Kinetic Parameter Identification Method, Device, Electronic Device and Computer Storage Medium

Abstract

The present application provides a method, apparatus, electronic device and computer storage medium for identifying dynamic parameters. The method includes: constructing a dynamic model through the centroid inertia tensor of a target moving part; determining physical feasibility constraints according to the dynamic model; updating the recursive least squares identification method based on the physical feasibility constraints; and identifying the dynamic parameters of each connecting rod of the target moving part according to the updated recursive least squares identification method. The present application constructs a dynamic model based on the centroid inertia tensor, taking into account the mass distribution, which can improve the accuracy and stability of the model. And directly using the centroid inertia tensor to reconstruct the dynamic model will generate a non-linear coupling between the dynamic parameters and non-dynamic quantities. Then, the non-linear coupling is transferred between the dynamic parameters through the dynamic parameters, and the transferred non-linearity is converted into a parameter constraint problem through parameter mapping and added to the physical feasibility constraints, which can reduce the dimension of the problem and enhance the feasibility of the model.

Description

Technical Field

[0001] This application relates to the field of data processing, and more particularly, to a method, device, electronic device, and computer storage medium for identifying dynamic parameters. Background Art

[0002] Dynamic parameter identification is a method for determining unknown parameters in a dynamic system through experiments, numerical simulations, theoretical derivations, etc. This technology is widely used in many fields such as mechanical engineering, automation, aerospace, and robotics. In the current field of parameter identification, dynamic parameter identification methods often ignore two important physical quantities: mass and center of mass.

[0003] However, in various application scenarios, especially when identifying parameters of complex mechanical systems (such as industrial robots and aerospace equipment) and electrical systems (such as permanent magnet synchronous motors), the neglect of mass and center of mass parameters often leads to model instability. Summary of the Invention

[0004] In view of this, an object of the embodiments of this application is to provide a method, device, electronic device, and computer storage medium for identifying dynamic parameters, which can improve model stability.

[0005] In a first aspect, an embodiment of this application provides a method for identifying dynamic parameters, including: constructing a dynamic model through the centroid inertia tensor of a target moving part; determining physical feasibility constraints according to the dynamic model; updating the recursive least squares identification method based on the physical feasibility constraints; and identifying the dynamic parameters of each joint of the target moving part according to the updated recursive least squares identification method.

[0006] In the above implementation process, by constructing a dynamic model based on the centroid inertia tensor, the dynamic model takes into account the mass distribution, which can improve the accuracy and stability of the dynamic model. In addition, directly reconstructing the dynamic model using the centroid inertia tensor will result in a non - linear coupling between dynamic parameters and non - dynamic quantities. Subsequently, the extended dynamic parameters can transfer this non - linear coupling between dynamic parameters, and through parameter mapping, the transferred non - linearity is converted into a parameter constraint problem and added to the physical feasibility constraints, which can reduce the dimension of the problem and enhance the feasibility of the model.

[0007] In one embodiment, the determining physical feasibility constraints according to the dynamic model includes: separating the linear term and the non - linear term of the dynamic model; determining the minimum inertia parameter set based on the dynamic model after separating the linear term and the non - linear term; and determining the physical feasibility constraints through the minimum inertia parameter set.

[0008] In the above implementation process, by separating the linear and non-linear terms of the dynamic model and determining the minimum inertia parameter set, redundant parameters can be reduced, and the dynamic behavior of the target moving part can still be fully described. While improving the accuracy of physical feasibility constraints, the parameters involved in the calculation are reduced, and the processing efficiency is improved.

[0009] In one embodiment, determining the physical feasibility constraints based on the minimum inertia parameter set includes: establishing a centroid inertia tensor constraint according to the dynamic model; establishing an equality constraint for the centroid and the quadratic terms of the centroid; determining a set of dynamic parameters that satisfy the centroid inertia tensor constraint and the equality constraint through the minimum inertia parameter set; and reconstructing the physical feasibility constraints according to the set of dynamic parameters.

[0010] In the above implementation process, determining a set of dynamic parameters that satisfy the centroid inertia tensor constraint and the equality constraint can, to a certain extent, place the centroid in the correct position and improve the accuracy of the set of dynamic parameters. Additionally, by reconstructing the physical feasibility constraints based on the minimum inertia parameter set and the set of dynamic parameters, a corresponding lower limit can be set for the mass, and then more reasonable dynamic parameters can be obtained, further improving the accuracy and authenticity of the set of dynamic parameters.

[0011] In one embodiment, updating the recursive least squares identification method based on the physical feasibility constraints includes: updating the minimum inertia parameter set according to the physical feasibility constraints; determining the least squares objective function based on the updated minimum inertia parameter set; and determining the recursive least squares identification method based on the least squares objective function and the forgetting factor.

[0012] In the above implementation process, through the recursive least squares identification method guided by physical feasibility constraints, the physical feasibility constraints are used to constrain and guide the parameter update direction. The dynamic parameters with physical feasibility can be identified online, and the accuracy and stability of the identification can be improved while ensuring physical feasibility. Additionally, by introducing the forgetting factor, the dependence on past data when new data appears can be gradually reduced, making the parameter estimation value more sensitive to the latest observation results and improving the identification accuracy.

[0013] In one embodiment, identifying the dynamic parameters of each link of the target moving part according to the updated recursive least squares identification method includes: compensating the recursive least squares identification method through a self-evolving fuzzy neural network; wherein the self-evolving fuzzy neural network is configured to compensate for the torque in the dynamic parameters; and identifying the dynamic parameters of each joint of the target moving part through the compensated recursive least squares identification method.

[0014] In the above implementation process, by using a self-evolving fuzzy neural network to compensate the recursive least squares identification method, and then realizing the compensation of the torque in the dynamic parameters, the control accuracy and robustness of the target moving part in a complex environment can be improved.

