A nonlinear-based industrial robot geometry parameter calibration method and system

Abstract

The application discloses a kind of industrial robot geometric parameter calibration method and system based on nonlinearity, the method includes: based on Standard D-H model, the position error of robot end effector is acquired and the low-order position error model based on SVD is constructed;The nonlinearity of robot is defined, the low-order position error model based on SVD is identified and processed, and the robot geometric parameter error identification result is obtained;In combination with ant colony algorithm, the robot geometric parameter error identification result is optimized and updated and robot calibration processing is carried out, and the robot geometric parameter calibration result is obtained.The application can improve the stability and accuracy of robot geometric parameter identification process, and then improve the absolute positioning accuracy and stability of heavy-duty industrial robot.The application is a kind of industrial robot geometric parameter calibration method and system based on nonlinearity, and can be widely applied to robot geometric parameter calibration technical field.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of robot geometric parameter calibration, and in particular to an industrial robot geometric parameter calibration method and system based on nonlinearity. BACKGROUND

[0002] In the application of heavy-duty industrial robots, the geometric parameters, dynamic parameters and control parameters of the robot system are coupled with each other, which means that the change of one parameter will often affect the performance of other parameters. For example, the change of joint angle will affect the position and attitude of the end effector of the robot arm, and such influence depends not only on the individual movement of the joint, but also on the change of other joint angles, and such coupling effect may cause the accumulation and amplification of calculation errors in the calibration process. Therefore, ignoring the parameter coupling effect or incorrectly linearizing the process will lead to inaccurate parameter identification, and ultimately affect the stability and accuracy of the robot system. The actual robot system is often affected by many unmodeled errors, which may be caused by various factors, including but not limited to: sensor errors, imperfections of mechanical structure, manufacturing tolerances, effects of external environmental changes on robot components, etc. The existence of unmodeled errors not only makes the behavior of the robot system deviate from the theoretical model, but also causes nonlinear behavior of the system.

[0003] In heavy-duty industrial robots, due to the coupling of system parameters and the existence of unmodeled errors, traditional calibration methods face great challenges. The nonlinearity of the system, the dynamically changing working environment and various unmodeled errors together cause the positioning accuracy of the robot to be unstable. In the calibration process, the interaction between unmodeled errors and nonlinearity may cause traditional algorithms to fall into local optimal solutions, further reducing the calibration accuracy and stability of the system. SUMMARY

[0004] To solve the above technical problems, the purpose of the present application is to provide an industrial robot geometric parameter calibration method and system based on nonlinearity, which can improve the stability and accuracy of the robot geometric parameter identification process, and further improve the absolute positioning accuracy and stability of the heavy-duty industrial robot.

[0005] The first technical solution adopted by the present application is: an industrial robot geometric parameter calibration method based on nonlinearity, comprising the following steps:

[0006] Based on the StandardD-H model, the position error of the robot end effector is obtained and a low-order position error model based on SVD is constructed;

[0007] The nonlinearity of the robot is defined, the low-order position error model based on SVD is identified, and the geometric parameter error identification result of the robot is obtained;

[0008] In combination with the ant colony algorithm, the geometric parameter error recognition result of the robot is optimized and updated, and the robot calibration processing is performed to obtain the geometric parameter calibration result of the robot.

[0009] Further, the step of obtaining the position error of the robot end effector and constructing a low-order position error model based on SVD based on the Standard D-H model specifically includes:

[0010] Based on the robot forward kinematics model, a multivariate nonlinear function of the position of the end effector with respect to the geometric parameters of the robot is obtained;

[0011] Based on the Standard D-H model, the multivariate nonlinear function is solved and calculated by the Monte Carlo method to obtain the theoretical position of the robot end effector;

[0012] The base coordinate system of the Standard D-H model is obtained, and the world coordinate system of the robot end effector position information is established according to the robot base;

[0013] According to the base coordinate system of the Standard D-H model and the world coordinate system of the robot end effector position information, a homogeneous transformation relationship matrix is constructed;

[0014] Drive the robot to move, and measure the actual position of the robot end effector in the world coordinate system by the laser tracker;

[0015] According to the actual position of the robot end effector in the world coordinate system, the actual position of the robot end effector is obtained in combination with the homogeneous transformation relationship matrix;

[0016] The difference between the actual position of the robot end effector and the theoretical position of the robot end effector is obtained to obtain the position error of the robot end effector;

[0017] Based on the position error of the robot end effector, a low-order position error model based on SVD is constructed in combination with the Jacobian matrix of the geometric parameters of the robot.

