Self-adaptive iterative learning method and system for high-precision position tracking of uncertain industrial robot
By constructing a dynamic model and an adaptive iterative learning control method, the problems of reduced positioning accuracy and motion instability of industrial robots caused by uncertainty are solved, and high-precision position tracking and stable control are achieved.
Patent Information
- Application Number
- CN202510917440.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-03
- Publication Date
- 2025-08-26
AI Technical Summary
Traditional control methods are difficult to effectively deal with the problems of reduced positioning accuracy and motion instability of industrial robots caused by uncertainty factors, especially in complex environments, which are difficult to achieve high-precision position tracking.
Adaptive iterative learning method for high-precision position tracking of uncertain industrial robots is adopted, and control input is gradually corrected to overcome the influence of uncertainty factors by constructing dynamic models, Fourier series expansion, fuzzy approximator and adaptive iterative learning control.
High-precision position tracking control over a limited time is realized, the system's anti-interference ability and robustness is improved, and the robot can quickly and accurately track the expected trajectory and maintain stable operation.
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Figure CN120533709A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of intelligent control, and in particular to an adaptive iterative learning system for high-precision position tracking of uncertain industrial robots. Background Art
[0002] Robots, a product of the concentrated application of modern science and technology, have permeated every aspect of our lives. A wide variety of robots, ranging from large industrial robots to tiny yet precise medical robots, are now in use. Robots of all shapes and sizes play a vital role in industrial robotics. Uncertainty in industrial robots primarily refers to the uncertainty inherent in industrial robotic systems. This uncertainty encompasses a variety of factors, such as environmental disturbances, parameter variations, and unmodeled dynamics. These factors lead to discrepancies between the robot model and the actual operating system, impacting aspects of the robot's high-precision positioning, motion control, and path planning. Therefore, the development of high-precision position tracking control technology within a limited time interval is a pressing priority.
[0003] Due to the existence of uncertainty factors, traditional linear or time-invariant control methods may not be able to effectively deal with this uncertainty. Uncertainty factors will also affect the positioning accuracy of the robot, causing the robot to be unable to reach the preset designated position, and various unstable phenomena such as jitter offset will occur during the movement, which will increase the difficulty of control. The methods usually used to deal with uncertain industrial robot models are robust control and adaptive sliding mode control. Robust control is to achieve system stability in the presence of uncertainty factors by designing a robust controller. Adaptive control is a control method that can spontaneously adjust parameters according to changes in external environmental factors and the system's own state. However, robust control has disadvantages such as limitations and flexibility, while adaptive control has disadvantages such as slow parameter convergence. Summary of the Invention
[0004] In response to the problems mentioned in the prior art, the present invention proposes an adaptive iterative learning and system for high-precision position tracking of uncertain industrial robots, which uses intelligent control technology to control the relative position of the robot, improve control accuracy, and thus achieve precise motion control of the robot.
[0005] In order to achieve the above object, the present invention adopts the following technical solutions: The present invention proposes an adaptive iterative learning method for high-precision position tracking of an uncertain industrial robot, comprising the following steps: Constructing a dynamic model of an industrial robot under uncertain working conditions, wherein the dynamic model includes unknown time-varying parameters, and generating a tracking error based on the dynamic model; Performing a Fourier series expansion on the unknown time-varying parameter to obtain a decomposition formula after the expansion, constructing a fuzzy approximator according to the decomposition formula, and generating an estimation error and an approximation error through the fuzzy approximator; Process the estimation error and approximation error to obtain the error function; A virtual control input is constructed according to the tracking error and the error function, and the actual control input is generated according to the virtual control input to realize the position control of the industrial robot.
[0006] As a further improvement of the present invention, the dynamic model of the industrial robot is as follows:
[0007] Where: It is the first nonlinear parameterized robot system i state variables; Represents the corresponding state vector The differential of is the control input of the nonlinear parameterized robot system; is the dynamic dimension of the system; is an unknown bounded external disturbance; Contains unknown time-varying parameters The unmodeled dynamics of Represents the robot's position state information, including model uncertainty and unknown time-varying disturbances; Indicates the actual trajectory output of the system; Indicates the number of iterations.
