A method and system for trajectory tracking of a robot arm based on interference estimation compensation

Abstract

This invention discloses a robotic arm trajectory tracking method and system based on interference estimation compensation, belonging to the field of trajectory tracking technology. The method includes: acquiring the desired trajectory information of the robotic arm, including the desired position q. d Based on the given total system disturbance d, a dynamic model of the robotic arm is established to determine the desired angular velocity and angular acceleration. A neural network disturbance observer is designed to estimate the total system disturbance and obtain the estimated system disturbance value y. A super-helical sliding mode controller and a globally non-singular terminal sliding surface s are designed to obtain the equivalent control torque u based on the desired trajectory information of the robotic arm and the given total system disturbance d. eq Based on the system disturbance estimate y and the equivalent control torque u eq This invention obtains the control law u of the robotic arm that satisfies Lyapunov stability analysis, thereby enabling robotic arm trajectory tracking. This invention improves the stability and trajectory tracking performance of the robotic arm system.

Description

Technical Field

[0001] This invention belongs to the field of trajectory tracking technology, specifically relating to a robotic arm trajectory tracking method and system based on interference estimation compensation. Background Technology

[0002] In the field of robotics, trajectory tracking is one of the key tasks in robotic arm control systems, with significant engineering and practical application implications. When performing complex operations such as assembly, welding, and grinding, robotic arms often require their end effectors to move precisely along a predetermined trajectory to ensure operational accuracy and efficiency. However, a robotic arm is a complex, nonlinear, and coupled system, frequently encountering interference and unknown errors during actual operation, greatly increasing the difficulty of precise control. Therefore, in the field of robotics, developing robust, fast-responding, and highly accurate robotic arm trajectory tracking control methods to address interference and errors during operation is a core technological foundation for improving the intelligence level of robotic arms and expanding their application scenarios.

[0003] To address the challenge of robotic arm trajectory tracking, scholars both domestically and internationally have proposed control methods such as PID control, sliding mode control, adaptive control, and deep learning-based intelligent control. PID control is simple in structure and easy to implement, but it is sensitive to changes in model parameters and external disturbances, exhibiting poor adaptability. Traditional sliding mode control, while achieving good results, is prone to chattering, leading to overheating of the robotic arm joint motors, accelerated wear, and even malfunction. Adaptive control enhances the system's ability to handle uncertainty, but its design is complex and parameter tuning is difficult. While deep learning-based intelligent control methods offer good predictive and estimation capabilities, they are computationally expensive and complex, placing high demands on the system's real-time performance. For robotic arm systems with external disturbances, dynamic errors, and uncertain modeling parameters, the methods proposed above cannot achieve the accuracy required in modern industrial manufacturing. Therefore, these robotic arm systems need to compensate for the total disturbance resulting from the combination of external disturbances, dynamic errors, and uncertain modeling parameters. Currently, most control methods use disturbance observers to compensate for the total disturbance; however, this approach, due to the limited performance of disturbance observers, cannot accurately estimate the total disturbance, ultimately affecting the trajectory tracking performance of the robotic arm.

[0004] Based on the above analysis, the main shortcomings of current research in related fields are: (1) The types of disturbances in robotic arm systems are diverse and dynamic changes are complex. Traditional trajectory tracking control algorithms are difficult to balance high precision and strong robustness, and cannot meet the dual requirements of precision and stability in modern industrial manufacturing; (2) Although some existing control algorithms perform well in certain performance indicators, such as control precision or response speed, they are often difficult to promote and apply in actual robotic arm systems due to problems such as high computational complexity, poor robustness, or excessive burden on the actuator; (3) In the control design for actual disturbance scenarios, there are still challenges in the effective estimation and compensation of total disturbances in the system, and there is a lack of reliable observation and compensation, which affects the stability of the system. Summary of the Invention

[0005] This invention addresses the shortcomings of existing technologies by providing a robotic arm trajectory tracking method and system based on interference estimation compensation, which can improve the stability and trajectory tracking performance of the robotic arm system.