[0018] Further, the step of constructing a low-order position error model based on SVD based on the position error of the robot end effector in combination with the Jacobian matrix of the geometric parameters of the robot specifically includes:

[0019] Based on the position error of the robot end effector, the geometric parameter error of the robot is obtained;

[0020] The Jacobian matrix is constructed according to the geometric parameter error of the robot;

[0021] The singular value SVD decomposition is performed on the Jacobian matrix to obtain the left and right orthogonal matrices and the singular value matrix.

[0022] A threshold is set to screen the singular value matrix to obtain a screened singular value matrix.

[0023] The screened singular value matrix is combined with left and right orthogonal matrices to reconstruct an optimized Jacobian matrix.

[0024] The optimized Jacobian matrix is combined with the geometric parameter error of the robot to construct a low-order position error model based on SVD.

[0025] Further, the step of defining the nonlinearity of the robot and identifying the low-order position error model based on SVD to obtain the geometric parameter error identification result of the robot includes:

[0026] The low-order position error model based on SVD is optimized by combining the logarithmic step size with the linear step size to obtain the optimal damping factor.

[0027] The low-order position error model based on SVD is used to obtain the position error variance of the robot geometric parameter and set the position error variance threshold and sliding window of the robot geometric parameter.

[0028] The size of the sliding window and the position error variance threshold of the robot geometric parameter are optimized by the grid search method to obtain the optimized sliding window and the optimized position error variance threshold of the robot geometric parameter.

[0029] The position error data of the robot geometric parameter is obtained through the optimized sliding window.

[0030] The nonlinearity of the robot is defined, the nonlinearity value of the robot is calculated, and the variance of the position error data of the robot geometric parameter is obtained.

[0031] If the variance of the position error data of the robot geometric parameter is greater than the optimized position error variance threshold of the robot geometric parameter, the low-order position error model based on SVD is identified by the LM algorithm combined with the optimal damping factor to obtain the first geometric parameter error identification result of the robot.

[0032] If the variance of the position error data of the robot geometric parameter is less than or equal to the optimized position error variance threshold of the robot geometric parameter, the low-order position error model based on SVD is identified by the LS algorithm to obtain the second geometric parameter error identification result of the robot.

[0033] The first geometric parameter error identification result of the robot is combined with the second geometric parameter error identification result of the robot to obtain the geometric parameter error identification result of the robot.

[0034] Further, the step of optimizing the low-order position error model based on SVD by combining the logarithmic step length with the linear step length to obtain the optimal damping factor specifically includes:

[0035] defining an optimization range and obtaining a target function of the low-order position error model based on SVD;

[0036] based on the optimization range, searching the target function by taking the logarithmic step length as a variable step length to obtain a preliminary search result;

[0037] based on the optimization range, performing a secondary search on the preliminary search result by taking the linear step length as a fixed step length to obtain the optimal damping factor.

[0038] Further, the definition expression of the nonlinearity of the robot is specifically as follows:

[0039]

[0040] In the above formula, δ represents the nonlinearity value, u represents the input excitation, represents the set of all linearization methods, represents the set of all input excitations, N[u] represents the measured system dynamic behavior, L[u] represents the corresponding linear system dynamic behavior, inf(·) represents the lower limit operation, sup(·) represents the upper limit operation, and L represents the set of linearization methods.

[0041] Further, the calculation expression of the variance of the position error data of the geometric parameters of the robot is specifically as follows:

[0042]

[0043] In the above formula, represents the variance of the position error data of the geometric parameters of the robot, represents the mean value of all error values in the window W t , N represents the window size, and ε t-i represents the error value at the t-i time in the window W t , t represents the current time, and i represents the time step offset from the current time t.

[0044] Further, the step of combining the ant colony algorithm, optimizing and updating the robot geometric parameter error identification result, and performing robot calibration processing to obtain the robot geometric parameter calibration result specifically includes:

[0045] optimizing the robot geometric parameter error identification result by the ant colony algorithm to obtain the optimized robot geometric parameter error identification result;

[0046] Update the Standard D-H model based on the optimized robot geometric parameter error identification result to obtain an updated Standard D-H model.

[0047] Calibrate the robot geometric parameters based on the updated Standard D-H model to obtain a robot geometric parameter calibration result.

[0048] The second technical solution adopted by the application is: an industrial robot geometric parameter calibration system based on nonlinearity, comprising:

[0049] The first module is configured to obtain the position error of the robot end effector based on the Standard D-H model and construct a low-order position error model based on SVD.

[0050] The second module is configured to define the nonlinearity of the robot, identify and process the low-order position error model based on SVD, and obtain a robot geometric parameter error identification result.

