Method and system for online identification of robot dynamics parameters
By combining the optimal bounded ellipsoid algorithm and a preset filter, the problems of noise sensitivity and slow convergence speed in traditional robot dynamic parameter identification methods are solved, and fast, stable and accurate online identification of robot dynamic parameters is achieved.
Patent Information
- Application Number
- CN202411741348.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-29
- Publication Date
- 2025-11-11
- Estimated Expiration
- 2044-11-29
AI Technical Summary
Traditional methods for identifying robot dynamic parameters are sensitive to noise, have large parameter estimation biases, and slow convergence speeds, especially when it comes to poor online identification of time-varying dynamic parameters.
The optimal bounded ellipsoid algorithm is adopted, combined with a preset filter, and the joint information of the robot in motion is acquired online. The minimum parameter set of the dynamic parameters to be identified is iteratively reduced until the maximum error of the predicted value of the control torque vector is less than the preset error value. The optimal bounded ellipsoid algorithm is used to continuously iterate to achieve rapid convergence and stable identification of parameters.
It enables rapid, stable, and accurate online identification of robot dynamic parameters, improving the stability and accuracy of parameter identification results.
Smart Images
Figure CN119526401B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of robot control technology, and in particular relates to a method and system for online identification of robot dynamic parameters. Background Technology
[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.
[0003] The dynamic models of robot systems typically contain unknown parameters, such as the inertia matrix, Coriolis matrix, and gravity vector. These parameters have a significant impact on the system's motion performance and control strategy design. Traditional parameter identification methods mainly rely on least squares and gradient descent methods. These methods often require a large number of data samples, are sensitive to noise, are prone to large parameter estimation biases, and suffer from slow parameter convergence speeds, resulting in poor online identification performance for time-varying dynamic parameters. Summary of the Invention
[0004] To address the aforementioned technical problems, this invention provides a method and system for online identification of robot dynamic parameters, which can improve the online identification effect of time-varying dynamic parameters.
[0005] To achieve the above objectives, the present invention adopts the following technical solution:
[0006] The first aspect of the present invention provides a method for online identification of robot dynamic parameters.
[0007] In one or more embodiments, a method for online identification of robot dynamic parameters is provided, including:
[0008] The robot is controlled to move along an ideal trajectory, and joint information during the robot's movement is acquired online; the joint information includes angle vector, joint angular velocity vector, angular acceleration vector, and control torque vector;
[0009] Based on the initial minimum parameter set of the dynamic parameters to be identified in the robot dynamics model and the joint information, the minimum parameter set of the dynamic parameters to be identified is continuously reduced using the optimal bounded ellipsoid algorithm until the maximum error of the predicted value of the control torque vector for a complete cycle of robot operation is less than the preset error value, thus obtaining the dynamic parameter identification result.
[0010] As one implementation method, the expression for the robot dynamics model is:
[0011]
[0012] In the formula Represents the joint angle vector. Represents the inertia matrix. Represents the centripetal-Coriolis matrix. and These represent the vectors of gravity, friction, and control torque, respectively. They are The first and second derivatives; , , and The known error range is denoted as , and the dynamic parameters to be identified are denoted as .
[0013] As one implementation method, the relationship between the control torque vector and the initial minimum parameter set of the dynamic parameters to be identified in the robot dynamics model is as follows:
[0014] The control torque vector is characterized by the transpose of the initial minimum parameter set of the dynamic parameters to be identified in the robot dynamics model and the product of the regression matrix.
[0015] As one implementation method, during the iterative reduction of the minimum parameter set of the dynamic parameters to be identified using the optimal bounded ellipsoid algorithm, a preset filter is used to remove noise from the angular acceleration vector, updating the expression of the robot dynamics model to:
[0016]
[0017] in, This represents the control torque vector after noise reduction; This represents the transpose of the matrix representing the optimal estimated value of the dynamic parameters to be identified, which minimizes the approximate error of the dynamic parameters to be identified. This represents the denoised regression matrix; This represents the approximate error of the dynamic parameters to be identified after noise reduction.
[0018] A second aspect of the present invention provides an online identification system for robot dynamic parameters.
