended to present the concept in a specific manner. In addition, in the embodiments of the present application, the meaning expressed by "and / or" can be both, or can be one of the two.

[0091] In the embodiments of the present application, "image" and "picture" can be used interchangeably at times, and it should be pointed out that the meanings expressed are consistent when the distinction is not emphasized. "Of", "corresponding" and "corresponding" can be used interchangeably at times, and it should be pointed out that the meanings expressed are consistent when the distinction is not emphasized.

[0092] In the embodiments of the present application, sometimes the subscript such as W1 can be written in the form of non-subscript such as W1, and the meanings expressed are consistent when the distinction is not emphasized.

[0093] In order to make the technical problems, technical solutions and advantages to be solved by the present application more clear, the following will be described in detail with reference to the drawings and specific embodiments.

[0094] The present application provides a flexible joint robot arm tracking control method of an adaptive neural network, which can be realized by a flexible joint robot arm tracking control device, which can be a terminal or a server. As shown in the flexible joint robot arm tracking control method flow chart of the adaptive neural network, the processing flow of the method can include the following steps: Figure 1

[0095] S1, a robot kinematics model is established.

[0096] In a feasible implementation manner, the D-H method is a standard method for establishing a robot kinematics model. Considering an n-link RMFJ model as:

[0097] ​

[0098] where D(γ) ∈ R n×n D (or abbreviated as D) represents a positive definite mass inertia matrix, R represents a real number, n represents a dimension, and γ ∈ R n represents a joint position vector, represents an acceleration of the joint position, P (or abbreviated as P) represents a Coriolis and centrifugal matrix, represents a velocity of the joint position, O(γ) ∈ R n O (or abbreviated as O) represents gravity, τ ∈ R n represents a control input vector, and satisfies where, respectively represent upper and lower bounds of

[0099] S2, based on a robot kinematics model, defining a trajectory tracking error, and designing a control input based on the robot kinematics model according to the tracking error.

[0100] In an available implementation, the application designs a trajectory tracking control algorithm for a flexible joint robot under full state feedback conditions. An adaptive bounded neural network is used to compensate for inherent uncertainties in the system, and a disturbance observer is introduced to enhance the robustness of the system, ensuring stable performance in the presence of external disturbances.

[0101] Specifically, the model-based control design:

[0102] Lemma 1: According to the approximation theory, if the number of nodes l is large enough and a suitable nonlinear activation function is used, then the neural network can approximate any continuous function with arbitrary precision. This approximation is represented as:

[0103]

[0104] where w * represents the desired weight vector:

[0105]

[0106] where ε(z) represents a bounded approximation error, satisfying

[0107] Lemma 2: Assuming f(μ) is an asymmetric saturation function, represented as:

[0108]

[0109] where, is the upper bound of τ, is the lower bound of τ. When or At this point, there exists a sharp corner. Therefore, a new smoothing function is introduced to approximate this saturation function:

[0110]

[0111] Here, the function L(τ) is bounded, and θ is a switching function:

[0112]

[0113] The trajectory tracking error is defined as:

[0114]

[0115] Wherein, α is a virtual controller:

[0116]

[0117] In the formula, e1 represents the first tracking error, γ1 represents the actual joint position vector, and γ d Let represent the ideal joint position vector, e2 represent the second tracking error, γ2 represent the actual joint velocity vector, α represent the virtual controller, and H = [(k1lncosh(e...]. 11 )) / tanh(e 11 )],…[(k n lncosh(e1n)) / tanh(e 1n )] T ∈R n T denotes matrix transpose, and K = diag[k1, ..., k] n ]∈R n×n It is a positive definite matrix. This represents the ideal joint velocity vector.

[0118] The derivative of the error is:

[0119]

[0120] Design a Lyapunov function as follows:

[0121]

[0122] In the formula, V1 represents the first Lyapunov function, n represents the dimension, and e 1i Let e1 represent the first tracking error of joint i, e2 represent the second tracking error, T represent the matrix transpose, and D represent the positive definite mass inertia matrix.