[0008] As a further improvement of the present invention, the tracking error is expressed as follows:
[0009] Where: represents the tracking error; Indicates the actual trajectory output of the system; represents the ideal trajectory.
[0010] As a further improvement of the present invention, the expanded decomposition formula is shown below:
[0011] Where: Represents the trigonometric function matrix about time; The weight matrix expressed as a Fourier series; is the residual error after Fourier series expansion; Indicates the upper bound; The fuzzy approximator is shown as follows:
[0012] in:
[0013] Where: It's about parameters and Fourier series of order fuzzy basis function vector; and is the weight matrix, where and is bounded; satisfies , , and is an unknown positive number; Represents the new FSE-FLS approximator With the original approximator The difference between express The transpose of Indicates the number of iterations.
[0014] As a further improvement of the present invention, the estimated error is expressed as follows:
[0015]
[0016] Where: and is an unknown quantity; and The unknown quantities and estimated value of; and is the estimation error; The approximation error is expressed as follows:
[0017] Where: for The derivative of is the residual error.
[0018] As a further improvement of the present invention, an error function is obtained, including: To deal with the unknown upper bounds of the estimation error and approximation error, a convergent series sequence is introduced: , , and satisfy:
[0019] At the beginning of each iteration, the initial error value should satisfy , ,in is a convergent series sequence; Therefore, the error function As shown in the following formula:
[0020] Where: represents the improved time-varying boundary layer; represents a saturation function.
[0021] As a further improvement of the present invention, a virtual control input is constructed according to the tracking error and the error function, and an actual control input is generated according to the virtual control input, including: The virtual control input is shown as follows:
[0022] Where: is the virtual control input; is the coefficient; is a convergent series sequence, ; represents the weight of the estimation error; represents the differential of the ideal trajectory; Introducing a first-order low-pass filter to the virtual control input , which is used to prevent gradient explosion caused by subsequent differentiation, as shown in the following formula:
[0023] Where: for The differential of represents the virtual control input, is the weight coefficient and satisfies ; The actual control input is shown as follows:
[0024] Where: 、 and The update rate of the table weight coefficient needs to be given; and represents the fuzzy basis function vector; represents the newly defined error function; is the coefficient; is a convergent series sequence; is the error function; For filter With state variables The difference between .
[0025] The present invention proposes an adaptive iterative learning system for high-precision position tracking of uncertain industrial robots, comprising: A construction module is used to construct a dynamic model of the industrial robot under uncertain working conditions, wherein the dynamic model includes unknown time-varying parameters and generates a tracking error according to the dynamic model; an error generation module, configured to perform a Fourier series expansion on the unknown time-varying parameter to obtain a decomposition formula after the expansion, construct a fuzzy approximator based on the decomposition formula, and generate an estimation error and an approximation error through the fuzzy approximator; Function generation module, used to process estimation error and approximation error to obtain error function; The control module constructs a virtual control input based on the tracking error and the error function, and generates an actual control input based on the virtual control input to realize the position control of the industrial robot.
[0026] The present invention proposes an adaptive iterative learning device for high-precision position tracking of an uncertain industrial robot, comprising a processor and a memory, wherein the processor implements the above-mentioned adaptive iterative learning method for high-precision position tracking of an uncertain industrial robot when executing a computer program stored in the memory.
[0027] A computer-readable storage medium is used to store a computer program, wherein when the computer program is executed by a processor, it implements the above-mentioned high-precision position tracking adaptive iterative learning method for uncertain industrial robots.
[0028] Compared with the prior art, the present invention has achieved the following technical effects: The present invention regards the uncertain industrial robot as a particle system and models it as a nonlinear parameterized system, and combines it with the filtered adaptive iterative learning control theory to achieve high-precision position tracking control of the robot within a limited time interval; compared with traditional control methods, due to the complex working environment of industrial robots, there are many uncertain factors such as environmental interference, changes in the robot's own parameters and unmodeled dynamics, which makes it difficult to achieve accurate tracking of the robot's position and cannot meet the needs of high-precision processing. The adaptive iterative learning control method adopted by the present invention can gradually correct the control input through continuous iterative learning, effectively overcoming the influence of these uncertain factors.