[0019] In one or more embodiments, a robot dynamics parameter online identification system includes:
[0020] The joint information online acquisition module is used to control the robot to move along an ideal trajectory and acquire joint information of the robot during its movement online; the joint information includes angle vector, joint angular velocity vector, angular acceleration vector and control torque vector;
[0021] The dynamic parameter identification module is used to iteratively reduce the minimum parameter set of the dynamic parameters to be identified based on the initial minimum parameter set of the dynamic parameters to be identified in the robot dynamic model and the joint information, using the optimal bounded ellipsoid algorithm, until the maximum error of the predicted value of the control torque vector for one complete cycle of robot operation is less than the preset error value, thus obtaining the dynamic parameter identification result.
[0022] As one implementation method, in the dynamic parameter identification module, the expression of the robot dynamic model is:
[0023]
[0024] In the formula Represents the joint angle vector. Represents the inertia matrix. Represents the centripetal-Coriolis matrix. and These represent the vectors of gravity, friction, and control torque, respectively. They are The first and second derivatives; , , and The known error range is denoted as , and the dynamic parameters to be identified are denoted as .
[0025] As one implementation, in the dynamic parameter identification module, the relationship between the control torque vector and the initial minimum parameter set of the dynamic parameters to be identified in the robot dynamic model is as follows:
[0026] The control torque vector is characterized by the transpose of the initial minimum parameter set of the dynamic parameters to be identified in the robot dynamics model and the product of the regression matrix.
[0027] As one implementation method, in the dynamic parameter identification module, during the process of iteratively narrowing down the minimum parameter set of the dynamic parameters to be identified using the optimal bounded ellipsoid algorithm, a preset filter is used to filter out noise in the angular acceleration vector, and the expression of the robot dynamic model is updated as follows:
[0028]
[0029] in, This represents the control torque vector after noise reduction; This represents the transpose of the matrix representing the optimal estimated value of the dynamic parameters to be identified, which minimizes the approximate error of the dynamic parameters to be identified. This represents the denoised regression matrix; This represents the approximate error of the dynamic parameters to be identified after noise reduction.
[0030] A third aspect of the present invention provides a computer-readable storage medium.
[0031] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the online identification method for robot dynamic parameters as described above.
[0032] A fourth aspect of the present invention provides an electronic device.
[0033] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps in the online robot dynamics parameter identification method described above.
[0034] Compared with the prior art, the beneficial effects of the present invention are:
[0035] This invention utilizes the initial minimum parameter set of the dynamic parameters to be identified in the robot's dynamic model and the joint information acquired online during the robot's motion. It iteratively reduces the minimum parameter set of the dynamic parameters to be identified using the optimal bounded ellipsoid algorithm, thereby accelerating the convergence of unknown parameters in online identification. It also ensures the stability and convergence of the parameter identification process, improving the stability and accuracy of the dynamic parameter identification results. Attached Figure Description
[0036] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.
[0037] Figure 1 This is a flowchart illustrating the online identification method for robot dynamic parameters according to an embodiment of the present invention;
[0038] Figure 2(a) shows the evolution trajectory of the parameter to be identified in an embodiment of the present invention;
[0039] Figure 2(b) shows the eigenvalues of the learning gain matrix in an embodiment of the present invention;
[0040] Figure 3 This is a schematic diagram of the structure of the online robot dynamics parameter identification system according to an embodiment of the present invention;
[0041] Figure 4 This is a schematic diagram of an electronic device according to an embodiment of the present invention. Detailed Implementation
[0042] The present invention will be further described below with reference to the accompanying drawings and embodiments.
[0043] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.
[0044] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.
[0045] Figure 1 This is a flowchart illustrating an online robot dynamics parameter identification method according to an embodiment of the present invention, as shown below. Figure 1 The online identification method for robot dynamic parameters shown in this embodiment may include:
[0046] S101, control the robot to move along an ideal trajectory, and acquire joint information of the robot during the movement online; the joint information includes angle vector, joint angular velocity vector, angular acceleration vector and control torque vector;
[0047] S102, based on the initial minimum parameter set of the dynamic parameters to be identified in the robot dynamics model and the joint information, the minimum parameter set of the dynamic parameters to be identified is continuously reduced using the optimal bounded ellipsoid algorithm until the maximum error of the predicted value of the control torque vector for one complete cycle of robot operation is less than the preset error value, thus obtaining the dynamic parameter identification result.
[0048] The expression for the robot's dynamics model is as follows:
[0049]
[0050] In the formula Represents the joint angle vector. Represents the inertia matrix. Represents the centripetal-Coriolis matrix. and These represent the vectors of gravity, friction, and control torque, respectively. They are The first and second derivatives; , , and The known error range is denoted as , and the dynamic parameters to be identified are denoted as .
