A data-driven based self-learning control method for a robot arm

Abstract

The present application belongs to the field of robot technology, and particularly relates to a mechanical arm self-learning control method based on data driving, which comprises the following steps: step one, establishing an n-dimensional mechanical arm data driving model; step two, designing a mechanical arm self-learning controller based on data driving; and step three, designing an RBF neural network disturbance estimator, so as to realize the control of mechanical arm self-learning. The present application can improve the control and adjustment ability of the joint angle position of the mechanical arm, change the traditional algorithm design mode relying on the model, and use the real-time data of the controlled system to study the controller, so that the complex system can also be effectively controlled.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of robot technology, in particular to a mechanical arm self-learning control method based on data driving. BACKGROUND

[0002] In recent years, with the development of intelligent machinery, the traditional manufacturing mode relying on machinery has changed, and the mechanical arm and its control technology have been widely applied and have become one of the most important technologies in the current intelligent manufacturing field of automobile automatic assembly, painting, glue coating, grabbing, etc. The emergence of intelligent machinery greatly reduces the labor cost, improves the industrial production efficiency, and the manufacturing process is also greatly improved with the development of technology. Intelligent machinery is entering a new era and developing towards more intelligent direction. From traditional control technology, it gradually changes to mechanical autonomous learning and execution of complex function tasks, and adapts to more complex working environment, which puts forward higher requirements for the "brain" of intelligent machinery.

[0003] The joint angle position tracking control ability of the mechanical arm is the premise of the mechanical arm to independently complete complex tasks. The traditional mechanical arm joint angle position tracking controller depends on accurate modeling technology, and the controller design becomes a big problem in the modeling difficulty and complex working environment. In the industrial process, a large amount of process data is obtained through sensors or other technologies, if the controller control process can utilize real-time data to adjust and update, the influence of model inaccuracy and complex environment on joint angle position control can be reduced, and the robustness of the system can be improved. The research on data-driven control algorithm provides a new idea for the joint angle control technology of the mechanical arm. SUMMARY

[0004] To solve the above technical problems, the present application provides a mechanical arm self-learning control method based on data driving, which can improve the control and adjustment ability of the joint angle position of the mechanical arm, change the traditional algorithm design method relying on model, and use the real-time data of the controlled system to research the controller, so that the complex system can also be effectively controlled.

[0005] The technical scheme of the present application is explained as follows in combination with the drawings:

[0006] The present application provides a mechanical arm self-learning control method based on data driving, comprising the following steps:

[0007] Step one, establish an n-dimensional mechanical arm data driving model;

[0008] Step two, design a mechanical arm self-learning controller based on data driving;

[0009] Step three, design a RBF neural network disturbance estimator, so as to realize the control of mechanical arm self-learning;

[0010] Wherein, the specific method of step one is as follows:

[0011] 11) Establish the relationship between the joint angle position and the input torque, as shown below:

[0012] q(t) = H(u(t))

[0013] Wherein, q(t) is the n-dimensional robot joint angle position column vector at time t; u(t) is the n-dimensional robot joint angle control torque column vector at time t; H is a nonlinear operator; q(t), u(t) are expressed as:

[0014]

[0015] 12) Express the n-dimensional robot joint angle nonlinear system in discrete form, as shown below:

[0016] q(k) = f(q(k-1),..., q(k-m q ), u(k-1),..., u(k-m u ))

[0017] In the formula, m is a positive integer; q(k) ∈ R is the current joint angle position of the robot; u(k) ∈ R is the input torque at the current time;

[0018] The specific method of step two is as follows:

[0019] 21) Set the nonlinear relationship between the nonlinear robot joint angle position and the control torque, which satisfies the following conditions:

[0020] (1) The partial derivative of the f function with respect to the (m q +2)th variable at k is continuous;

[0021] (2) The system satisfies the generalized Lipschitz condition, which is mathematically expressed as:

[0022] |q(k1+1)-q(k2+1)|≤b|u(k1)-u(k2)|

[0023] Wherein, k1 ≠ k2, and k1, k2 are greater than zero, and b is a positive number;

[0024] 22) The relationship between the joint angle position and the control torque is dynamically linearized, and the joint angle position increment is expressed as:

[0025] Δq(k+1) = f c (k)·Δu(k)