[0015] In one embodiment, the compensation of the recursive least squares identification method by the self-evolving fuzzy neural network includes: performing a fuzzification operation on the input variables through a Gaussian membership function; performing a fuzzy intersection operation on the input variables after the fuzzification operation using an algebraic product operation; generating a result output according to the external input state and the input variables after the fuzzy intersection operation, where the result output is configured to determine the error between the actual network output and the desired output; and compensating the recursive least squares identification method based on the error.

[0016] In one embodiment, before the compensation of the recursive least squares identification method by the self-evolving fuzzy neural network, the method further includes: updating the antecedent layer in the self-evolving fuzzy neural network by the gradient descent method; and / or updating the consequent layer in the self-evolving fuzzy neural network according to the physical feasibility constraint; and / or updating the optimization rule according to the activation intensity threshold.

[0017] In the above implementation process, by selecting corresponding update methods for different network layers for updating, the self-evolving fuzzy neural network can be updated online and the compensation torque can be generated in real time to compensate the torque of the identified extended dynamics, thereby improving the accuracy and robustness of parameter identification.

[0018] In a second aspect, an embodiment of the present application further provides a dynamic parameter identification device, including: a construction module for constructing a dynamic model through the centroid inertia tensor of the target moving part; a determination module for determining a physical feasibility constraint according to the dynamic model; a first update module for updating the recursive least squares identification method based on the physical feasibility constraint; and an identification module for identifying the dynamic parameters of each link of the target moving part according to the updated recursive least squares identification method.

[0019] In a third aspect, an embodiment of the present application further provides an electronic device, including: a processor and a memory, where the memory stores machine-readable instructions executable by the processor, and when the electronic device runs, the machine-readable instructions are executed by the processor to perform the steps of the method in the first aspect or any possible implementation manner of the first aspect.

[0020] Fourthly, an embodiment of the present application further provides a computer-readable storage medium, on which a computer program is stored. When the computer program is run by a processor, it executes the steps of the kinetic parameter identification method in the above first aspect or any possible implementation manner of the first aspect.

[0021] To make the above objects, features, and advantages of the present application more obvious and understandable, specific embodiments are hereinafter given and described in detail in conjunction with the accompanying drawings. Description of the Drawings

[0022] To more clearly illustrate the technical solutions of the embodiments of the present application, the accompanying drawings required for the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present application and should not be regarded as limiting the scope. For those of ordinary skill in the art, other related drawings can be obtained based on these drawings without creative efforts.

[0023] Figure 1 It is a block diagram of the electronic device provided by the embodiment of the present application;

[0024] Figure 2 It is a flowchart of the kinetic parameter identification method provided by the embodiment of the present application;

[0025] Figure 3 It is a schematic diagram of the self-evolving fuzzy neural network provided by the embodiment of the present application;

[0026] Figure 4 It is a schematic diagram of the functional modules of the kinetic parameter identification device provided by the embodiment of the present application. Detailed Embodiments

[0027] Next, the technical solutions in the embodiments of the present application will be described in conjunction with the drawings in the embodiments of the present application.

[0028] It should be noted that similar reference numerals and letters indicate similar items in the following drawings. Therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings. At the same time, in the description of the present application, terms such as "first" and "second" are only used for distinguishing descriptions and cannot be understood as indicating or implying relative importance.

[0029] Dynamic parameter identification can be divided into model-free identification and model-based identification. Model-free identification does not require a predefined mathematical model of the robotic arm in advance. Instead, it relies on the measurement of the joint positions and torques of the robotic arm, treating the robotic arm as an unknown nonlinear multi-input multi-output system. Typical model-free identification methods include multi-layer perceptron network compensator, Gaussian process regression, radial basis function network compensator, etc. The advantage of model-free identification is that it is more flexible and does not require complex mathematical derivations. However, compared with model-based identification, it requires more computational resources and has lower accuracy, and the identified dynamic model cannot cover all physical effects.

[0030] Model-based identification, on the other hand, can establish a comprehensive and stable dynamic model by using the known predefined mathematical model of the system to describe the physical behavior and properties of the system. Since the dynamic model of the robotic arm is linear with respect to the dynamic parameters, linear regression techniques can be applied. Common methods include least squares, weighted least squares, maximum likelihood estimation, etc. Although these methods can quickly estimate the dynamic parameters, they all rely on the availability of accurate measurements, and the uncertainty of the data may lead to biased or inaccurate parameter estimates. In recent years, the concept of online parameter identification has received increasing attention, which allows the continuous update of the dynamic model based on real-time data. A series of online methods and their improvements, such as extended Kalman filter, unscented Kalman filter, etc., are used to model the dynamics to obtain better estimation functions. However, these online methods still have problems. Especially in open and changing scenarios, the dynamic characteristics of the system may change continuously, resulting in performance degradation.

[0031] In view of this, the present application proposes a dynamic parameter identification method. By constructing a dynamic model based on the centroid inertia tensor, the dynamic model takes into account the distribution of length and mass, which can improve the accuracy and stability of the dynamic model. In addition, directly reconstructing the dynamic model using the centroid inertia tensor will result in a nonlinear coupling between the dynamic parameters and non-dynamic quantities. The subsequent extended dynamic parameters can transfer this nonlinear coupling to between the dynamic parameters, and through parameter mapping, the transferred nonlinearity is converted into a parameter constraint problem and added to the physical feasibility constraints, which can reduce the dimension of the problem and enhance the feasibility of the model.

[0032] To facilitate the understanding of this embodiment, the electronic device for implementing the dynamic parameter identification method disclosed in the embodiments of the present application will be introduced in detail first.

[0033] As Figure 1 shown, it is a block diagram of the electronic device. The electronic device 100 may include a memory 111 and a processor 113. Those of ordinary skill in the art can understand that Figure 1The structure shown is only illustrative and does not limit the structure of the electronic device 100. For example, the electronic device 100 may also include more or fewer components than those shown in Figure 1 or have a different configuration from that shown in Figure 1 .