[0051] Assumption and It is measurable. For the desired output vector, Both are bounded. Define a tracking error. ) and its filtered tracking error in This represents a positive diagonal matrix. It is an auxiliary signal. Let , col indicates column vector concatenation;
[0052] In this embodiment, M(p) is symmetric and positive definite, and it satisfies in They are some constants.
[0053] In this embodiment, .
[0054] In some alternative embodiments, the minimum parameter set and regression matrix of the robot dynamics parameters can be obtained by existing methods. The relationship between the control torque vector and the initial minimum parameter set of the unidentified dynamic parameters of the robot dynamics model is: the control torque vector is characterized by the multiplication of the transpose of the initial minimum parameter set of the unidentified dynamic parameters of the robot dynamics model and the regression matrix.
[0055] Formula (1) can then be modified as follows:
[0056]
[0057] in, Transpose of the initial minimum parameter set of the dynamic parameters to be identified; Represents the regression matrix; express The first derivative, This represents the joint angular velocity.
[0058] Define the excitation trajectory, ideal trajectory, tracking error, and parameters to be identified as bounded, and define corresponding compact sets for each. , .
[0059]
[0060]
[0061] in, The initial minimum parameter set for the dynamic parameters to be identified In Number of columns; , , This indicates the upper limit of the corresponding parameter.
[0062] Define the approximate error of the parameter to be identified :
[0063]
[0064]
[0065]
[0066]
[0067]
[0068] in and The corresponding approximation errors are given respectively. The optimal estimate of the parameters to be identified by minimizing the absolute value. . , , , and These are all regression matrices corresponding to the approximation errors. Among them, It means: the representation of the corresponding parameter, that is, equal to.
[0069] Use variable substitution The robot dynamics model can be rewritten as follows:
[0070]
[0071] in, To identify the approximate error of the dynamic parameters; All are regression matrices.
[0072] To avoid using noisy acceleration signals in equation (2) Apply a stabilizing filter to equation (2) ,in Let c be the filter parameters, and c be a complex variable. Then, we can obtain...
[0073]
[0074] in, This represents the control torque vector after noise reduction; This represents the transpose of the matrix representing the optimal estimated value of the dynamic parameters to be identified, which minimizes the approximate error of the dynamic parameters to be identified. This represents the denoised regression matrix; This represents the approximate error of the dynamic parameters to be identified after noise reduction.
[0075] That It can be calculated in the following ways:
[0076]
[0077] The left side of the equal sign in formula (4) are respectively The first derivative;
[0078] Approximation error of the optimal parameter to be identified in It is a constant.
[0079] According to the above theorem, the approximate error of the optimal parameter value to be identified is... by Constraints, therefore its filtered corresponding items It is also bounded, that is ,in yes The i-th element, It is a constant, i = 1~n.
[0080] From equation (4), we can see that the control torque of the i-th joint can be written as follows:
[0081]
[0082] in express The i-th column, i = 1~n. Then, with... ellipsoid set centered It can be defined as follows:
[0083]
[0084] in i = 1~n. It is chosen as a sufficiently large value, such that Belongs to the ellipsoid set The approximate value of the control torque for the i-th joint is:
[0085] in for The estimated value. The filtered recognition error of the i-th joint is defined as...
[0086]
[0087] A recognition algorithm with fast parameter convergence:
[0088]
[0089]
[0090]
[0091]
[0092]
[0093]
[0094] in, Represents the projection operator; Indicates an intermediate physical quantity; To learn the gain matrix; This is the denoised regression matrix; This represents the recognition error after filtering. The coefficient is constant. For the cause of forgetting; For intermediate parameters; It is a unit diagonal matrix; , For intermediate parameters; This is the preset filtered recognition error value.
[0095] Is it satisfied with Gain greater than 1, Satisfying 0 < A fixed forgetting factor less than 1 These are two freely chosen parameters that satisfy... . They represent The upper and lower limits. i = 1~n.
[0096] (15)
[0097] and It is by
[0098] (16)
[0099] The learning gain matrix in this embodiment Bounded, that is , The estimated parameters to be identified are bounded by a predefined elliptic set, i.e., formula (6). .