[0026] wherein, Δq(k+1) represents the displacement increment of the joint angle position of the robot arm at the next time, Δu(k) represents the input difference between the current time and the last time, f c (k) represents the pseudo partial derivative value at the current k time, and the update law thereof is designed by the pseudo partial derivative estimation method;

[0027] 23) update the joint angle of the robot arm, as follows:

[0028] q(k+1) = q(k) + Δq(k+1)

[0029] wherein, q(k) is the joint angle position of the robot arm at the current time; q(k+1) is the position of the joint angle position under the action of the control system; and Δq(k+1) is the joint angle position increment of the robot arm at the next time compared with the current time;

[0030] 24) consider the control torque update law design method in the controller, first propose the error cost function as shown in the following formula, as follows:

[0031] J(q(k)) = |q * (k+1) - q(k+1)| 2 + λ |u(k) - u(k-1)| 2

[0032] wherein, q * (k+1) is the desired joint angle position of the robot arm; q*(k+1) - q(k+1) is the difference between the desired joint angle position at the next time and the actual joint angle position at the next time; u(k) - u(k-1) is the difference between the control torque at the current sampling time and the control torque at the last sampling time; and λ is a weight factor related to the control torque variation, which is used to adjust the change rate of the input torque and is a positive number other than zero;

[0033] 25) substitute the joint angle position update law of the robot arm into the error cost function of the pseudo partial derivative, and take the partial derivative of J(u(k)) with respect to u(k) after substitution, so that the equation after derivation is zero to obtain the data-driven model-free control law:

[0034]

[0035] wherein, is the pseudo partial derivative estimation update law, λ is a weight factor related to the control torque variation, and q(k) is the joint angle position of the robot arm;

[0036] 26) introduce a step factor to adjust the torque increment, γ is a non-zero value, and obtain a new control torque update law, as follows:

[0037]

[0038] where γ is a step factor and λ is a weight factor related to the control torque variation;

[0039] 27) The pseudo-derivative value f c (k) is updated;

[0040] The error cost function of the pseudo-derivative estimation update law:

[0041]

[0042] where is the estimation update rate of the pseudo-derivative f c (k-1); n is a weight factor related to the pseudo-derivative; according to the design method of the control torque update law, the partial derivative of J(f c (k)) with respect to f c (k) is taken and the equation is set to zero, a second step factor h is introduced to adjust the change of the pseudo-derivative output, and the pseudo-derivative estimation expression is obtained:

[0043]

[0044] where the reset algorithm is used to limit , if or |Δu(k-1)|≤c, c is a given constant value, and when any of the above conditions occurs

[0045] 28) A feedforward controller is introduced, and its control law is:

[0046] u2(k) = W(k)Q(k)

[0047] where W(k) is the learning parameter vector of the feedforward controller, and the weight value is updated through the steepest descent algorithm; Q(k) is the parameter vector of the desired position; the types of W(k) and Q(k) are defined as follows:

[0048] W(k) = [w0(k), w1(k), …, w N (k)]

[0049] W(k) = W(k-1) + μ(k-1)Q T (k-1)e(k-1)

[0050] Q(k) = [q * (k), q * (k-1), …, q * (k-N)] T

[0051] ​29) The composite controller combining feedforward control and feedback control is designed as follows:

[0052] u(k) = u1(k) + u2(k)

[0053] Specifically, it is expressed as follows:

[0054]

[0055] In the formula, q(k) is the joint angle position of the robotic arm, W(k) is the learned parameter vector of the feedforward controller, and Q(k) is the parameter vector of the desired position.

[0056] The specific method for step three is as follows:

[0057] 31) Considering the characteristics of generalized disturbances, a disturbance estimation method based on RBF neural network is introduced; the dynamic linearization data model of joint angle position considering the existence of generalized disturbances is expressed as:

[0058]

[0059] In the formula, q e (k) represents the generalized uncertain disturbance; Δq(k+1) represents the displacement increment of the joint angle position of the robot arm at the next moment;

[0060] 32) Regarding q e (k) An online identification is performed using a 1-3-1 layer RBF neural network. According to the mathematical principles of radial basis function neural networks, the expression for the generalized perturbation is written as:

[0061] q e (k)=w(k) T h(k)

[0062] In the formula, w(k) represents the weights of the neural network; h(k) represents the activation function of the neural network; and the estimation expression for the perturbation is:

[0063]

