A robot dynamic parameter identification method, system, device and medium

Abstract

This invention belongs to the field of robot dynamic parameter identification technology. To address the problems of poor accuracy and robustness of existing identification methods, a robot dynamic parameter identification method, system, device, and medium are proposed. The method establishes a robot joint torque model; uses a finite Fourier series to generate the robot excitation trajectory, optimizes the robot excitation trajectory while satisfying the physical limitations of the robot body and the collision constraints of real physical space, and then determines it as the input data for identification; establishes a logarithmic Euclidean metric convex approximation regularization term of the physical consistency matrix; uses sigmoid as a weight to weight the least squares method, and alternately solves the inertia parameters and the nonlinear friction model using a double inner loop until the residual converges. This method can quickly achieve identification accuracy comparable to long-term excitation without requiring pre-identification of the nonlinear friction model, significantly improving computational efficiency.

Description

Technical Field

[0001] The present invention belongs to the technical field of robot dynamic parameter identification, and in particular relates to a robot dynamic parameter identification method, system, equipment and medium. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] Dynamic parameter identification plays a critical role in robotic control and dynamic analysis. Only by obtaining parameters that best match the robot's dynamic performance can control algorithms be optimized to improve motion efficiency and ensure the system's responsiveness and stability during dynamic operation. For multi-degree-of-freedom robots, key parameters to be identified typically include the inertia tensor, the center of mass positions of each link, and the nonlinear characteristics of joint friction. These parameters directly determine the reliability of the dynamic model, profoundly impacting the controller's tracking accuracy and overall performance.

[0004] In offline identification, the only system input is the excitation trajectory. The choice of the excitation trajectory has a decisive influence on the accuracy and robustness of the identification parameters. At the same time, physical consistency usually chooses the generation of linear matrix inequality (LMI) constrained least squares or weighted least squares solutions to ensure that the identification values ​​are physically interpretable. The identification process minimizes the error between the model prediction value and the actual measurement value by adjusting the inertia parameters.

[0005] Prior art has proposed convex approximation regularization methods to improve the problem of semidefinite programming, where rigid constraints cause estimated parameters to be on the edge of physical consistency. However, the repeated changes in the SPD matrix reference point during iteration can lead to numerical instability. Physical feasibility constraints and semidefinite programming have also been proposed to address the physical feasibility of inertial parameters. However, identifying the inertial parameters of a body without complex nonlinear friction can introduce additional errors, resulting in biased estimates.

[0006] Current identification methods have certain problems: Problem 1: In scenarios where the excitation process is limited by acquisition time and spatial geometry, it is difficult to truly restore the dynamic performance of the robot body parameters, resulting in poor accuracy and robustness of the identification results. Problem 2: Uncertain factors such as robot flexibility, imprecise friction models, and sensor noise will introduce additional errors, causing least squares or weighted least squares to over-consider the poorly fitted parts, resulting in biased estimates that reduce the body's identification accuracy. In addition, when considering iterative weighted least squares based on linear matrix inequalities (LMI) for Problems 1 and 2, on the one hand, the imposed rigid convex constraints on parameter physical consistency will cause the final estimated parameters to be on the edge of physical consistency and only short-term excitations will accelerate them into the physically infeasible region. On the other hand, the traditional Huber robust weight function often lacks specific parameter adjustment standards. Summary of the Invention

[0007] In order to overcome the above-mentioned deficiencies of the prior art, the present invention provides a robot dynamic parameter identification method, system, equipment and medium, which can obtain identification accuracy equivalent to long-term excitation in a short time without the need for pre-identification of the nonlinear friction model, thereby greatly improving the computational efficiency.

[0008] In order to achieve the above object, the present invention adopts the following technical solutions:

[0009] In a first aspect, the present invention provides a method for identifying robot dynamic parameters, comprising:

[0010] Establish a rigid body dynamics model of the robot, and establish a robot joint torque model based on the rigid body dynamics linear model of the robot, the motor inertia model and the nonlinear friction model;

[0011] Generate the robot's excitation trajectory based on the finite Fourier series, optimize the robot's excitation trajectory while satisfying the physical limitations of the robot body and the collision constraints of the real physical space, and obtain the robot's motion parameters based on the optimized excitation trajectory as the input data for identification;

[0012] Establish the robot's physical consistency matrix, describe the log-Euclidean metric based on the SPD manifold, and establish the convex approximation regularization term of the log-Euclidean metric of the physical consistency matrix;

[0013] A weight matrix is ​​established based on the Sigmoid function. Combining the robot joint torque model and the logarithmic Euclidean convex approximation regularization term, the inertia parameter identification optimization objective function in the first inner loop is constructed and solved iteratively to identify the minimum inertia parameter set and motor inertia.

[0014] The friction torque in the residual torque is estimated based on the parameters identified in the first inner loop, and the friction torque is fitted using a nonlinear friction model. The nonlinear friction model optimization objective function is constructed and solved until the exponential factor of the nonlinear friction model converges, thereby obtaining the nonlinear friction parameter set identified in the second inner loop.