[0123] The derivative of V1 is as follows:

[0124]

[0125] Then, the model-based control input is:

[0126]

[0127] where,

[0128]

[0129]

[0130] where τ = [τ1,..., τN]T∈ RN n ] T ∈ R n denotes the control input vector, K1 = diag[k1,..., kN] ∈ RN 11 denotes a positive definite matrix, 1n n×n holds, θ i is a switching function:

[0131]

[0132] Thus, the equation can be rewritten as:

[0133]

[0134] Define a function According to Lemma 2, where L(τ) denotes the approximation error, and it is assumed that L(τ) has an upper bound where is an unknown positive constant. Thus,

[0135]

[0136] According to Taylor expansion, it can be known that:

[0137]

[0138] where, and within the interval , is a positive constant. According to Young's inequality, the equation can be restated as:

[0139]

[0140] Thus, it is proved that the output error can converge to a small range.

[0141] ​​S3, compensating the model uncertainty by using neural network, estimating the unknown disturbance in control input by using disturbance observer, obtaining adaptive bounded neural network control based on state feedback.

[0142] In one feasible implementation, the adaptive bounded neural network control based on state feedback is designed as:

[0143] Considering the uncertainty of parameters O, P and D, the direct application of control strategy (12) and auxiliary variable which depends on these model parameters becomes impractical. Therefore, neural network is used to approximate the value of .

[0144]

[0145] In the formula, w * represents the desired weight vector, T represents matrix transpose, e1 represents the first tracking error, γ1 represents the actual joint position vector, γ d represents the ideal joint position vector, e2 represents the second tracking error, γ2 represents the actual joint velocity vector, represents the auxiliary variable, ε(z) represents the approximation error, and satisfies is a known positive constant. In addition, a disturbance observer is used to estimate the unknown disturbance τ d . Therefore, the control input is:

[0146]

[0147] In the formula, K1=diag[k 11 , …k 1n ] ∈ R n×n is a positive definite matrix, θ is a switching function:

[0148]

[0149] wherein represents the estimated value of the weight, which is the estimation of w * , and satisfies

[0150] is a disturbance observer, which is used to approximate the unknown disturbance τ d . Its update law is defined as:

[0151]

[0152] wherein, represents the estimated value of the unknown disturbance, which is the estimation of d* According to the estimation, the satisfaction χ1 and χ2 represent a constant.

[0153] A new Lyapunov function is defined as:

[0154]

[0155] The derivative of the function is ultimately It can be proved that the designed closed-loop system is semi-global uniformly ultimately bounded.

[0156] The application designs an adaptive bounded neural network controller for estimating the uncertainty in the model parameters, the boundary of which is known and can adapt to the constraints of the actuator.

[0157] By using the hyperbolic tangent function (tanh), a bounded control signal is realized, thereby avoiding the adverse effects of input saturation by designing an auxiliary system to offset the input saturation, thereby simplifying the controller design process.

[0158] By introducing a disturbance observer to estimate external disturbances, the robustness and stability of the system are significantly enhanced.

[0159] S4, build a robot system platform to verify the feasibility and effectiveness of the adaptive bounded neural network control method based on state feedback, and define a Lyapunov function to prove the stability of the closed-loop system of the adaptive bounded neural network based on state feedback.

[0160] In a feasible implementation, a simulation experiment platform is built:

[0161] In order to verify the feasibility and effectiveness of the proposed control method, the application will compare and analyze the simulation results of the proposed control method with the simulation results of error feedback control and neural network control on a computer equipped with Ubuntu 16.04 operating system and ROS Noetic 20.04 environment in Gazebo simulation platform. In the Gazebo simulation environment, the Baxter robot is simulated, mainly involving the following steps: loading the model of the Baxter robot in Gazebo, which contains the geometric shape, joint information and physical properties of the robot; communicate with the Baxter robot through the ROS interface, you can write ROS nodes to control the joint motion of the robot, send motion instructions, and receive sensor data; start simulation, Gazebo will update the state of the robot and the dynamic changes of the environment according to the calculation results of the physical engine, you can monitor the behavior of the robot in real time through the ROS node, and adjust the control strategy as needed.

[0162] Specifically, the operation steps are as follows:

[0163] First, the device information in the baxter.sh script file is modified to ensure that the simulation platform can connect with the IP address of the computer, as shown in Figure 2 .

[0164] Next, run the environment configuration script in the command line interface of the linux system to start the simulation environment of the Baxter robot. Through the launch file, Gazebo can be started and the simulation model of the robot can be loaded, as shown in Figure 3 . The interface after successful startup is shown in Figure 4 .

