Dynamic parameter identification method and device, electronic equipment and computer storage medium

Abstract

The invention provides a kinetic parameter identification method and device, electronic equipment and a computer storage medium, and the method comprises the steps: constructing a kinetic model through the mass center inertia tensor of a target moving part; determining a physical feasibility constraint according to the kinetic model; updating the recursive least square identification method based on the physical feasibility constraint; and according to the updated recursive least square identification method, identifying kinetic parameters of each connecting rod of the target moving part. The dynamic model is constructed based on the centroid inertia tensor, mass distribution is considered, and the accuracy and stability of the model can be improved. The mass center inertia tensor is directly used for reconstructing the kinetic model, nonlinear coupling between kinetic parameters and non-kinetic quantities can be generated, then the nonlinear coupling is transferred between the kinetic parameters through the kinetic parameters, the transferred nonlinearity is converted into a parameter constraint problem through parameter mapping, and the parameter constraint problem is added into physical feasibility constraint; the dimensionality of the problem can be reduced, and the feasibility of the model is enhanced.

Description

Technical Field

[0001] The present application relates to the field of data processing, and in particular to a method, device, electronic device and computer storage medium for dynamic parameter identification. Background Art

[0002] Dynamic parameter identification is a method to determine unknown parameters in a dynamic system through experiments, numerical simulations or theoretical derivations. 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 the two important physical quantities of mass and center of mass.

[0003] However, in many application scenarios, especially when it comes to parameter identification of complex mechanical systems (such as industrial robots, 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 the present application is to provide a dynamic parameter identification method, device, electronic device and computer storage medium, which can improve model stability.

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

[0006] In the above implementation process, by constructing a dynamic model based on the mass center inertia tensor, the dynamic model takes into account the distribution of mass, which can improve the accuracy and stability of the dynamic model. In addition, directly using the mass center inertia tensor to reconstruct the dynamic model will produce nonlinear coupling between dynamic parameters and non-dynamic quantities, and the subsequent extended dynamic parameters can transfer the nonlinear coupling between dynamic parameters, and convert the transferred nonlinearity into a parameter constraint problem through parameter mapping and add it to the physical feasibility constraint, which can reduce the dimension of the problem and enhance the feasibility of the model.

[0007] In one embodiment, determining the physical feasibility constraint based on the dynamic model includes: separating the linear terms and nonlinear terms of the dynamic model; determining a minimum inertia parameter set based on the dynamic model after separating the linear terms and nonlinear terms; and determining the physical feasibility constraint through the minimum inertia parameter set.

[0008] In the above implementation process, by separating the linear terms and nonlinear 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 parts can still be fully described. While improving the accuracy of the physical feasibility constraints, the parameters involved in the calculation are reduced, thereby improving processing efficiency.

[0009] In one embodiment, determining the physical feasibility constraint through the minimum inertia parameter set includes: establishing a center of mass inertia tensor constraint based on the dynamic model; establishing an equality constraint for the center of mass and the quadratic term of the center of mass; determining a dynamic parameter set that satisfies the center of mass inertia tensor constraint and the equality constraint through the minimum inertia parameter set; and reconstructing the physical feasibility constraint based on the dynamic parameter set.

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

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

[0012] In the above implementation process, the recursive least squares identification method guided by physical feasibility constraints uses physical feasibility constraints to constrain and guide the parameter update direction, and can identify dynamic parameters with physical feasibility online, which can improve the accuracy and stability of identification while ensuring physical feasibility. In addition, 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 most recent observation results, and improving the accuracy of identification.

[0013] In one embodiment, the dynamic parameters of each connecting rod of the target moving part are identified based on the updated recursive least squares identification method, including: 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, the recursive least squares identification method is compensated by using a self-evolving fuzzy neural network, and then the torque in the dynamic parameters is compensated, which can improve the accuracy and robustness of the control of the target moving part in a complex environment.

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

[0016] In one embodiment, before compensating 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 strength threshold.

[0017] In the above implementation process, the corresponding update method is selected for different network layers to update the self-evolving fuzzy neural network online, and the compensation torque is generated in real time to perform torque compensation on the identified extended dynamics, thereby improving the accuracy and robustness of parameter identification.