[0029] This invention utilizes filtering technology to process system state and error information during each iteration, improving the system's anti-interference capability and robustness. After multiple iterations, the robot can quickly and accurately track the desired trajectory and achieve precise position control. Furthermore, this control method exhibits excellent adaptability, automatically adjusting the control strategy based on changes in robot parameters to ensure stable system operation. BRIEF DESCRIPTION OF THE DRAWINGS
[0030] Figure 1 It is a schematic diagram of the overall process of the present invention; Figure 2 The displacement error curve within 500ms of the industrial robot during 100 iterations provided for the simulation verification of the method of the present invention; Figure 3 Schematic diagram of the method of the present invention. DETAILED DESCRIPTION
[0031] The present invention will be further described in detail below with reference to the accompanying drawings and examples. It will be understood that the specific embodiments described herein are intended only to illustrate the present invention and are not intended to limit the present invention. It should also be noted that, for ease of description, the accompanying drawings only illustrate portions relevant to the present invention, not all structures.
[0032] See also Figure 1 and Figure 3 The present invention proposes an adaptive iterative learning method for high-precision position tracking of an uncertain industrial robot, comprising the following steps: Constructing a dynamic model of an industrial robot under uncertain working conditions, wherein the dynamic model includes unknown time-varying parameters, and generating a tracking error based on the dynamic model; Performing a Fourier series expansion on the unknown time-varying parameter to obtain a decomposition formula after the expansion, constructing a fuzzy approximator according to the decomposition formula, and generating an estimation error and an approximation error through the fuzzy approximator; Process the estimation error and approximation error to obtain the error function; A virtual control input is constructed according to the tracking error and the error function, and the actual control input is generated according to the virtual control input to realize the position control of the industrial robot.
[0033] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments: Step 1: Construct a dynamic model of the uncertain robot.
[0034] Considering the robot as a mass point system and considering uncertain working conditions (such as load changes and hydraulic pressure fluctuations), the dynamic model is established through dynamic research on uncertain robots as follows:
[0035] Where: are the state variables of the nonlinear parameterized robot system; is the control input of the nonlinear parameterized robot system; is the dynamic dimension of the system; is an unknown bounded external disturbance; Contains unknown time-varying parameters The unmodeled dynamics of Represents the corresponding state vector The differential of Represents the robot's position state information, including model uncertainty and unknown time-varying disturbances; Indicates the actual trajectory output of the system; Indicates the number of iterations.
[0036] Step 2: Based on the approximation theory, an intelligent model is established for the uncertain part of the uncertain industrial robot model, and the position tracking error of the robot is determined. The tracking error in the embodiment is shown as follows:
[0037] Where: represents the tracking error; Indicates the actual trajectory output of the system; represents the ideal trajectory.
[0038] This embodiment considers the robot position tracking control under the conditions of model uncertainty and unknown interference and initial state error in each iteration, and only provides theoretical reference.
[0039] Step 2.1: Processing of unknown time-varying parameters in uncertain industrial robot models: In a finite time interval, the unknown time-varying parameters are regarded as periodic signals, so Expanded into a Fourier series .
[0040] Where: is the weight matrix of the Fourier series; Represents the trigonometric function matrix about time; is the residual error after Fourier series expansion; Indicates the upper bound.
[0041] Step 2.2: Create a new fuzzy approximator and and They are modeled as:
[0042] in:
[0043] Where: It's about parameters and Fourier series of order fuzzy basis function vector; and is the weight matrix, where and is bounded; satisfies , , and is an unknown positive number; Represents the new FSE-FLS approximator With the original approximator The difference between express The transpose of Indicates the number of iterations.
[0044] The estimated error in the embodiment is shown as follows:
[0045]
[0046]
[0047] Where: 、 and is an unknown quantity; 、 and is an estimate of the unknown quantity; 、 and is the estimation error; ,in represents the sum of higher-order terms in the Taylor series expansion.
[0048] The approximation error of the embodiment is:
[0049] In the above formula:
[0050] Where: , , ; Remainder The boundary is .
[0051] Step 2.3, error function design and unknown bound processing: For the treatment of the unknown upper bound of each error term, the following typical convergent series sequence is introduced: , ,satisfy .