[0051] The third module is configured to combine the ant colony algorithm, optimize and update the robot geometric parameter error identification result, and perform robot calibration processing to obtain a robot geometric parameter calibration result.

[0052] The method and system have the following beneficial effects: the method and system obtain the position error of the robot end effector based on the Standard D-H model and construct a low-order position error model based on SVD, in the process of establishing the position error model, the SVD is used to reduce the dimension of the Jacobian matrix, the redundant information is removed by retaining the significant eigenvalues, the accuracy of the Jacobian matrix in the iterative identification process is ensured, and the singularity of the matrix is avoided, the nonlinearity of the robot is further defined, the low-order position error model based on SVD is identified and processed, a robot geometric parameter error identification result is obtained, and finally the ant colony algorithm is combined to optimize and update the robot geometric parameter error identification result and perform robot calibration processing, the nonlinearity is alternately identified, the ant colony algorithm is introduced as a subsequent optimization step, the ant colony algorithm optimizes the geometric parameters after identification and correction by simulating the group intelligence mechanism of ants foraging, can effectively avoid local optimal solution, and improves the absolute positioning accuracy and stability of the heavy-duty industrial robot. BRIEF DESCRIPTION OF DRAWINGS

[0053] Figure 1 is a step flowchart of the industrial robot geometric parameter calibration method based on nonlinearity of the application;

[0054] Figure 2 is a structural block diagram of the industrial robot geometric parameter calibration system based on nonlinearity of the application;

[0055] Figure 3 is a flowchart of an industrial robot geometric parameter calibration process provided by an embodiment of the present application;

[0056] Figure 4 is a schematic diagram of a grid search method for optimizing a logarithmic step length according to an embodiment of the present application;

[0057] Figure 5 is a schematic diagram of a grid search method for optimizing a linear step length according to an embodiment of the present application;

[0058] Figure 6 is a comparative schematic diagram of direction errors of a grid search method according to an embodiment of the present application;

[0059] Figure 7 is a comparative schematic diagram of direction errors of an optimization recognition algorithm based on nonlinearity and an ant colony algorithm according to an embodiment of the present application;

[0060] Figure 8 is a comparative schematic diagram of position errors of an optimization recognition algorithm based on nonlinearity and an ant colony algorithm according to an embodiment of the present application. DETAILED DESCRIPTION

[0061] The present application will be further described in detail below with reference to the accompanying drawings and specific embodiments. For the step numbers in the following embodiments, only the setting for facilitating the description is provided, and the order between the steps is not limited in any way, and the execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0062] Referring to Figure 1 , the present application provides an industrial robot geometric parameter calibration method based on nonlinearity, which comprises the following steps:

[0063] S100, based on a Standard D-H model, acquiring a position error of a robot end effector and constructing a low-order position error model based on SVD;

[0064] Specifically, the position error is acquired, the joint angle of the target point is used to calculate the theoretical position of the end effector by using the Standard D-H model and driving the robot to move in the workspace, and then measuring the actual position of the robot end effector by using a laser tracker and the difference between the two is the position error ΔP.

[0065] In the embodiment, based on a robot forward kinematics model, a position of an end effector is obtained as a multivariate nonlinear function of robot geometric parameters; based on a Standard D-H model, the multivariate nonlinear function is solved and calculated by a Monte Carlo method to obtain a theoretical position of the robot end effector; a base coordinate system of the Standard D-H model is obtained, and a world coordinate system of the robot end effector position information is established according to a robot base; a homogeneous transformation relationship matrix is constructed according to the base coordinate system of the Standard D-H model and the world coordinate system of the robot end effector position information; the robot is driven to move, and an actual position of the robot end effector in the world coordinate system is measured and obtained by a laser tracker; the actual position of the robot end effector in the world coordinate system is combined with the homogeneous transformation relationship matrix to obtain an actual position of the robot end effector; a difference between the actual position of the robot end effector and the theoretical position of the robot end effector is obtained to obtain a position error of the robot end effector; and based on the position error of the robot end effector, a low-order position error model based on SVD is constructed in combination with a Jacobian matrix of the robot geometric parameters.

[0066] It needs to be further explained that, according to robot forward kinematics, the position P of the end effector is a multivariate nonlinear function of the robot geometric parameters, which is written as a function relationship as follows:

[0067] P=f(θ,d,a,α)

[0068] wherein 0=[01,θ2,…,θ6] T , d=[d1,d2,…,d6] T , a=[a1,a2,…,a6] T , and α=[α1,α2,…,α6] T .