[0018] In the second aspect, an embodiment of the present application also provides a dynamic parameter identification device, including: a construction module, used to construct a dynamic model through the center of mass inertia tensor of the target moving part; a determination module, used to determine the physical feasibility constraints based on the dynamic model; a first update module, used to update the recursive least squares identification method based on the physical feasibility constraints; 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.

[0019] In a third aspect, an embodiment of the present application further provides an electronic device, comprising: 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 the method in the above-mentioned first aspect, or any possible implementation of the first aspect.

[0020] In a fourth aspect, 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 executed by a processor, the steps of the kinetic parameter identification method in the above-mentioned first aspect, or any possible implementation of the first aspect are executed.

[0021] In order to make the above-mentioned objects, features and advantages of the present application more obvious and understandable, embodiments are given below and described in detail with reference to the attached drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments will be briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without paying creative work.

[0023] Figure 1 A block diagram of an electronic device provided in an embodiment of the present application; Figure 2 A flow chart of a kinetic parameter identification method provided in an embodiment of the present application; Figure 3 A schematic diagram of a self-evolving fuzzy neural network provided in an embodiment of the present application; Figure 4 A schematic diagram of the functional modules of the kinetic parameter identification device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0024] The technical solutions in the embodiments of the present application will be described below in conjunction with the accompanying drawings in the embodiments of the present application.

[0025] It should be noted that similar reference numerals and letters represent similar items in the following drawings, so 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 this application, the terms "first", "second", etc. are only used to distinguish the description and cannot be understood as indicating or implying relative importance.

[0026] Dynamic parameter identification can be divided into model-free identification and model-based identification. Model-free identification does not require the mathematical model of the robot to be defined in advance, but relies on the measurement of the joint position and torque of the robot, and regards the robot as an unknown nonlinear multi-input and 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 derivation. However, compared with model-based identification, it requires more computing resources and has lower accuracy, and the identified dynamic model cannot cover all physical effects.

[0027] Model-based identification 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 manipulator 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 gained increasing attention, which allows the dynamic model to be continuously updated based on real-time data. A series of online methods and their improvements, such as extended Kalman filtering, unscented Kalman filtering, 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.

[0028] In view of this, the present application proposes a method for identifying dynamic parameters. By constructing a dynamic model based on the mass center 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 using the mass center inertia tensor to reconstruct the dynamic model will produce nonlinear coupling between dynamic parameters and non-dynamic quantities, and the subsequent extended dynamic parameters can transfer the nonlinear coupling between dynamic parameters, and convert the transferred nonlinearity into a parameter constraint problem through parameter mapping and add it to the physical feasibility constraint, which can reduce the dimension of the problem and enhance the feasibility of the model.

[0029] To facilitate understanding of this embodiment, firstly, an electronic device for executing the dynamic parameter identification method disclosed in the embodiment of the present application is introduced in detail.

[0030] like Figure 1 , which is a block diagram of an electronic device. The electronic device 100 may include a memory 111 and a processor 113. A person skilled in the art may understand that Figure 1The structure shown is only for illustration and does not limit the structure of the electronic device 100. For example, the electronic device 100 may further include Figure 1 More or fewer components as shown, or with Figure 1 Different configurations shown.

[0031] The memory 111 and the processor 113 are directly or indirectly electrically connected to each other to achieve data transmission or interaction. For example, these elements can be electrically connected to each other via one or more communication buses or signal lines. The processor 113 is used to execute the executable module stored in the memory.

[0032] The memory 111 may be, but is not limited to, a random access memory (RAM), a read only memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable read-only memory (EEPROM), etc. The memory 111 is used to store programs, and the processor 113 executes the program after receiving an execution instruction. 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.

[0033] The processor 113 may be an integrated circuit chip with signal processing capability. The processor 113 may be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it may also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components. The methods, steps and logic block diagrams disclosed in the embodiments of the present application may be implemented or executed. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0034] The electronic device 100 in this embodiment can be used to execute each step in each method provided in the embodiments of the present application. The implementation process of the kinetic parameter identification method is described in detail below through several embodiments.

[0035] First, before introducing the kinetic parameter identification method provided in the embodiment of the present application, the basic concept of kinetic parameter identification is introduced: Dynamic parameter identification refers to a method of determining unknown parameters in a dynamic system through experiments, numerical simulations or theoretical derivations. It identifies the model parameters in the system (such as the mass, center of mass, inertia tensor, friction, etc. of each arm of the robot) based on the input and output data of the system (such as the displacement, velocity, acceleration, force, etc. of each joint of the robot arm), aiming to improve the accuracy, stability and performance of the system.