[0034] The above-mentioned memory 111 and the processor 113 are electrically connected directly or indirectly to each other to achieve data transmission or interaction. For example, these elements can be electrically connected to each other through one or more communication buses or signal lines. The above-mentioned processor 113 is used to execute the executable module stored in the memory.

[0035] Among them, the memory 111 can be, but is not limited to, a random access memory (Random Access Memory, abbreviated as RAM), a read-only memory (Read Only Memory, abbreviated as ROM), a programmable read-only memory (Programmable Read-Only Memory, abbreviated as PROM), an erasable programmable read-only memory (Erasable Programmable Read-Only Memory, abbreviated as EPROM), an electrically erasable programmable read-only memory (Electric Erasable Programmable Read-Only Memory, abbreviated as EEPROM), etc. Among them, the memory 111 is used to store a program, and after receiving an execution instruction, the processor 113 executes the program. The method executed by the electronic device 100 defined by the process disclosed in any embodiment of the present application can be applied to the processor 113 or implemented by the processor 113.

[0036] The above-mentioned processor 113 may be an integrated circuit chip with signal processing capabilities. The above-mentioned processor 113 can be a general-purpose processor, including a central processing unit (Central Processing Unit, abbreviated as CPU), a network processor (Network Processor, abbreviated as NP), etc.; it can also be a digital signal processor (digital signal processor, abbreviated as DSP), an application-specific integrated circuit (Application Specific Integrated Circuit, abbreviated as ASIC), a field programmable gate array (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components. It can implement or execute the various methods, steps and logic block diagrams disclosed in the embodiments of the present application. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor, etc.

[0037] The electronic device 100 in this embodiment can be used to execute each step in the various methods provided by the embodiments of the present application. The implementation process of the dynamic parameter identification method will be described in detail through several embodiments below.

[0038] First, before introducing the dynamic parameter identification method provided by the embodiments of the present application, the basic concept of dynamic parameter identification will be introduced first:

[0039] Dynamic parameter identification refers to a method of determining unknown parameters in a dynamic system through experiments, numerical simulations, theoretical derivations, etc. It identifies the model parameters in the system (such as the mass, center of mass, inertia tensor, friction force, etc. of each arm of the robotic arm) based on the input and output data of the system (such as the displacement, velocity, acceleration, force, etc. of each joint of the robotic arm), aiming to improve the accuracy, stability, and performance of the system.

[0040] Please refer to Figure 2 , which is the flowchart of the dynamic parameter identification method provided by the embodiments of the present application. The following will elaborate on the Figure 2 specific process shown in detail.

[0041] Step 201, construct a dynamic model through the inertia tensor of the center of mass of the target moving part.

[0042] Among them, the inertia tensor of the center of mass is a tensor that describes the inertia of a rigid body when rotating around its center of mass.

[0043] The target moving part here refers to the component for which the dynamic parameters need to be determined. For example, a robotic arm, a gripper, etc.

[0044] Existing dynamic parameter identification needs to identify parameters such as the mass, center of mass, and link inertia tensor of each component of the target moving part. Among them, a link refers to a rigid structural part that connects two adjacent components in the target moving part, and each link strictly corresponds to a kinematic link in the target moving part, and its length and mass distribution will directly affect the motion performance of the target moving part.

[0045] For example, if the target moving part is a robotic arm, then the dynamic parameter identification needs to identify parameters such as the mass, center of mass, and link inertia tensor of each arm of the robotic arm. Among them, a link refers to a rigid structural part that connects two adjacent arms in the robotic arm, and each link strictly corresponds to a kinematic link in the robotic arm.

[0046] In the embodiments of the present application, it is necessary to identify the mass, center of mass, quadratic term of the center of mass, and inertia tensor of the center of mass of each link. Among them, the link inertia tensor is defined relative to the origin of the coordinate system of the link, and the inertia tensor of the center of mass is defined relative to the center of mass.

[0047] It should be understood that for a target moving part with a rotating joint, if the inertia tensor of the center of mass is used, the dynamic model is non-linear. If the inertia tensor of the connecting rod is used, the non-linear part can be eliminated by the parallel axis theorem to obtain a linear model. The inertia tensor of the connecting rod can indeed simplify the dynamic model, but the physical feasibility constraints established therefrom have a coupling of mass, center of mass, and inertia tensor of the connecting rod, resulting in that the physical feasibility constraints can only constrain the physical properties (positivity, positive definiteness) of the three, and it is difficult to constrain the ranges of mass and center of mass. If considering directly using the inertia tensor of the center of mass to reconstruct the dynamic model, this will generate a non-linear coupling between the dynamic parameters and the non-dynamic quantities, and the subsequent extended dynamic parameters can transfer this non-linear coupling to between the dynamic parameters, and convert the transferred non-linearity into a parameter constraint problem through parameter mapping and add it to the physical feasibility constraints.

[0048] In one embodiment, the dynamic model can be constructed in the following manner:

[0049] Add the quadratic terms of the center of mass to the original dynamic parameter set to form the dynamic parameter set:

[0050] ;

[0051] ;

[0052] Among them, is to form the dynamic parameter set, is the component of the center of mass vector on the axis in its coordinate system, is the component of the center of mass vector on the axis in its coordinate system, is the component of the center of mass vector on the axis in its coordinate system, is a 1×6 vector composed of the upper triangular elements of the inertia tensor of the center of mass, is the th mass of the connecting rod, is the th dynamic parameter of the connecting rod, is the center of mass vector.

[0053] The magnitude of the above center of mass vector is 1×3, and the center of mass vector includes axis, axis and axis components. Among them, .