[0006] This invention provides the following technical solution:

[0007] Firstly, a robotic arm trajectory tracking method based on disturbance estimation compensation is provided, including:

[0008] S1: Obtain the desired trajectory information of the robotic arm, including the desired position q. d Desired angular velocity Desired angular acceleration

[0009] S2: Based on the given total system disturbance d, establish a dynamic model of the robotic arm;

[0010] S3: Design a neural network disturbance observer to estimate the total system disturbance and obtain the system disturbance estimate y;

[0011] S4: Design a superhelical sliding mode controller and a globally nonsingular terminal sliding surface s, and obtain the equivalent control torque u based on the desired trajectory information of the robotic arm and the given total system disturbance d. eq ;

[0012] S5: Based on the system disturbance estimate y and equivalent control torque u eq We obtain the control law u of the robotic arm that satisfies the Lyapunov stability analysis, and realize the trajectory tracking of the robotic arm.

[0013] Optionally, the dynamic model of the robotic arm is:

[0014]

[0015] Among them, q, and These represent the angular position, angular velocity, and angular acceleration of each joint of the robotic arm, respectively, and τ is the torque applied to each joint of the robotic arm. These are estimates of the centrifugal force and Coriolis force matrices. This is an estimate of the gravity matrix. It is an estimate of the inverse matrix of a positive definite symmetric bounded inertia matrix.

[0016] Optionally, step S3 specifically includes:

[0017] S31: The neural network disturbance observer consists of an input layer, two hidden layers, and an output layer; the input layer receives input signals related to the system state (position and status) and control signals;

[0018] The output R of the k-th neuron in the first hidden layer k (t) is:

[0019]

[0020] Where, φ k (·) is the activation function for the first hidden layer. This represents the weighted connection from the l-th neuron in the input layer to the k-th hidden neuron in the first hidden layer, where k ranges from [1, m]. l (t) represents the output of the l-th neuron in the input layer;

[0021] The output S of the j-th neuron in the second hidden layer j (t) is:

[0022]

[0023] Where j takes values ​​in the range [1, n], ψ represents the weighted connection from the k-th neuron in the first hidden layer to the j-th neuron in the second hidden layer. j (·) is the activation function for the second hidden layer;

[0024] The output y(t) of the output layer is:

[0025]

[0026] in, This represents the weight connection from the j-th neuron in the second hidden layer to the output layer;

[0027] S32: Train a neural network disturbance observer using the training data, and use the trained neural network disturbance observer to estimate the total system disturbance and obtain the system disturbance estimate y.

[0028] Optionally, in step S32, the weights of the output layer and the two hidden layers are updated during training, specifically as follows:

[0029]

[0030] Where d(t) is the total system disturbance at time t, and η is the neural network learning rate.

[0031] Optionally, step S4 specifically includes:

[0032] S41: Design the globally non-singular terminal sliding surface s;

[0033]

[0034] Where e is the position tracking error, For angular velocity tracking error, c and b are two diagonal constant coefficient matrices;

[0035] S42: The design of a super-spiral sliding mode controller is as follows:

[0036]

[0037] in, Let v be the derivative of the sliding surface. The integral of λ and α represents the first and second control gains, respectively, and sign(·) is the sign function;

[0038] S43: Using the globally nonsingular terminal sliding surface s and the robotic arm dynamics model, the derivative of the sliding surface is... The conversion is performed, and the equivalent control torque u for robotic arm trajectory tracking is obtained. eq ;

[0039]

[0040] Optionally, step S5 specifically includes:

[0041] S51: Based on the system disturbance estimate y and equivalent control torque u eq To obtain the control law u of the robotic arm, the expression is:

[0042]

[0043] Where s is the sliding surface. v is The integral of , where e is the position tracking error. For angular velocity tracking error, c and b are two diagonal constant coefficient matrices;

[0044] S52: Set the Lyapunov stability function as follows:

[0045]

[0046] Among them, w h For neural network weights, It is the ideal weight, γ h represents the Lyapunov weighting factor, h = 1, 2, 3;

[0047] S53: Differentiate the Lyapunov stability function to obtain the constraints for asymptotic stability of the robotic arm system and the constraints for convergence within the effective time.

[0048] S54: Based on the constraints of asymptotic stability of the robotic arm system and the constraints of convergence within the effective time, the control law u of the robotic arm that satisfies the constraints is derived.

[0049] Optionally, step S53 specifically includes:

[0050] S531: Differentiate the Lyapunov stable function;

[0051]

[0052] Where η is the neural network learning rate, dw h Let J be the difference between the gradient value at the previous time step and the current time step, and Tr represent the trace of the matrix.