[0036] See also Figure 2 , is a flow chart of the kinetic parameter identification method provided in the embodiment of the present application. Figure 2 The specific process shown is described in detail.

[0037] Step 201, constructing a dynamic model through the mass center inertia tensor of the target moving part.

[0038] Among them, the center-of-mass inertia tensor is a tensor that describes the magnitude of inertia when a rigid body rotates around its center of mass.

[0039] The target moving part here refers to the component whose dynamic parameters need to be determined, for example, a robot arm, a gripper, etc.

[0040] The existing dynamic parameter identification requires the identification of parameters such as the mass, center of mass and connecting rod inertia tensor of each element of the target moving part. Among them, the connecting rod refers to the rigid structural part connecting two adjacent elements in the target moving part. Each connecting rod 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.

[0041] For example, if the target moving part is a robotic arm, the dynamic parameter identification needs to identify the mass, center of mass, and inertia tensor of each arm of the robotic arm. Among them, the connecting rod refers to the rigid structural part connecting two adjacent arms in the robotic arm, and each connecting rod strictly corresponds to a kinematic link in the robotic arm.

[0042] In the embodiment of the present application, it is necessary to identify the mass, center of mass, center of mass quadratic term and center of mass inertia tensor of each connecting rod. Among them, the connecting rod inertia tensor is defined relative to the origin of the connecting rod coordinate system, and the center of mass inertia tensor is defined relative to the center of mass.

[0043] It should be understood that for a target moving part with a rotating joint, if the center of mass inertia tensor is used, the dynamic model is nonlinear. If the connecting rod inertia tensor is used, the nonlinear part can be eliminated through the parallel axis theorem to obtain a linear model. The connecting rod inertia tensor can indeed simplify the dynamic model, but the physical feasibility constraint established by this has the coupling of mass, center of mass, and connecting rod inertia tensor, resulting in the physical feasibility constraint only constraining the physical properties (positive and negative, positive definiteness) of the three, and it is difficult to constrain the range of mass and center of mass. If we consider directly using the center of mass inertia tensor to reconstruct the dynamic model, this will produce nonlinear coupling between dynamic parameters and non-dynamic quantities, and the subsequent extended dynamic parameters can transfer this nonlinear coupling between dynamic parameters, and convert the transferred nonlinearity into a parameter constraint problem through parameter mapping and add it to the physical feasibility constraint.

[0044] In one embodiment, the kinetic model can be constructed by: Add the quadratic term of the center of mass to the original dynamic parameter set, and the dynamic parameter set becomes: ; ; in, To form the kinetic parameter set, is the centroid vector in its coordinate system The weight of the axis, is the centroid vector in its coordinate system The weight of the axis, is the centroid vector in its coordinate system The weight of the axis, is a 1×6 vector consisting of the upper triangular elements of the center-of-mass inertia tensor, For the The mass of the connecting rod, For the The dynamic parameters of the connecting rod, is the centroid vector.

[0045] The size of the above centroid vector is 1×3, and the centroid vector includes axis, Axis and The components of the axis. Among them, .

[0046] The total set of kinetic parameters here is , then the dynamic model can be expressed as: ; ; ; in, For the The connecting rod is applied to the The force on the connecting rod, For the The connecting rod is applied to the The torque on the connecting rod, For the The mass of the connecting rod, is the centroid vector, To form the kinetic parameter set, is the connecting rod inertia tensor, is the orthogonal rotation matrix (the The vector in the coordinate system is transformed to coordinate systems), is an antisymmetric matrix, is the rotation matrix, For the The connecting rod center of mass is The acceleration in the coordinate system, For the The connecting rod is The angular acceleration in the coordinate system is For the The origin of the coordinate system is The position in the coordinate system, and It is an intermediate quantity (with no actual physical meaning).

[0047] In one embodiment, ; ; in, refer to In the corresponding coordinate system The weight on the axis, refer to In the corresponding coordinate system The weight on the axis, refer to In the corresponding coordinate system The weight on the axis, refer to In the corresponding coordinate system The weight on the axis, refer to In the corresponding coordinate system The weight on the axis, refer to In the corresponding coordinate system The weight on the axis, express No. Line Elements of a column.