[0165] Finally, in a new terminal window, execute the Baxter simulation command and robot enable instruction. After the robot is enabled, run the self-written Python code to start the simulation experiment, as shown in Figure 5 .

[0166] Further, data settings: the basic parameters are shown in Table 1, and the parameter settings of the robot are as follows:

[0167] Table 1

[0168]

[0169]

[0170]

[0171]

[0172]

[0173] wherein, s3=Q2L1L c2 ,s4=Q1L c2 +Q2L1,s5=Q2L c2 . The initial position is set as: The reference trajectory is:

[0174] 1) Error feedback control: Error Feedback Control (EFC) is a feedback control algorithm that quickly responds to errors through a proportional term and suppresses oscillations through a differential term, thereby enhancing the stability and response speed of the system. The error feedback controller is designed as follows:

[0175]

[0176] wherein, K p is the proportional gain, K d is the differential gain, and Kp = 0.8, K d = 0.15.

[0177] 2) Neural Network Control: In order to enhance the credibility of the experiment, neural networks (NN) are introduced as a control group. Neural network control has strong adaptability, learning ability, nonlinear mapping ability, robustness and fault tolerance. In addition, radial basis function (RBF) is used to compensate for system uncertainty, effectively improving the control accuracy and robustness of the system. The design of the neural network controller is as follows:

[0178]

[0179] where w represents the weight of the neural network, and R(z) represents the radial basis function. The number of nodes of the neural network is 256, the center parameter is ±1, the variance of the center is δ = 1.98, the learning rate σ = 0.001, Γ i = 0.15, χ1 = 0.005, χ2 = 1, the initial weight is (i = 1, 2,..., 256).

[0180] 3) Adaptive Bounded Neural Network Control: The adaptive bounded neural network (ABNN) controller can estimate the uncertainty in the model parameters and adjust the controller gain to adapt to the limitations of the actuator, thereby ensuring effective trajectory tracking of the system, and a disturbance observer is designed to estimate and compensate for unknown external disturbances. The design of the adaptive bounded neural network controller is as follows:

[0181]

[0182] where the adaptive bounded neural network has 256 nodes, the center parameter is ±1, the variance of the center is δ = 1.8, the learning rate σ = 0.001, Γ i = 0.15, χ1 = 0.005, χ2 = 1, K1 = diag[0.1, 0.1], the initial weight is (i = 1, 2,..., 256).

[0183] Further, the trajectory tracking simulation experiment of the robotic arm:

[0184] Figure 6 and Figure 7 represent the trajectory tracking curve and error curve of joint 1, Figure 8 and Figure 9The figure shows the trajectory tracking curve and error curve of joint 2. As shown in the figure, for joint 1, at the approach of three peak values, when t = 4.84s, the tracking error of EFC is 0.1076 rad, the tracking error of NN is 0.0021 rad, and the tracking error of ABNN is 0.0014 rad; when t = 10s, the tracking errors of the three control methods are 0.0105 rad, 0.0086 rad and 0.0049 rad respectively; when t = 16.2, the tracking errors of the three control methods are 0.0039 rad, 0.0053 rad and 0.0019 rad respectively.

[0185] Further, as shown in the figure, for joint 2, at the approach of three peak values, when t = 4s, the tracking error of EFC is 0.0046 rad, the tracking error of NN is 0.0042 rad, and the tracking error of ABNN is 0.0008 rad; when t = 10s, the tracking errors of the three control methods are 0.0120 rad, 0.0106 rad and 0.0049 rad respectively; when t = 15, the tracking errors of the three control methods are 0.0070 rad, 0.0130 rad and 0.0068 rad respectively. Thus, the tracking errors of the NN and EFC control methods are larger than that of the ABNN control method, so the algorithm of the application has good tracking performance and anti-interference ability.

[0186] The application proposes a trajectory tracking algorithm based on an adaptive bounded neural network for a flexible joint robot, and the effectiveness of the proposed control method is verified through simulation experiments on a Gazebo platform. In addition, through Lyapunov stability analysis, the semi-global asymptotic uniform boundedness of the closed-loop system is proved. The experimental results show that:

[0187] In the simulation experiment, the control algorithm proposed in the application can effectively realize trajectory tracking and has good anti-interference performance.

