Output feedback nonlinear control method for multi-degree-of-freedom electrically controlled heavy-duty robot arm

Abstract

The application provides a multi-degree-of-freedom electric control heavy-load mechanical arm output feedback nonlinear control method, which comprises the following steps: step S100, a mathematical model of a multi-degree-of-freedom electric control heavy-load mechanical arm is established, including a heavy-load mechanical arm mechanical system dynamics model and a Solidworks-Simulink joint simulation model; step S200, based on the mathematical model of the multi-degree-of-freedom electric control heavy-load mechanical arm, a neural network observer is designed to compensate for modeling uncertainty, external disturbance and joint angular velocity of the mechanical arm system; and step S300, a multi-degree-of-freedom electric control heavy-load mechanical arm nonlinear controller based on the neural network observer is designed.

Description

Technical Field

[0001] This invention relates to servo control technology for electrically controlled heavy-duty robotic arms, and in particular to a method for output feedback nonlinear control of multi-degree-of-freedom electrically controlled heavy-duty robotic arms. Background Technology

[0002] Multi-degree-of-freedom electrically controlled heavy-duty robotic arms play an irreplaceable role in core fields such as industrial manufacturing, disaster relief and rescue, and large-scale engineering construction due to their advantages of strong load-bearing capacity, large working space and high flexibility. The electrically controlled heavy-duty robotic arm driven by a servo motor is a typical complex dynamic system with highly nonlinear, strong coupling and time-varying parameters. In practical engineering applications, its high-precision motion control faces severe challenges: (1) Complex matching and mismatch uncertainties: During the operation of the heavy-duty robotic arm, there is extremely strong dynamic coupling between the joints, complex nonlinear friction inside the servo motor and reducer, and the end of the robotic arm often faces unknown load changes and external time-varying interference; these complex matching and mismatch uncertainties make it difficult for traditional control methods based on nominal mathematical models to guarantee the tracking accuracy of the system. (2) Limitations of state measurement and noise amplification effect: Electrically controlled heavy-duty robotic arms in industrial settings are usually only equipped with position sensors such as photoelectric encoders to measure joint angles, lacking high-precision joint speed sensors. If conventional numerical differentiation methods are used to obtain speed signals, the measurement noise of the sensors will inevitably be amplified, resulting in a large number of high-frequency glitches in the feedback signal, which will seriously pollute the control closed loop and degrade control performance. In summary, existing control strategies, when dealing with the control of electrically controlled heavy-duty robotic arms, cannot simultaneously take into account high-precision observation under conditions without speed sensors, strong robustness to complex nonlinearities, and low-jitter control output. Summary of the Invention

[0003] The purpose of this invention is to provide a method for output feedback nonlinear control of a multi-degree-of-freedom electrically controlled heavy-duty robotic arm, comprising the following steps: Step S100: Establish a mathematical model of a multi-degree-of-freedom electrically controlled heavy-duty manipulator, including a dynamic model of the heavy-duty manipulator's mechanical system and a Solidworks-Simulink co-simulation model. Step S200: Based on the mathematical model of the multi-degree-of-freedom electrically controlled heavy-duty manipulator, design a neural network observer to compensate for the modeling uncertainty of the manipulator system, external disturbances, and joint angular velocities. Step S300: Design a nonlinear controller for a multi-degree-of-freedom electrically controlled heavy-duty robotic arm based on a neural network observer.

[0004] Furthermore, in step S100, establishing the mathematical model of the multi-degree-of-freedom electrically controlled heavy-duty robotic arm specifically includes the following steps: Step S110: Establish a mathematical model of the multi-degree-of-freedom electrically controlled heavy-duty robotic arm based on the Newton-Euler dynamics modeling method; Step S120: Establish a Solidworks 3D model of the electrically controlled heavy-duty robotic arm, import it into Adams to determine the joint coordination and motion relationships, use joint torque as input and joint angle as output to export it to Matlab-Simulink for joint simulation. Step S130: The established mathematical model of the multi-degree-of-freedom electrically controlled heavy-duty robotic arm is converted into a state-space equation.