[0015] The residual between the measured torque and the predicted torque determined by the identification parameters in the first inner loop and the identification parameters in the second inner loop is calculated, and the solution is iterated continuously until the residual converges, and finally the identified minimum inertia parameter set and nonlinear friction parameters are obtained.

[0016] In a second aspect, the present invention provides a robot dynamic parameter identification system, comprising:

[0017] A model building module is configured to: establish a rigid body dynamics model of the robot, and establish a joint torque model of the robot based on the rigid body dynamics linear model of the robot, the motor inertia model and the nonlinear friction model;

[0018] An excitation trajectory optimization module is configured to generate an excitation trajectory of the robot based on a finite Fourier series, optimize the excitation trajectory of the robot while satisfying the physical limitations of the robot body and the collision constraints of the real physical space, and obtain the robot's motion parameters based on the optimized excitation trajectory as input data for identification;

[0019] A log-Euclidean metric convex approximation module is configured to: establish a physical consistency matrix of the robot, describe the log-Euclidean metric based on the SPD manifold, and establish a log-Euclidean metric convex approximation regularization term of the physical consistency matrix;

[0020] The first inner loop module is configured to: establish a weight matrix based on the Sigmoid function, combine the robot joint torque model and the logarithmic Euclidean metric convex approximation regularization term, construct the inertia parameter identification optimization objective function in the first inner loop, and perform iterative solution to identify the minimum inertia parameter set and motor inertia;

[0021] a second inner loop module configured to estimate the friction torque in the residual torque based on the parameters identified in the first inner loop, fit the friction torque using a nonlinear friction model, construct an optimization objective function for the nonlinear friction model, and solve the function until the exponential factor of the nonlinear friction model converges, thereby obtaining a nonlinear friction parameter set identified by the second inner loop;

[0022] The outer loop module is configured to calculate the residual between the measured torque and the predicted torque determined by the identification parameters in the first inner loop and the identification parameters in the second inner loop, and continuously iterate the solution until the residual converges, and finally obtain the identified minimum inertia parameter set and nonlinear friction parameters.

[0023] In a third aspect, the present invention provides an electronic device comprising a memory and a processor, and computer instructions stored in the memory and executed on the processor, wherein the computer instructions, when executed by the processor, perform the method described in the first aspect.

[0024] In a fourth aspect, the present invention provides a computer-readable storage medium for storing computer instructions, wherein when the computer instructions are executed by a processor, the method described in the first aspect is performed.

[0025] In a fifth aspect, the present invention provides a computer program product, comprising a computer program, which implements the method described in the first aspect when executed by a processor.

[0026] One or more of the above technical solutions have the following beneficial effects:

[0027] In the present invention, a weight function is designed based on the Sigmoid function, and an inertial parameter identification optimization objective function in the first inner loop is established. Compared with the traditional Huber robust weight function, it helps to show parameter adjustability when facing different residual scenarios, thereby better giving outlier residuals smaller weights, and helping to reduce the adverse effects of outliers caused by model uncertainty, imprecise models, noise, etc. on inertial parameter identification, thereby achieving the purpose of unbiased estimation and robust estimation.

[0028] In the present invention, the logarithmic Euclidean metric convex approximation is used as a regularization term to ensure the optimal solution in global optimization. It can correctly reflect the geometric distance between the current estimated parameter value and the nominal value on the SPD manifold, which helps to achieve good identification effects in under-excitation scenarios where there is only a short period of excitation and the excitation trajectory is constrained by environmental geometry. Compared with the traditional Euclidean distance regularization method, the RMSE is significantly reduced.

[0029] The geometric convex regularization method proposed in this invention is combined with a robust iterative identification method. The convexity of the convex regularization can quickly converge to the global optimal solution. The geometric properties can capture the geometric characteristics of the physical consistency matrix composed of inertia parameters, and promote the numerical flow to conform to the geometric characteristic distribution of the SPD manifold instead of being projected to the boundary of the feasible domain, thereby ensuring the realistic rationality of the physical values.

[0030] Advantages of additional aspects of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0032] Figure 1 This is a flow chart of the robot dynamic parameter identification method in Example 1 of the present invention;

[0033] Figure 2 : This is a corresponding relationship diagram between the Sigmoid weight function and the probability density of the joint torque residual in the first embodiment of the present invention;

[0034] FIG3 (a) is a schematic diagram of visualization of the logarithmic metric convex approximation regularization in Example 1 of the present invention;

[0035] FIG3 ( b ) is a schematic diagram of visualization of the traditional Euclidean canonical rule in the first embodiment of the present invention;

[0036] Figure 4 The results of iterative identification processes for two regularization methods under long-term and short-term excitation scenarios in Example 1 of the present invention are as follows;

[0037] FIG5 (a) is a comparison diagram of the predicted torque of joint 1 on an industrial robot and the actual measured torque using the method provided in Example 1 of the present invention;

