Industrial robot geometric parameter calibration method and system based on nonlinearity

Abstract

The invention discloses an industrial robot geometric parameter calibration method and system based on nonlinearity, and the method comprises the steps: obtaining a position error of an end effector of a robot based on a Standard D-H model, and constructing a low-order position error model based on SVD; defining the nonlinearity of the robot, and performing identification processing on the SVD-based low-order position error model to obtain a geometric parameter error identification result of the robot; and in combination with an ant colony algorithm, optimizing and updating the robot geometric parameter error identification result, and carrying out robot calibration processing to obtain a robot geometric parameter calibration result. According to the method, the stability and accuracy of the geometric parameter identification process of the robot can be improved, and then the absolute positioning precision and stability of the heavy-load industrial robot are improved. The industrial robot geometric parameter calibration method and system based on nonlinearity can be widely applied to the technical field of robot geometric parameter calibration.

Description

Technical Field

[0001] The present invention relates to the technical field of robot geometric parameter calibration, and in particular to a method and system for calibrating geometric parameters of an industrial robot based on nonlinearity. Background Art

[0002] In the application of heavy-duty industrial robots, the geometric parameters, dynamic parameters and control parameters of the robot system are coupled to each other, which means that the change of one parameter often affects the performance of other parameters. For example, the change of joint angle will affect the position and posture of the end effector of the robot arm, and this effect depends not only on the individual movement of the joint, but also on the change of other joint angles. This coupling effect may lead to the accumulation and amplification of calculation errors during the calibration process. Therefore, ignoring the parameter coupling effect or incorrectly linearizing it will lead to inaccurate parameter identification, which will eventually affect the stability and accuracy of the robot system. The actual robot system is often affected by many unmodeled errors, which may come from a variety of factors, including but not limited to: sensor errors, imperfections in mechanical structures, manufacturing tolerances, and the impact of external environmental changes on robot components. 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, traditional calibration methods face great challenges due to the coupling of system parameters and the existence of unmodeled errors. The nonlinearity of the system, the dynamically changing working environment, and various unmodeled errors work together to cause the robot's positioning accuracy to be unstable. During the calibration process, the interaction between unmodeled errors and nonlinearity may cause traditional algorithms to fall into a local optimal solution, further reducing the calibration accuracy and system stability. Summary of the invention

[0004] In order to solve the above technical problems, the purpose of the present invention 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 thus improve the absolute positioning accuracy and stability of the heavy-load industrial robot.

[0005] The first technical solution adopted by the present invention is: a method for calibrating geometric parameters of an industrial robot 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] 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;

[0008] Combined with the ant colony algorithm, the robot geometric parameter error identification results are optimized and updated, and the robot calibration is performed to obtain the robot geometric parameter calibration results.

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

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

[0011] Based on the Standard DH model, the Monte Carlo method is used to solve and calculate the multivariate nonlinear function to obtain the theoretical position of the robot's end effector.

[0012] Obtain the base coordinate system of the Standard DH model and establish the world coordinate system of the robot end effector position information based on the robot base;

[0013] According to the base coordinate system of the Standard DH 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 use the laser tracker to measure and obtain the actual position of the robot's end effector in the world coordinate system;

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

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

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

[0018] Furthermore, the step of constructing a low-order position error model based on SVD based on the position error of the robot end effector and the Jacobian matrix of the robot's geometric parameters specifically includes:

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

[0020] Construct the Jacobian matrix based on the geometric parameter errors of the robot;

[0021] Perform singular value SVD decomposition on the Jacobian matrix to obtain the left and right orthogonal matrices and the singular value matrix;

[0022] Set a threshold, filter the singular value matrix, and obtain a filtered singular value matrix;

[0023] Combine the selected singular value matrix with the left and right orthogonal matrices to reconstruct the optimized Jacobian matrix;

[0024] Combining the robot's geometric parameter errors with the optimized Jacobian matrix, a low-order position error model based on SVD is constructed.