[0005] Further, in step S110, the mechanical system dynamics model of the multi-degree-of-freedom electrically controlled heavy-duty manipulator is obtained according to the Euler-Lagrange method: (1) in, For the joint angle of the robotic arm, Let be the angular velocity of the robotic arm joint. Let be the angular acceleration vector of the robotic arm joint. D ( q ) represents the inertia matrix of the robotic arm. The matrix of centrifugal force and Coriolis force of the robotic arm. G ( q ) represents the gravitational torque of the robotic arm. f d This refers to the total disturbance experienced by the robotic arm from external sources. τ This is the control torque vector of the robotic arm. For the degrees of freedom of the robotic arm.

[0006] Further, in step S120, a three-dimensional model of the multi-degree-of-freedom electrically controlled heavy-duty manipulator is created using Solidworks, and its joint coordinate system is established using the robot MDH method to obtain the dynamic parameters of the multi-degree-of-freedom electrically controlled heavy-duty manipulator. The dynamic parameters are then imported into Adams software to assign rotational joints, joint torques, and joint angles to the manipulator, and exported to the Matlab-Simulink workspace for co-simulation.

[0007] Furthermore, step S130 specifically includes the following processes: Step S131, Define state variables Let the variable ,variable The mathematical model of the multi-degree-of-freedom electrically controlled heavy-duty robotic arm can be described by the following state-space equation: (2) in, D , C , GThese are the robotic arm inertia matrix, the robotic arm centrifugal force and Coriolis force matrix, and the robotic arm gravitational torque; Step S132, using nominal value D n , C n , G n Torque feedforward is performed, and the uncertainty in system modeling is estimated using a neural network. After processing, the result is... (3) make ,have to (4) in, u For controlling the joint torque of the robotic arm, t It is time. n = G n -1 C n x 2, Modeling uncertainties in robotic arm dynamics h ( t ) is the perturbation function.

[0008] Furthermore, in step S200, a neural network is designed to compensate for the uncertainties in the dynamic modeling of the robotic arm. The specific process includes: Step S211: Construct a real-time estimation function to approximate the uncertainties and unknown external disturbances in the dynamic modeling of the robotic arm. , (5) in, This is the current estimate matrix of the true values ​​of the neural network weights. To obtain the feature vector after processing by the hidden layers of the neural network, X =[ x 1 T , x 2 T ]; Step S212: Estimate the true values ​​of the neural network weights and joint angular velocities, as expressed below. (6) in, This is the input vector of the neural network. for x The estimated value of 2, This represents the approximation error of the neural network. Step S213: Obtain the adaptive rate of neural network weights. , (7) in, It is a constant. B 2 represents the correction gain term. β The nonlinear gain coefficient of the observer, P It is a positive definite symmetric matrix. , , ; Step S214, utilize the adaptive rate of neural network weights. The Euler first-order forward integral method is used to update the true values ​​of the neural network weights, and the updated true values ​​of the neural network weights are substituted into formula (5) to replace the original values. To achieve uncertainty in the dynamics modeling of robotic arms Compensation will be provided.

[0009] Furthermore, the specific process of designing the neural network to compensate for external disturbances and joint angular velocity in step S200 includes: The mathematical model of a multi-degree-of-freedom electrically controlled heavy-duty robotic arm is converted into a model using state variables. Design: (8) in, l 1. l 2. l 3 are respectively , , The diagonal gain coefficient matrix, ω 0 represents the observer gain. I It is the identity matrix. , , They are respectively x 1. x 2. x The estimated value of 3, for The estimated value; make Subtracting equations (4) and (8) gives us... (9) in ; make ,have to (10) Rewriting formula (10) in matrix multiplication form, and simplifying, we get... (11) in, ξ For observation estimation error; Let be a Huiwitz matrix, satisfying the existence of a matrix , making ; choose , making , For neural networks The upper bound of the 2-norm, express Q The smallest eigenvalue of a matrix. and They are P The maximum and minimum eigenvalues ​​of a matrix, h max This represents the upper bound of the disturbance. This represents the minimum observer gain. This represents the upper bound of the estimation error of the neural network. c 1. c 2 is a constant.