[0048] Here and It is an intermediate quantity generated to separate kinetic parameters from non-kinetic terms.

[0049] Assume that the force and torque at the end of the connecting rod are 0, let Indicates the forces and moments borne by each component. The overall process of calculating the forces and moments of the dynamic model can be expressed as: ; in, express , For the Extended dynamic parameters of the connecting rod.

[0050] Simplified expression: ; in, is the total force and moment ( ), for The matrix defined ( ), is the extended kinetic parameter ( ), is the set of real numbers, represents the real number set as a 36×1 real number matrix, represents the real number set as a 96×1 real number matrix, is the angle of the joint, is the angular velocity of the joint, is the angular acceleration of the joint.

[0051] When the target moving part is a rotating element, the torque applied is only in the z-axis direction, while the calculated torque has three directions: x, y, and z. Therefore, the torque calculation can be performed based on the following matrix: ; in, is the joint torque ( , represents the real number set as a 6×1 real number matrix), for The matrix consisting of rows in the same direction as the joint torque ( , represents the real number set as a 6×96 real number matrix), The total dynamic parameter set composed of the dynamic parameter set of the connecting rod (the direction selection mainly depends on the above ).

[0052] Step 202: determine physical feasibility constraints based on the dynamics model.

[0053] Among them, the physical feasibility constraint requires that the dynamic parameters have a reasonable numerical range to meet 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 maximum linearly independent group, that is, the minimum inertia parameter set.

[0054] The object of dynamic parameter identification here is the minimum inertia parameter set. The introduction of physical feasibility constraints is to find a reasonable complete dynamic parameter set through the minimum inertia parameter set.

[0055] The existing physical feasibility constraints mainly represent the center-of-mass inertia tensor by the connecting rod inertia tensor and the center of mass, and indirectly constrain the positivity of the center-of-mass inertia tensor. However, this method ignores the range of mass and center of mass, and outliers in mass and center of mass may still lead to model instability.

[0056] In one embodiment, the positivity of the center-of-mass inertia tensor is directly constrained.

[0057] Step 203: updating the recursive least squares identification method based on the physical feasibility constraint.

[0058] The recursive least squares identification method here is a method to estimate the system model parameters by minimizing the sum of squares of the errors between the actual observations and the model predictions.

[0059] Step 204 , identifying the dynamic parameters of each connecting rod of the target moving part according to the updated recursive least squares identification method.

[0060] Among them, the recursive least squares identification method can be used to determine the dynamic parameters of each component of the target moving part.

[0061] The updated recursive least squares identification method here refers to the recursive least squares identification method after the update iteration condition is met, for example, the iteration reaches the iteration number, the parameters after the iteration meet the parameter preset condition, etc.

[0062] In the above implementation process, by constructing a dynamic model based on the mass center inertia tensor, the dynamic model takes into account the distribution of mass, which can improve the accuracy and stability of the dynamic model. In addition, directly using the mass center inertia tensor to reconstruct the dynamic model will produce nonlinear coupling between dynamic parameters and non-dynamic quantities, and the subsequent extended dynamic parameters can transfer the nonlinear coupling between dynamic parameters, and convert the transferred nonlinearity into a parameter constraint problem through parameter mapping and add it to the physical feasibility constraint, which can reduce the dimension of the problem and enhance the feasibility of the model.

[0063] In a possible implementation, step 202 includes: separating linear terms and nonlinear terms of the dynamic model; determining a minimum inertia parameter set based on the dynamic model after separating the linear terms and nonlinear terms; and determining a physical feasibility constraint through the minimum inertia parameter set.

[0064] In one embodiment, assuming The Chinese Communist Party Linearly independent columns, the dynamic model after separating linear terms and nonlinear terms can be expressed as: ; in, for The independent columns of , Represents the set of real numbers as 36× ), for The relevant columns of , Represents the set of real numbers as 36× ), is the total force and moment ( , represents the real number set as a 36×1 real number matrix), for The matrix defined ( , represents the real number set as a 36×96 real number matrix), is a maximal linearly independent group, are other linearly related terms, is the angle of the joint, is the angular velocity of the joint, is the angular acceleration of the joint.