[0100] In this embodiment, the optimal bounded ellipsoid algorithm is used to iteratively reduce the minimum parameter set of the dynamic parameters to be identified. The process of online identification of dynamic parameters is as follows:
[0101] The dynamic parameters to be identified are defined as bounded. Then, the robot is made to move along an ideal trajectory. During the robot's movement, joint angles, joint angular velocities, angular accelerations, and control torques are collected and calculated according to formula (4). The filtered recognition error is obtained according to formulas (5) to (8). Then, according to formulas (10) to (16), we obtain get The integral is obtained Then repeat the above process, iterating continuously until the maximum error of the predicted control torque vector for a complete robot cycle is less than the preset error value, thus obtaining the dynamic parameter identification result.
[0102] As shown in Figure 2(a), to study the performance under time-varying parameters, a load of 0.8 kg was added to the end effector of the robot's manipulator. The 0.8 kg load was added to the end effector of the robot's manipulator via a gripper at a time of t=20 seconds. The evolution trajectory of the parameters to be identified is shown in Figure 2(a), and the eigenvalues of the learning gain matrix are shown in Figure 2(b). It can be seen from the figures that the parameters exhibit good convergence after using the improved optimal bounded ellipsoid algorithm.
[0103] This embodiment uses the initial minimum parameter set of the dynamic parameters to be identified in the robot dynamics model and the joint information acquired online during the robot's motion. It then uses the optimal bounded ellipsoid algorithm to iteratively reduce the minimum parameter set of the dynamic parameters to be identified, thereby accelerating the convergence of unknown parameters in online identification. This also ensures the stability and convergence of the parameter identification process, improving the stability and accuracy of the dynamic parameter identification results.
[0104] Figure 3 This is a schematic diagram of the structure of an online robot dynamics parameter identification system according to an embodiment of the present invention. This embodiment is similar to... Figure 1 Corresponding to the online identification method for robot dynamic parameters, such as Figure 3 As shown, the online robot dynamics parameter identification system in this embodiment may include:
[0105] The joint information online acquisition module 301 is used to control the robot to move along an ideal trajectory and acquire joint information of the robot during its movement online; the joint information includes angle vector, joint angular velocity vector, angular acceleration vector and control torque vector.
[0106] The dynamic parameter identification module 302 is used to iteratively reduce the minimum parameter set of the dynamic parameters to be identified based on the initial minimum parameter set of the dynamic parameters to be identified in the robot dynamic model and the joint information, using the optimal bounded ellipsoid algorithm, until the maximum error of the predicted value of the control torque vector for one complete cycle of robot operation is less than the preset error value, thus obtaining the dynamic parameter identification result.
[0107] In the dynamic parameter identification module 302, the expression for the robot dynamic model is:
[0108]
[0109] In the formula Represents the joint angle vector. Represents the inertia matrix. Represents the centripetal-Coriolis matrix. and These represent the vectors of gravity, friction, and control torque, respectively. They are The first and second derivatives; , , and The known error range is denoted as , and the dynamic parameters to be identified are denoted as .
[0110] In the dynamic parameter identification module 302, the relationship between the control torque vector and the initial minimum parameter set of the dynamic parameters to be identified in the robot dynamic model is as follows:
[0111] The control torque vector is characterized by the transpose of the initial minimum parameter set of the dynamic parameters to be identified in the robot dynamics model and the product of the regression matrix.
[0112] In the dynamic parameter identification module 302, during the iterative process of using the optimal bounded ellipsoid algorithm to narrow down the minimum parameter set of the dynamic parameters to be identified, a preset filter is used to filter out noise in the angular acceleration vector, and the expression of the robot dynamic model is updated as follows:
[0113]
[0114] in, This represents the control torque vector after noise reduction; This represents the transpose of the matrix representing the optimal estimated value of the dynamic parameters to be identified, which minimizes the approximate error of the dynamic parameters to be identified. This represents the denoised regression matrix; This represents the approximate error of the dynamic parameters to be identified after noise reduction.
[0115] It should be noted here that, Figure 3 The various modules in the online robot dynamics parameter identification system, and Figure 1 Each step in the online identification method for robot dynamic parameters corresponds to the previous one, and their specific implementation process is the same, so it will not be repeated here.
[0116] Reference Figure 4 A schematic diagram of an electronic device is provided. It should be noted that... Figure 4 The electronic device 400 shown is merely an example and should not be construed as limiting the functionality and scope of use of the embodiments of the present invention.