[0010] Furthermore, the specific process of designing the nonlinear controller for the multi-degree-of-freedom electrically controlled heavy-duty robotic arm based on a neural network observer in step S300 includes: Step S310, Define Then a sliding surface can be defined. (12) in, e 1 represents the angle tracking error. e 2 represents the angular velocity tracking error. x 1d for x The expected value of 1 and All are positive definite diagonal parameter matrices with a value greater than 0. ; Step S320, for Differentiating gives (13) Wherein, the derivative of the position error is (14) Observer velocity estimation error Then there is Substitute The expression is obtained (15) Step S330, obtain the derivative of the joint velocity observation value as follows: (16) Step S340, let Design the joint control torque of the robotic arm. (17) in, , in, K 1. K 2 are diagonal gain matrices; Step S350, substitute the derivative of the velocity error have to (18) Step S360, will and Substitute into the sliding surface function The equation yields (19) Expanding and simplifying formula (19), since The constant holds true, thus yielding the nonlinear controller equations for the multi-degree-of-freedom electrically controlled heavy-duty robotic arm. (20) Compared with the prior art, the significant advantages of this invention are: (1) It uses a neural network observer to process the mismatch uncertainty and external disturbance of the system, which can avoid modeling the strong coupling dynamics and complex nonlinear friction between multiple joints and facilitate the implementation of the controller; (2) It adopts an output feedback control strategy, which eliminates the need for joint speed sensors; (3) It combines a neural network observer and sliding mode control to process the mismatch and matching uncertainty of the system at the same time, which can achieve better tracking performance. Attached Figure Description

[0011] Figure 1 This is a schematic diagram of the method of the present invention.

[0012] Figure 2 This is a schematic diagram of the trajectory tracking test of the multi-degree-of-freedom electrically controlled heavy-duty robotic arm of the present invention.

[0013] Figure 3 This is a diagram showing the tracking effect of the six joints of the multi-degree-of-freedom electrically controlled heavy-duty robotic arm based on a neural network observer, designed in this invention, on the desired command.

[0014] Figure 4 This is a comparison curve of the tracking error of the six joints under the action of the controller designed in this invention and the traditional PID controller.

[0015] Figure 5 This is the control input diagram of the six joints under the action of the output feedback controller of the multi-degree-of-freedom electrically controlled heavy-duty robotic arm based on a neural network observer designed in this invention.

[0016] Figure 6 The neural network observer designed in this invention analyzes the angular velocity signals of the six joints. The observation effect diagram. Detailed Implementation

[0017] Combination Figure 1 A method for output feedback nonlinear control of a multi-degree-of-freedom electrically controlled heavy-duty robotic arm includes the following steps: Step 1: Establish a mathematical model of the multi-degree-of-freedom electrically controlled heavy-duty manipulator, including the dynamic model of the heavy-duty manipulator's mechanical system and the Solidworks-Simulink co-simulation model. Step 2: Based on the mathematical model of the multi-degree-of-freedom electrically controlled heavy-duty manipulator, design a neural network observer to compensate for the modeling uncertainty of the manipulator system, external disturbances, and joint angular velocities. Step 3: Design a nonlinear controller for a multi-degree-of-freedom electrically controlled heavy-duty robotic arm based on a neural network observer; Step 4: Apply Lyapunov stability theory to perform stability analysis on the nonlinear controller of the multi-degree-of-freedom heavy-duty robotic arm based on the neural network observer, and obtain the result that the system is bounded and stable.

[0018] Step 1: Establish a mathematical model of the multi-degree-of-freedom electrically controlled heavy-duty robotic arm, including the dynamic model of the heavy-duty robotic arm's mechanical system and the Solidworks-Simulink co-simulation model.