[0069] Further, for obtaining the theoretical position, the geometric parameter error identification sample points and the precision verification points are obtained by the Monte Carlo method based on the Standard D-H model.

[0070] For obtaining the actual position, the world coordinate system of the measurement robot end effector position information is established according to the robot base, the robot is driven to move based on the joint angle parameters of the sample points, and the end effector position based on the world coordinate system is measured and obtained by the laser tracker

[0071] The following homogeneous transformation relationship exists between the world coordinate system and the base coordinate system of the Standard D-H model, and the expression is as follows:

[0072]

[0073] Wherein, the rotation matrix R, due to the non-rotation relationship, the rotation matrix is a unit matrix, and its expression is:

[0074]

[0075] The translation vector t represents the displacement of the origin of the base coordinate system relative to the origin of the world coordinate system, and its expression is:

[0076]

[0077] For a point In the world coordinate system, its position in the base coordinate system is It is calculated by the following formula:

[0078]

[0079] In the above formula, represents the actual position of the robot end effector, represents the actual position of the robot end effector in the world coordinate system, T WB represents the homogeneous transformation matrix.

[0080] More specifically, a low-order position error model based on SVD is established, a Jacobian matrix J about the geometric parameters of the robot is established based on differential kinematics, and dimensionality reduction processing is performed on it through SVD, significant eigenvalues are retained, redundant information is reduced, and then a position error model ΔP = J·ΔX is established.

[0081] In this embodiment, based on the position error of the robot end effector, the geometric parameter error of the robot is obtained; a Jacobian matrix is constructed according to the geometric parameter error of the robot; singular value SVD decomposition is performed on the Jacobian matrix to obtain left and right orthogonal matrices and a singular value matrix; a threshold is set, and the singular value matrix is filtered to obtain a filtered singular value matrix; the filtered singular value matrix and the left and right orthogonal matrices are combined to reconstruct an optimized Jacobian matrix; and a low-order position error model based on SVD is constructed by combining the geometric parameter error of the robot and the optimized Jacobian matrix.

[0082] Further, it should be noted that the geometric parameter error ΔX to be identified has the expression:

[0083] ΔX = [Δθ, Δd, Δa, Δa] T

[0084] Wherein, Δθ = [Δθ1, Δθ2, …, Δθ6] T , Δd = [Δd1, Δd2, …, Δd6] T , Δa = [Δa1, Δa2, …, Δa6] T,Δα=[Δα1,Δα2,…,Δα6] T .

[0085] The Jacobian matrix J is expressed as:

[0086] J0 = [M θ M d M α M α ]

[0087] Where M θ M d M a M α Both are 3×6 matrices, and their elements are functions consisting of 24 robot geometric parameters.

[0088] To ensure the accuracy of the Jacobian matrix during the iterative identification process and to avoid matrix singularity, singular value decomposition is performed on it to obtain:

[0089] J0 = U·S·V T

[0090] Where, U∈R m×m and V∈R n×n These are left and right orthogonal matrices, respectively; S∈R m×n It is a diagonal matrix, and its diagonal elements σ i They are singular values, and satisfy σ1≥σ2≥…≥σ r ≥0 (r is the rank of the singular value).

[0091] Based on the set threshold μ, the singular values ​​σ i The process involves filtering, retaining singular values ​​greater than μ, and setting singular values ​​less than μ to 0. The resulting diagonal matrix is ​​represented as:

[0092]

[0093] Using the filtered singular value matrix S', combined with orthogonal matrices U and V, the optimized Jacobian matrix J is reconstructed, and its expression is:

[0094] J = U·S′·V T

[0095] This leads to a low-order position error model: ΔP = J·ΔX.

[0096] S200. Define the nonlinearity of the robot, identify the low-order position error model based on SVD, and obtain the identification results of the robot's geometric parameter errors.

[0097] Specifically, an optimization identification model based on nonlinearity evaluation is established: the LM algorithm can quickly converge to a better local optimal solution when there is a large difference between the initial estimated value and the true value, so it is set as the initial identification algorithm, and the initial data to be evaluated is obtained using a sliding window. When the nonlinearity is large, the LM algorithm is used for geometric parameter error identification to enhance the anti-interference ability of the algorithm to unmodeled errors; when the nonlinearity is small, the LS algorithm is used to improve the identification efficiency and accuracy. Through continuous iterative identification, when the difference between the theoretical position and the actual position meets the accuracy requirement, the geometric parameter error obtained by identification is output.