[0054] The total dynamic parameter set here is , then the dynamic model can be expressed as:

[0055] ;

[0056] ;

[0057] ;

[0058] wherein, is the force exerted by the -th link on the -th link, is the torque exerted by the -th link on the -th link, is the mass of the -th link, is the centroid vector, forms a set of dynamic parameters, is the link inertia tensor, is an orthogonal rotation matrix (transforming a vector in the -th coordinate system to the -th coordinate system), is a skew-symmetric matrix, is a rotation matrix, is the acceleration of the centroid of the -th link in the -th coordinate system, is the angular acceleration of the -th link in the -th coordinate system, is the position of the origin of the -th coordinate system in the -th coordinate system, and are intermediate quantities (having no actual physical meaning).

[0059] In one embodiment,

[0060] ;

[0061] ;

[0062] wherein, refers to the component on the axis in the corresponding coordinate system, refers to the component on the axis in the corresponding coordinate system, refers to the component on the axis in the corresponding coordinate system, refers to the component on the axis in the corresponding coordinate system, refers to the component on the refers to the component on the axis in the corresponding coordinate system The component on the axis Refers to In the corresponding coordinate system The component on the axis Refers to In the corresponding coordinate system The component on the axis Represents The Row and Column element.

[0063] Here, And Are intermediate quantities generated to separate the dynamic parameters from the non-dynamic terms.

[0064] Assuming that the force and moment at the end of the connecting rod are 0, let Represent the force and moment borne by each component. The total process of calculating the dynamic model force and moment can be expressed as:

[0065] ;

[0066] Where, Represents , Is the Extended dynamic parameter of the

[0067] Simplified to:

[0068] ;

[0069] Where, Is the total force and moment ( ), Is The defined matrix ( ), Is the extended dynamic parameter ( ), Is the set of real numbers, Represents that the set of real numbers is a 36×1 real matrix, Represents that the set of real numbers is a 96×1 real matrix, Is the angle of the joint, Is the angular velocity of the joint, Is the angular acceleration of the joint.

[0070] In the case where the component of the target moving part is a rotating component, the applied moment has only one direction of the z-axis, while the calculated moment has three directions of x, y, and z. Therefore, the calculation of the moment can be based on the following matrix:

[0071] ;

[0072] Among them, is the joint torque ( , indicating that the real number set is a 6×1 real number matrix), is the matrix composed of the rows in that are in the same direction as the joint torque ( indicating that the real number set is a 6×96 real number matrix), is the total dynamic parameter set composed of the dynamic parameter sets of the connecting rods (the direction selection mainly depends on the above ).

[0073] Step 202, determine the physical feasibility constraints according to the dynamic model.

[0074] Among them, the physical feasibility constraints require that the dynamic parameters have reasonable numerical ranges, satisfy the physical constraints of the dynamic model, and ensure that the model can truly reflect the actual motion characteristics. Since the dynamic parameter set is a linearly dependent set, it is necessary to find its maximal linearly independent group, that is, the minimum inertia parameter set.

[0075] The identification object of the dynamic parameter identification here is the minimum inertia parameter set. Among them, the introduction of the physical feasibility constraints is to find a reasonable complete dynamic parameter set through the minimum inertia parameter set.

[0076] The existing physical feasibility constraints mainly represent the centroid inertia tensor with the connecting rod inertia tensor and the centroid, and indirectly constrain the positive definiteness of the centroid inertia tensor. However, this method ignores the ranges of the mass and the centroid, and the mass and centroid of outliers may still cause the instability of the model.

[0077] In one embodiment, directly constrain the positive definiteness of the centroid inertia tensor.

[0078] Step 203, update the recursive least squares identification method based on the physical feasibility constraints.

[0079] The recursive least squares identification method here is a method for estimating the system model parameters by minimizing the sum of the squares of the errors between the actual observed values and the model predicted values.

[0080] Step 204, identify the dynamic parameters of each connecting rod of the target moving part according to the updated recursive least squares identification method.

[0081] Among them, the recursive least squares identification method can be used to determine the dynamic parameters of each component of the target moving part.

[0082] The updated recursive least squares identification method here refers to the recursive least squares identification method after meeting the update iteration conditions. For example, the iteration reaches the number of iterations, and the parameters after iteration reach the preset parameter conditions, etc.

[0083] In the above implementation process, by constructing a dynamic model based on the centroid inertia tensor, the dynamic model takes into account the mass distribution, which can improve the accuracy and stability of the dynamic model. In addition, directly reconstructing the dynamic model using the centroid inertia tensor will result in a non-linear coupling between the dynamic parameters and non-dynamic quantities. Subsequently, the extended dynamic parameters can transfer this non-linear coupling to between the dynamic parameters, and through parameter mapping, the transferred non-linearity is converted into a parameter constraint problem and added to the physical feasibility constraints, which can reduce the dimension of the problem and enhance the feasibility of the model.

[0084] In one possible implementation manner, step 202 includes: separating the linear term and the non-linear term of the dynamic model; determining the minimum inertia parameter set based on the dynamic model after separating the linear term and the non-linear term; and determining the physical feasibility constraint through the minimum inertia parameter set.

[0085] In one embodiment, assume There are linearly independent columns in, and the dynamic model after separating the linear term and the non-linear term can be expressed as:

[0086] ;

[0087] Among them, is 's independent column ( , represents the real number set as a 36× real number matrix), is 's related column ( , represents the real number set as a 36× real number matrix), is the total force and moment ( , represents the real number set as a 36×1 real number matrix), is 's defined matrix ( , represents the real number set as a 36×96 real number matrix), is the maximal linearly independent group, is other linearly related terms, is the angle of the joint, is the angular velocity of the joint, is the angular acceleration of the joint.

[0088] In one embodiment, the relevant columns can be expressed as: .

[0089] Here, corresponds to the matrix , corresponds to the matrix .