[0188] Compared with the EFC and NN control algorithms, the trajectory tracking effect of the algorithm proposed in the application is better.

[0189] In the embodiment of the application, an adaptive neural network controller is designed to estimate the uncertainty of the model parameters, the boundary of which is known and can adapt to the constraints of the actuator.

[0190] The application introduces a hyperbolic tangent function (tanh) to realize a bounded control signal, avoids the adverse effects of additional design auxiliary systems to offset input saturation, and thus simplifies the design process of the controller.

[0191] The application considers an interference observer to estimate external interference, which significantly improves the robustness and stability of the system.

[0192] The robot system platform based on ROS realizes real-time monitoring and control of joint states of the robot through efficient communication mechanism and software and hardware integration, has strong perception, decision and execution capabilities, and can efficiently complete tasks in complex environments.

[0193] The application proves the stability of the closed-loop system by defining a Lyapunov function, and ensures efficient and stable control of the system by optimizing the design parameters.

[0194] Figure 10 A flexible joint robot arm tracking control device for an adaptive neural network is shown in a block diagram according to an exemplary embodiment, and the device is used for a flexible joint robot arm tracking control method of an adaptive neural network. Figure 10 The device includes a building module 310, a design module 320, a control module 330 and a proving module 340.

[0195] The building module 310 is used to build a robot kinematic model.

[0196] The design module 320 is used to define a trajectory tracking error based on the robot kinematic model, and to design a control input based on the robot kinematic model according to the tracking error.

[0197] The control module 330 is used to compensate for the uncertainty of the neural network model, and to estimate unknown disturbances in the control input by using a disturbance observer, to obtain an adaptive bounded neural network control based on state feedback.

[0198] The proving module 340 is used to build a robot system platform to verify the feasibility and effectiveness of the adaptive bounded neural network control method based on state feedback, and to define a Lyapunov function to prove the stability of the closed-loop system of the adaptive bounded neural network based on state feedback.

[0199] In the embodiment of the application, an adaptive neural network controller is designed to estimate the uncertainty of the model parameters, the boundary of which is known and can adapt to the constraints of the actuator.

[0200] The application introduces a hyperbolic tangent function (tanh) to realize a bounded control signal, avoids additional design of an auxiliary system to offset the adverse effects of input saturation, and thus simplifies the design process of the controller.

[0201] The application considers a disturbance observer to estimate external disturbances, and significantly improves the robustness and stability of the system.

[0202] The robot system platform based on ROS realizes real-time monitoring and control of joint states of the robot through efficient communication mechanism and software and hardware integration, has strong perception, decision and execution capabilities, and can efficiently complete tasks in complex environments.

[0203] This invention proves the stability of a closed-loop system by defining a Lyapunov function, and ensures efficient and stable control of the system by optimizing design parameters.

[0204] Figure 11 This is a schematic diagram of the structure of a flexible joint robotic arm tracking and control device provided in an embodiment of the present invention, as shown below. Figure 11 As shown, the flexible joint robotic arm tracking and control device may include the above-mentioned Figure 10 The adaptive neural network-based flexible joint robotic arm tracking control device is shown. Optionally, the flexible joint robotic arm tracking control device 410 may include a first processor 2001.

[0205] Optionally, the flexible joint robotic arm tracking control device 410 may also include a memory 2002 and a transceiver 2003.

[0206] The first processor 2001, memory 2002, and transceiver 2003 can be connected via a communication bus.

[0207] The following is combined with Figure 11 The following is a detailed description of each component of the flexible joint robotic arm tracking and control device 410:

[0208] The first processor 2001 is the control center of the flexible joint robotic arm tracking and control device 410. It can be a single processor or a collective term for multiple processing elements. For example, the first processor 2001 can be one or more central processing units (CPUs), application-specific integrated circuits (ASICs), or one or more integrated circuits configured to implement embodiments of the present invention, such as one or more digital signal processors (DSPs), or one or more field-programmable gate arrays (FPGAs).

[0209] Optionally, the first processor 2001 can perform various functions of the flexible joint robotic arm tracking control device 410 by running or executing software programs stored in the memory 2002 and calling data stored in the memory 2002.