[0064] In the formula, Let w(k) be the estimated value; ε is the estimation error between the estimated value of the disturbance and the actual disturbance under the desired condition;

[0065] 33) The estimation error of the perturbation estimator is used as the input to the neural network; after introducing the neural network, in order to determine... The value of is used to define the error cost function for the weight update of the RBF neural network:

[0066] E(k) = 1 / 2ε 2

[0067] In the formula, E(k) is error cost function output, and the estimated error between disturbance estimation value under expected condition and actual disturbance is epsilon;

[0068] 34) mathematical expression is obtained through actual feedback value and model output; according to gradient descent method, w(k) is adjusted is updated as follows:

[0069]

[0070] In the formula, w(k) is the estimation value of w(k), and eta is learning rate; is partial derivative of E(k);

[0071] 35) after the weight value update is substituted into the data model with generalized uncertain disturbance variable, the same model-free adaptive controller design method is used to obtain new controller pseudo partial derivative and control torque update law:

[0072]

[0073] In the formula, w(k) is the weight value of neural network, and h(k) is the activation function of neural network;

[0074] 36) the new pseudo partial derivative update law is substituted into the new control torque update law, so that the manipulator joint angle position controller with disturbance estimation compensation is obtained, and the control of manipulator self-learning is realized.

[0075] The beneficial effects of the present application are:

[0076] 1) the present application has high control precision, strong anti-interference ability, and does not need complex modeling process;

[0077] 2) the present application studies a model-free adaptive positioning control strategy based on data driving aiming at the influence of uncertain disturbance and other factors under manipulator working environment, a data driving model is established according to the relationship between joint angle position of the manipulator and input torque, and a self-learning feedforward controller is designed based on the model, in order to compensate the influence of external disturbance on control precision, a model-free adaptive feedback controller based on RBF neural network disturbance estimator is proposed, a composite controller is designed by combining the two, and the stability of the controller is proved by using limit theory. BRIEF DESCRIPTION OF DRAWINGS

[0078] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed to be used in the embodiments will be briefly introduced as follows. It should be understood that the following drawings only show some of the embodiments of the present application, and therefore should not be regarded as a limitation on the scope. Other related drawings can also be obtained by those of ordinary skill in the art without creative labor on the basis of these drawings.

[0079] Figure 1 A schematic diagram of a data-driven based joint angle tracking control method for a mechanical arm of the present application. DETAILED DESCRIPTION

[0080] The present application will be further described in detail below in combination with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application, and not to limit the present application. In addition, it should be noted that, for the convenience of description, only the parts related to the present application are shown in the drawings, not all the structures.

[0081] Referring to Figure 1 A data-driven based self-learning control method for a mechanical arm, comprising the following steps:

[0082] Step 1, establish a data-driven model of an n-dimensional mechanical arm, the specific method is as follows:

[0083] 11) Establish the relationship between the joint angle position and the input torque, as shown below:

[0084] q(t)=H(u(t))

[0085] Where q(t) is the n-dimensional mechanical arm joint angle position column vector at time t; u(t) is the n-dimensional mechanical arm joint angle control torque column vector at time t; H is a nonlinear operator; q(t), u(t) are represented as:

[0086]

[0087] 12) Express the n-dimensional mechanical arm joint angle nonlinear system in discrete form, as shown below:

[0088] q(k)=f(q(k-1),...,q(k-m q ),u(k-1),...,u(k-m u ))

[0089] In the formula, m is a positive integer; q(k)∈R is the current time mechanical arm joint angle position; u(k)∈R is the current time input torque.

[0090] Step 2, design a data-driven based mechanical arm self-learning controller, as follows:

[0091] 21) Set the nonlinear relationship between the nonlinear mechanical arm joint angle position and the control torque, which satisfies the following conditions:

[0092] (1) The partial derivative of the function f with respect to the first (m q

[0093] (2) The system satisfies the generalized Lipschitz condition, which is mathematically expressed as:

[0094] |q(k1+1)-q(k2+1)|≤b|u(k1)-u(k2)

[0095] Where k1≠k2, and k1, k2 are greater than zero, and b is a positive number;

[0096] 22) The relationship between the mechanical arm joint angle position and the control torque is dynamically linearized, and the joint angle position increment is expressed as:

[0097] Δq(k+1)=f c (k)·Δu(k)