[0038] FIG5( b ) is a comparison diagram of the predicted torque of joint 2 on the industrial robot and the actual measured torque using the method provided in Example 1 of the present invention;

[0039] FIG5( c ) is a comparison diagram of the torque prediction diagram of joint 3 on the industrial robot and the actual measured torque diagram according to the method provided in Example 1 of the present invention;

[0040] FIG5( d ) is a comparison diagram of the predicted torque of joint 4 on the industrial robot and the actual measured torque using the method provided in Example 1 of the present invention;

[0041] FIG5( e ) is a comparison diagram of the torque prediction diagram of the joint 5 of the industrial robot and the actual measured torque according to the method provided in the first embodiment of the present invention;

[0042] FIG5( f ) is a comparison diagram of the torque prediction diagram of the joint 6 of the industrial robot and the actual measured torque using the method provided in the first embodiment of the present invention. DETAILED DESCRIPTION

[0043] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which the present invention belongs.

[0044] It should be noted that the terms used herein are for describing particular embodiments only and are not intended to limit the exemplary embodiments according to the present invention.

[0045] In the absence of conflict, the embodiments of the present invention and the features thereof may be combined with each other.

[0046] Example 1

[0047] This embodiment discloses a method for identifying robot dynamic parameters, including:

[0048] Establish a rigid body dynamics model of the robot, and establish a robot joint torque model based on the rigid body dynamics linear model of the robot, the motor inertia model and the nonlinear friction model;

[0049] Generate the robot's excitation trajectory based on the finite Fourier series, optimize the robot's excitation trajectory while satisfying the physical limitations of the robot body and the collision constraints of the real physical space, and obtain the robot's motion parameters based on the optimized excitation trajectory as the input data for identification;

[0050] Establish the robot's physical consistency matrix, describe the log-Euclidean metric based on the SPD manifold, and establish the convex approximation regularization term of the log-Euclidean metric of the physical consistency matrix;

[0051] A weight matrix is ​​established based on the Sigmoid function. Combining the robot joint torque model and the logarithmic Euclidean convex approximation regularization term, the inertia parameter identification optimization objective function in the first inner loop is constructed and solved iteratively to identify the minimum inertia parameter set and motor inertia.

[0052] The friction torque in the residual torque is estimated based on the parameters identified in the first inner loop, and the friction torque is fitted using a nonlinear friction model. The nonlinear friction model optimization objective function is constructed and solved until the exponential factor of the nonlinear friction model converges, thereby obtaining the nonlinear friction parameter set identified in the second inner loop.

[0053] The residual between the measured torque and the predicted torque determined by the identification parameters in the first inner loop and the identification parameters in the second inner loop is calculated. If the calculated residual does not reach the convergence tolerance, the predicted friction torque is calculated based on the nonlinear friction parameters identified in the second inner loop and substituted into the next round of identification in the first inner loop. The outer loop is combined with the first and second inner loops, and the solution is continuously iterated until the residual converges, and finally the minimum inertia parameter set and nonlinear friction parameters are obtained.

[0054] This embodiment establishes a robot joint torque model based on the robot rigid body dynamics model, motor inertia model, and nonlinear friction model; uses a finite Fourier series to generate the robot excitation trajectory, and optimizes the robot excitation trajectory while satisfying the physical limitations of the robot body and the collision constraints of the real physical space; introduces the logarithmic Euclidean metric on the SPD manifold, constructs the logarithmic Euclidean metric convex approximation regularization term, and establishes the inertia parameter identification optimization objective function together with the physical consistency constraint; uses Sigmoid as the weight to weight the least squares, and uses a double inner loop to alternately solve the inertia parameters and the nonlinear friction model until the residual converges. This embodiment only requires 3s of data to achieve identification accuracy comparable to long-term excitation and does not require pre-identification of the nonlinear friction model, significantly improving computational efficiency.

[0055] The following combination Figure 1 A robot dynamic parameter identification method proposed in this embodiment is described in detail:

[0056] S1: Establish a linearized rigid body dynamics linear model of the robot, and combine the nonlinear friction model, motor inertia model and linearized rigid body dynamics model to form an iteratively solvable joint torque model.

[0057] S1 specifically includes:

[0058] For the joint space motion variables, namely position, velocity and acceleration and subject to generalized force The n-degree-of-freedom multi-body dynamics system can be derived by recursively deducing the inverse dynamics model of Newton-Euler to obtain the following equation:

[0059]

[0060] in, represents the generalized inertia matrix, are the Coriolis force and centripetal force matrices, is the gravity moment vector, is a linearized non-full-rank observation matrix, vector is the standard parameter set for robot dynamics, where is a set of relationship parameters for a single link, specifically:

[0061]

[0062] in, Defined as the moment of inertia matrix of the connecting rod in the fixed coordinate system {B}, represents the center of mass position of the connecting rod in the fixed coordinate system {B}, represents the mass of the i-th connecting rod.