[0117] like Figure 4As shown, the electronic device 400 includes a central processing unit (CPU) 401, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 402 or a program loaded from a storage section 408 into a random access memory (RAM) 403. The RAM 403 also stores various programs and data required for system operation. The CPU 401, ROM 402, and RAM 403 are interconnected via a bus 404. An input / output (I / O) interface 405 is also connected to the bus 404.
[0118] The following components are connected to I / O interface 405: an input section 406 including a keyboard, mouse, etc.; an output section 407 including a cathode ray tube (CRT), liquid crystal display (LCD), etc., and speakers, etc.; a storage section 408 including a hard disk, etc.; and a communication section 409 including a network interface card such as a local area network (LAN) card, modem, etc. The communication section 409 performs communication processing via a network such as the Internet. A drive 410 is also connected to I / O interface 405 as needed. A removable medium 411, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., is installed on drive 410 as needed so that computer programs read from it can be installed into storage section 408 as needed.
[0119] When the central processing unit 401 in the electronic device of this embodiment executes the program, it achieves the following: Figure 1 The steps in the online identification method for robot dynamic parameters are shown.
[0120] Specifically, according to embodiments of this application, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of this application include a computer program product comprising a computer program carried on a computer-readable medium, the computer program including functions for executing... Figure 1 The program code for the method shown. In such an embodiment, the computer program can be downloaded and installed from a network via communication section 409, and / or installed from removable medium 411. When the computer program is executed by central processing unit 401, it performs the various functions defined in the apparatus of this application.
[0121] in, Figure 1 The computer program instructions corresponding to the method shown may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in the process. Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.
[0122] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM), etc.
[0123] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A method for online identification of robot dynamic parameters, characterized in that, include: Control the robot to move along an ideal trajectory and acquire joint information of the robot during its movement online; The joint information includes angle vector, joint angular velocity vector, angular acceleration vector, and control torque vector; Based on the initial minimum parameter set of the dynamic parameters to be identified in the robot dynamics model and the joint information, the minimum parameter set of the dynamic parameters to be identified is continuously reduced by using the optimal bounded ellipsoid algorithm until the maximum error of the predicted value of the control torque vector for one complete cycle of robot operation is less than the preset error value, thus obtaining the dynamic parameter identification result. The process of online identification of dynamic parameters involves iteratively narrowing down the minimum parameter set to be identified using the optimal bounded ellipsoid algorithm. The dynamic parameters to be identified are defined as bounded. The robot is then guided to move along an ideal trajectory. During the robot's motion, joint angles, angular velocities, angular accelerations, and control torques are collected and calculated using the following formula. The left side of the equal sign are respectively The first derivative; The filtered recognition error is calculated using the following formula. : The control torque of the i-th joint can be written as follows: in, This represents the control torque vector after noise reduction; This represents the transpose of the matrix representing the optimal estimated value of the dynamic parameters to be identified, which minimizes the approximate error of the dynamic parameters to be identified. This represents the denoised regression matrix; This represents the approximate error of the dynamic parameters to be identified after noise reduction. yes The i-th element; express Let the i-th column be a sequence of numbers, where i = 1 to n; then, let the i-th column be a sequence of numbers, where i = 1 to n. ellipsoid set centered It can be defined as follows: in i = 1~n; It is chosen as a sufficiently large value, such that Belongs to the ellipsoid set The approximate value of the control torque for the i-th joint is: in for The estimated value; the filtered recognition error of the i-th joint is defined as... Then, according to the following formula, we obtain... : A recognition algorithm with fast parameter convergence: ； ； ； in, Represents the projection operator; Indicates an intermediate physical quantity; To learn the gain matrix; This is the denoised regression matrix; This represents the recognition error after filtering. The coefficient is constant. For the cause of forgetting; For intermediate parameters; It is a unit diagonal matrix; , For intermediate parameters; This is the preset filtered recognition error value; Is it satisfied with Gain > 1 Satisfying 0 < A fixed forgetting factor < 1 These are two freely chosen parameters that satisfy... ; They represent The upper and lower limits; i = 1~n; and It is by in, Indicates the upper limit of the parameter to be identified; get : Points earned Then repeat the above process, iterating continuously until the maximum error of the predicted control torque vector for a complete robot cycle is less than the preset error value, thus obtaining the dynamic parameter identification result.