[0098] Where Δq(k+1) represents the displacement increment of the mechanical arm joint angle position at the next time, Δu(k) represents the input difference between the current time and the previous time, f c (k) represents the pseudo partial derivative value at the current k time, and its update law is designed by the pseudo partial derivative estimation method;

[0099] 23) Update the mechanical arm joint angle, as shown below:

[0100] q(k+1)=q(k)+Δq(k+1)

[0101] Where q(k) is the joint angle position increment of the mechanical arm at the current time, q(k+1) is the joint angle position increment under the action of the control system; and Δq(k+1) is the joint angle position increment of the mechanical arm at the next time compared with the current time;

[0102] 24) Considering the control torque update law design method in the controller, first propose the error cost function as shown in the following formula, which is as follows:

[0103] J(q(k))=|q * (k+1)-q(k+1)| 2 +λ|u(k)-u(k-1)| 2

[0104] Where q * ​(k+1) is the desired joint angle position of the robot arm; q*(k+1)-q(k+1) is the difference between the desired joint angle position at the next time and the actual joint angle position at the next time; u(k)-u(k-1) is the difference between the control torque at the current sampling time and the control torque at the last sampling time; λ is a weight factor related to the change of the control torque, which is used to adjust the change rate of the input torque, and is a positive number other than zero;

[0105] 25) Substitute the joint angle position update law of the robot arm into the error cost function of the pseudo partial derivative, and take the partial derivative of J(u(k)) with respect to u(k) after substitution, and set the derived equation to zero to obtain the data-driven model-free control law:

[0106]

[0107] wherein, is the pseudo partial derivative estimation update law, λ is a weight factor related to the change of the control torque, q(k) is the joint angle position of the robot arm, and u(k) is the input torque;

[0108] 26) Introduce a step factor to adjust the torque increment, γ is a non-zero value, and obtain a new control torque update law, as follows:

[0109]

[0110] wherein, γ is a step factor;

[0111] 27) Design the pseudo partial derivative f c (k) update law;

[0112] Error cost function of the pseudo partial derivative estimation update law:

[0113]

[0114] wherein, is the estimated value of the pseudo partial derivative f c (k); m is a weight factor related to the pseudo partial derivative; according to the design method of the control torque update law, take the partial derivative of J(f c (k)) with respect to f c (k) and set the equation to zero, introduce a second step factor h to adjust the change of the pseudo partial derivative output, and obtain the pseudo partial derivative estimation expression:

[0115]

[0116] wherein, the reset algorithm is used to limit , if or |Δu(k-1)|≤c, c is a given constant value, and Any of the above conditions occurs to make

[0117] 28) Introducing a feedforward controller, the control law is:

[0118] u2(k) = W(k)Q(k)

[0119] In the formula, W(k) is the learning parameter vector of the feedforward controller, and the weight value is updated by the steepest descent algorithm; Q(k) is the parameter vector of the desired position; The type of W(k), Q(k) is defined as follows:

[0120] W(k) = [w0(k), w1(k), …, w N (k)]

[0121] W(k) = W(k-1) + μ(k-1)Q T (k-1)e(k-1)

[0122] Q(k) = [q * (k), q * (k-1), …, q * (k-N)] T ;

[0123] 29) Combined feedforward control and feedback control design composite controller as follows:

[0124] u(k) = u1(k) + u2(k)

[0125] Specifically represented as:

[0126]

[0127] In the formula, q(k) is the joint angle position of the robot arm, W(k) is the learning parameter vector of the feedforward controller, and Q(k) is the parameter vector of the desired position.

[0128] Step three, design RBF neural network disturbance estimator, so as to realize the control of robot arm self-learning, as follows:

[0129] 31) Considering the characteristics of generalized disturbance, a kind of RBF neural network disturbance estimation method is introduced; For the joint angle position dynamic linearization data model considering the existence of generalized disturbance, it is expressed as:

[0130]

[0131] In the formula, q e (k) is the generalized uncertain disturbance; Δq(k+1) represents the displacement increment of the joint angle position of the robot arm at the next time;

[0132] 32) For q e(k) An online identification is performed using a 1-3-1 layer RBF neural network. According to the mathematical principles of radial basis function neural networks, the expression for the generalized perturbation is written as:

[0133] q e (k)=w(k) T h(k)

[0134] In the formula, w(k) represents the weights of the neural network; h(k) represents the activation function of the neural network; and the estimation expression for the perturbation is:

[0135]

[0136] In the formula, ε is the estimated value of w(k); ε is the estimation error between the estimated value of the disturbance and the actual disturbance under the desired condition.