[0052] At the beginning of each iteration, the initial error value should satisfy , ,in is a convergent series sequence; Constructing error function for:
[0053] in, is a saturation function, and its expression is
[0054] in, It is an improved time-varying layer boundary.
[0055] Step 3: Based on the adaptive iterative learning control theory, a finite-time high-precision position tracking control strategy for the uncertain industrial robot is proposed. The specific implementation steps are as follows: Step 3.1: Design virtual control input
[0056] Designing a new error function and ( )as follows:
[0057]
[0058] Where: and is the newly defined error function, is the error compensation mechanism, is a first-order low-pass filter, is the error function, is an improved time-varying layer boundary, is a convergent series sequence, is the design error coefficient.
[0059] For the first subsystem of the robot model:
[0060] According to the position tracking error, the Lyapunov function is selected as ; In order to make Semi-negative definite, the virtual control input is designed as follows:
[0061] Where: is the virtual control input; is the coefficient; is a convergent series sequence, Step 3.2: Introduce a first-order low-pass filter , removing the gradient explosion problem:
[0062] Where: for The differential of represents the virtual control input, is the weight coefficient and satisfies .
[0063] Step 3.3: Design the actual control input and parameter adaptation law
[0064] Designing a new error function for:
[0065] Select the Lyapunov function:
[0066] Taking its derivative we get:
[0067] in
[0068] Where: is the expected value of the weight matrix of the dynamic model, is the expected value of the weight matrix of external interference, The expected value of the evidence for the weights of the Fourier coefficients, is the expected value of the error coefficient weight matrix, and represents the fuzzy basis function vector, 、 、 and are the coefficients of the designed Lyapunov function, is a convergent series, is the newly defined error function; is the time-dependent trigonometric matrix, is the number of iterations.
[0069] The actual control input is designed as:
[0070] Where: 、 and The update rate of the table weight coefficient needs to be given; and represents the fuzzy basis function vector; is the newly defined error function; is the coefficient; is a convergent series sequence; Error function; For filter With state variables The difference between .
[0071] Select the parameter update law as:
[0072] Where: is the expected value of the weight matrix of the dynamic model, is the expected value of the weight matrix of external interference, The expected value of the evidence for the weights of the Fourier coefficients, is the expected value of the error coefficient weight matrix, and represents the fuzzy basis function vector, 、 、 and are the coefficients of the designed Lyapunov function, is a convergent series, is the newly defined error function; is the time-dependent trigonometric matrix, is the number of iterations.
[0073] Step 4: Stability Proof and Simulation Analysis This section is a detailed proof of Theorem 1. The specific process is as follows: According to hypothesis 1, . Take the Lyapunov function as ,have
[0074] in, , , , , .
[0075] definition , so the above formula can be rewritten as
[0076] According to the properties of convergent series, we know that ,therefore, is bounded, and has ,therefore
[0077] It is arbitrary, for , we can get
[0078] is bounded. Through the concept of convergent series sequence, is bounded, and has , so we can get It is also bounded.
[0079] for , , and .
[0080] For any , we can get is bounded, so we can get It is bounded.
[0081] Most importantly, for any , is bounded, so we have , , and They are all bounded. is also bounded. Bounded, and by It is uniformly continuous, so it can be proved that in a finite time interval and under uncertain working conditions, the robot's position tracking error can converge to zero as the number of iterations increases, that is, the task of high-precision tracking is completed.
[0082] Simulation verification: This section verifies the effectiveness of the designed control strategy through numerical examples. The state equation of the uncertain robot is:
[0083] in, .
[0084] The reference model of the system is:
[0085] In the formula is the displacement of the robot. is the velocity of the robot. The desired target trajectory given by the reference model is .
[0086] The adaptive iterative learning control strategy is selected as follows
[0087] And determine the parameter update law
[0088] In the formula , , , , , , , . First, define three fuzzy flags , they evenly cover the input domain. , corresponding to the four inputs of the system. Represents the three fuzzy sets corresponding to a certain input of the system. When using fuzzy logic to approximate a function, the following three membership functions are taken: For input , we choose the membership function as: , , . For input , we choose the membership function as: , , ,. For input , we choose the membership function as: , , . For the uncertain items in the system, the fuzzy IF-THEN rules are selected as follows:
[0089] in , , .