2. The online identification method for robot dynamic parameters as described in claim 1, characterized in that, The expression for the robot's dynamics model is: In the formula Represents the joint angle vector. Represents the inertia matrix. Represents the centripetal-Coriolis matrix. and These represent the vectors of gravity, friction, and control torque, respectively. They are The first and second derivatives; , , and The known error range is denoted as , and the dynamic parameters to be identified are denoted as .
3. The online identification method for robot dynamic parameters as described in claim 1, characterized in that, The relationship between the control torque vector and the initial minimum parameter set of the dynamic parameters to be identified in the robot dynamics model is as follows: The control torque vector is characterized by the transpose of the initial minimum parameter set of the dynamic parameters to be identified in the robot dynamics model and the product of the regression matrix.
4. An online identification system for robot dynamic parameters, characterized in that, include: The joint information online acquisition module is used to control the robot to move along an ideal trajectory and to acquire joint information of the robot during its movement online. The joint information includes angle vector, joint angular velocity vector, angular acceleration vector, and control torque vector; The dynamic parameter identification module is used to iteratively reduce the minimum parameter set of the dynamic parameters to be identified based on the initial minimum parameter set of the dynamic parameters to be identified in the robot dynamic model and the joint information, using the optimal bounded ellipsoid algorithm, until the maximum error of the predicted value of the control torque vector for one complete cycle of robot operation is less than the preset error value, thus obtaining the dynamic parameter identification result. The process of online identification of dynamic parameters involves iteratively narrowing down the minimum parameter set to be identified using the optimal bounded ellipsoid algorithm. The dynamic parameters to be identified are defined as bounded. The robot is then guided to move along an ideal trajectory. During the robot's motion, joint angles, angular velocities, angular accelerations, and control torques are collected and calculated using the following formula. The left side of the equal sign are respectively The first derivative; The filtered recognition error is calculated using the following formula. : The control torque of the i-th joint can be written as follows: in, This represents the control torque vector after noise reduction; This represents the transpose of the matrix representing the optimal estimated value of the dynamic parameters to be identified, which minimizes the approximate error of the dynamic parameters to be identified. This represents the denoised regression matrix; This represents the approximate error of the dynamic parameters to be identified after noise reduction. yes The i-th element; express Let the i-th column be a sequence of numbers, where i = 1 to n; then, let the i-th column be a sequence of numbers, where i = 1 to n. ellipsoid set centered It can be defined as follows: in i = 1~n; It is chosen as a sufficiently large value, such that Belongs to the ellipsoid set The approximate value of the control torque for the i-th joint is: in for The estimated value; the filtered recognition error of the i-th joint is defined as... Then, according to the following formula, we obtain... : A recognition algorithm with fast parameter convergence: ； ； ； in, Represents the projection operator; Indicates an intermediate physical quantity; To learn the gain matrix; This is the denoised regression matrix; This represents the recognition error after filtering. The coefficient is constant. For the cause of forgetting; For intermediate parameters; It is a unit diagonal matrix; , For intermediate parameters; This is the preset filtered recognition error value; Is it satisfied with Gain > 1 Satisfying 0 < A fixed forgetting factor < 1 These are two freely chosen parameters that satisfy... ; They represent The upper and lower limits; i = 1~n; and It is by in, Indicates the upper limit of the parameter to be identified; get : Points earned Then repeat the above process, iterating continuously until the maximum error of the predicted control torque vector for a complete robot cycle is less than the preset error value, thus obtaining the dynamic parameter identification result.
5. The online robot dynamics parameter identification system as described in claim 4, characterized in that, In the dynamic parameter identification module, the expression for the robot's dynamic model is: In the formula Represents the joint angle vector. Represents the inertia matrix. Represents the centripetal-Coriolis matrix. and These represent the vectors of gravity, friction, and control torque, respectively. They are The first and second derivatives; , , and The known error range is denoted as , and the dynamic parameters to be identified are denoted as .
6. The online robot dynamics parameter identification system as described in claim 4, characterized in that, In the dynamic parameter identification module, the relationship between the control torque vector and the initial minimum parameter set of the dynamic parameters to be identified in the robot dynamic model is as follows: The control torque vector is characterized by the transpose of the initial minimum parameter set of the dynamic parameters to be identified in the robot dynamics model and the product of the regression matrix.
7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps in the online identification method for robot dynamic parameters as described in any one of claims 1-3.
8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the online identification method for robot dynamic parameters as described in any one of claims 1-3.