[0137] 33) The estimation error of the perturbation estimator is used as the input to the neural network; after introducing the neural network, in order to determine... The value of is used to define the error cost function for the weight update of the RBF neural network:

[0138] E(k) = 1 / 2ε 2

[0139] In the formula, E(k) is the output of the error cost function, and ε is the estimation error between the disturbance estimate and the actual disturbance under the desired condition;

[0140] 34) Obtain the mathematical expression by comparing the actual feedback values ​​with the model output; adjust the expression according to the gradient descent method. The update is as follows:

[0141]

[0142] In the formula, Let w(k) be the estimated value, and η be the learning rate; for Partial derivatives with respect to E(k);

[0143] 35) After substituting the updated weights into the data model with generalized uncertain disturbance variables, and following the same model-free adaptive controller design method, we obtain the new controller pseudo-partial derivatives and the update law of the control torque:

[0144]

[0145] In the formula, w(k) represents the weights of the neural network; h(k) represents the activation function of the neural network.

[0146] 36) The new pseudo-derivative update law is substituted into the new control torque update law to obtain a manipulator joint angle position controller with disturbance estimation compensation, and the control of the manipulator self-learning is realized.

[0147] In conclusion, the data-driven model is established according to the relationship between the joint angle position and the input torque of the manipulator, and a self-learning feedforward controller is designed based on the model. In order to compensate the influence of external disturbance on the control accuracy, a model-free adaptive feedback controller based on RBF neural network disturbance estimator is proposed, and a compound controller is designed by combining the two, and the stability of the controller is proved by using limit theory.