[0053] S532: Order The constraint condition for the asymptotic stability of the robotic arm system is and Negative definite;

[0054] When dw h and When the directions are the same, then

[0055] When sv-α·v·sign(s)≤0, or sv-α·v·sign(s)>0 and satisfies α≥s max At that time, Negative definite;

[0056] S533: The constraint condition for convergence within the effective time is:

[0057] Where ε is the convergence rate parameter, ε > 0, and γ is the fractional power parameter, 0 < γ < 1.

[0058] Secondly, a robotic arm trajectory tracking system based on interference estimation compensation is provided, including:

[0059] Desired trajectory information acquisition module: Acquires the desired trajectory information of the robotic arm, including the desired position q. dDesired angular velocity Desired angular acceleration

[0060] Model building module: Based on the given total system disturbance d, establish the dynamic model of the robotic arm;

[0061] Disturbance estimation module: Design a neural network disturbance observer to estimate the total system disturbance and obtain the system disturbance estimate y;

[0062] Equivalent control torque acquisition module: Design a super-helical sliding mode controller and a globally non-singular terminal sliding surface s to acquire the equivalent control torque u based on the desired trajectory information of the robotic arm and the given total system disturbance d. eq ;

[0063] Trajectory tracking module: based on system disturbance estimate y and equivalent control torque u eq We obtain the control law u of the robotic arm that satisfies the Lyapunov stability analysis, and realize the trajectory tracking of the robotic arm.

[0064] Thirdly, a computer device is provided, including a processor and a memory; wherein, when the processor executes a computer program stored in the memory, it implements the steps of the robotic arm trajectory tracking method based on interference estimation compensation as described in any one of the first aspects.

[0065] Fourthly, a computer-readable storage medium is provided for storing a computer program; when the computer program is executed by a processor, it implements the steps of the robotic arm trajectory tracking method based on interference estimation compensation as described in any one of the first aspects.

[0066] Compared with the prior art, the beneficial effects of the present invention are:

[0067] This invention compensates for errors in a robotic arm system, including external disturbances and dynamic errors, using a neural network disturbance observer. It also utilizes a global super-helical sliding mode controller to compensate for unobservable errors in the robotic arm system, i.e., modeling uncertain parameter errors, ultimately achieving stability and improved trajectory tracking performance, thus enhancing the accuracy of trajectory tracking. The neural network reduces the computational cost of trajectory tracking. The introduction of an integral term effectively reduces chattering during the sliding mode control process. The disturbance observer and sliding mode controller ensure the stability of the robotic arm system. This invention balances high precision with strong robustness, meeting the dual requirements of precision and stability in modern industrial manufacturing. Attached Figure Description

[0068] Figure 1 This is a flowchart of the robotic arm trajectory tracking method based on interference estimation compensation according to the present invention;

[0069] Figure 2This is a diagram showing the composition of the neural network interference observer of the present invention;

[0070] Figure 3 This is a comparison chart of interference observer estimation provided by an embodiment of the present invention;

[0071] Figure 4 This is a tracking error curve provided by an embodiment of the present invention;

[0072] Figure 5 This is a control torque output curve provided by an embodiment of the present invention. Detailed Implementation

[0073] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0074] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the term "comprising" and any variations thereof are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0075] Example 1

[0076] like Figure 1 As shown, a robotic arm trajectory tracking method based on disturbance estimation compensation is provided, including:

[0077] S1: Obtain the desired trajectory information of the robotic arm, including the desired position q. d Desired angular velocity Desired angular acceleration

[0078] The acquisition of desired trajectory information can refer to existing technologies. Optionally, the desired position of each joint of the robotic arm can be set as q. d1 =q d2 =q d3 =10sin(0.5πt)+10sin(πt), q d4 =q d5 =q d6 =5sin(0.1πt), expected angular velocity of each joint The expected angular acceleration of each joint can be obtained by taking the first derivative of the expected trajectory of each joint. The second derivative can be obtained from the expected trajectory of each joint.

[0079] S2: Based on the given total system disturbance d, establish a dynamic model of the robotic arm.