[0065] In one embodiment, The relevant columns can be expressed as: .

[0066] Here Correspondence Matrix , Correspondence Matrix .

[0067] Through a permutation matrix ( , represents the real number set as a 96×96 real number matrix), and It can be expressed as: ; ; Preset: ; Then the dynamic model can be rewritten as: ; Then the minimum inertia parameter set can be expressed as: ; in, is the kinetic parameter set, is the minimum inertia parameter set, for The matrix defined is, is the permutation matrix, for Independent columns of for The relevant columns of is a maximal linearly independent group, are other linearly related terms, To map the complete kinetic parameters to the matrix of the minimum set of relational parameters, for and ratio.

[0068] The above is the permutation matrix List, is the permutation matrix divided by The minimum inertia parameter set here is the minimum dynamic parameter set that can fully characterize the given system. In the 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.

[0069] The minimum inertia parameter set is obtained by identifying the linearly correlated parameters in the system and eliminating redundant parameters.

[0070] Alternatively, the physical feasibility constraints can be determined by finding a complete set of dynamic parameters that meets the constraints through a minimum set of inertia parameters.

[0071] In the above implementation process, by separating the linear terms and nonlinear 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 parts can still be fully described. While improving the accuracy of the physical feasibility constraints, the parameters involved in the calculation are reduced, thereby improving processing efficiency.

[0072] In one possible implementation, the physical feasibility constraints are determined through a minimum inertia parameter set, including: establishing a center of mass inertia tensor constraint based on a dynamic model; establishing an equality constraint for the center of mass and the quadratic term of the center of mass; determining a dynamic parameter set that satisfies the center of mass inertia tensor constraint and the equality constraint through a minimum inertia parameter set; and reconstructing the physical feasibility constraints based on the dynamic parameter set.

[0073] In one embodiment, the physical feasibility constraint is mainly to express the center-of-mass inertia tensor by the connecting rod inertia tensor and the center of mass, thereby indirectly constraining the positivity of the center-of-mass inertia tensor.

[0074] For example, let , according to the parallel axis theorem, the physical feasibility constraint can be expressed as: ; in," "express is a positive definite matrix.

[0075] By using Schur's complement theorem, the above physical feasibility constraint can be rewritten as: ; ; Furthermore, the physical feasibility constraint can also rewrite the linear matrix inequality shown in the following formula: ; in, For the The moment of inertia of the center of mass of the connecting rod is, is the connecting rod inertia tensor, For the The mass of the connecting rod, For the The center of mass of the connecting rod, is an antisymmetric matrix, is the connecting rod-based inertia tensor of the connecting rod, The center of mass is The dynamic parameters of the direction, The center of mass is The dynamic parameters of the direction, The center of mass is Directional dynamic parameters.

[0076] Here Equivalent to , this physical feasibility constraint can be transformed into a semi-definite programming problem.

[0077] In another embodiment, the physical feasibility constraint is determined by directly constraining the positivity of the center-of-mass inertia tensor.

[0078] The physical feasibility constraint here can be expressed as: ; in, It is a 3-order square matrix.

[0079] If you express No. The value of the principal minor of the order is, according to the Sylvester criterion, The equivalence is that the principal minors of all orders are greater than 0.

[0080] Further, can be expressed as an inequality constraint: ; At the same time, due to the dynamic parameter set Existence center of mass The quadratic term with the centroid , so it is necessary to add equality constraints related to the center of mass: ; Since the minimum inertia parameter set is identified , so it cannot be directly To constrain, but to Find the complete set of dynamic parameters that satisfy the constraints . So the verification of physical feasibility constraints can be expressed as: ; ; ; in, For the Inequality constraints on all the dynamic parameters of the connecting rod, For the The equality constraints for all the dynamic parameters of the connecting rod, For the The set of all dynamic parameters of a connecting rod.

[0081] Understandably, the center-of-mass quadratic term and the center-of-mass constraint of the extended kinetic parameter This can ensure that the center of mass is in the correct position to a certain extent. At the same time, a lower limit can be set for the mass, that is, .in, express In this way, a more reasonable set of dynamic parameters can be obtained.