[0148] Although the embodiments of the present application have been shown and described, it will be understood by those of ordinary skill in the art that various changes, modifications, substitutions and alterations can be made thereto without departing from the principles and spirit of the present application, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A data-driven based self-learning control method for a robot arm, characterized in that, The method comprises the following steps: Step one, establishing a data-driven model of n-dimensional robot arm; Step two, designing a data-driven robot arm self-learning controller; Step three, designing a RBF neural network disturbance estimator, so as to realize self-learning control of the robot arm; The specific method of step one is as follows: 11) the relationship between joint angle position and input torque is established, as shown in the following formula: q(t) = H(u(t)) Wherein, q(t) is the joint angle position column vector of the n-dimensional robot arm at time t; u(t) is the joint angle control torque column vector of the n-dimensional robot arm at time t; H is a nonlinear operator; q(t) and u(t) are expressed as: 12) the n-dimensional robot arm joint angle nonlinear system is expressed in discrete form, as shown in the following formula: q(k) = f(q(k - 1),..., q(k - m q ), u(k - 1),..., u(k - m u )) Wherein, m is a positive integer; q(k) is the joint angle position of the robot arm at the current time; u(k) is the input torque at the current time; The specific method of step two is as follows: 21) the nonlinear relationship between the nonlinear robot arm joint angle position and the control torque is set, which satisfies the following conditions: (1) the partial derivatives of the function f with respect to the first (m q +2) variables are continuous at the value k; (2) the system satisfies the generalized Lipschitz condition, and the mathematical expression is: |q(k1+1)-q(k2+1)|≤b|u(k1)-u(k2) Wherein, k1≠k2, and k1 and k2 are greater than zero, and b is a positive number; 22) the relationship between the joint angle position and the control torque of the robot arm is processed by dynamic linearization, and the joint angle position increment is expressed as: Δq(k + 1) = f c (k) · Δu(k) In the formula, △q(k+1) represents the displacement increment of the joint angle position of the robot arm at the next time, △u(k) represents the input difference between the current time and the previous time, f c (k) represents the pseudo partial derivative value at the current k time, and the update law thereof is designed by a pseudo partial derivative estimation method. 23) the joint angle of the robot arm is updated, as shown in the following formula: q(k+1) = q(k) +△q(k+1) Wherein, q(k) is the joint angle position of the robot arm at the current time; q(k+1) is the position of the joint angle position under the action of the control system;△q(k+1) is the joint angle position increment of the robot arm at the next time compared with the current time; 24) considering the control torque updating law design method in the controller, first, the error cost function is proposed as shown in the following formula: J(q(k)) = |q * (k+1)-q(k+1)| 2 +λ|u(k)-u(k-1)| 2 wherein q * (k+1) is the desired joint angle position of the robot arm; q*(k+1) - q(k+1) is the difference between the desired joint angle position at the next time and the actual joint angle position at the next time; u(k) - u(k-1) is the difference between the control torque at the current sampling time and the control torque at the last sampling time; and λ is a weight factor related to the control torque variation, which is used to adjust the change rate of the input torque and is a positive non-zero number. 25) the joint angle position updating law of the robot arm is substituted into the error cost function of the pseudo partial derivative, and the partial derivative of J(u(k)) about u(k) is taken, so that the equation after derivation is zero to obtain the model-free control law based on data driving: wherein is the pseudo-derivative update law, λ is a weighting factor related to the control torque variation, and q(k) is the joint angle position of the robot arm. 26) a step factor is introduced to adjust the torque increment, and γ is a non-zero value, so that a new control torque updating law is obtained, which is specifically as follows: Wherein, γ is a step factor; 27) the pseudo-derivative value f at the current k time instant c (k) the update law is designed; The error cost function of the pseudo partial derivative estimation updating law is: In the formula, For pseudo-partial derivatives f c The estimated update law of (k-1); n is the weighting factor with respect to the pseudo-partial derivative; according to the design method of the control torque update law, for J(f c (k) Find information about f c After taking the partial derivative of (k), the equation is set to zero. A second step factor h is introduced to adjust the change in the pseudo-partial derivative output, resulting in the pseudo-partial derivative estimation expression: where the reset algorithm is applied to is limited if or |△u(k-1)|≤c, c being a given constant value, and is set to zero whenever any of the above conditions occurs 28) a feedforward controller is introduced, and its control law is: u2(k) = W(k)Q(k) Wherein, W(k) is the learning parameter vector of the feedforward controller, which is updated by the steepest descent algorithm; Q(k) is the parameter vector of the expected position; the types of W(k) and Q(k) are defined as shown in the following formula: W(k) = [w0(k), w1(k),..., w N (k)] W(k) = W(k - 1) + μ(k - 1)Q T (k - 1)e(k - 1) Q(k) = [q * (k), q * (k-1),..., q * (k-N)] T ; 29) a compound controller is designed by combining feedforward control and feedback control, as shown in the following formula: u(k) = u1(k) + u2(k) Specifically expressed as: Wherein, q(k) is the joint angle position of the robot arm, W(k) is the learning parameter vector of the feedforward controller, and Q(k) is the parameter vector of the expected position; The specific method of step three is as follows: 31)Considering the generalized disturbance characteristics, a disturbance estimation method based on RBF neural network is introduced. The dynamic linearization data model of joint angle position considering the existence of generalized disturbance is expressed as: where q e (k) is a generalized uncertain disturbance; and Δq(k + 1) represents a displacement increment of the joint angle position of the robot arm at the next time. 32) for q e (k) An online identification is performed using a 1-3-1 layer RBF neural network. According to the mathematical principle of the radial basis function neural network, the expression of the generalized disturbance is written as q e (k) = w(k) T h(k) where w(k) is the weight of neural network; h(k) is the activation function of neural network; the estimation expression of disturbance is: wherein is an estimate of w(k); and ε is an estimate of the error between the disturbance estimate under the expectation condition and the actual disturbance. 33) the estimation error of the perturbation estimator as input to a neural network; after introducing the neural network, define an error cost function for the RBF neural network weight update as the value of ​ E(k) = 1 / 2 ε 2 where E(k) is the error cost function output, and ε is the estimation error between the estimated value of disturbance under the expected condition and the actual disturbance; 34) Obtain a mathematical expression by actual feedback value and model output; adjust according to gradient descent method Update as follows: wherein is an estimate of w(k), and η is a learning rate; is with respect to the partial derivative of E(k). 35)After the weight update is substituted into the data model with generalized uncertain disturbance variables, the new controller pseudo partial derivative and control torque update law are obtained according to the same model-free adaptive controller design method: where w(k) is the weight of neural network; h(k) is the activation function of neural network; 36)The new pseudo partial derivative update law is substituted into the new control torque update law to obtain the joint angle position controller of the manipulator with disturbance estimation compensation, and the control of manipulator self-learning is realized.

Images