[0210] In a specific implementation, as one example, the first processor 2001 may include one or more CPUs, for example... Figure 11 CPU0 and CPU1 are shown in the diagram.

[0211] In a specific implementation, as one example, the flexible joint robotic arm tracking and control device 410 may also include multiple processors, such as... Figure 11 The first processor 2001 and the second processor 2004 are shown in the diagram. Each of these processors can be a single-core processor (single-CPU) or a multi-core processor (multi-CPU). Here, "processor" can refer to one or more devices, circuits, and / or processing cores used to process data (e.g., computer program instructions).

[0212] The memory 2002 is used to store the software program that executes the present invention, and is controlled by the first processor 2001 to execute it. The specific implementation method can be referred to the above method embodiment, and will not be repeated here.

[0213] Optionally, the memory 2002 may be a read-only memory (ROM) or other type of static storage device capable of storing static information and instructions, random access memory (RAM) or other type of dynamic storage device capable of storing information and instructions, or electrically erasable programmable read-only memory (EEPROM), compact disc read-only memory (CD-ROM) or other optical disc storage, optical disc storage (including compressed optical discs, laser discs, optical discs, digital universal optical discs, Blu-ray discs, etc.), magnetic disk storage media or other magnetic storage devices, or any other medium capable of carrying or storing desired program code in the form of instructions or data structures and accessible by a computer, but not limited thereto. The memory 2002 may be integrated with the first processor 2001 or may exist independently, and may be controlled via the interface circuit of the flexible joint robotic arm tracking control device 410. Figure 11 (Not shown in the figure) is coupled to the first processor 2001, and the embodiments of the present invention do not specifically limit this.

[0214] The transceiver 2003 is used to communicate with network devices or with terminal devices.

[0215] Alternatively, transceiver 2003 may include a receiver and a transmitter. Figure 11 (Not shown separately). The receiver is used to implement the receiving function, and the transmitter is used to implement the transmitting function.

[0216] Optionally, the transceiver 2003 can be integrated with the first processor 2001, or exist independently, and be coupled with the first processor 2001 through an interface circuit (not shown in the figure) of the flexible joint mechanical arm tracking control device 410, and the embodiments of the present application do not make specific limitations hereon. Figure 11

[0217] It should be noted that, Figure 11 The structure of the flexible joint mechanical arm tracking control device 410 shown in the figure does not constitute a limitation on the router, and the actual knowledge structure identification device can include more or fewer components than those shown in the figure, or combine certain components, or different component arrangements.

[0218] In addition, the technical effects of the flexible joint mechanical arm tracking control device 410 can refer to the technical effects of the adaptive neural network flexible joint mechanical arm tracking control method described in the above method embodiments, which will not be repeated here.

[0219] It should be understood that the first processor 2001 in the embodiments of the present application can be a central processing unit (CPU), and the processor can also be other general-purpose processors, digital signal processors (DSP), application specific integrated circuits (ASIC), field programmable gate arrays (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor.

[0220] ​It should also be understood that the memory in the embodiments of the present application can be volatile or nonvolatile memory, or can include both volatile and nonvolatile memory. The nonvolatile memory can be read-only memory (ROM), programmable ROM (PROM), erasable PROM (EPROM), electrically EPROM (EEPROM), or flash memory. The volatile memory can be random access memory (RAM) used as external cache. By way of example, and not limitation, many forms of random access memory (RAM) are available, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous dynamic RAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM), and direct rambus RAM (DR RAM).

[0221] The above-described embodiments can be implemented in whole or in part by software, hardware (e.g., circuitry), firmware, or any combination thereof. When implemented in software, the above-described embodiments can be implemented in the form of a computer program product. The computer program product includes one or more computer instructions or computer programs. When the computer instructions or computer programs are loaded and executed on a computer, the processes or functions described in the embodiments of the present application are wholly or partially generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. The computer instructions can be stored in a computer-readable storage medium or transferred from one computer-readable storage medium to another computer-readable storage medium, for example, the computer instructions can be transferred from one website, computer, server, or data center to another website, computer, server, or data center through wired (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium accessible by a computer or a data storage device such as a server, data center, etc. containing one or more available medium collections. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium. The semiconductor medium can be a solid-state disk.