[0082] In the above implementation process, determining the dynamic parameter set that satisfies the center of mass inertia tensor constraint and the equality constraint can, to a certain extent, place the center of mass in the correct position and improve the accuracy of the dynamic parameter set. In addition, by reconstructing the physical feasibility constraint based on the minimum inertia parameter set and the dynamic parameter set, a corresponding lower limit can be set for the mass, thereby obtaining more reasonable dynamic parameters and further improving the accuracy and authenticity of the dynamic parameter set.

[0083] In a possible implementation, 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 a forgetting factor.

[0084] Among them, when the error of the identified torque is not within the allowable error range, the dynamic parameter set is updated according to the following formula: ; ; ; in, is the kinetic parameter set, is the minimum inertia parameter set, To map the complete kinetic parameters to the matrix of the minimum set of relational parameters, For the Inequality constraints on all the dynamic parameters of the connecting rod, For the The equality constraints for all the dynamic parameters of the connecting rod, For the The set of all dynamic parameters of a connecting rod.

[0085] And update the minimum inertia parameter set according to the following formula: ; in, is the minimum inertia parameter set, is the kinetic parameter set, is the minimum inertia parameter set.

[0086] It should be understood that when the error of the identification torque is within the allowable error range, it is determined that the update meets the iteration condition, and the minimum inertia parameter set corresponding to the error of the identification torque within the allowable error range is the updated minimum inertia parameter set.

[0087] In one embodiment, according to the minimum inertia parameter set, the least squares objective function can be expressed by the following formula: ; in, is the identified basic inertial parameter set, is the total number of sampling points, is the actual torque minus the friction torque, For the forgetting factor.

[0088] According to the kinetic model, The moment and force of the first element are the same as the moment and force of the first element to the The components are irrelevant.

[0089] Therefore, the recursive least square method can be used to identify the kinetic parameters of each element up to the first element in turn.

[0090] element The iterative update process can be expressed as: ; ; in, Forgetting Factor , For the moment, through the The minimum inertia parameter set obtained by the moment of each element, For the Moment, The covariance matrix of the elements (used in the recursive least squares update procedure).

[0091] Initial covariance matrix Indicates that the uncertainty of the initial estimate is large ( ), which is initially set to a large positive number times the identity matrix.

[0092] Understandably, unlike least squares and weighted least squares, which need to process and solve the entire data set at once, 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 estimate instead of recalculating the entire data set. This recursive nature reduces computational complexity. In addition, the least squares objective function can continuously adapt to changing system dynamics. For example, noise or external interference in the robot manipulator. At the same time, the introduction of the forgetting factor can gradually reduce the dependence on past data when new data appears, making the parameter estimates more sensitive to recent observations.

[0093] In the above implementation process, the recursive least squares identification method guided by physical feasibility constraints uses physical feasibility constraints to constrain and guide the parameter update direction, and can identify dynamic parameters with physical feasibility online, which can improve the accuracy and stability of identification while ensuring physical feasibility. In addition, 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 most recent observation results, and improving the accuracy of identification.

[0094] In a possible implementation, step 204 includes: compensating the updated recursive least squares identification method by a self-evolving fuzzy neural network; and identifying the dynamic parameters of each joint of the target moving part by the compensated recursive least squares identification method.

[0095] Among them, the self-evolving fuzzy neural network configuration position compensates the torque in the dynamic parameters.

[0096] 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. Unlike traditional methods, the evolutionary fuzzy neural network can dynamically adjust its structure and parameters online, making it suitable for handling time-varying dynamics and uncertainties in robotic systems.

[0097] Due to the complexity of the target moving parts and the existence of nonlinear factors such as external interference, it is difficult to achieve high-precision recognition based only on traditional dynamic models. Therefore, it is necessary to compensate for the unmodeled dynamics and nonlinear interference.

[0098] Considering that the compensation error is affected by joint angle, velocity, acceleration and torque, the input and output of the self-evolving fuzzy neural network are: ; ; in, is the first estimated value of the identified dynamic model The torque of the joint, is the error between the actual torque and the acquired torque, is the angle of the joint, is the angular velocity of the joint, is the angular acceleration of the joint.

[0099] In one embodiment, if Figure 3 As shown, the self-evolving fuzzy neural network may include an input layer, a precondition layer, an activation layer, a postcondition layer and an output layer.