[0063] Considering that the linear friction model does not include more detailed speed-dependent characteristics such as the Stribeck effect, which cannot well capture the nonlinear friction phenomenon at low speed, a nonlinear friction model is used and expressed as:

[0064]

[0065] Among them, the function The Stribeck curve reflects the Stribeck effect. is the Coulomb friction coefficient, is the coefficient of static friction, represents the Stribeck speed, The exponential factor that expresses the curve shaping. Function represents viscous friction, which is usually proportional to angular velocity; is the linear viscosity coefficient. For the convenience of representation, the nonlinear friction parameter set is , where the single joint friction parameter set is .

[0066] Combining the linearized rigid body dynamics model, motor inertia model and nonlinear friction model, the robot joint torque model is finally established, which is specifically expressed as:

[0067]

[0068] in, and are the full rank regression matrix and the minimum inertia parameter set after numerical decomposition, Expressing diagonal block matrix operations, is the inertia vector of the joint motor, is the nonlinear friction torque.

[0069] S2: Generate the robot excitation trajectory based on the finite Fourier series, optimize the robot excitation trajectory while satisfying the physical limitations of the robot body and the collision constraints of the real physical space, and obtain the robot's motion parameters according to the optimized excitation trajectory as the input data for identification.

[0070] S2 specifically includes:

[0071] Finite Fourier series are usually used as the excitation trajectory of the robot, specifically:

[0072]

[0073] in, is the initial position of each joint, are the optimization coefficients of the finite Fourier series, is the fundamental frequency of the excitation trajectory, N is the order of the finite Fourier series,t is the time step. In this example, let is the fundamental angular frequency of the excitation trajectory, N=5 The 5th-order finite Fourier series excitation trajectory with a time step of 20s.

[0074] When optimizing the excitation trajectory, the physical constraints of the robot and the geometric constraints of the surrounding environment should be considered. The optimization condition can be written as:

[0075]

[0076] in, Respectively represent the position limit, velocity limit, and acceleration limit of the i-th joint, x 、 y 、 z They represent the position of the end effector in Cartesian space, Represent the zero moment and the end moment of the excitation trajectory respectively. Therefore, by optimizing the finite Fourier series coefficients The robot excitation trajectory can be obtained. A commonly used excitation trajectory optimization problem can be described by the observation matrix condition number:

[0077]

[0078] in, is the adjustment coefficient, Represents the calculation of the matrix condition number.

[0079] After the excitation trajectory is optimized, the excitation trajectory can be executed through the robot control interface and the robot joint angle can be measured. , joint speed , true torque .

[0080] In this example, a zero-phase third-order Butterworth filter is used, and the cutoff frequency is set to 5 Hz to smooth the noise of the data and to measure the robot joint angle. Use the second-order central difference method to obtain the joint acceleration , the joint angle , joint speed , true torque and joint acceleration as input for system identification.

[0081] S3: Establish the physical consistency matrix of the robot, describe the log-Euclidean metric based on the SPD manifold, and establish the log-Euclidean metric convex approximation regularization term of the physical consistency matrix.

[0082] S3 specifically includes:

[0083] Define the commonly used physical consistency matrix in robotics and use it to constrain the generation of solution sets in the convex optimization process. Specifically:

[0084]

[0085] in, is the matrix trace operator, represents the identity matrix, is the inertia tensor of the rigid body, and The mass and center of mass of the i-th connecting rod respectively, expressed When the physical consistency matrix satisfies the basic physical constraints, the matrix remains symmetric and positive, that is, On the fourth-order symmetric positive definite matrix manifold Above, the relationship can be expressed as , and the manifold Considered as embedded in the SPD manifold middle.

[0086] For SPD manifolds The logarithmic Euclidean measure (LEM) is a The Lie group structure of is derived from group operations, where At the same time, in the logarithmic-Euclidean framework, for ,connect X and Y The geodesic of is defined as:

[0087]

[0088] in, represents the matrix exponential operation, Represents the logarithm operation of a matrix. and The geodesic distance between two points on the SPD manifold using the log-Euclidean metric can be described as:

[0089]

[0090] in, The Frobenius matrix norm derived from the Frobenius matrix inner product. It represents the log-Euclidean metric, but since the combination of the F-norm and the operator concavity is not always guaranteed to be convex, the resulting solution set is often spread over local minimum points. Therefore, it is necessary to establish a log-Euclidean metric convex approximation as a regularization term to ensure that the optimal solution is obtained in the global optimization, so as to correctly reflect the geometric distance between the current estimated parameter value and the nominal value on the SPD manifold.