[0098] In the embodiment, the low-order position error model based on SVD is optimized by combining the logarithmic step size with the linear step size to obtain an optimal damping factor; the low-order position error model based on SVD is used to obtain the position error variance of the robot geometric parameters and set the position error variance threshold of the robot geometric parameters and the sliding window; the size of the sliding window and the position error variance threshold of the robot geometric parameters are optimized by the grid search method to obtain the optimized sliding window and the optimized position error variance threshold of the robot geometric parameters; the position error data of the robot geometric parameters are obtained through the optimized sliding window; the nonlinearity of the robot is defined, the nonlinearity value of the robot is calculated, and the variance of the position error data of the robot geometric parameters is obtained; if the variance of the position error data of the robot geometric parameters is greater than the optimized position error variance threshold of the robot geometric parameters, the low-order position error model based on SVD is identified by the LM algorithm combined with the optimal damping factor to obtain a first robot geometric parameter error identification result; if the variance of the position error data of the robot geometric parameters is less than or equal to the optimized position error variance threshold of the robot geometric parameters, the low-order position error model based on SVD is identified by the LS algorithm to obtain a second robot geometric parameter error identification result; the robot geometric parameter error identification result is obtained by combining the first robot geometric parameter error identification result and the second robot geometric parameter error identification result.

[0099] wherein the optimization range is defined and the objective function of the low-order position error model based on SVD is obtained; based on the optimization range, the objective function is searched by using the logarithmic step size as a variable step size to obtain a preliminary search result; based on the optimization range, the preliminary search result is searched again by using the linear step size as a fixed step size to obtain the optimal damping factor.

[0100] Further, it needs to be noted that the LM algorithm is sensitive to the damping factor, and the exhaustive method is used to optimize it before identification.

[0101] The optimization range is set to [10 -10 ,1], and the range cannot be too small to avoid singularity of the Jacobian matrix. The following steps are taken:Figure 4 and Figure 5 The optimization is performed in a way that combines the logarithmic step with the linear step. The root mean square error (RMSE) of the position error is taken as the objective function, and the optimization process is performed by minimizing the objective function, where λ is the damping factor to be optimized, and the function is defined as follows:

[0102]

[0103] The logarithmic step is a variable step search that quickly locks the optimal range, and the linear step is a constant step search that searches around the optimal range twice. The optimal damping factor λ is obtained by exhaustive search, and the size is 10 -10 .

[0104] The sliding window is a sliding data set with a fixed size, and the window contains the position error data calculated in the last N iterations. Let the position error calculated in each iteration be ε k (where k represents the iteration step number), and the sliding window size is N. Then, at any time t, the error data in the window can be represented as:

[0105] W t = {ε t-N+1 , ε t-N+2 , …, ε t}

[0106] With the calculation of each new error data ε t , the window slides one step forward, and the earliest error value ε t-N+1 is removed, and the new value ε t is added to the window, and the updated window data set is:

[0107] W t+1 = {ε t-N+2 , ε t-N+3 , …, ε t+1}

[0108] Definition of nonlinearity:

[0109]

[0110] In the above formula, δ represents the nonlinearity value, u represents the input excitation, represents the set of all linearization methods, represents the set of all input excitations, N[u] represents the dynamic behavior of the measured system, L[u] represents the dynamic behavior of the corresponding linear system, and inf(·) represents the lower bound, i.e. in all linearization method sets , find the linearization method that minimizes the error, and sup(·) represents the upper bound, i.e. in all input excitation sets In this paper, the input excitation that maximizes the error is found, and L represents the set of linearization methods.

[0111] It is known that LS algorithm is suitable for parameter identification of linear system, and LM algorithm is suitable for parameter identification of nonlinear system. Therefore, the numerical simulation based on LS algorithm identification obtains the dynamic behavior information of linear system, and the position error variance σ0 of linear system is regarded as linear behavior, and the threshold σ threshold of position error variance of measured system is regarded as dynamic behavior. Combined with the definition of nonlinearity, the nonlinearity δ0 of geometric parameter error identification system is calculated as follows:

[0112] δ0=σ threshold -σ0

[0113] The error data W t in the window is calculated, and the variance of error data in the window is calculated. The expression is as follows:

[0114]

[0115] In the above formula, σ represents the variance of position error data of robot geometric parameters, μ represents the mean of all error values in the window W t , N represents the window size, and ε t-i represents the error value at the t-i moment in the window W t , t represents the current moment, and i represents the time step offset from the current moment t.