[0019] Step 1.1: The linkage motion of the electrically controlled heavy-duty robotic arm is driven by linear and rotary actuators controlled by servo motors. Based on the multibody dynamics of the robotic arm linkages and the dynamics of the motor actuators, a mathematical model of the multi-degree-of-freedom electrically controlled heavy-duty robotic arm is established, as follows: Based on the Euler-Lagrange method, the dynamic model of the mechanical system of the multi-degree-of-freedom electrically controlled heavy-duty robotic arm is described as follows: (1) in, For the joint angle of the robotic arm, , Let be the angular velocity of the robotic arm joint. , Let be the angular acceleration vector of the robotic arm joint. robotic arm inertial matrix Centrifugal force and Coriolis force matrix of robotic arm The gravitational torque vector of the robotic arm The total disturbance experienced by the robotic arm, such as joint friction. Robotic arm control torque vector , For the degrees of freedom of the robotic arm, It is the set of real numbers.

[0020] Step 1.2: A 3D model of the multi-degree-of-freedom electrically controlled heavy-duty manipulator is created. After the model is established, its joint coordinate system is established in Solidworks using the Robot MDH method, thereby obtaining the dynamic parameters of the multi-degree-of-freedom electrically controlled heavy-duty manipulator, such as mass and inertia tensor. The mating relationships are determined and imported into Adams software to assign rotational joints, joint torques, and joint angles to the manipulator. These parameters are then exported to the Matlab-Simulink workspace for co-simulation.

[0021] Step 1.3: To facilitate controller design, define state variables and transform the established mathematical model of the multi-degree-of-freedom valve-controlled hydraulic manipulator into state-space equations, as follows: Define state variables Let the variable ,variable The mathematical model of the multi-degree-of-freedom electrically controlled heavy-duty robotic arm can be described by the following state-space equation: (2) Since the dynamic parameters of the robotic arm cannot be accurately obtained, their nominal values ​​are used. D n , C n , G n Torque feedforward is performed, and the uncertainty in system modeling is estimated using a neural network. After processing, the result is obtained. (3) make The equation can be rewritten as (4) in, u For controlling the joint torque of the robotic arm, n = G n -1 C n x 2, Modeling uncertainties in robotic arm dynamics h ( t ) is the perturbation function.

[0022] Step 2: Based on the mathematical model of the multi-degree-of-freedom electrically controlled heavy-duty robotic arm, design a neural network observer to compensate for the modeling uncertainty of the robotic arm system, external disturbances, and joint angular velocities.

[0023] Step 2.1: Design a neural network to compensate for uncertainties in the dynamic modeling of the robotic arm. The details are as follows: Neural networks can be used to approximate any continuous function. There exists an optimal weight vector. , making (5) Since the optimal value and joint angular velocity cannot be accurately known, their true values ​​are estimated, and the expression is as follows: (6) in, This is the input vector of the neural network. For neural network activation functions, These are estimates of the true values ​​of the neural network weights. This represents the approximation error of the neural network. The design of the neural network weights is adaptive. (7) in, It is a constant. It is a state The observation error, B 2 represents the correction gain term. β The nonlinear gain coefficient of the observer, P It is a positive definite symmetric matrix. , ; Adaptive weights of neural networks The Euler first-order forward integral method is used to update the true values ​​of the neural network weights, and the updated true values ​​of the neural network weights are substituted into formula (5) to replace the original values. To achieve uncertainty in the dynamics modeling of robotic arms Compensation will be provided.

[0024] Step 2.2: Design an extended state observer to estimate the external disturbances experienced by the robotic arm. and joint velocity The details are as follows: Since the sensor only provides a position signal, an output feedback observer is designed here, using only... The observer can be designed as follows: (8) make Subtracting equations (2) from equation (2) yields... (9) make , can be obtained (10) Organized ; (11) in, l 1. l 2. l 3 are respectively , , The diagonal gain coefficient matrix, ω 0 represents the observer gain. I It is the identity matrix. , , They are respectively x 1. x 2. x The estimated value of 3, for The estimated value, , ξ To estimate the error of observation, Let be a Huiwitz matrix, satisfying the existence of a matrix , making ; For neural networks The upper bound of the 2-norm, express Q The smallest eigenvalue of a matrix. and They are P The maximum and minimum eigenvalues ​​of a matrix, h max This represents the upper bound of the disturbance. This represents the minimum observer gain. This represents the upper bound of the neural network estimation error. Define the above parameters and choose appropriate ones. , making This is used for subsequent stability verification, and the parameter observer designed accordingly can accurately observe the angular velocity of the robotic arm joints. With the disturbance .