[0091] The convex approximation formula based on the logarithmic Euclidean metric can be described as:

[0092]

[0093] in, represents the logarithm operation of the matrix, expresses a convex approximation to the log-Euclidean metric, represents the Hadamard product operation, Represents the symmetric positive definite matrix X The eigenvalues ​​after eigendecomposition and the corresponding orthogonal matrix and its transpose. Represents The first-order difference quotient matrix of is:

[0094]

[0095] Identify the inertia parameters of the i-th link in a multi-body dynamic system with n degrees of freedom The convex optimization regularization term of can be expressed as:

[0096]

[0097] in, , The inertia parameter value of the i-th connecting rod is obtained by convex optimization calculation and through Mapping, is the nominal value of the inertia parameter of the i-th link and through Mapping.

[0098] For the full parameter set of n-degree-of-freedom multi-body dynamics system The regularization term of convex optimization under identification can be simply expressed as the sum of convex approximations of the logarithmic Euclidean metric, specifically:

[0099]

[0100] in, They represent the identification value and the nominal value of the standard parameter set obtained after convex optimization, Respectively represent i The inertia parameter identification value and the nominal value of the inertia parameter of each connecting rod, n represents the n-degree-of-freedom multi-body dynamic system.

[0101] S4: Establish a weight matrix based on the Sigmoid function, combine the robot joint torque model and the logarithmic Euclidean metric convex approximation regularization term, construct the inertia parameter identification optimization objective function in the first inner loop, and perform iterative solution to identify the minimum inertia parameter set and motor inertia.

[0102] S4 specifically includes:

[0103] According to the joint torque model proposed by S1 The logarithmic Euclidean metric convex approximation regularization term of the n-degree-of-freedom multi-body dynamic system proposed by S3 , establish the inertia parameter identification optimization objective function in the first inner loop, specifically:

[0104]

[0105]

[0106] in, The observation matrices are and the diagonal block matrix Stacked, The nonlinear friction torque is and the measured torque stacked; are the minimum inertia parameter set and motor rotor inertia obtained by iterative identification; is the penalty coefficient of the regularization term; After the symbol, expression The matrix is ​​positive definite. is the weight matrix of the ath iteration in the first inner loop, and its initial value is 1.

[0107] It is a more flexible weight function designed based on the Sigmoid function Calculated, specifically:

[0108]

[0109] in, e To identify the joint torque residual, k and They respectively control the speed of change of weights and the position of the inflection point of the Sigmoid function, and As the inflection point position, the weight change speed k can be controlled, that is:

[0110]

[0111] in, , L represents the value of the S function at the asymptotic zero line.

[0112] As a weight function, it can be expressed in a data quantile table In this example, , corresponding to the 90% quantile; , corresponding to the 99% quantile; , can be achieved by controlling the weight change speed k .

[0113] According to the weight function and the minimum operator Update the weight matrix ,Right now:

[0114]

[0115] Update the minimum parameter set and motor inertia and use the weight function Calculate new weights , calculate the weight matrix of the two generations before and after deviation, that is:

[0116]

[0117] In this example, the weight convergence tolerance is set ,when Meet the convergence tolerance , then returns the minimum parameter set of the last generation in the first inner loop and motor inertia estimated value.

[0118] S5: Estimate the friction torque in the residual torque based on the parameters identified in the first inner loop, fit the friction torque using the nonlinear friction model, construct the nonlinear friction model optimization objective function, and solve until the exponential factor of the nonlinear friction model converges to obtain the nonlinear friction parameter set identified by the second inner loop.

[0119] S5 specifically includes:

[0120] Based on the minimum inertia parameter set identified in the first inner loop of S4 and motor inertia , and then estimate the friction torque in the remaining torque, specifically:

[0121]

[0122] in, It is the residual torque obtained by subtracting the identified torque from the measured torque.

[0123] The nonlinear friction model proposed in S1 is used to fit , the nonlinear friction torque of the i-th joint can be written as:

[0124]

[0125] in, is the Coulomb friction coefficient, is the coefficient of static friction, represents the Stribeck speed, An exponential factor expressing the curve shaping, is the linear viscosity coefficient, function Represents viscous friction.

[0126] The objective function of the nonlinear friction model optimization for the i-th joint can be expressed as:

[0127]

[0128]

[0129] in, is the fitting friction torque of the i-th joint, is the residual torque related to friction at the i-th joint.

[0130] Exponential factor to shape the curve As the convergence benchmark, the exponential factors of the two generations before and after the iterative cycle are judged. deviation, that is:

[0131]

[0132] Among them, the exponential factor Recorded as In this example, the friction convergence tolerance is set ,when Meet the convergence tolerance , then the nonlinear friction parameter set in the second inner loop is returned estimated value.

[0133] S6: Calculate the residual between the measured torque and the predicted torque determined by the identification parameters in the first inner loop and the identification parameters in the second inner loop. If the calculated residual does not reach the convergence tolerance, calculate the predicted friction torque based on the nonlinear friction parameters identified in the second inner loop and substitute it into the next round of identification in the first inner loop. Through the outer loop combined with the first and second inner loops, continuously iterate and solve until the residual converges, and finally obtain the identified minimum inertia parameter set and nonlinear friction parameters.