[0222] It should be understood that the term "and / or" herein merely describes an association relationship of associated objects, which means that there can be three relationships, for example, A and / or B can represent the following three cases: A exists alone, A and B exist together, and B exists alone, where A and B can be singular or plural. In addition, the character " / " herein generally represents an "or" relationship between the associated objects before and after it, but it can also represent an "and / or" relationship, which can be understood according to the context before and after it.

[0223] In the present application, "at least one" means one or more, and "multiple" means two or more. "At least one of the following" or the like means any combination of the items, including any combination of single or multiple items. For example, at least one of a, b, or c can represent a, b, c, a-b, a-c, b-c, or a-b-c, where a, b, and c can be single or multiple.

[0224] It should be understood that in various embodiments of the present application, the size of the sequence number of the above-described processes does not mean the order of execution, and the execution order of the processes should be determined according to their functions and inherent logic, and should not constitute any limitation on the implementation process of the embodiments of the present application.

[0225] Those skilled in the art can clearly understand that the units and algorithm steps of each example described in combination with the embodiments disclosed herein can be realized by electronic hardware or a combination of computer software and electronic hardware. Whether the functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of the present application.

[0226] Those skilled in the art can clearly understand that, for the convenience and brevity of the description, the specific working processes of the devices, apparatuses and units described above can refer to the corresponding processes in the foregoing method embodiments, which will not be repeated here.

[0227] In several embodiments provided by the present application, it should be understood that the disclosed devices, apparatuses and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely schematic, for example, the division of the units is only a logical function division, and actual implementation can have another division manner, for example, multiple units or components can be combined or integrated into another device, or some features can be ignored or not executed. In addition, the coupling or direct coupling or communication connection between the units shown or discussed can be indirect coupling or communication connection through some interfaces, devices or units, which can be electrical, mechanical or other forms.

[0228] The units described as separate components can or can not be physically separated, and the components shown as units can or can not be physical units, that is, they can be located in one place, or can be distributed on multiple network units. Part or all of the units can be selected according to actual needs to achieve the purpose of the embodiment scheme.

[0229] In addition, each functional unit in each embodiment of the present application can be integrated into a processing unit, or each unit can exist physically independently, or two or more units can be integrated into one unit.

[0230] If the functions are realized in the form of software function units and sold or used as independent products, they can be stored in a computer readable storage medium. Based on this understanding, the technical solutions of the present application or the parts of the present application that essentially contribute to the prior art or the parts of the technical solutions can be embodied in the form of software products. The computer software product is stored in a storage medium and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method described in the various embodiments of the present application. The aforementioned storage medium includes a U disk, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk, and various media that can store program codes.