[0090] Through a permutation matrix ( , represents a real matrix of 96×96 for the set of real numbers), and can be expressed as:

[0091] ;

[0092] ;

[0093] Preset:

[0094] ;

[0095] Then the dynamic model can be rewritten as:

[0096] ;

[0097] Then the minimum inertia parameter set can be expressed as:

[0098] ;

[0099] Among them, is the dynamic parameter set, is the minimum inertia parameter set, is the defined matrix, is the permutation matrix, is the independent column of, is the relevant column of, is the maximal linearly independent group, is the other linearly related terms, is the matrix that maps the complete dynamic parameters to the minimum relation parameter set, is the ratio of and

[0100] The above-mentioned is the first columns of the permutation matrix, is the part of the permutation matrix except the first Other columns than the column. The minimum inertia parameter set here is the minimum set of dynamic parameters that can fully characterize a given system. In dynamic parameter identification, determining the minimum inertia parameter set of each component of the target moving part can reduce redundant parameters while ensuring that these parameters can still fully describe the dynamic behavior of the system.

[0101] Among them, the minimum inertia parameter set is obtained by identifying linearly dependent parameters in the system and eliminating redundant parameters.

[0102] Optionally, a complete set of dynamic parameters that meet the constraints can be found through the minimum inertia parameter set, and then the physical feasibility constraints can be determined.

[0103] In the above implementation process, by separating the linear term and the non-linear term of the dynamic model and then determining the minimum inertia parameter set, redundant parameters can be reduced and the dynamic behavior of the target moving part can still be fully described. While improving the accuracy of the physical feasibility constraints, the parameters involved in the calculation are reduced, and the processing efficiency is improved.

[0104] In a possible implementation manner, determining the physical feasibility constraints through the minimum inertia parameter set includes: establishing a centroid inertia tensor constraint according to the dynamic model; establishing an equality constraint for the centroid and the quadratic term of the centroid; determining a set of dynamic parameters that meet the centroid inertia tensor constraint and the equality constraint through the minimum inertia parameter set; and reconstructing the physical feasibility constraints according to the set of dynamic parameters.

[0105] In one embodiment, the physical feasibility constraint mainly represents the centroid inertia tensor in terms of the link inertia tensor and the centroid, and then indirectly constrains the positive definiteness of the centroid inertia tensor.

[0106] Exemplarily, let , according to the parallel axis theorem, the physical feasibility constraint can be expressed as:

[0107] ;

[0108] Among them, " " represents is a positive definite matrix.

[0109] Through the Schur complement theorem, the above physical feasibility constraint can be rewritten as:

[0110] ;

[0111] ;

[0112] Furthermore, the physical feasibility constraint can be rewritten as the following linear matrix inequality:

[0113] ;

[0114] Among them, is the centroid inertia tensor of the th connecting rod, is the connecting rod inertia tensor, is the th mass of the connecting rod, is the centroid of the th connecting rod, is an anti-symmetric matrix, is the connecting rod-based inertia tensor of the connecting rod, is the dynamic parameter of the centroid in the direction, is the dynamic parameter of the centroid in the direction, is the dynamic parameter of the centroid in the direction.

[0115] Here is equivalent to , and this physical feasibility constraint can be transformed into a semi-definite programming problem.

[0116] In another embodiment, the physical feasibility constraint is determined by directly constraining the positive definiteness of the centroid inertia tensor.

[0117] The physical feasibility constraint here can be expressed as:

[0118] ;

[0119] Among them, is a 3rd-order square matrix.

[0120] If is used to represent the value of the th leading principal minor of , then according to the Sylvester criterion, is equivalent to each leading principal minor being greater than 0.

[0121] Furthermore, can be expressed as an inequality constraint:

[0122] ;

[0123] At the same time, since there is a centroid and a quadratic term of the centroid in the dynamic parameter set , it is necessary to add an equality constraint related to the centroid:

[0124] ;

[0125] Since the minimum inertia parameter set is identified , so it is not possible to directly impose constraints on , but rather to find a complete set of dynamic parameters that satisfy the constraints through . Therefore, the verification of physical feasibility constraints can be expressed as: .

[0126] ;

[0127] ;

[0128] ;

[0129] where is the inequality constraint on all the dynamic parameters of the th link, is the equality constraint on all the dynamic parameters of the th link, is the set of all the dynamic parameters of the th link.

[0130] It can be understood that the quadratic term of the center of mass and the center of mass constraint of the extended dynamic parameters can ensure to a certain extent that the center of mass is in the correct position. At the same time, a lower limit can be set for the mass, that is . Where represents the preset lower limit. In this way, a more reasonable set of dynamic parameters can be obtained.

[0131] In the above implementation process, determining the set of dynamic parameters that satisfy the center of mass inertia tensor constraint and the equality constraint can make the center of mass in the correct position to a certain extent and improve the accuracy of the set of dynamic parameters. In addition, by reconstructing the physical feasibility constraint according to the minimum inertia parameter set and the set of dynamic parameters, a corresponding lower limit can be set for the mass, and then a more reasonable set of dynamic parameters can be obtained, further improving the accuracy and authenticity of the set of dynamic parameters.

[0132] In a possible implementation manner, based on the physical feasibility constraint, the recursive least squares identification method is updated, including: updating the minimum inertia parameter set according to the physical feasibility constraint; determining the least squares objective function according to the minimum inertia parameter set; and determining the recursive least squares identification method based on the least squares objective function and the forgetting factor.

[0133] Where, when the error of the identified torque is not within the allowable error range, the set of dynamic parameters is updated according to the following formula:

[0134] ;

[0135] ;

[0136] ;

[0137] wherein, is the set of kinetic parameters, is the set of minimum inertia parameters, is the matrix that maps the complete kinetic parameters to the set of minimum relationship parameters, is the inequality constraint of all the kinetic parameters of the th link, is the equality constraint of all the kinetic parameters of the th link, is the th link of all the kinetic parameter sets.

[0138] And update the set of minimum inertia parameters according to the following formula: ;

[0139] wherein, is the set of minimum inertia parameters, is the set of kinetic parameters, is the set of minimum inertia parameters.