[0134] S6 specifically includes:

[0135] The first inner loop proposed by S4 and the second inner loop proposed by S5 are connected in series in the outer loop, and the minimum inertia parameter set identified based on the first inner loop of S4 is obtained. and motor inertia , and the nonlinear friction parameter set based on the second inner loop identification in S5 , calculate the joint torque residual of each generation of the outer loop , specifically:

[0136]

[0137] in, are the measured torque and the identified nonlinear friction torque, The identified body torque and motor inertia torque are respectively. Save the residuals of each generation in the outer loop ,calculate The deviation of the two generations of residuals, that is:

[0138]

[0139] In this example, the residual convergence tolerance is set ,when Meet the convergence tolerance , output the minimum inertia parameter set obtained by the first inner loop iterative identification and the nonlinear friction parameters obtained by the second inner loop iterative identification; when Convergence tolerance not met The friction parameters identified by the second inner loop iteration are substituted into the nonlinear friction model to obtain the predicted nonlinear friction force, and then brought into the first inner loop of the next round to participate in the identification.

[0140] Table 1 Comparison of identification error results of different weight functions

[0141]

[0142] As shown in Table 1, the Sigmoid weight function and the traditional Huber robust weight function used in the present invention are respectively used to identify the robot dynamic parameters. The Sigmoid weight function helps to improve the identification accuracy.

[0143] In the present invention, a joint torque model is established based on the full-rank linear dynamic model, nonlinear friction model, and motor inertia after numerical decomposition; a finite Fourier series is used to plan the excitation trajectory that satisfies the joint limits and collision constraints, with the goal of minimizing the observation matrix condition number, and the filtered posture and torque data are collected; a logarithmic Euclidean metric is introduced on the SPD manifold, a logarithmic Euclidean metric convex approximation regularization term is constructed, and an inertia parameter identification optimization objective function is established together with the physical consistency constraint; Sigmoid is used as a weight to weight the least squares, and a double inner loop is used to alternately solve the inertia parameters and the nonlinear friction model until the residual converges. Only 3s of data are needed to obtain identification accuracy comparable to long-term excitation and there is no need to pre-identify the nonlinear friction model, which greatly improves computational efficiency.

[0144] like Figure 2As shown in Figure 1, a schematic diagram of the weighting of the least squares method using the Sigmoid weight function in an example of the present invention is shown. As can be seen from the figure, the 90% residual data quantile is the inflection point of the Sigmoid weight function, and the 99% residual data quantile is where the Sigmoid weight asymptotically approaches the zero line. As the residual continues to increase, the weight continues to decrease, thereby suppressing the influence of outlier residuals on inertial parameter identification. The adjustability of the data quantile is more flexible than the traditional Huber robust weight function.

[0145] As shown in Figures 3(a) and 3(b), the examples of the present invention use a logarithmic Euclidean metric convex approximation and a traditional Euclidean distance for iterative identification. Although the use of a traditional Euclidean regularizer and a physical consistency matrix can satisfy the most basic physical constraints and stay away from the boundary zero value, the numerical changes of the various inertial parameters are unrelated to each other, making it impossible to form a set of physically meaningful values. Even if the regularization penalty coefficient is continuously increased, a normal manipulator configuration cannot be formed. The logarithmic Euclidean metric convex approximation not only stays away from the boundary zero value, but also naturally forms a manipulator configuration based on the intrinsic geometric changes of the inertia tensor, center of mass, and mass associated with the SPD manifold.

[0146] like Figure 4 As shown, the present invention uses a 3s excitation duration as the example. The bar chart results show that, in scenarios with only 3s of excitation and subject to environmental geometry constraints, the logarithmic Euclidean distance convex approximation regularization method achieves comparable recognition accuracy to that achieved with a full 20s excitation, while the traditional Euclidean regularization method achieves far lower recognition accuracy than the logarithmic Euclidean distance convex approximation regularization method. This demonstrates that the logarithmic Euclidean metric convex approximation method proposed in this invention can be used in short-duration excitation scenarios and exhibits improved iterative numerical stability.

[0147] As shown in Figure 5 (a) to Figure 5 (f), the example of the present invention uses 20s excitation duration to iteratively identify the robot arm joint torque prediction model. The NMAE error obtained by comparing the predicted test trajectory is within 5%, and the obtained joint torque prediction model has high accuracy.