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

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

[0027] Based on the low-order position error model of SVD, the position error variance of the robot's geometric parameters is obtained and the position error variance threshold and sliding window of the robot's geometric parameters are set;

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

[0029] The position error data of the robot's geometric parameters are obtained through the optimized sliding window;

[0030] Define the nonlinearity of the robot, calculate the nonlinearity value of the robot and obtain the variance of the position error data of the robot's geometric parameters;

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

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

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

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

[0035] Define the optimization range and obtain the objective function of the low-order position error model based on SVD;

[0036] Based on the optimization range, the objective function is searched by using a logarithmic step size as a variable step size to obtain preliminary search results;

[0037] Based on the optimization range, a secondary search is performed on the preliminary search results by taking the linear step size as a fixed step size to obtain the optimal damping factor.

[0038] Furthermore, 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 stimuli, N[u] represents the measured system dynamic behavior, L[u] represents the corresponding linear system dynamic behavior, inf(·) represents the infimum operation, sup(·) represents the supremum operation, and L represents the set of linearization methods.

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

[0042]

[0043] In the above formula, represents the variance of the position error data of the robot's geometric parameters, Represents window W t The mean of all error values ​​in, N represents the window size, ε t-i Represents window W t The error value at the ti-th moment, t represents the current moment, and i represents the number of time steps offset from the current moment t.

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

[0045] The robot geometric parameter error identification results are optimized by using the ant colony algorithm to obtain the optimized robot geometric parameter error identification results;

[0046] The Standard DH model is updated based on the optimized robot geometric parameter error identification results to obtain an updated Standard DH model;

[0047] Based on the updated Standard D-H model, the robot geometric parameters are calibrated to obtain the robot geometric parameter calibration results.

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

[0049] The first module is used to obtain the position error of the robot end effector based on the Standard DH model and build a low-order position error model based on SVD;

[0050] The second module is used 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;

[0051] The third module is used to optimize and update the robot geometric parameter error identification results and perform robot calibration processing in combination with the ant colony algorithm to obtain the robot geometric parameter calibration results.

[0052] The beneficial effects of the method and system of the present invention are as follows: based on the Standard DH model, the present invention obtains the position error of the robot end effector and constructs 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, and by retaining significant eigenvalues ​​and eliminating redundant information, the accuracy of the Jacobian matrix in the iterative identification process is guaranteed and the singularity of the matrix is ​​avoided. The nonlinearity of the robot is further defined, and the low-order position error model based on SVD is identified to obtain the robot geometric parameter error identification result. Finally, in combination with the ant colony algorithm, the robot geometric parameter error identification result is optimized and updated and the robot calibration is performed. Alternate identification is performed based on nonlinearity, and the ant colony algorithm is introduced as a subsequent optimization step. The ant colony algorithm optimizes the identified and corrected geometric parameters by simulating the group intelligence mechanism of ant foraging, which can effectively avoid local optimal solutions and improve the absolute positioning accuracy and stability of heavy-duty industrial robots. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 It is a flow chart of the steps of a method for calibrating geometric parameters of an industrial robot based on nonlinearity of the present invention;

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

[0055] Figure 3 It is a schematic diagram of the process of calibrating geometric parameters of an industrial robot provided by a specific embodiment of the present invention;

[0056] Figure 4 It is a schematic diagram of optimizing the logarithmic step length by exhaustive method provided by a specific embodiment of the present invention;

[0057] Figure 5 It is a schematic diagram of the exhaustive linear step optimization provided by a specific embodiment of the present invention;

[0058] Figure 6 is a comparative schematic diagram of the directional error of the grid search method provided by a specific embodiment of the present invention;

[0059] Figure 7 It is a schematic diagram comparing the directional errors of the optimization identification algorithm based on nonlinearity and the ant colony algorithm provided in a specific embodiment of the present invention;

[0060] Figure 8 It is a schematic diagram comparing the position errors of the nonlinear optimization identification algorithm and the ant colony algorithm provided in a specific embodiment of the present invention. DETAILED DESCRIPTION

[0061] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. The step numbers in the following embodiments are only provided for the convenience of explanation and description, and the order between the steps is not limited in any way. The execution order of each step in the embodiment can be adaptively adjusted according to the understanding of those skilled in the art.