[0116] Based on the nonlinearity δ0 of the system, an optimization identification algorithm combining LM algorithm and LS algorithm is constructed, and different methods are selected for geometric parameter error identification according to the nonlinearity of the system, and the selection principle is as follows:

[0117] If there exists such that δ>δ0, the nonlinearity of the current system is large, and the LM algorithm is selected for identification; if there exists such that δ≤δ0, the nonlinearity of the current system is small, and the LS algorithm is selected for identification.

[0118] The window size N is the sample number for calculating the variance, and the setting of the variance threshold σ threshold will affect the selection of the algorithm. Therefore, in order to further improve the adaptability and accuracy of the identification algorithm, the grid search method is used to optimize the sliding window size N and the variance threshold σ threshold . The root mean square error RMSE of position error is taken as the objective function, and the optimization process is carried out by minimizing the objective function, wherein the window size N and the variance threshold σ threshold are the parameters to be optimized, and the function is defined as follows:

[0119]

[0120] The optimal window size N is 9 and the optimal variance threshold σ is 0.007 obtained by the grid search method threshold The corresponding direction error ratio is as shown in the following table 1 Figure 6 .

[0121] S300, in combination with the ant colony algorithm, the robot geometric parameter error identification result is optimized and updated, and the robot calibration processing is performed to obtain the robot geometric parameter calibration result.

[0122] Specifically, after completing the geometric parameter error identification, the ant colony algorithm is introduced, and the geometric parameter error is optimized through the group intelligence mechanism of simulating ant foraging, so as to avoid the problem that the identification method may fall into local optimum, and further improve the absolute positioning accuracy and the stability of the system.

[0123] In this embodiment, the robot geometric parameter error identification result is optimized by the ant colony algorithm to obtain the optimized robot geometric parameter error identification result; the Standard D-H model is updated based on the optimized robot geometric parameter error identification result to obtain the updated Standard D-H model; and the robot geometric parameter is calibrated based on the updated Standard D-H model to obtain the robot geometric parameter calibration result.

[0124] Further, it needs to be noted that the basic parameters of the ant colony algorithm are set, including the number of ants, the maximum number of iterations, the initial value of pheromone, the pheromone evaporation coefficient, the heuristic information influence factor and the pheromone concentration influence factor, etc. The identification corrected geometric parameter is taken as the input of the ant colony algorithm, and the root mean square error RMSE of the position error is taken as the fitness function, and the optimal geometric parameter error ΔX is output. The optimization process is performed by minimizing the fitness function, and the function definition is as shown below:

[0125]

[0126] After the identified geometric parameter is optimized by the ant colony algorithm, the corresponding direction error ratio is as shown in the following table 1 Figure 7 The position error ratio is as shown in the following table 2 Figure 8As shown, wherein, according to the comparative experimental results, the position error is reduced from 13.03mm to 1.80mm by combining the LM algorithm and the LS algorithm based on the nonlinearity for geometric error parameter identification. After optimizing the geometric parameters by the ant colony algorithm, the position error is further reduced from 1.80mm to 1.21mm, and the absolute positioning accuracy is improved by 90.71%. Therefore, the embodiment of the present application not only combines the advantages of the LM algorithm and the LS algorithm based on the nonlinearity, but also demonstrates that the present application has certain geometric parameter calibration accuracy.

[0127] Based on the optimized geometric parameter error, the Standard D-H model is updated, and the calibration effect is verified on the machine.

[0128] As shown in the above, Figure 3 The present application calculates the theoretical position and the actual position measured by the laser tracker to obtain the position error through the Standard D-H model; the Jacobian matrix is processed by SVD for dimension reduction, and a low-order position error model is established; the LM algorithm or the LS algorithm is selected for geometric parameter error identification according to the nonlinearity evaluation of the system, the LM algorithm is used for identification when the nonlinearity is high, and the LS algorithm is used when the nonlinearity is low; the ant colony algorithm is used to optimize the geometric parameters after identification and correction. The present application not only improves the robustness of the heavy-duty industrial robot in the process of geometric parameter calibration, but also avoids local optimal solution and improves the calibration accuracy.

[0129] The embodiment of the present application has the following advantages compared with the prior art:

[0130] 1) In the process of establishing the position error model, the Jacobian matrix J is processed by SVD for dimension reduction. By retaining the characteristic values with significant values and eliminating redundant information, the accuracy of the Jacobian matrix J in the iterative identification process is ensured and the singularity of the matrix is avoided.

[0131] 2) The damping factor lambda of the LM algorithm is optimized by the exhaustive method, which avoids the sensitivity of the LM algorithm to the initial setting of the damping factor lambda; the grid search method is used to optimize the sliding window N and the threshold value sigma threshold of the error variance, which ensures the applicability of the nonlinearity and ensures that the system can quickly and accurately change the identification algorithm.