[0148] Example 2

[0149] The purpose of this embodiment is to provide a robot dynamic parameter identification system, including:

[0150] A model building module is configured to: establish a rigid body dynamics model of the robot, and establish a joint torque model of the robot based on the rigid body dynamics linear model of the robot, the motor inertia model and the nonlinear friction model;

[0151] An excitation trajectory optimization module is configured to generate an excitation trajectory of the robot based on a finite Fourier series, optimize the excitation trajectory of the robot while satisfying the physical limitations of the robot body and the collision constraints of the real physical space, and obtain the robot's motion parameters based on the optimized excitation trajectory as input data for identification;

[0152] A log-Euclidean metric convex approximation module is configured to: establish a physical consistency matrix of the robot, describe the log-Euclidean metric based on the SPD manifold, and establish a log-Euclidean metric convex approximation regularization term of the physical consistency matrix;

[0153] The first inner loop module is configured to: establish a weight matrix based on the Sigmoid function, combine the robot joint torque model and the logarithmic Euclidean metric convex approximation regularization term, construct the inertia parameter identification optimization objective function in the first inner loop, and perform iterative solution to identify the minimum inertia parameter set and motor inertia;

[0154] a second inner loop module configured to: estimate the friction torque in the residual torque based on the parameters identified by the first inner loop, and fit the friction torque using a nonlinear friction model until the exponential factor of the nonlinear friction model converges, thereby obtaining a nonlinear friction parameter set identified by the second inner loop;

[0155] The outer loop module is configured to calculate the residual between the measured torque and the predicted torque determined by the identification parameters in the first inner loop and the identification parameters in the second inner loop, and continuously iterate the solution until the residual converges, and finally obtain the identified minimum inertia parameter set and nonlinear friction parameters.

[0156] In further embodiments, there is also provided:

[0157] An electronic device includes a memory and a processor, and computer instructions stored in the memory and executed by the processor. When the computer instructions are executed by the processor, the method described in Example 1 is performed. For the sake of brevity, no further details are given here.

[0158] It should be understood that in this embodiment, the processor may be a central processing unit (CPU), or may be other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), off-the-shelf field-programmable gate arrays (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or any conventional processor, etc.

[0159] The memory may include a read-only memory and a random access memory, and provides instructions and data to the processor. A portion of the memory may also include a non-volatile random access memory. For example, the memory may also store information about the device type.

[0160] A computer-readable storage medium is used to store computer instructions, and when the computer instructions are executed by a processor, the method described in embodiment 1 is performed.

[0161] The method in Example 1 can be directly implemented as being executed by a hardware processor, or by a combination of hardware and software modules within the processor. The software module can be located in a storage medium well-established in the art, such as random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, or registers. The storage medium is located in the memory, and the processor reads the information in the memory and, in conjunction with its hardware, completes the steps of the above method. To avoid repetition, a detailed description is not given here.

[0162] Those skilled in the art will appreciate that the units and algorithm steps of the various examples described in conjunction with this embodiment can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professionals and technicians can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0163] Although the above describes the specific embodiments of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without any creative work are still within the scope of protection of the present invention.

Claims

1. A method for identifying robot dynamic parameters, characterized in that: include: Establish a rigid body dynamics model of the robot, and establish a joint torque model of the robot based on the rigid body dynamics linear model, motor inertia model and nonlinear friction model; Generate the robot's excitation trajectory based on the finite Fourier series, optimize the robot's excitation trajectory while satisfying the physical limitations of the robot body and the collision constraints of the real physical space, and obtain the robot's motion parameters based on the optimized excitation trajectory as the input data for identification; Establish the robot's physical consistency matrix, describe the log-Euclidean metric based on the SPD manifold, and establish the convex approximation regularization term of the log-Euclidean metric of the physical consistency matrix; A weight matrix is ​​established based on the Sigmoid function. Combining the robot joint torque model and the logarithmic Euclidean convex approximation regularization term, the inertia parameter identification optimization objective function in the first inner loop is constructed and solved iteratively to identify the minimum inertia parameter set and motor inertia. The friction torque in the residual torque is estimated based on the parameters identified in the first inner loop, and the friction torque is fitted using a nonlinear friction model. The nonlinear friction model optimization objective function is constructed and solved until the exponential factor of the nonlinear friction model converges, thereby obtaining the nonlinear friction parameter set identified in the second inner loop. The residual between the measured torque and the predicted torque determined by the identification parameters in the first inner loop and the identification parameters in the second inner loop is calculated, and the solution is iterated continuously until the residual converges, and finally the identified minimum inertia parameter set and nonlinear friction parameters are obtained.

2. A robot dynamic parameter identification method according to claim 1, characterized in that: Establish the physical consistency matrix of the robot, specifically: ， in, is the matrix trace operator, represents the identity matrix, is the inertia tensor of the rigid body, and Separate i The mass and center of mass of each connecting rod, expressed The mapping relationship, superscript T means transpose.

3. A robot dynamic parameter identification method according to claim 2, characterized in that: Based on the SPD manifold description of the logarithmic Euclidean metric, the logarithmic Euclidean metric convex approximation regularization term of the physical consistency matrix is ​​established, specifically: ， in, They represent the identification value and the nominal value of the standard parameter set obtained after convex optimization, Respectively represent i The inertia parameter identification value and the inertia parameter nominal value of each connecting rod, The inertia parameter value of the i-th connecting rod is obtained by convex optimization calculation and through Mapping, is the nominal value of the inertia parameter of the i-th link and through Mapping, represents the logarithm operation of the matrix, represents the Hadamard product operation, Represents log( ), is the Frobenius matrix norm derived from the Frobenius matrix inner product, Represented respectively The eigenvalues ​​after eigendecomposition and the corresponding orthogonal matrix and transpose.