[0231] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art can easily think of changes or replacements within the technical scope disclosed by the present application, which should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A tracking control method for a flexible joint robotic arm using an adaptive neural network, characterized in that, The method includes: S1. Establish the robot's kinematic model; The robot kinematic model in S1 is shown in equation (1) below: In the formula, D(γ)∈R n×n Let R denote the positive definite mass-inertia matrix, where R is a real number, n represents the dimension, and γ∈R. n Represents the joint position vector. The acceleration representing the joint position. Represents the Coriolis and centrifugal matrices. The velocity representing the joint position, O(γ)∈R n Represents gravity, τ∈R n τ represents the control input vector. d Indicates unknown interference; S2. Based on the robot kinematics model, define the trajectory tracking error, and design a control input based on the robot kinematics model according to the tracking error; The trajectory tracking error in S2 is shown in equation (2) below: in, In the formula, e1 represents the first tracking error, γ1 represents the actual joint position vector, and γ d Let represent the ideal joint position vector, e2 represent the second tracking error, γ2 represent the actual joint velocity vector, α represent the virtual controller, and H = [(k1 lncosh(e 11 )) / tanh(e 11 )],…[(k n lncosh(e 1n )) / tanh(e 1n )]T∈R n T denotes matrix transpose, and K = diag[k1, ..., k] n ]∈R n×n R represents a real number, and n represents the dimension. Represents the ideal joint velocity vector; The control input based on the robot kinematics model in S2 is shown in equation (4) below: in, In the formula, τ=[τ1,…,τ n ] T ∈R n Let K1 represent the control input vector, R represent real numbers, n represent the dimension, T represent matrix transpose, e1 represent the first tracking error, and K1 = diag[k 11 , ...k 1n ]∈R n×n Let e2 be a positive definite matrix, e2 be the second tracking error, and A be the process variable. τ represents an auxiliary variable. d To represent unknown interference, θ i Represents the switching function. and Let O represent negative and positive constants, P represent the Coriolis and centrifugal matrices, α represent the virtual controller, and D represent the positive definite mass inertia matrix. The derivative of the virtual controller; S3. The uncertainty of the model is compensated by a neural network, and the unknown disturbance in the control input is estimated by a disturbance observer to obtain an adaptive bounded neural network control based on state feedback. The uncertainty of the model in S3 is compensated by a neural network, as shown in equation (7) below: In the formula, w * Represents the expected weight vector, R represents a real number, n represents the dimension, T represents the matrix transpose, e1 represents the first tracking error, γ1 represents the actual joint position vector, and γ d Let represent the ideal joint position vector, e2 represent the second tracking error, γ2 represent the actual joint velocity vector, and R(z) represent the radial basis function. Let z represent the auxiliary variable, and ε(z) represent the approximation error. The adaptive bounded neural network control based on state feedback in S3 is shown in equation (8) below: In the formula, τ=[τ1,…,τ n ] T ∈R n Let K1 represent the control input vector, R represent real numbers, n represent the dimension, T represent matrix transpose, e1 represent the first tracking error, and K1 = diag[k 11 , ..., k 1n ]∈R n×n Let e2 be a positive definite matrix, e2 be the second tracking error, and A be the process variable. Represents auxiliary variables. Indicates the interference observer. This represents the estimated value of the auxiliary variable. Let R(z) represent the estimated weights, and let R(z) represent the radial basis functions. Γ represents the update rate of the estimated weights. i (i = 1, 2, ..., n) represents a positive definite matrix, e 2i Let represent the second tracking error of joint i, and σ represent a small positive constant. This represents the estimated weight of joint i. θ is a switching function. and These represent negative and positive constants, respectively. Among them, disturbance compensator For approximate unknown disturbance τ d Its renewal law is defined as: Where χ1 and χ2 represent constants; S4. Build a robot system platform to verify the feasibility and effectiveness of the adaptive bounded neural network control method based on state feedback, and define the Lyapunov function to prove the stability of the closed-loop system based on the adaptive bounded neural network. The definition of the Lyapunov function in S4 includes: Define the first Lyapunov function to prove that the trajectory tracking error can converge to a small range, as shown in equation (9): In the formula, V1 represents the first Lyapunov function, n represents the dimension, and e 1i Let e1 represent the first tracking error of joint i, e2 represent the second tracking error, T represent the matrix transpose, and D represent the positive definite mass-inertia matrix. Define a second Lyapunov function to prove the stability of the closed-loop system based on state feedback adaptive bounded neural network, as shown in equation (10): In the formula, V2 represents the second Lyapunov function. Γ represents the error of the weights. i (i = 1, 2, ..., n) represents a positive definite matrix, and χ² represents a constant. This indicates the error caused by interference.

2. A flexible joint robotic arm tracking control device based on an adaptive neural network, wherein the adaptive neural network flexible joint robotic arm tracking control device is used to implement the flexible joint robotic arm tracking control method based on an adaptive neural network as described in claim 1, characterized in that, The device includes: Establish a module for building the robot's kinematic model; The design module is used to define the trajectory tracking error based on the robot's kinematic model, and to design the control input based on the robot's kinematic model according to the tracking error; The control module is used to compensate for model uncertainties using neural networks, estimate unknown disturbances in the control input using disturbance observers, and obtain adaptive bounded neural network control based on state feedback. The proof module is used to build a robot system platform to verify the feasibility and effectiveness of the state feedback-based adaptive bounded neural network control method, and to define the Lyapunov function to prove the stability of the closed-loop system based on the state feedback-based adaptive bounded neural network.

3. A flexible joint robotic arm tracking and control device, characterized in that, The flexible joint robotic arm tracking and control device includes: processor; A memory storing computer-readable instructions that, when executed by the processor, implement the method as described in claim 1.

4. A computer-readable storage medium, characterized in that, The computer-readable storage medium contains program code that can be invoked by a processor to execute the method as described in claim 1.

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