[0140] It should be understood that when the error of the identified torque is within the error tolerance range, it is determined that the update reaches the iteration condition, and the set of minimum inertia parameters corresponding to the error of the identified torque within the error tolerance range is determined as the updated set of minimum inertia parameters.

[0141] In one embodiment, according to the set of minimum inertia parameters, it is determined that the least squares objective function can be expressed by the following formula:

[0142] ;

[0143] wherein, is the identified set of basic inertia parameters, is the total number of sampling points, is the actual torque minus the friction torque, is the forgetting factor.

[0144] According to the kinetic model, the torque and force of the th component are independent of the components from the 1st component to the th component.

[0145] Therefore, the kinetic parameters of each component to the 1st component can be sequentially identified by using the recursive least squares method.

[0146] The iterative update process of the component can be expressed as:

[0147] ;

[0148] ;

[0149] wherein, is the forgetting factor , is the th moment, and the minimum inertia parameter set is obtained by the moment of the th element, is the th moment, and the th covariance matrix of the element (used for the recursive least squares update process).

[0150] Initial covariance matrix indicates that the uncertainty of the initial estimate is relatively large ( ), and it is initially set to a large positive number multiplied by the identity matrix.

[0151] It can be understood that, different from the least squares method and the weighted least squares method that need to process and solve the entire data set at one time, the least squares objective function gradually updates the parameter estimates as new data arrives, making it very suitable for real-time dynamic systems. It only needs to update the previous estimates instead of recalculating the entire data set, and this recursive feature reduces the computational complexity. In addition, the least squares objective function can continuously adapt to the changing system dynamics. For example, the noise or external interference in a robot manipulator. At the same time, introducing the forgetting factor can gradually reduce the dependence on past data when new data appears, making the parameter estimates more sensitive to the most recent observations.

[0152] In the above implementation process, through the recursive least squares identification method guided by physical feasibility constraints, using physical feasibility constraints to constrain and guide the parameter update direction, the dynamic parameters with physical feasibility can be identified online, and while ensuring physical feasibility, the accuracy and stability of identification can be improved. In addition, by introducing the forgetting factor, the dependence on past data when new data appears can be gradually reduced, making the parameter estimates more sensitive to the most recent observations and improving the identification accuracy.

[0153] In a possible implementation manner, step 204 includes: compensating the updated recursive least squares identification method through a self-evolving fuzzy neural network; identifying the dynamic parameters of each joint of the target moving part through the compensated recursive least squares identification method.

[0154] wherein, the self-evolving fuzzy neural network is configured to compensate the moment in the dynamic parameters.

[0155] The self-evolving fuzzy neural network here is a method that can adapt to dynamic changes. It combines the adaptive learning ability of neural networks with the interpretability and robustness of fuzzy systems. Different from traditional methods, the evolving fuzzy neural network can dynamically adjust its structure and parameters online to make it suitable for dealing with time-varying dynamics and uncertainties in robotic systems.

[0156] Due to the complexity of the target moving parts and the existence of non-linear factors such as external disturbances, it is very difficult to achieve high-precision identification based only on traditional dynamic models. Therefore, it is necessary to compensate for the unmodeled dynamics and non-linear disturbances.

[0157] Considering that the compensation error is affected by joint angles, velocities, accelerations, and torques, the input and output of the self-evolving fuzzy neural network are:

[0158] ;

[0159] ;

[0160] Among them, is the torque of the joint estimated by the identified dynamic model, is the error between the actual torque and the collected torque, is the joint angle, is the joint angular velocity, is the joint angular acceleration.

[0161] In one embodiment, as Figure 3 shown, the self-evolving fuzzy neural network may include an input layer, a antecedent layer, an activation layer, a consequent layer, and an output layer.

[0162] Among them, each node in the input layer is a clear input variable, and the input variable is input to this layer; each node in the antecedent layer can perform a fuzzification operation using a type-1 Gaussian membership function; each node in the activation layer represents its fuzzy rules and functions; each node in the consequent layer is called a result node, describing a linear model with exogenous inputs; the node in the output layer corresponds to an output linguistic variable, and this output function combines the outputs of the activation layer and the consequent layer.

[0163] The above self-evolving fuzzy neural network can be updated along with the dynamic parameter identification and generate compensation torque in real time.

[0164] In the above implementation process, by using the self-evolving fuzzy neural network to compensate the recursive least squares identification method, and then realizing the compensation of the torque in the dynamic parameters, the accuracy and robustness of the control of the target moving parts in a complex environment can be improved.

[0165] In a possible implementation, the recursive least squares identification method is compensated by a self-evolving fuzzy neural network, including: performing a fuzzification operation on the input variables through a Gaussian membership function; performing a fuzzy intersection operation on the input variables after the fuzzification operation using an algebraic product operation; generating a result output according to the external input state and the input variables after the fuzzy intersection operation; compensating the recursive least squares identification method based on the error.

[0166] Among them, the result output is configured to determine the error between the actual network output and the desired output.

[0167] The fuzzification operation here can be implemented by the following formula:

[0168] ;

[0169] Among them, is the function value, is the center of the Gaussian function, is the standard deviation of the Gaussian function.

[0170] The function value here is a type-1 Gaussian membership function. The standard deviation of the Gaussian function is used to represent the width of the Gaussian function.

[0171] It can be understood that in order to obtain the activation strength , each node uses the algebraic product operation to perform a fuzzy intersection operation on the inputs from the antecedent layer.

[0172] Then, the calculation formula for performing the fuzzy intersection operation on the input variables after the fuzzification operation using the algebraic product operation can be as follows:

[0173] ;

[0174] The output of the result node is a linear combination of the external input states and can be expressed as:

[0175] ;

[0176] Among them, is the activation strength of the fuzzy rule, is the function value, is the function parameter to be optimized, is the output corresponding to the th rule, and are in the form of a linear function,

[0177] The above result output can be expressed by the following formula:

[0178] ;

[0179] ;

[0180] It should be understood that the purpose of the self-evolving fuzzy neural network is to determine the minimization of the error function. Among them, the minimization of the error function can be expressed as:

[0181] ;

[0182] Among them, is the result after normalization of the activation intensity ; is the minimization of the error function is the actual network output is the desired output represents the total number of rules.