[0025] Step 3: Design a nonlinear controller for a multi-degree-of-freedom electrically controlled heavy-duty robotic arm based on a neural network observer.

[0026] Design a nonlinear controller for a multi-degree-of-freedom electrically controlled heavy-duty robotic arm based on a neural network observer, as follows: definition Then a sliding surface can be defined. (12) in, e 1 represents the angle tracking error. e 2 represents the angular velocity tracking error. and All are positive definite diagonal parameter matrices with a value greater than 0. ; right Taking the derivative, (13) According to the system state equation, the derivative of the position error is: (14) Considering the velocity estimation error of the observer Then there is Substitute The expression yields (15) From the dynamic equations of the extended state observer, the derivative of the joint velocity observations is: (16) make Design the joint control torque of the robotic arm. (17) in ; in, K 1. K 2 are diagonal gain matrices; Substitute the derivative of the velocity error achievable (18) Will and Substitute into the sliding surface function The equation yields (19) Expand and simplify it, because If it holds true, then we can obtain (20) Step 4: Apply Lyapunov stability theory to perform stability analysis on the nonlinear controller of the multi-degree-of-freedom heavy-duty robotic arm based on the neural network observer, and obtain the result that the system is bounded and stable.

[0027] Step 4.1 Proof of the stability of the neural network observer, specifically including: Define Lyapunov functions for ,(twenty one) Differentiating gives ,(twenty two) Expand ,(twenty three) ;(twenty four) Organized (25) in (26) By applying Lyapunov's stability theory, the stability of the observer is proven, and the result is that the observer is bounded and stable. Therefore, by adjusting the control parameters, the tracking error of the system tends to 0 as time approaches infinity.

[0028] Step 4.2, Controller stability proof, can be obtained from step 3 above: Define Lyapunov functions as (27) Differentiating gives (28) because All are positive definite parameters, and It can be further reduced to (29) in, For matrix The smallest eigenvalue, For matrix The minimum eigenvalue; based on the stability proof of the neural network observer in step 4.1, the velocity estimation error of the observer. It is bounded and stable, and exists. , making From this, we can conclude that... (30) If robust gain switching Large enough to overcome the observation residuals, i.e., the matrix parameters satisfy... , Then the following equation always holds true: (31) Using Lyapunov's stability theory to prove stability, we can see that... This holds true. According to the LaSalle invariance principle and finite-time stability theory, the state of the closed-loop control system will reach the sliding surface within a finite time. And converges asymptotically along the sliding surface. Therefore, adjusting the control parameters reduces the system's position tracking error. With speed tracking error Under finite time conditions, the time constant tends to 0, resulting in a globally asymptotically stable system. Proof complete.

[0029] Assumption 1: Ideal weights for neural networks Neural network activation functions Approximation error of neural networks All are bounded and their upper bounds are known; express The Frobenius norm; express The 2-norm; Assumption 2: Desired system reference signal and its first derivative It is smooth and bounded.

[0030] Lemma 1: If the function It is continuous, then in The Lipschitz condition is satisfied within the actual range of variation: Example 1: To evaluate the performance of the designed controller, this example uses the Matlab-Adams simulation platform to build a six-degree-of-freedom electrically controlled heavy-duty robotic arm platform to verify the effectiveness of the proposed control strategy.

[0031] The mechanical parameters of the electrically controlled heavy-duty robotic arm are shown in Table 1.

[0032] Table 1 Mechanical parameters of the electrically controlled heavy-duty robotic arm in For each link quality For each link MDH modeling parameters, Let be the inertial tensor of each link about its joint coordinate system. Link by The joint coordinate system is the reference centroid position.