[0062] Reference Figure 1 The present invention provides a method for calibrating geometric parameters of an industrial robot based on nonlinearity, the method comprising the following steps:

[0063] S100, based on the Standard DH model, obtain the position error of the robot end effector and build a low-order position error model based on SVD;

[0064] Specifically, the position error is obtained, and the theoretical position of the end effector is calculated using the Standard DH model based on the joint angle of the target point. The robot is driven to move in the workspace, and the laser tracker is used to measure the actual position of the robot end. and The difference is the position error ΔP.

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

[0066] It should be further explained that, from the robot's forward kinematics, we know that the position P of the end effector is a multivariate nonlinear function of the robot's geometric parameters, which can be expressed as a functional relationship:

[0067] P=f(θ,d,a,α)

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

[0069] Furthermore, to obtain the theoretical position, based on the Standard D-H model, the Monte Carlo method is used to obtain the geometric parameter error identification sample points and accuracy verification points.

[0070] To obtain the actual position, a world coordinate system is established based on the robot base to measure the position information of the end effector of the robot arm. The robot is driven to move based on the joint angle parameters of the sample points. The laser tracker measures and obtains the end effector position based on the world coordinate system.

[0071] There is the following homogeneous transformation relationship between the world coordinate system and the base coordinate system of the Standard DH model, which is expressed as follows:

[0072]

[0073] Among them, the rotation matrix R, due to the lack of rotation relationship, is the 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. Its expression is:

[0076]

[0077] For a point Its position in the world coordinate system, its position in the base coordinate system 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 a homogeneous transformation matrix.

[0080] More specifically, a low-order position error model based on SVD is established, and the Jacobian matrix J of the robot's geometric parameters is established based on differential kinematics. The dimensionality reduction is performed on it through SVD to retain the eigenvalues ​​with significant contributions and reduce redundant information. Then, a position error model ΔP=J·ΔX is established.

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

[0082] Furthermore, it should be noted that the geometric parameter error ΔX to be identified is expressed as:

[0083] ΔX=[Δθ,Δd,Δa,Δa] T

[0084] Among them, 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] Among them, M θ ,M d ,M a ,M α They are all 3×6 matrices whose elements are functions of the 24 robot geometric parameters.

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

[0089] J0=U·S·V T

[0090] Among them, U∈R m×m and V∈R n×n are left and right orthogonal matrices respectively; S∈R m×n is a diagonal matrix whose diagonal elements σ i is a singular value and satisfies σ1≥σ2≥…≥σ r ≥0 (r is the rank of the singular value).

[0091] According to the set threshold μ, the singular value σ i Screening is performed to retain singular values ​​greater than μ and set singular values ​​less than μ to 0. The diagonal matrix after screening is expressed as:

[0092]

[0093] The optimized Jacobian matrix J is reconstructed by using the screened singular value matrix S' and combining the orthogonal matrices U and V. Its expression is:

[0094] J=U·S′·V T

[0095] Then a low-order position error model is constructed: ΔP=J·ΔX.

[0096] S200, defining the nonlinearity of the robot, performing identification processing on a low-order position error model based on SVD, and obtaining a robot geometric parameter error identification result;

[0097] Specifically, an optimization identification model based on nonlinear evaluation is established: the LM algorithm can quickly converge to a good 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 sliding window is used to obtain the initial data to be evaluated. When the nonlinearity is large, the LM algorithm is used for geometric parameter error identification to enhance the algorithm's anti-interference ability for 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 requirements, the geometric parameter error obtained by identification is output.

[0098] In this 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 the optimal damping factor; based on the low-order position error model of SVD, the position error variance of the robot's geometric parameters is obtained and the position error variance threshold and sliding window of the robot's geometric parameters are set; the size of the sliding window and the position error variance threshold of the robot's 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's geometric parameters; the position error data of the robot's 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 position of the robot's geometric parameters is obtained variance of error data; if the variance of the position error data of the robot's geometric parameters is greater than the position error variance threshold of the optimized robot's geometric parameters, then combined with the optimal damping factor, the low-order position error model based on SVD is identified through the LM algorithm to obtain the first robot geometric parameter error identification result; if the variance of the position error data of the robot's geometric parameters is less than or equal to the position error variance threshold of the optimized robot's geometric parameters, then the LS algorithm is used to identify the low-order position error model based on SVD to obtain the second robot geometric parameter error identification result; the first robot geometric parameter error identification result is combined with the second robot geometric parameter error identification result to obtain the robot geometric parameter error identification result.