[0132] 3) Based on the nonlinearity, the LM algorithm and the LS algorithm are alternately identified, when the nonlinearity of the system is high, the LM algorithm with strong robustness is selected for error identification; when the nonlinearity of the system is low, the LS algorithm with higher accuracy is selected, which ensures the stability and accuracy of the identification process.

[0133] 4) Introduce the ant colony algorithm as a subsequent optimization step, the ant colony algorithm optimizes the geometric parameters after recognition by simulating the group intelligence mechanism of ant foraging, which can effectively avoid local optimal solution, further improve the absolute positioning accuracy and stability of heavy industrial robots.

[0134] Reference Figure 2 A nonlinear-based industrial robot geometric parameter calibration system, comprising:

[0135] The first module 201 is configured to obtain the position error of the robot end effector and construct a low-order position error model based on SVD based on the Standard D-H model;

[0136] The second module 202 is configured to define the nonlinearity of the robot, identify the low-order position error model based on SVD, and obtain the robot geometric parameter error identification result;

[0137] The third module 203 is configured to combine the ant colony algorithm, optimize and update the robot geometric parameter error identification result, and perform robot calibration processing to obtain the robot geometric parameter calibration result.

[0138] The contents in the above method embodiments are applicable to the system embodiments, the system embodiments specifically realize the same functions as the above method embodiments, and achieve the same beneficial effects as the above method embodiments.

[0139] The above is a specific description of the preferred implementation of the present application, but the present application is not limited to the above embodiments. Those skilled in the art can make various equivalent modifications or replacements without departing from the spirit of the present application. These equivalent modifications or replacements are all included in the scope defined by the claims of the present application.

Claims

1. A method for calibrating geometric parameters of an industrial robot based on non-linearity, characterized by, The method comprises the following steps: Based on the Standard D-H model, the position error of the robot end effector is obtained, and a low-order position error model based on SVD is constructed; The low-order position error model based on SVD is optimized by combining the logarithmic step length with the linear step length, and the optimal damping factor is obtained; Based on the low-order position error model based on SVD, the position error variance of the robot geometric parameter is obtained, and the position error variance threshold and the sliding window of the robot geometric parameter are set; The size of the sliding window and the position error variance threshold of the robot geometric parameter are optimized by the grid search method, and the optimized sliding window and the optimized position error variance threshold of the robot geometric parameter are obtained; The position error data of the robot geometric parameter is obtained through the optimized sliding window; The nonlinearity of the robot is defined, the nonlinearity value of the robot is calculated, and the variance of the position error data of the robot geometric parameter is obtained; If the variance of the position error data of the robot geometric parameter is greater than the optimized position error variance threshold of the robot geometric parameter, the low-order position error model based on SVD is identified by the LM algorithm combined with the optimal damping factor, and the first robot geometric parameter error identification result is obtained; If the variance of the position error data of the robot geometric parameter is less than or equal to the optimized position error variance threshold of the robot geometric parameter, the low-order position error model based on SVD is identified by the LS algorithm, and the second robot geometric parameter error identification result is obtained; The robot geometric parameter error identification result is obtained by combining the first robot geometric parameter error identification result and the second robot geometric parameter error identification result; The robot geometric parameter error identification result is optimized and updated by combining the ant colony algorithm, and the robot calibration processing is performed, and the robot geometric parameter calibration result is obtained.

2. The method for calibrating geometric parameters of an industrial robot based on non-linearity according to claim 1, characterized in that, The step of obtaining the position error of the robot end effector based on the Standard D-H model and constructing the low-order position error model based on SVD comprises the following steps: Based on the robot forward kinematics model, a multivariate nonlinear function of the position of the end effector with respect to the robot geometric parameter is obtained; Based on the Standard D-H model, the multivariate nonlinear function is calculated by the Monte Carlo method, and the theoretical position of the robot end effector is obtained; The base coordinate system of the Standard D-H model is obtained, and the world coordinate system of the robot end effector position information is established according to the robot base; According to the base coordinate system of the Standard D-H model and the world coordinate system of the robot end effector position information, a homogeneous transformation relationship matrix is constructed; The robot is driven to move, and the actual position of the robot end effector in the world coordinate system is measured and obtained by a laser tracker; According to the actual position of the robot end effector in the world coordinate system, the actual position of the robot end effector is obtained combined with the homogeneous transformation relationship matrix; The difference between the actual position of the robot end effector and the theoretical position of the robot end effector is obtained, and the position error of the robot end effector is obtained. Based on the position error of the robot end effector, combined with the Jacobian matrix of the robot geometric parameters, a low-order position error model based on SVD is constructed.