[0080] Specifically, S21: Establish the dynamic model of the robotic arm, as shown below:

[0081]

[0082] In the formula, q, Let M(q) represent the angular position, angular velocity, and angular acceleration of each joint of the robotic arm, respectively. M(q) is a positive definite symmetric bounded inertia matrix. G(q) is the centrifugal force and Coriolis force matrix, G(q) is the gravity matrix, τ is the torque applied to each joint of the robotic arm, and d is the total disturbance of the system.

[0083] For example, the initial system state is set to q = [0,0,0,0,0,0]. T ,

[0084] S22: The robotic arm system has modeling errors, as shown below:

[0085]

[0086] in, and M(q), respectively And the estimated value of G(q);

[0087] Therefore, the total disturbance of the system can be written as:

[0088]

[0089] in This is dynamic error;

[0090] For example, let the dynamic error Let external interference τ d =[τ d1 ,τ d2 ,τ d3 ,τ d4 ,τ d5 ,τ d6 ] T , where τ d1 =0.04sin(πt), τ d2 =0.04sin(0.5πt)+0.4sin(πt),τ d3=0.04sin(πt)+0.4sin(0.5πt),τ d4 =0.01cos(0.2πt)+0.01cos(0.4πt),τ d5 =0.01cos(0.5πt), τ d6 =0.01cos(πt). The modeling uncertainty parameters are set as ΔM = 0.2M, ΔC = 0.2C, and ΔG = 0.2G.

[0091] S23: The dynamic model of the robotic arm is rewritten in the following form:

[0092]

[0093] S3: Design a neural network disturbance observer to estimate the total system disturbance and obtain the system disturbance estimate y.

[0094] S31: The neural network disturbance observer consists of an input layer, two hidden layers, and an output layer; the input layer receives input signals related to the system state (position and status) and control signals.

[0095] like Figure 2 As shown, the input layer is set to have i neurons, which receive input signals related to the system state and control signals. The output of the l-th neuron is a. l (t), where l takes values ​​in the range [1, i];

[0096] For example, i = 7, and the range of l is [1, 7].

[0097] If the first hidden layer has m neurons, then the output R of the k-th neuron is... k (t) is:

[0098]

[0099] Where, φ k (·) is the activation function for the first hidden layer. For the weighted connection from the l-th neuron in the input layer to the k-th hidden neuron in the first hidden layer, k takes values ​​in the range [1, m]; alternatively, m = 10, and k takes values ​​in the range [1, 10], φ k (·) = tanh(·).

[0100] Let the second hidden layer have n neurons, and let the output S of the j-th neuron in the second hidden layer be... j (t) is:

[0101]

[0102] Where j takes values ​​in the range [1, n], ψ represents the weighted connection from the k-th neuron in the first hidden layer to the j-th neuron in the second hidden layer. j (·) is the activation function for the second hidden layer; alternatively, n = 5, j takes values ​​in the range [1, 5], and φ k (·) = tanh(·).

[0103] The output y(t) of the output layer is:

[0104]

[0105] in, This represents the weight connection from the j-th neuron in the second hidden layer to the output layer.

[0106] S32: Train a neural network disturbance observer using the training data, and use the trained neural network disturbance observer to estimate the total system disturbance and obtain the system disturbance estimate y.

[0107] The weights of the output layer and the two hidden layers are updated during training, specifically as follows:

[0108]

[0109] Where d(t) is the total system disturbance at time t, and η is the neural network learning rate.

[0110] The specific training process of the neural network interference observer is based on existing technologies, as is the acquisition of training data.

[0111] Figure 3 In the figures (a)-(f), the interference observer estimates for the six joints of the robotic arm are compared. Figure 3 In the diagram, the solid red lines represent the interference values ​​of each joint, the dotted blue lines represent the estimation results of the interference values ​​by the neural network interference observer method provided by this invention, and the dashed black lines represent the estimation results of the interference values ​​by the nonlinear interference observer design method. Figure 3 It is evident that this application significantly improves the estimation results of interference values.

[0112] S4: Design a superspiral sliding mode controller and a globally nonsingular terminal sliding surface s, and obtain the equivalent control torque u based on the given total system disturbance d. eq .