[0099] Among them, 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 taking the logarithmic step size as a variable step size to obtain preliminary search results; based on the optimization range, the preliminary search results are searched secondary by taking the linear step size as a fixed step size to obtain the optimal damping factor.

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

[0101] The optimization range is set to [10 -10 ,1], in order to avoid the Jacobian matrix from being singular, the range cannot be smaller. Figure 4 and Figure 5 The optimization is performed by combining the logarithmic step size with the linear step size. The root mean square error RMSE of the position error is used 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 definition is as follows:

[0102]

[0103] The logarithmic step size is a variable step size search, which quickly locks the optimal range. The linear step size is a fixed step size search, which searches twice near the optimal range. The optimal damping factor λ is obtained by exhaustive method, which is 10 -10 .

[0104] The sliding window is a sliding data set with a fixed size, which 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 number of iterations), the sliding window size is N, then at any time t, the error data in the window can be expressed as:

[0105] W t ={ε t-N+1 ,ε t-N+2 ,…,ε t}

[0106] With each new error data ε t The calculation window will slide forward one step, and the earliest error value ε t-N+1 is removed, the new value ε t After adding the window, 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 stimuli, N[u] represents the measured system dynamic behavior, L[u] represents the corresponding linear system dynamic behavior, and inf(·) represents the lower bound, that is, in the set of all linearization methods In the linearization method, we find the method that minimizes the error. sup(·) represents the supremum, that is, in all input stimulus sets In , find the input stimulus that maximizes the error, and L represents the set of linearization methods.

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

[0112] δ0=σ threshold -σ0

[0113] The error data W in the window t , calculate the variance of the error data within the window Its expression is:

[0114]

[0115] In the above formula, represents the variance of the position error data of the robot's geometric parameters, Represents window W t The mean of all error values ​​in, N represents the window size, ε t-i Represents window W t The error value at the ti-th moment, t represents the current moment, and i represents the number of time steps offset from the current moment t.

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

[0117] If exists If δ>δ0, the nonlinearity of the current system is large, and the LM algorithm is selected for identification; if there is If 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 number of samples for calculating the variance, and the variance threshold σ threshold The setting will affect the choice of algorithm. Therefore, in order to further improve the adaptability and accuracy of the identification algorithm, the grid search method is used to adjust the sliding window size N and the variance threshold σ threshold The root mean square error RMSE of the position error is used as the objective function, and the optimization process is performed by minimizing the objective function, where the window size N and the variance threshold σ threshold is the parameter 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 obtained by grid search. threshold is 0.007, and the corresponding direction error is Figure 6 .

[0121] S300, 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.

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

[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 DH model is updated based on the optimized robot geometric parameter error identification result to obtain the updated Standard D-H model; based on the updated Standard DH model, the robot geometric parameters are calibrated to obtain the robot geometric parameter calibration result.

[0124] Furthermore, it should 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 volatility coefficient, the heuristic information influencing factor, and the pheromone concentration influencing factor. The geometric parameters after identification and correction are used as the input of the ant colony algorithm, the root mean square error RMSE of the position error is used as the fitness function, and the optimal geometric parameter error ΔX is output. The optimization process is carried out by minimizing the fitness function, and the function definition is as follows:

[0125]

[0126] After optimizing the identified geometric parameters through the ant colony algorithm, the corresponding direction error is Figure 7 As shown, the position error is Figure 8As shown, the comparison of experimental results shows that the position error is reduced from 13.03mm to 1.80mm by combining the LM algorithm and the LS algorithm for geometric error parameter identification based on nonlinearity. 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 comprehensively improved by 90.71%. Therefore, the embodiment of the present invention not only combines the advantages of the LM algorithm and the LS algorithm based on nonlinearity, but also illustrates that the present invention has a certain geometric parameter calibration accuracy through the embodiment.