[0033] like Figure 2As shown, the desired trajectory in the task space is set as a composite trajectory of fixed-point control and circular trajectory: The trajectory planning steps are as follows: The robotic arm moves from its initial position to a fixed point. Exercise Then, using this as the starting point for circular motion, with a radius of 0.5m, the motion revolves around the center. It moves in a circular trajectory.

[0034] The following controller is used for comparison in the simulation: The controller parameters are as follows: (ESO+RBF Output Feedback Controller EROFC based on neural network observers) PID controller: The controller parameters are as follows: The tracking effect of the robotic arm's task space trajectory under EROFC is as follows: Figure 3 As shown, the expected command and the actual joint angles are basically coincident, and the expected task space trajectory and the actual task space trajectory are also basically coincident, indicating good tracking performance; the comparison diagram of the tracking errors of the six joints under the action of EROFC and PIDController is shown below. Figure 4 As shown, it can be seen that the controller proposed in this embodiment has a significant improvement in control performance compared to the traditional PID controller, and has excellent tracking performance.

[0035] Figure 5 This is a graph showing the change of control input of an electrically controlled heavy-duty robotic arm system over time under the action of EROFC. As can be seen from the graph, the obtained control input is a low-frequency continuous signal, which is more conducive to execution in practical applications. Figure 6 The six-joint angular velocity estimated by the neural network observer. For ideal angular velocity The observation diagram shows that the neural network observer can accurately observe the ideal signal, reducing the need for joint angular velocity sensors and making the controller easier to deploy in practical applications.

Claims

1. A method for output feedback nonlinear control of a multi-degree-of-freedom electrically controlled heavy-duty robotic arm, characterized in that, Includes the following steps: Step S100: Establish a mathematical model of a multi-degree-of-freedom electrically controlled heavy-duty manipulator, including a dynamic model of the heavy-duty manipulator's mechanical system and a Solidworks-Simulink co-simulation model. Step S200: Based on the mathematical model of the multi-degree-of-freedom electrically controlled heavy-duty manipulator, design a neural network observer to compensate for the modeling uncertainty of the manipulator system, external disturbances, and joint angular velocities. Step S300: Design a nonlinear controller for a multi-degree-of-freedom electrically controlled heavy-duty robotic arm based on a neural network observer; In step S100, establishing the mathematical model of the multi-degree-of-freedom electrically controlled heavy-duty robotic arm specifically includes the following steps: Step S110: Establish a mathematical model of the multi-degree-of-freedom electrically controlled heavy-duty robotic arm based on the Newton-Euler dynamics modeling method; Step S120: Establish a Solidworks 3D model of the electrically controlled heavy-duty robotic arm, import it into Adams to determine the joint coordination and motion relationships, use joint torque as input and joint angle as output to export it to Matlab-Simulink for joint simulation. Step S130: The established mathematical model of the multi-degree-of-freedom electrically controlled heavy-duty robotic arm is converted into a state-space equation. In step S110, the mechanical system dynamics model of the multi-degree-of-freedom electrically controlled heavy-duty manipulator is obtained according to the Euler-Lagrange method: ， （1） in, For the joint angle of the robotic arm, Let be the angular velocity of the robotic arm joint. Let be the angular acceleration vector of the robotic arm joint, and D(q) be the robotic arm inertia matrix. Let G(q) be the matrix of centrifugal force and Coriolis force of the robotic arm, and f be the gravitational torque of the robotic arm. d Let τ be the total disturbance experienced by the robotic arm from external forces, and τ be the control torque vector of the robotic arm. For the degrees of freedom of the robotic arm; In step S120, a three-dimensional model of the multi-degree-of-freedom electrically controlled heavy-duty manipulator is created using Solidworks. Its joint coordinate system is established using the robot MDH method to obtain the dynamic parameters of the multi-degree-of-freedom electrically controlled heavy-duty manipulator. The dynamic parameters are then imported into Adams software to assign rotational joints, joint torques, and joint angles to the manipulator, and exported to the Matlab-Simulink workspace for co-simulation. Step S130 specifically includes the following process: Step S131, Define state variables Let the variable ,variable The mathematical model of the multi-degree-of-freedom electrically controlled heavy-duty robotic arm can be described by the following state-space equation: ， （2） Where D, C, and G are the inertia matrix of the robotic arm, the centrifugal force and Coriolis force matrix of the robotic arm, and the gravitational torque of the robotic arm, respectively. Step S132, using the nominal value D of D, C, and G. n C n G n Torque feedforward is performed, and the uncertainty in system modeling is estimated using a neural network. After processing, the result is... ， （3） make ,have to ， （4） Where u is the joint control torque of the robotic arm, and t is time. , To model the uncertainties in the dynamics of the robotic arm, h(t) is the disturbance function; In step S200, a neural network is designed to compensate for the uncertainty in the dynamic modeling of the robotic arm. The specific process includes: Step S211: Construct a real-time estimation function to approximate the uncertainties and unknown external disturbances in the dynamic modeling of the robotic arm. , ， （5） in, This is the current estimate matrix of the true values ​​of the neural network weights. To obtain the feature vector after processing by the hidden layers of the neural network, X=[x1 T x2 T ]; Step S212: Estimate the true values ​​of the neural network weights and joint angular velocities, as expressed below. ， （6） in, This is the input vector of the neural network. This is an estimate of x2. This represents the approximation error of the neural network. Step S213: Obtain the adaptive rate of neural network weights. , ， （7） in, B2 is a constant, B2 is the correction gain term, β is the nonlinear gain coefficient of the observer, and P is a positive definite symmetric matrix. , , ; Step S214, utilize the adaptive rate of neural network weights. The Euler first-order forward integral method is used to update the true values ​​of the neural network weights, and the updated true values ​​of the neural network weights are substituted into formula (5) to replace the original values. To achieve uncertainty in the dynamics modeling of robotic arms Compensation will be provided.