[0100] 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 fuzzification operations using the 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 input; the node in the output layer corresponds to an output linguistic variable, and the output function combines the outputs of the activation layer and the consequent layer.

[0101] The self-evolving fuzzy neural network can be updated along with the dynamic parameter identification and generate compensation torque in real time.

[0102] In the above implementation process, the recursive least squares identification method is compensated by using a self-evolving fuzzy neural network, and then the torque in the dynamic parameters is compensated, which can improve the accuracy and robustness of the control of the target moving part in a complex environment.

[0103] In a possible implementation, the recursive least squares identification method is compensated by a self-evolving fuzzy neural network, including: performing fuzzification operations on input variables through a Gaussian membership function; using algebraic product operations to perform fuzzy intersection operations on the input variables after the fuzzification operation; generating result outputs based on external input states and the input variables after the fuzzy intersection operation; and compensating the recursive least squares identification method based on errors.

[0104] Among them, the result output is configured to determine the error between the actual network output and the expected output.

[0105] The fuzzification operation here can be achieved by the following formula: ; in, is the function value, is the center of the Gaussian function, is the standard deviation of the Gaussian function.

[0106] 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.

[0107] Understandably, in order to obtain the activation strength Each node uses the algebraic product operation to perform Performs a fuzzy intersection operation on the inputs.

[0108] Then the calculation formula for performing fuzzy intersection operation on the input variables after fuzzification operation using algebraic product operation can be as follows: ; The output of the result node is a linear combination of the external input states and can be expressed as: ; in, is the activation strength of the fuzzy rule, is the function value, are the function parameters that need to be optimized, For the The output corresponding to the rule is, and In the form of a linear function, are the coefficients of the linear function.

[0109] The above result output can be expressed by the following formula: ; ; It should be understood that the purpose of the self-evolving fuzzy neural network is to determine the minimization error function. The minimization error function can be expressed as: ; in, The activation intensity The normalized result is To minimize the error function, is the actual network output, is the expected output, Indicates the total number of rules.

[0110] In one possible implementation, before compensating the recursive least squares identification method by the self-evolving fuzzy neural network, the method also 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 strength threshold.

[0111] Among them, the update of the front layer can be achieved in the following ways: make Represents input variables Middle Antecedent parameters in Gaussian fuzzy sets and In this case, the antecedent can be updated by gradient descent: ; The subsequent update here can be achieved in the following ways: Will The output in is converted into a row vector, then: ; in, is the learning rate of gradient descent, is the subsequent part. Therefore, It can also be updated by recursive least squares identification method, expressed as: ; ; in, For the forgetting factor, is the covariance matrix.

[0112] The above-mentioned optimization rule update mainly includes rule pruning and rule generation.

[0113] In one implementation, the activation intensity threshold Can be used to determine rule generation, when The maximum value is less than the threshold , a new rule is generated.

[0114] For regular pruning, the historical average activation strength is an evaluation indicator, which represents the average activation intensity from the beginning of rule generation to now. , it means that the rule is rarely activated and should be pruned.

[0115] In the above implementation process, the corresponding update method is selected for different network layers to update the self-evolving fuzzy neural network online, and the compensation torque is generated in real time to perform torque compensation on the identified extended dynamics, thereby improving the accuracy and robustness of parameter identification.

[0116] Based on the same application concept, a kinetic parameter identification device corresponding to the kinetic parameter identification method is also provided in the embodiment of the present application. Since the principle of solving the problem by the device in the embodiment of the present application is similar to that in the aforementioned kinetic parameter identification method embodiment, the implementation of the device in this embodiment can refer to the description in the embodiment of the above method, and the repeated parts will not be repeated.

[0117] See also Figure 4, is a functional module diagram of the kinetic parameter identification device provided in the embodiment of the present application. The modules in the kinetic parameter identification device in this embodiment are used to execute the steps in the above method embodiment. The kinetic parameter identification device includes a construction module 301, a determination module 302, an update module 303, and an identification module 304; wherein, The construction module 301 is used to construct a dynamic model through the mass center inertia tensor of the target moving part.

[0118] The determination module 302 is used to determine the physical feasibility constraints according to the dynamic model.

[0119] The first updating module 303 is used to update the recursive least squares identification method based on the physical feasibility constraint.

[0120] The identification module 304 is used to identify the dynamic parameters of each connecting rod of the target moving part according to the updated recursive least squares identification method.