[0127] Based on the optimized geometric parameter errors, the Standard DH model is updated and the calibration effect is verified on the computer.

[0128] In summary, if Figure 3 As shown, the embodiment of the present invention calculates the theoretical position and the actual position measured by the laser tracker through the Standard DH model to obtain the position error; performs dimension reduction processing on the Jacobian matrix through SVD to establish a low-order position error model; selects the LM algorithm or the LS algorithm for geometric parameter error identification according to the nonlinearity evaluation of the system, and uses the LM algorithm for identification when the nonlinearity is high, and uses the LS algorithm when it is low; and uses the ant colony algorithm to optimize the geometric parameters after identification and correction. The present invention not only improves the robustness of heavy-duty industrial robots in the process of geometric parameter calibration, but also avoids local optimal solutions and improves the calibration accuracy.

[0129] Compared with the prior art, the embodiments of the present invention have the following advantages:

[0130] 1) In the process of establishing the position error model, SVD is used to reduce the dimension of the Jacobian matrix J. By retaining significant eigenvalues ​​and eliminating redundant information, the accuracy of the Jacobian matrix J in the iterative identification process is guaranteed and the singularity of the matrix is ​​avoided.

[0131] 2) The damping factor λ of the LM algorithm is optimized by exhaustive search, which avoids the characteristic that the LM algorithm is sensitive to the damping factor λ set initially; the threshold σ of the sliding window N and the error variance is optimized by grid search. threshold , ensuring the applicability of nonlinearity and ensuring 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 used alternately for identification. When the system nonlinearity is high, the more robust LM algorithm is used for error identification; when the system nonlinearity is low, the more accurate LS algorithm is used to ensure the stability and accuracy of the identification process.

[0133] 4) The ant colony algorithm is introduced as a subsequent optimization step. The ant colony algorithm optimizes the identified and corrected geometric parameters by simulating the group intelligence mechanism of ants foraging, which can effectively avoid local optimal solutions and further improve the absolute positioning accuracy and stability of heavy-load industrial robots.

[0134] Reference Figure 2 , a geometric parameter calibration system of an industrial robot based on nonlinearity, comprising:

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

[0136] The second module 202 is used 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 used to optimize and update the robot geometric parameter error identification result and perform robot calibration processing in combination with the ant colony algorithm to obtain the robot geometric parameter calibration result.

[0138] The contents of the above method embodiments are all applicable to the present system embodiments. The functions specifically implemented by the present system embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

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

Claims

1. A method for calibrating geometric parameters of an industrial robot based on nonlinearity, characterized in that: The following steps are involved: Based on the Standard DH model, the position error of the robot end effector is obtained and a low-order position error model based on SVD is constructed; 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; Combined with the ant colony algorithm, the robot geometric parameter error identification results are optimized and updated, and the robot calibration is performed to obtain the robot geometric parameter calibration results.

2. The method for calibrating geometric parameters of an industrial robot based on nonlinearity according to claim 1, characterized in that: The step of obtaining the position error of the robot end effector based on the Standard DH model and constructing a low-order position error model based on SVD specifically includes: Based on the robot forward kinematics model, the multivariate nonlinear function of the end effector position with respect to the robot geometric parameters is obtained; Based on the Standard DH model, the Monte Carlo method is used to solve and calculate the multivariate nonlinear function to obtain the theoretical position of the robot's end effector. Obtain the base coordinate system of the Standard DH model and establish the world coordinate system of the robot end effector position information based on the robot base; According to the base coordinate system of the Standard DH model and the world coordinate system of the robot end effector position information, a homogeneous transformation relationship matrix is ​​constructed; Drive the robot to move, and use the laser tracker to measure and obtain the actual position of the robot's end effector in the world coordinate system; According to the actual position of the robot end effector in the world coordinate system, combined with the homogeneous transformation relationship matrix, the actual position of the robot end effector is obtained; Obtain the difference between the actual position of the robot end effector and the theoretical position of the robot end effector to obtain the position error of the robot end effector; Based on the position error of the robot end effector and the Jacobian matrix of the robot's 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 and 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 the Jacobian matrix based on the geometric parameter errors of the robot; Perform singular value SVD decomposition on the Jacobian matrix to obtain the left and right orthogonal matrices and the singular value matrix; Set a threshold, filter the singular value matrix, and obtain a filtered singular value matrix; Combine the selected singular value matrix with the left and right orthogonal matrices to reconstruct the optimized Jacobian matrix; Combining the robot's geometric parameter errors with the optimized Jacobian matrix, a low-order position error model based on SVD is constructed.