2. The method according to claim 1, characterized in that, The specific process of designing a neural network to compensate for external disturbances and joint angular velocities in step S200 includes: The mathematical model of a multi-degree-of-freedom electrically controlled heavy-duty robotic arm is converted into a model using state variables. Design: ， （8） Wherein, l1, l2, and l3 are respectively , , The diagonal gain coefficient matrix, where ω0 is the observer gain and I is the identity matrix. , , Let x1, x2, and x3 be the estimated values, respectively. for The estimated value; make Subtracting equations (4) and (8) gives us... ， （9） in ; make ,have to ，（10） Rewriting formula (10) in matrix multiplication form, and simplifying, we get... ， （11） Where ξ is the observation estimation error; Let be a Huiwitz matrix, satisfying the existence of a matrix , making ; choose , making , For neural networks The upper bound of the 2-norm, This represents the smallest eigenvalue of the Q matrix. and These are the maximum and minimum eigenvalues ​​of matrix P, h, and h, respectively. max This represents the upper bound of the disturbance. This represents the minimum observer gain. c1 and c2 represent the upper bound of the neural network estimation error, and are constants.

3. The method according to claim 2, characterized in that, The specific process of designing the nonlinear controller for a multi-degree-of-freedom electrically controlled heavy-duty robotic arm based on a neural network observer in step S300 includes: Step S310, Define Then a sliding surface can be defined. ， （12） Where e1 is the angle tracking error, e2 is the angular velocity tracking error, and x 1d Let x1 be the expected value. and All are positive definite diagonal parameter matrices with a value greater than 0. ; Step S320, for Differentiating gives ， （13） Wherein, the derivative of the position error is ， （14） Observer velocity estimation error Then there is Substitute The expression is ， （15） Step S330, obtain the derivative of the joint velocity observation value as follows: ； （16） Step S340, let Design the joint control torque of the robotic arm. ， （17） in, ， Where K1 and K2 are diagonal gain matrices, respectively; Step S350, substitute the derivative of the velocity error have to ， （18） Step S360, will and Substitute into the sliding surface function The equation yields ，（19） Expanding and simplifying formula (19), since The constant holds true, thus yielding the nonlinear controller equations for the multi-degree-of-freedom electrically controlled heavy-duty robotic arm. （20）。

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