[0183] In a possible implementation, before compensating the recursive least squares identification method through the self-evolving fuzzy neural network, the method further includes: updating the antecedent layer in the self-evolving fuzzy neural network by the gradient descent method; and / or, updating the consequent layer in the self-evolving fuzzy neural network according to the physical feasibility constraint; and / or, updating the optimization rules according to the activation intensity threshold.

[0184] Among them, the update of the antecedent layer can be achieved in the following way:

[0185] Let represent the input variable in the th Gaussian fuzzy set of the antecedent parameters and . In this case, the antecedent part can be updated by the gradient descent:

[0186] ;

[0187] The consequent update here can be achieved in the following way:

[0188] Convert the output in to a row vector, then there is:

[0189] ;

[0190] Among them, is the learning rate of the gradient descent is the consequent part. Therefore, can also be updated by the recursive least squares identification method, expressed as:

[0191] ;

[0192] ;

[0193] Among them, is the forgetting factor, is the covariance matrix.

[0194] The above update of the optimization rules mainly includes rule pruning and rule generation.

[0195] In one implementation, the activation intensity threshold can be used to judge rule generation. When the maximum value of is less than the threshold

[0196] For rule pruning, the historical average activation intensity is an evaluation index, which represents the average value of the activation intensity from the start of rule generation to the present. If , it means that the rule is rarely activated and should be pruned.

[0197] In the above implementation process, by selecting the corresponding update method for different network layers for update, the self-evolving fuzzy neural network can be updated online, and the compensation torque can be generated in real time to compensate the identified extended dynamics, thereby improving the accuracy and robustness of parameter identification.

[0198] Based on the same application concept, an embodiment of the present application also provides a dynamic parameter identification device corresponding to the dynamic parameter identification method. Since the principle of solving problems by the device in the embodiment of the present application is similar to that of the foregoing embodiment of the dynamic parameter identification method, the implementation of the device in this embodiment can refer to the description in the foregoing method embodiment, and the repeated parts will not be described again.

[0199] Please refer to Figure 4 , which is a schematic diagram of the functional modules of the dynamic parameter identification device provided by the embodiment of the present application. Each module in the dynamic parameter identification device in this embodiment is used to execute each step in the foregoing method embodiment. The dynamic parameter identification device includes a construction module 301, a determination module 302, an update module 303, and an identification module 304; among them,

[0200] The construction module 301 is used to construct a dynamic model through the centroid inertia tensor of the target moving part.

[0201] The determination module 302 is used to determine the physical feasibility constraint according to the dynamic model.

[0202] The first update module 303 is used to update the recursive least squares identification method based on the physical feasibility constraint.

[0203] The recognition module 304 is used to recognize the dynamic parameters of each connecting rod of the target moving part according to the updated recursive least squares identification method.

[0204] In a possible implementation manner, the determination module 302 is further configured to: separate the linear term and the non-linear term of the dynamic model; determine the minimum inertia parameter set based on the dynamic model after separating the linear term and the non-linear term; and determine the physical feasibility constraint through the minimum inertia parameter set.

[0205] In a possible implementation manner, the determination module 302 is specifically configured to: establish a centroid inertia tensor constraint according to the dynamic model; establish an equality constraint of the centroid and the quadratic term of the centroid; determine a set of dynamic parameters that satisfy the centroid inertia tensor constraint and the equality constraint through the minimum inertia parameter set; and reconstruct the physical feasibility constraint according to the set of dynamic parameters.

[0206] In a possible implementation manner, the determination module 302 is specifically configured to: update the minimum inertia parameter set according to the physical feasibility constraint; determine a least squares objective function according to the updated minimum inertia parameter set; and determine the recursive least squares identification method based on the least squares objective function and the forgetting factor.

[0207] In a possible implementation manner, the recognition module 304 is further configured to: compensate the recursive least squares identification method through a self-evolving fuzzy neural network; wherein the self-evolving fuzzy neural network is configured to compensate the torque in the dynamic parameters; and recognize the dynamic parameters of each joint of the target moving part through the compensated recursive least squares identification method.

[0208] In a possible implementation manner, the recognition module 304 is specifically configured to: perform a fuzzification operation on the input variable through a Gaussian membership function; perform a fuzzy intersection operation on the input variable after performing the fuzzification operation using an algebraic product operation; generate a result output according to the external input state and the input variable after performing the fuzzy intersection operation; wherein the result output is configured to determine the error between the actual network output and the expected output; and compensate the recursive least squares identification method based on the error.

[0209] In a possible implementation manner, the dynamic parameter identification device further includes: a second update module, configured to update the antecedent layer in the self-evolving fuzzy neural network by using the gradient descent method; and / or update the consequent layer in the self-evolving fuzzy neural network according to the physical feasibility constraint; and / or update the optimization rule according to the activation intensity threshold.

[0210] In addition, an embodiment of the present application further provides a computer-readable storage medium, on which a computer program is stored. When the computer program is run by a processor, it executes the steps of the dynamic parameter identification method described in the above method embodiment.

[0211] A computer program product of the dynamic parameter identification method provided by an embodiment of the present application includes a computer-readable storage medium storing program code. The instructions included in the program code can be used to execute the steps of the dynamic parameter identification method described in the above method embodiment. For details, refer to the above method embodiment and will not be elaborated herein.