4. The method for calibrating geometric parameters of an industrial robot based on nonlinearity according to claim 3, characterized in that: The step of defining the nonlinearity of the robot, identifying the low-order position error model based on SVD, and obtaining the robot geometric parameter error identification result specifically includes: The low-order position error model based on SVD is optimized by combining logarithmic step size with linear step size to obtain the optimal damping factor; Based on the low-order position error model of SVD, the position error variance of the robot's geometric parameters is obtained and the position error variance threshold and sliding window of the robot's geometric parameters are set; The size of the sliding window and the position error variance threshold of the robot's geometric parameters are optimized by the grid search method to obtain the optimized sliding window and the position error variance threshold of the robot's geometric parameters; The position error data of the robot's geometric parameters are obtained through the optimized sliding window; Define the nonlinearity of the robot, calculate the nonlinearity value of the robot and obtain the variance of the position error data of the robot's geometric parameters; If the variance of the position error data of the robot geometric parameters is greater than the position error variance threshold of the optimized robot geometric parameters, the low-order position error model based on SVD is identified by the LM algorithm in combination with the optimal damping factor to obtain the first robot geometric parameter error identification result; If the variance of the position error data of the robot's geometric parameters is less than or equal to the position error variance threshold of the optimized robot's geometric parameters, the LS algorithm identifies the low-order position error model based on SVD to obtain the second robot's geometric parameter error identification result; The geometric parameter error identification result of the first robot is combined with the geometric parameter error identification result of the second robot to obtain the robot geometric parameter error identification result.

5. The method for calibrating geometric parameters of an industrial robot based on nonlinearity according to claim 4, characterized in that: The step of optimizing the low-order position error model based on SVD by combining the logarithmic step size with the linear step size 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, the objective function is searched by using a logarithmic step size as a variable step size to obtain preliminary search results; Based on the optimization range, a secondary search is performed on the preliminary search results by taking the linear step size as a fixed step size to obtain the optimal damping factor.

6. The method for calibrating geometric parameters of an industrial robot based on nonlinearity according to claim 5, characterized in that: The definition expression of the nonlinearity of the robot is specifically as follows: 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 stimuli, N[u] represents the measured system dynamic behavior, L[u] represents the corresponding linear system dynamic behavior, inf(·) represents the infimum operation, sup(·) represents the supremum operation, and L represents the set of linearization methods.

7. The method for calibrating geometric parameters of an industrial robot based on nonlinearity according to claim 6, 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, represents the variance of the position error data of the robot's geometric parameters, Represents window W t The mean of all error values ​​in, N represents the window size, ε t-W Represents window W t The error value at the ti-th moment, t represents the current moment, and i represents the number of time steps offset from the current moment t.

8. The method for calibrating geometric parameters of an industrial robot based on nonlinearity according to claim 7, 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 processing to obtain the robot geometric parameter calibration result specifically includes: The robot geometric parameter error identification results are optimized by using the ant colony algorithm to obtain the optimized robot geometric parameter error identification results; Based on the optimized robot geometric parameter error identification results, the Standard DH model is updated to obtain the updated Standard D-H model; Based on the updated Standard DH model, the robot geometric parameters are calibrated to obtain the robot geometric parameter calibration results.

9. A geometric parameter calibration system for industrial robots based on nonlinearity, characterized in that: Includes the following modules: The first module is used to obtain the position error of the robot end effector based on the Standard DH model and build a low-order position error model based on SVD; The second module is used 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; The third module is used to optimize and update the robot geometric parameter error identification results and perform robot calibration processing in combination with the ant colony algorithm to obtain the robot geometric parameter calibration results.

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