[0113] Specifically, S41: Design the globally non-singular terminal sliding surface s;

[0114]

[0115] Where e is the position tracking error, For angular velocity tracking error, c and b are two diagonal constant coefficient matrices;

[0116] Alternatively, c = diag[2,2,2,2,2,2] and b = diag[3,3,3,3,3,3], where diag[·] represents the values ​​inside the diagonal, and all elements outside the diagonal are 0.

[0117] S42: The design of a super-spiral sliding mode controller is as follows:

[0118]

[0119] in, Let v be the derivative of the sliding surface. The integral of λ and α is the first and second control gain, respectively, and sign(·) is the sign function, satisfying λ, α≥0;

[0120] For example, λ = 1, α = 1.

[0121] S43: Using the globally nonsingular terminal sliding surface s and the robotic arm dynamics model, the derivative of the sliding surface is... The conversion is performed, and the equivalent control torque u for robotic arm trajectory tracking is obtained. eq .

[0122] Specifically, based on the robotic arm's desired trajectory information obtained in step S1, including the desired position q... d Desired angular velocity Desired angular acceleration The position tracking error e and the angular velocity tracking error are obtained. and angular acceleration tracking error As shown below:

[0123]

[0124] Based on the derivative of the superspiral sliding mode controller with respect to the globally non-singular terminal sliding surface s:

[0125]

[0126] The equivalent control u for robotic arm trajectory tracking is obtained. eq :

[0127]

[0128] S5: Based on the system disturbance estimate y and equivalent control torque u eq We obtain the control law u of the robotic arm that satisfies the Lyapunov stability analysis, and realize the trajectory tracking of the robotic arm.

[0129] S51: Based on the system disturbance estimate y and equivalent control torque u eq To obtain the control law u of the robotic arm, the expression is:

[0130]

[0131] Where s is the sliding surface. v is The integral of , where e is the position tracking error. Let c be the angular velocity tracking error, and b be two diagonal constant coefficient matrices.

[0132] S52: Set the Lyapunov stability function as follows:

[0133]

[0134] Among them, w h For neural network weights, It is the ideal weight, γ h represents the Lyapunov weighting factor, h = 1, 2, 3;

[0135] S53: Differentiate the Lyapunov stability function to obtain the constraints for asymptotic stability of the robotic arm system and the constraints for convergence within the effective time.

[0136] Step S53 is as follows:

[0137] S531: Differentiate the Lyapunov stable function;

[0138]

[0139] Where η is the neural network learning rate, dw h Let J be the difference between the previous and current values ​​of the gradient, and Tr denote the trace over the matrix; as a choice of location, the gradient J is...

[0140] S532: Order in Used to analyze the stability of superspiral sliding mode control. The constraints for asymptotic stability of the robotic arm system, used to analyze the stability of a neural network disturbance observer, are as follows: and Negative definite;

[0141] When dw h and When the directions are the same, then

[0142] When sv-α·v·sign(s)≤0, or sv-α·v·sign(s)>0 and satisfies α≥s max At that time, Negative definite;

[0143] S533: The constraint condition for convergence within the effective time is:

[0144] Where ε is the convergence rate parameter, ε > 0, and γ is the fractional power parameter, 0 < γ < 1.

[0145] That is, the robotic arm system is asymptotically stable and satisfies If the form is given, where ε > 0 and 0 < γ < 1, then the system has an effective time T. f Convergence;

[0146] in

[0147] S54: Based on the constraints of asymptotic stability of the robotic arm system and the constraints of convergence within the effective time, the control law u of the robotic arm that satisfies the constraints is derived.

[0148] Figure 4 In the figure, (a)-(f) are the tracking error curves of the six joints of the robotic arm, respectively. Figure 4 In the diagram, the solid red lines represent the joint tracking error curves of the traditional sliding mode control method based on neural network disturbance observation; the dashed purple lines represent the joint tracking error curves of the non-singular terminal sliding mode control method based on neural network disturbance observation; the dotted blue lines represent the joint tracking error curves of the fast non-singular terminal sliding mode control method based on neural network disturbance observation; and the solid black lines represent the joint tracking error curves of the robotic arm trajectory tracking method based on a neural network disturbance observer and global super-helical sliding mode control provided by this invention. Figure 4 It can be seen that the robotic arm trajectory tracking method based on neural network disturbance observer and global superhelical sliding mode control proposed in this application has the lowest tracking error for each joint.