[0090] You can get:
[0091] in is a matrix A parameter in . Introducing vector , formula (91) is written as:
[0092] in is a 216-dimensional vector, where The elements are:
[0093] The simulation results are as follows Figure 2 As shown in the figure, with the increase of the number of iterations, the robot can achieve high-precision position tracking.
[0094] Based on the same inventive concept, an embodiment of the present invention also provides an uncertain industrial robot high-precision position tracking adaptive iterative learning system. Since the principle of solving the problem by the uncertain industrial robot high-precision position tracking adaptive iterative learning system is similar to the aforementioned uncertain industrial robot high-precision position tracking adaptive iterative learning method, the implementation of the uncertain industrial robot high-precision position tracking adaptive iterative learning system can refer to the implementation of the uncertain industrial robot high-precision position tracking adaptive iterative learning method, and the repeated parts will not be repeated.
[0095] In specific implementation, the embodiment of the present invention provides a high-precision position tracking adaptive iterative learning system for uncertain industrial robots, specifically including: A construction module is used to construct a dynamic model of the industrial robot under uncertain working conditions, wherein the dynamic model includes unknown time-varying parameters and generates a tracking error according to the dynamic model; an error generation module, configured to perform a Fourier series expansion on the unknown time-varying parameter to obtain a decomposition formula after the expansion, construct a fuzzy approximator based on the decomposition formula, and generate an estimation error and an approximation error through the fuzzy approximator; Function generation module, used to process estimation error and approximation error to obtain error function; The control module constructs a virtual control input based on the tracking error and the error function, and generates an actual control input based on the virtual control input to realize the position control of the industrial robot.
[0096] Correspondingly, an embodiment of the present invention also provides an adaptive iterative learning device for high-precision position tracking of an uncertain industrial robot, comprising a processor and a memory, wherein when the processor executes the computer program stored in the memory, it implements the adaptive iterative learning method for high-precision position tracking of an uncertain industrial robot as provided in an embodiment of the present invention.
[0097] For more specific details about the above method, please refer to the corresponding contents disclosed in the aforementioned embodiments, which will not be described again here.
[0098] Accordingly, an embodiment of the present invention further provides a computer-readable storage medium for storing a computer program, wherein, when the computer program is executed by a processor, the adaptive iterative learning method for high-precision position tracking of an uncertain industrial robot as provided in an embodiment of the present invention is implemented.
[0099] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from the other embodiments. References to the same or similar portions of the various embodiments will be sufficient. The systems, devices, and storage media disclosed in the embodiments are described briefly because they correspond to the methods disclosed in the embodiments. For relevant details, refer to the method descriptions.
[0100] Professionals may further appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of the two. In order to clearly illustrate the interchangeability of hardware and software, the above description has generally described the components and steps of each example according to their functions. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professionals and technicians may use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.
[0101] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein may be implemented directly using hardware, a software module executed by a processor, or a combination of the two. The software module may be placed in random access memory (RAM), internal memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, a hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art.
[0102] Finally, it should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, method, article, or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or device. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not preclude the presence of additional identical elements in the process, method, article, or device comprising the element.
[0103] The above is a detailed introduction to the high-precision position tracking adaptive iterative learning method, system, device and storage medium for uncertain industrial robots provided by the present invention. Specific examples are used in this article to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea; at the same time, for general technical personnel in this field, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.
Claims
1. An adaptive iterative learning method for high-precision position tracking of uncertain industrial robots, characterized by: The following steps are involved: Constructing a dynamic model of an industrial robot under uncertain working conditions, wherein the dynamic model includes unknown time-varying parameters, and generating a tracking error based on the dynamic model; Performing a Fourier series expansion on the unknown time-varying parameter to obtain a decomposition formula after the expansion, constructing a fuzzy approximator according to the decomposition formula, and generating an estimation error and an approximation error through the fuzzy approximator; Process the estimation error and approximation error to obtain the error function; A virtual control input is constructed according to the tracking error and the error function, and the actual control input is generated according to the virtual control input to realize the position control of the industrial robot.