4. A robot dynamic parameter identification method according to claim 1, characterized in that: The inertia parameter identification optimization objective function in the first inner loop is specifically: ， ， in, The observation matrices are and the diagonal block matrix Stacked, The nonlinear friction torque and the measured torque stacked; are the minimum inertia parameter set and motor rotor inertia obtained by iterative identification; is the penalty coefficient of the regularization term; The first inner loop a The weight matrix of the iteration, is the weight matrix, Represents the regularization term of the log-Euclidean metric convex approximation of the physical consistency matrix.

5. A robot dynamic parameter identification method according to claim 1 or 4, characterized in that: The weight matrix is ​​established according to the Sigmoid function, specifically: ， ， Among them, e is the residual of the identified joint torque, k and Control the speed of change of weights and the position of the inflection point of the Sigmoid function respectively. , L represents the value of the S function at the asymptotic zero line.

6. A robot dynamic parameter identification method according to claim 1, characterized in that: The friction torque in the residual torque is estimated based on the parameters identified in the first inner loop, and the friction torque is fitted using the nonlinear friction model. The nonlinear friction model optimization objective function is constructed and solved until the exponential factor of the nonlinear friction model converges. The nonlinear friction parameter set identified in the second inner loop is obtained, specifically: Estimate the friction torque in the residual torque based on the parameters identified in the first inner loop, and fit the friction torque using a nonlinear friction model; The objective function of nonlinear friction model optimization is constructed with the goal of minimizing the F-norm of the difference between the fitted friction torque and the corresponding friction-coherent residual torque. In the iterative solution of the nonlinear friction model optimization objective function, it is determined whether the deviation of the exponential factors of the previous and next generations of nonlinear friction models meets the convergence tolerance. If so, the nonlinear friction parameter set of the second inner loop identification is obtained.

7. A robot dynamic parameter identification method according to claim 1, characterized in that: The residual between the measured torque and the predicted torque determined by the identification parameters in the first inner loop and the identification parameters in the second inner loop is calculated. The solution is iterated continuously until the residual converges, and the minimum inertia parameter set and nonlinear friction parameters are finally obtained. Specifically, Based on the residuals calculated from the identified parameters in the first inner loop and the identified parameters in the second inner loop, the residuals of the joint torques in each generation of the outer loop are calculated; If the calculated residual does not reach the convergence tolerance, the predicted friction torque is calculated based on the nonlinear friction parameters of the second inner loop identification and substituted into the next round of the first inner loop identification; By combining the outer loop with the first inner loop and the second inner loop, the solution is iterated continuously until the residual converges, and finally the minimum inertia parameter set and nonlinear friction parameters are obtained.

8. A robot dynamic parameter identification system, characterized in that: include: A model building module is configured to: establish a rigid body dynamics model of the robot, and establish a joint torque model of the robot based on the rigid body dynamics linear model of the robot, the motor inertia model and the nonlinear friction model; An excitation trajectory optimization module is configured to generate an excitation trajectory of the robot based on a finite Fourier series, optimize the excitation trajectory of the robot while satisfying the physical limitations of the robot body and the collision constraints of the real physical space, and obtain the robot's motion parameters based on the optimized excitation trajectory as input data for identification; A log-Euclidean metric convex approximation module is configured to: establish a physical consistency matrix of the robot, describe the log-Euclidean metric based on the SPD manifold, and establish a log-Euclidean metric convex approximation regularization term of the physical consistency matrix; The first inner loop module is configured to: establish a weight matrix based on the Sigmoid function, combine the robot joint torque model and the logarithmic Euclidean metric convex approximation regularization term, construct the inertia parameter identification optimization objective function in the first inner loop, and perform iterative solution to identify the minimum inertia parameter set and motor inertia; a second inner loop module configured to estimate the friction torque in the residual torque based on the parameters identified in the first inner loop, fit the friction torque using a nonlinear friction model, construct an optimization objective function for the nonlinear friction model, and solve the function until the exponential factor of the nonlinear friction model converges, thereby obtaining a nonlinear friction parameter set identified by the second inner loop; The outer loop module is configured to calculate the residual between the measured torque and the predicted torque determined by the identification parameters in the first inner loop and the identification parameters in the second inner loop, and continuously iterate the solution until the residual converges, and finally obtain the identified minimum inertia parameter set and nonlinear friction parameters.

9. An electronic device, characterized in that: The method comprises a memory and a processor, and computer instructions stored in the memory and executed on the processor, wherein when the computer instructions are executed by the processor, the method according to any one of claims 1 to 7 is completed.

10. A computer-readable storage medium, characterized in that Used to store computer instructions, which, when executed by a processor, complete the method according to any one of claims 1 to 7.

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