[0149] like Figure 5 As shown, the control torque output curve provided by this invention is in Figure 5 In the figures, (a) is the joint control torque output curve of the traditional sliding mode control method based on neural network disturbance observation; (b) is the joint control torque output curve of the non-singular terminal sliding mode control method based on neural network disturbance observation; (c) is the joint control torque output curve of the fast non-singular terminal sliding mode control method based on neural network disturbance observation; and (d) is the joint control torque output curve of the robotic arm trajectory tracking method based on neural network disturbance observer and global superhelical sliding mode control provided by this invention. Figure 5 It can be seen that the output of the control torque in this application is more stable and avoids the phenomenon of vibration.

[0150] Example 2

[0151] A robotic arm trajectory tracking system based on disturbance estimation compensation includes:

[0152] Desired trajectory information acquisition module: Acquires the desired trajectory information of the robotic arm, including the desired position q. d Desired angular velocity Desired angular acceleration

[0153] Model building module: Based on the given total system disturbance d, establish the dynamic model of the robotic arm;

[0154] Disturbance estimation module: Design a neural network disturbance observer to estimate the total system disturbance and obtain the system disturbance estimate y;

[0155] Equivalent control torque acquisition module: Design a super-helical sliding mode controller and a globally non-singular terminal sliding surface s to acquire the equivalent control torque u based on the desired trajectory information of the robotic arm and the given total system disturbance d. eq ;

[0156] Trajectory tracking module: based on system disturbance estimate y and equivalent control torque u eq We obtain the control law u of the robotic arm that satisfies the Lyapunov stability analysis, and realize the trajectory tracking of the robotic arm.

[0157] For more detailed information on the above methods, please refer to the relevant content disclosed in the foregoing embodiments, which will not be repeated here.

[0158] Example 3

[0159] The present invention provides a computer device, including a processor and a memory; wherein, when the processor executes a computer program stored in the memory, it implements the steps of the above-described robotic arm trajectory tracking method based on interference estimation compensation.

[0160] For more detailed information on the above methods, please refer to the relevant content disclosed in the foregoing embodiments, which will not be repeated here.

[0161] Example 4

[0162] The present invention provides a computer-readable storage medium for storing a computer program; when the computer program is executed by a processor, it implements the steps of the above-described robotic arm trajectory tracking method based on interference estimation compensation.

[0163] For more detailed information on the above methods, please refer to the relevant content disclosed in the foregoing embodiments, which will not be repeated here.

[0164] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. The systems, devices, and storage media disclosed in the embodiments are described simply because they correspond to the methods disclosed in the embodiments; relevant details can be found in the method section.

[0165] Those skilled in the art will clearly understand that the techniques in the embodiments of the present invention can be implemented using software plus necessary general-purpose hardware platforms. Based on this understanding, the technical solutions in the embodiments of the present invention, or the parts that contribute to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in various embodiments or certain parts of the embodiments of the present invention.

[0166] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A robotic arm trajectory tracking method based on disturbance estimation compensation, characterized in that, include: S1: Obtain the desired trajectory information of the robotic arm, including the desired position. Desired angular velocity Desired angular acceleration ; S2: Based on the given total system disturbance Establish a dynamic model of the robotic arm; S3: Design a neural network disturbance observer to estimate the total system disturbance and obtain the system disturbance estimate. ; S4: Design a superspiral sliding mode controller and a globally non-singular terminal sliding surface. s To obtain information based on the desired trajectory of the robotic arm and the total disturbance of the given system. Equivalent control torque ; S5: Based on system disturbance estimation and equivalent control torque Obtain the control law of the robotic arm that satisfies Lyapunov stability analysis. To achieve trajectory tracking of the robotic arm; The dynamic model of the robotic arm is as follows: in, , and These are the angular positions, angular velocities, and angular accelerations of each joint of the robotic arm. To apply torque to each joint of the robotic arm, These are estimates of the centrifugal force and Coriolis force matrices. This is an estimate of the gravity matrix. It is an estimate of the inverse matrix of a positive definite symmetric bounded inertia matrix; Step S4 is as follows: S41: Design a globally nonsingular terminal sliding surface s ; in, For position tracking error, For angular velocity tracking error, and These are two diagonal matrices with constant coefficients; S42: The design of a super-spiral sliding mode controller is as follows: in, For sliding surface s The derivative of v for The points, and These are the first and second control gains, respectively. It is a symbolic function; S43: Utilizing a globally non-singular terminal sliding surface s And the robotic arm dynamics model, the derivative of the sliding surface The process involves conversion and obtaining the equivalent control torque for robotic arm trajectory tracking. ; ； Step S5 is as follows: S51: Based on system disturbance estimation and equivalent control torque Obtain the control law of the robotic arm The expression is: in, For sliding surface, , v for The points, For position tracking error, For angular velocity tracking error, and These are two diagonal matrices with constant coefficients; S52: Set the Lyapunov stability function as follows: in, For neural network weights, It is the ideal weight. For Lyapunov weighting factors, ; S53: Differentiate the Lyapunov stability function to obtain the constraints for asymptotic stability of the robotic arm system and the constraints for convergence within the effective time. S54: Based on the constraints of asymptotic stability and convergence within the effective time of the robotic arm system, the control law of the robotic arm that satisfies the constraints is derived. .