2. The adaptive iterative learning method for high-precision position tracking of an uncertain industrial robot according to claim 1, characterized in that: The dynamic model of the industrial robot is as follows: Where: It is the first nonlinear parameterized robot system i state variables; Represents the corresponding state vector The differential of is the control input of the nonlinear parameterized robot system; is the dynamic dimension of the system; is an unknown bounded external disturbance; It contains unknown time-varying parameters The unmodeled dynamics of Represents the robot's position state information, including model uncertainty and unknown time-varying disturbances; Indicates the actual trajectory output of the system; Indicates the number of iterations.
3. The adaptive iterative learning method for high-precision position tracking of an uncertain industrial robot according to claim 1, characterized in that: The tracking error is expressed as follows: Where: represents the tracking error; Indicates the actual trajectory output of the system; represents the ideal trajectory.
4. The adaptive iterative learning method for high-precision position tracking of an uncertain industrial robot according to claim 1, characterized in that: The expanded decomposition formula is shown below: Where: Represents the trigonometric function matrix about time; The weight matrix expressed as a Fourier series; is the residual error after Fourier series expansion; Indicates the upper bound; The fuzzy approximator is shown as follows: in: Where: It's about parameters and Fourier series of order fuzzy basis function vector; and is the weight matrix, where and is bounded; satisfies , , and is an unknown positive number; Represents the new FSE-FLS approximator With the original approximator The difference between express The transpose of Indicates the number of iterations.
5. The method for adaptive iterative learning of high-precision position tracking of an uncertain industrial robot according to claim 4, characterized in that: The estimated error is expressed as follows: Where: and is an unknown quantity; and The unknown quantities and estimated value of; and is the estimation error; The approximation error is expressed as follows: Where: for The derivative of is the residual error.
6. The method for adaptive iterative learning of high-precision position tracking of an uncertain industrial robot according to claim 1, characterized in that: Get the error function, including: To deal with the unknown upper bounds of the estimation error and approximation error, a convergent series sequence is introduced: , , and satisfy: At the beginning of each iteration, the initial error value should satisfy , ,in is a convergent series sequence; Therefore, the error function As shown in the following formula: Where: represents the improved time-varying boundary layer; represents a saturation function.
7. The adaptive iterative learning method for high-precision position tracking of an uncertain industrial robot according to claim 1, characterized in that: Constructing a virtual control input based on the tracking error and the error function, and generating an actual control input based on the virtual control input, including: The virtual control input is shown as follows: Where: is the virtual control input; is the coefficient; is a convergent series sequence, ; represents the weight of the estimation error; represents the differential of the ideal trajectory; Introducing a first-order low-pass filter to the virtual control input , which is used to prevent gradient explosion caused by subsequent differentiation, as shown in the following formula: Where: for The differential of represents the virtual control input, is the weight coefficient and satisfies ; The actual control input is shown as follows: Where: 、 and The update rate of the table weight coefficient needs to be given; and represents the fuzzy basis function vector; represents the newly defined error function; is the coefficient; is a convergent series sequence; is the error function; For filter With state variables The difference between .
8. An adaptive iterative learning system for high-precision position tracking of uncertain industrial robots, characterized by: include: A construction module is used to construct a dynamic model of the industrial robot under uncertain working conditions, wherein the dynamic model includes unknown time-varying parameters and generates a tracking error according to the dynamic model; an error generation module, configured to perform a Fourier series expansion on the unknown time-varying parameter to obtain a decomposition formula after the expansion, construct a fuzzy approximator based on the decomposition formula, and generate an estimation error and an approximation error through the fuzzy approximator; Function generation module, used to process estimation error and approximation error to obtain error function; The control module constructs a virtual control input based on the tracking error and the error function, and generates an actual control input based on the virtual control input to realize the position control of the industrial robot.
9. An adaptive iterative learning device for high-precision position tracking of uncertain industrial robots, characterized in that: The method comprises a processor and a memory, wherein when the processor executes the computer program stored in the memory, the method for adaptive iterative learning of high-precision position tracking of an uncertain industrial robot according to any one of claims 1 to 7 is implemented.
10. A computer-readable storage medium, characterized in that Used to store a computer program, wherein when the computer program is executed by a processor, it implements the adaptive iterative learning method for high-precision position tracking of an uncertain industrial robot according to any one of claims 1 to 7.