3. The method for calibrating geometric parameters of an industrial robot based on nonlinearity according to claim 2, characterized in that, The step of constructing a low-order position error model based on SVD based on the position error of the robot end effector, combined with the Jacobian matrix of the robot geometric parameters, specifically includes: Based on the position error of the robot end effector, the geometric parameter error of the robot is obtained; Construct a Jacobian matrix according to the geometric parameter error of the robot; Singular value SVD decomposition is performed on the Jacobian matrix to obtain left and right orthogonal matrices and a singular value matrix; Set a threshold value and filter the singular value matrix to obtain a filtered singular value matrix; Combine the filtered singular value matrix with the left and right orthogonal matrices to reconstruct the optimized Jacobian matrix; Combine the geometric parameter error of the robot with the optimized Jacobian matrix to construct a low-order position error model based on SVD.

4. The method for calibrating geometric parameters of an industrial robot based on nonlinearity according to claim 3, characterized in that, The step of optimizing the low-order position error model based on SVD by combining the logarithmic step length with the linear step length to obtain the optimal damping factor, specifically includes: Define the optimization range and obtain the objective function of the low-order position error model based on SVD; Based on the optimization range, search the objective function by variable step length with logarithmic step length to obtain the preliminary search result; Based on the optimization range, perform a second search on the preliminary search result by fixed step length with linear step length to obtain the optimal damping factor.

5. The method for calibrating geometric parameters of an industrial robot based on non-linearity according to claim 4, characterized in that, The definition expression of the nonlinearity of the robot is specifically as follows: ； In the above formulae, denotes the nonlinearity value, denotes the input excitation, denotes the set of all linearization methods, denotes the set of all input excitations, denotes the measured system dynamics, denotes the corresponding linear system dynamics, denotes the lower bound operation, denotes the upper bound operation, denotes the set of linearization methods.

6. The method for calibrating geometric parameters of an industrial robot based on non-linearity according to claim 5, characterized in that, The calculation expression of the variance of the position error data of the robot geometric parameters is specifically as follows: ； in the above formula, a variance of the position error data representing the robot geometry parameters, a mean of all error values within the window a mean of all error values within the window, a window size, a window error values at the time step, a current time, a current time a number of time steps to offset forward from the current time.

7. The method for calibrating geometric parameters of an industrial robot based on non-linearity according to claim 6, characterized in that, The step of optimizing and updating the robot geometric parameter error identification result by combining the ant colony algorithm and performing robot calibration to obtain the robot geometric parameter calibration result, specifically includes: Optimize the robot geometric parameter error identification result by ant colony algorithm to obtain the optimized robot geometric parameter error identification result; Update the Standard D-H model based on the optimized robot geometric parameter error identification result to obtain the updated Standard D-H model; Calibrate the robot geometric parameters based on the updated Standard D-H model to obtain the robot geometric parameter calibration result.

8. A non-linearity based industrial robot geometry parameter calibration system, characterized by, It includes the following modules: The first module is used to obtain the position error of the robot end effector based on the Standard D-H model and construct a low-order position error model based on SVD; The second module is used to optimize the low-order position error model based on SVD by combining the logarithmic step length with the linear step length to obtain the optimal damping factor; The low-order position error model based on SVD obtains the position error variance of the robot geometric parameters and sets the position error variance threshold and sliding window of the robot geometric parameters; Optimize the size of the sliding window and the position error variance threshold of the robot geometric parameters by grid search method to obtain the optimized sliding window and the optimized position error variance threshold of the robot geometric parameters; Obtain the position error data of the robot geometric parameters through the optimized sliding window; defining nonlinearity of the robot, calculating nonlinearity value of the robot, and obtaining variance of position error data of the robot geometric parameters; if the variance of the position error data of the robot geometric parameters is greater than the optimized position error variance threshold of the robot geometric parameters, then the first robot geometric parameter error identification result is obtained by identifying the low-order position error model based on SVD through the LM algorithm combined with the optimal damping factor; if the variance of the position error data of the robot geometric parameters is less than or equal to the optimized position error variance threshold of the robot geometric parameters, then the second robot geometric parameter error identification result is obtained by identifying the low-order position error model based on SVD through the LS algorithm; combining the first robot geometric parameter error identification result and the second robot geometric parameter error identification result, the robot geometric parameter error identification result is obtained; the third module is used for combining the ant colony algorithm, optimizing and updating the robot geometric parameter error identification result, and performing robot calibration processing to obtain the robot geometric parameter calibration result.

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