2. The robotic arm trajectory tracking method based on interference estimation compensation according to claim 1, characterized in that, Step S3 is as follows: S31: The neural network disturbance observer consists of an input layer, two hidden layers, and an output layer; the input layer receives input signals related to the system state (position and status) and control signals; The first hidden layer k The output of each neuron for: in, The activation function for the first hidden layer. For the input layer The first hidden layer contains 1 neuron. k The weight connections of the hidden neurons, k The range of values ​​for is [1, ...]. m ], For the input layer The output of each neuron; The second hidden layer j The output of each neuron for: in, j The range of values ​​for is [1, ...]. n ], This represents the first hidden layer. k The first neuron is connected to the second hidden layer. j The weight connections of each neuron, This is the activation function for the second hidden layer; Output of the output layer for: in, This indicates the second hidden layer. j Weight connections from each neuron to the output layer; S32: Train a neural network disturbance observer using the training data, and use the trained neural network disturbance observer to estimate the total system disturbance and obtain the system disturbance estimate. .

3. The robotic arm trajectory tracking method based on interference estimation compensation according to claim 2, characterized in that, Step S32 involves updating the weights of the output layer and the two hidden layers during training, specifically as follows: in, Let t be the total system disturbance at time t. This represents the learning rate of the neural network.

4. The robotic arm trajectory tracking method based on interference estimation compensation according to claim 1, characterized in that, Step S53 is as follows: S531: Differentiate the Lyapunov stable function; in, For the neural network learning rate, gradient The difference between the previous time value and the current time value, Represents the trace of a matrix; S532: Order , , The constraint condition for the asymptotic stability of the robotic arm system is: and Negative definite; when and When the directions are the same, then ; when ,or And satisfy , At that time, Negative definite; S533: The constraint condition for convergence within the effective time is: in, For the convergence rate parameter, , For fractional power parameters, .

5. A robotic arm trajectory tracking system based on interference estimation compensation, comprising the steps of the robotic arm trajectory tracking method based on interference estimation compensation as described in any one of claims 1-4, characterized in that, include: Desired trajectory information acquisition module: Acquires the desired trajectory information of the robotic arm, including the desired position. Desired angular velocity Desired angular acceleration ; Model building module: based on the total disturbance of the given system Establish a dynamic model of the robotic arm; Disturbance estimation module: Designs a neural network disturbance observer to estimate the total system disturbance and obtain the system disturbance estimate. ; Equivalent control torque acquisition module: Design of super-helical sliding mode controller and globally non-singular terminal sliding surface s To obtain information based on the desired trajectory of the robotic arm and the total disturbance of the given system. Equivalent control torque ; Trajectory tracking module: based on system disturbance estimates and equivalent control torque Obtain the control law of the robotic arm that satisfies Lyapunov stability analysis. This enables the tracking of the robotic arm's trajectory.

6. A computer device, characterized in that, It includes a processor and a memory; wherein, when the processor executes the computer program stored in the memory, it implements the steps of the robotic arm trajectory tracking method based on interference estimation compensation as described in any one of claims 1-4.

7. A computer-readable storage medium, characterized in that, Used to store computer programs; when the computer programs are executed by a processor, they implement the steps of the robotic arm trajectory tracking method based on interference estimation compensation as described in any one of claims 1-4.

Images