[0121] In a possible implementation, the determination module 302 is further used to: separate the linear terms and the nonlinear terms of the dynamic model; determine a minimum inertia parameter set based on the dynamic model after separating the linear terms and the nonlinear terms; and determine the physical feasibility constraint through the minimum inertia parameter set.

[0122] In one possible implementation, the determination module 302 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.

[0123] In a possible implementation, the determination module 302 is specifically used to: update 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; and determine the recursive least squares identification method based on the least squares objective function and the forgetting factor.

[0124] In a possible implementation, the identification module 304 is also used 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 for the torque in the dynamic parameters; and identify the dynamic parameters of each joint of the target moving part through the compensated recursive least squares identification method.

[0125] In one possible implementation, the identification module 304 is specifically used to: perform fuzzification operations on input variables through a Gaussian membership function; perform fuzzy intersection operations on the input variables after the fuzzification operations using algebraic product operations; generate result outputs based on external input states and the input variables after the fuzzy intersection operations; 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.

[0126] In a possible implementation, the kinetic parameter identification device further includes: a second updating module, used to update the antecedent layer in the self-evolving fuzzy neural network by a gradient descent method; and / or to update the consequent layer in the self-evolving fuzzy neural network according to the physical feasibility constraint; and / or to update the optimization rules according to an activation strength threshold.

[0127] In addition, an embodiment of the present application also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of the kinetic parameter identification method described in the above method embodiment are executed.

[0128] The computer program product of the kinetic parameter identification method provided in the embodiment of the present application includes a computer-readable storage medium storing program code, and the instructions included in the program code can be used to execute the steps of the kinetic parameter identification method described in the above method embodiment. For details, please refer to the above method embodiment, which will not be repeated here.

[0129] In several embodiments provided in 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 schematic. For example, the flowcharts and block diagrams in the accompanying drawings show the possible architecture, functions and operations of the devices, methods and computer program products according to multiple embodiments of the present application. In this regard, each box in the flowchart or block diagram can represent a module, a program segment or a part of a code, and the module, a program segment or a part of a 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 box can also occur in a different order from the order marked in the accompanying drawings. For example, two consecutive boxes can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and / or flowchart, and the combination of boxes in the block diagram and / or flowchart can be implemented with a dedicated hardware-based system that performs a specified function or action, or can be implemented with a combination of dedicated hardware and computer instructions.

[0130] In addition, the functional modules in the various embodiments of the present application may be integrated together to form an independent part, or each module may exist separately, or two or more modules may be integrated to form an independent part.

[0131] If the function is implemented in the form of a software function module and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application can be essentially or partly embodied in the form of a software product that contributes to the prior art. The computer software product is stored in a storage medium, including several instructions to enable a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present application. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, etc. Various media that can store program codes. It should be noted that in this article, relational terms such as first and second, etc. 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 terms "include", "comprises" or any other variation thereof are intended to cover non-exclusive inclusion, so that a process, method, article or apparatus that includes a series of elements includes not only those elements, but also includes other elements not explicitly listed, or also includes elements inherent to such process, method, article or apparatus. In the absence of more restrictions, the elements defined by the sentence "includes..." do not exclude the presence of other identical elements in the process, method, article or apparatus that includes the elements.

[0132] The above description is only a preferred embodiment of the present application and is not intended to limit the present application. For those skilled in the art, the present application may have various changes and variations. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application. It should be noted that similar numbers and letters represent similar items in the following drawings, so once an item is defined in one drawing, it does not need to be further defined and explained in the subsequent drawings.

[0133] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art who is familiar with the present technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on 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; According to the updated recursive least squares identification method, the dynamic parameters of each connecting rod of the target moving part are identified.

2. The method according to claim 1, characterized in that 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; The physical feasibility constraint is determined by the minimum inertia parameter set.

3. The method according to claim 2, characterized in that 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.

4. The method according to claim 2, 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.

5. The method according to any one of claims 1 to 4, 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.

6. The method according to claim 5, 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.

7. The method according to claim 5, 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.

8. 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; The identification module is used to identify the dynamic parameters of each connecting rod of the target moving part according to the updated recursive least squares identification method.

9. 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 7.

10. 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 the method according to any one of claims 1 to 7 are executed.

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