[0212] In several embodiments provided by the present application, it should be understood that the disclosed devices and methods can also be implemented in other ways. The device embodiments described above are merely illustrative. For example, the flowcharts and block diagrams in the accompanying drawings show the possible architectures, functions, and operations of devices, methods, and computer program products according to multiple embodiments of the present application. In this regard, each block in the flowchart or block diagram can represent a module, a program segment, or a part of code, and the module, program segment, or part of code contains one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than marked in the accompanying drawings. For example, two consecutive blocks can actually be executed substantially in parallel, and they can sometimes be executed in the reverse order, depending on the functions involved. It should also be noted that each block in the block diagram and / or flowchart, as well as the combination of blocks in the block diagram and / or flowchart, can be implemented by a dedicated hardware-based system for performing the specified functions or actions, or can be implemented by a combination of dedicated hardware and computer instructions.

[0213] In addition, in each embodiment of the present application, the various functional modules can be integrated together to form an independent part, or each module can exist alone, or two or more modules can be integrated to form an independent part.

[0214] When the above-mentioned functions are implemented in the form of software function modules and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a part of this technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in various embodiments of this application. The foregoing storage medium includes: various media such as USB flash drives, mobile hard disks, read-only memories (ROM, Read-Only Memory), random access memories (RAM, Random Access Memory), magnetic disks, or optical discs that can store program codes. It should be noted that in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements not only includes those elements, but also includes other elements not expressly listed, or also includes elements inherent to such process, method, article or device. Without further limitation, the elements defined by the statement "comprising..." do not exclude the existence of additional identical elements in the process, method, article or device comprising the said elements.

[0215] The foregoing are only the preferred embodiments of this application and are not used to limit this application. For those skilled in the art, this application can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of this application shall be included within the protection scope of this application. It should be noted that similar reference numerals and letters denote similar items in the following drawings. Therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings.

[0216] The above is only the specific implementation manner of this application, but the protection scope of this application is not limited thereto. Any person skilled in the art can easily think of changes or replacements within the technical scope disclosed by this application and should be covered by the protection scope of this application. Therefore, the protection scope of this application shall be subject to the protection scope of the claims.

Claims

1. A method for identifying kinetic parameters, characterized in that: include: The dynamic model is constructed through the mass center inertia tensor of the target moving part; determining physical feasibility constraints based on the kinetic model; Based on the physical feasibility constraint, updating the recursive least squares identification method; Identifying the dynamic parameters of each connecting rod of the target moving part according to the updated recursive least squares identification method; Determining physical feasibility constraints according to the kinetic model includes: separating linear and nonlinear terms of the kinetic model; Determine the minimum inertia parameter set based on the dynamic model after separating the linear terms and the nonlinear terms; Determining the physical feasibility constraint through the minimum inertia parameter set; Determining the physical feasibility constraint by using the minimum inertia parameter set includes: According to the dynamic model, establishing a mass center inertia tensor constraint; Establish equality constraints on the centroid and the quadratic term of the centroid; Determining a dynamic parameter set that satisfies the mass center inertia tensor constraint and the equality constraint through the minimum inertia parameter set; The physical feasibility constraints are reconstructed based on the set of dynamic parameters.

2. The method according to claim 1, characterized in that The updating of the recursive least squares identification method based on the physical feasibility constraint comprises: updating the minimum inertia parameter set according to the physical feasibility constraint; Determine the least squares objective function according to the updated minimum inertia parameter set; The recursive least squares identification method is determined based on the least squares objective function and the forgetting factor.

3. The method according to any one of claims 1 to 2, characterized in that: The step of identifying the dynamic parameters of each connecting rod of the target moving part according to the updated recursive least squares identification method includes: The recursive least squares identification method is compensated by a self-evolving fuzzy neural network; wherein the self-evolving fuzzy neural network is configured to compensate for the torque in the dynamic parameters; The dynamic parameters of each joint of the target moving part are identified by using a compensated recursive least squares identification method.

4. The method according to claim 3, characterized in that The compensating the recursive least squares identification method by the self-evolving fuzzy neural network includes: Fuzzification is performed on input variables through Gaussian membership function; Use algebraic product operation to perform fuzzy intersection operation on the input variables after fuzzification operation; Generate a result output according to the external input state and the input variable after performing the fuzzy intersection operation; wherein the result output is configured to determine the error between the actual network output and the expected output; The recursive least squares identification method is compensated based on the error.

5. The method according to claim 3, characterized in that: Before compensating the recursive least squares identification method by the self-evolving fuzzy neural network, the method further comprises: Updating the antecedent layer in the self-evolving fuzzy neural network by gradient descent method; and / or updating the consequent layer in the self-evolving fuzzy neural network according to the physical feasibility constraint; And / or updating the optimization rule according to the activation strength threshold.

6. A kinetic parameter identification device, characterized in that: include: A construction module is used to construct a dynamic model through the mass center inertia tensor of the target moving part; A determination module, used for determining physical feasibility constraints according to the dynamic model; A first updating module, configured to update a recursive least squares identification method based on the physical feasibility constraint; an identification module, used to identify the dynamic parameters of each connecting rod of the target moving part according to the updated recursive least squares identification method; The determination module is further used to: separate the linear terms and nonlinear terms of the kinetic model; Determine a minimum inertia parameter set based on a dynamic model after separating linear terms and nonlinear terms; determine the physical feasibility constraint through the minimum inertia parameter set; The determination module is specifically used to: establish a center of mass inertia tensor constraint based on the dynamic model; establish an equality constraint between the center of mass and the quadratic term of the center of mass; determine a dynamic parameter set that satisfies the center of mass inertia tensor constraint and the equality constraint through the minimum inertia parameter set; and reconstruct the physical feasibility constraint based on the dynamic parameter set.

7. An electronic device, characterized in that: include: A processor and a memory, wherein the memory stores machine-readable instructions executable by the processor, and when the electronic device is running, the machine-readable instructions are executed by the processor to perform the steps of any method described in claims 1 to 5.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of any method according to claim 1 to 5 are executed.

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