A method for kinematic calibration of an industrial robot

Abstract

The application discloses a kind of kinematics calibration methods of industrial robot, comprising the following steps: S1, pre-calibration base coordinate system and tool coordinate system;S2, establish kinematics error model, solve the number of redundant parameters of interference model;S3, determine specific redundant parameter, eliminate specific redundant parameter;S4, iteration identification is carried out to the remaining to-be-identified geometric error parameter after eliminating redundant parameter;S5, the result of iteration identification is converted into actual geometric parameter error, and is compensated to robot controller.The application realizes the quick conversion of measuring coordinate system {w} And base coordinate system {b}, reduce calibration time, when identifying robot parameter error, the problem of being sensitive to initial parameter condition is overcome by MIEKF algorithm, the preset parameter error can be identified, with the characteristics of high identification precision, fast convergence speed and high robustness, effectively improve calibration precision.

Description

Technical Field

[0001] This invention relates to the field of robotics, and in particular to a kinematic calibration method for industrial robots. Background Technology

[0002] Industrial robots are widely used in industries such as automotive, logistics, aerospace, and medical surgery due to their high flexibility. These industries have high requirements for the absolute positioning accuracy of robots. However, due to factors such as the manufacturing precision of core components, assembly precision, and environmental conditions, the absolute positioning accuracy of robots is usually at the millimeter level, which is difficult to meet the high-precision work requirements of these industries.

[0003] Robot kinematic calibration methods involve establishing an error parameter model based on the robot's kinematics, then using appropriate algorithms to identify and compensate for the main geometric parameter errors in the model, thereby improving positioning accuracy. While calibration compensation cannot completely eliminate errors, it effectively improves the robot's positioning accuracy, and this method is widely used by robot manufacturers.

[0004] However, the above methods also have certain technical drawbacks. Before calibration, each joint needs to be rotated individually in the robot's zero-position state to collect end-effector position data. Then, the base coordinate system and tool coordinate system are obtained through axis fitting, which increases the calibration steps and data acquisition time, and also reduces calibration efficiency. In addition, traditional calibration methods involve complex and time-consuming calculations and derivations when analyzing redundant parameters of the kinematic error model, and lack high-precision identification algorithms when identifying geometric parameter errors in the error model. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a kinematic calibration method for industrial robots.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: a kinematic calibration method for an industrial robot, comprising the following steps:

[0007] S1. Pre-calibrate the robot base coordinate system {b} and the robot end-effector coordinate system {t} to obtain the pose of the robot base coordinate system {b} relative to the measurement coordinate system {w}.

[0008] posture Depend on Obtained by inverse, To measure the pose of coordinate system {w} relative to robot base coordinate system {b}. Solving equation (1) yields the following results:

[0009]

[0010] in, To measure the attitude transformation of coordinate system {w} relative to robot base coordinate system {b}. To measure the position transformation of coordinate system {w} relative to robot base coordinate system {b};

[0011] S2. Establish a kinematic error model, measure the motion poses of m groups of robots, and identify the Jacobian matrix J in equation (2). m Singular value decomposition is performed to calculate the number of redundant parameters in solving the interference model;

[0012] ΔP m =J m ΔX (2)

[0013] Where, ΔP m Let denot be the total positional deviation of the m groups of robots' motion poses, and let ΔX be the column vector of errors for each parameter.

[0014] S3. Combine the number of redundant parameters obtained in step S2, and determine the specific redundant parameters through correlation and multicollinearity analysis, and then remove the specific redundant parameters.

[0015] S4. Iteratively identify the remaining geometric error parameters to be identified after removing redundant parameters;

[0016] Since the robot's motion pose is measured in m sets, the Jacobian matrix J is identified. m Composed of m calibration points, the Jacobian matrix J is identified by solving equation (3). m The scaling factor for each column after compression is l j Then, the diagonal variance matrix D formed by the scaling factors of each column is solved by equation (4);

[0017]

[0018] Where j is the number of geometric error parameters to be identified.

[0019] D = diag(l1, l2, ..., l) 33 (4)

[0020] Substitute the obtained diagonal variance matrix D into equation (5) to transform the identification Jacobian matrix of each calibration point into the system observation matrix H. k Substitute the obtained diagonal variance matrix D into equation (6) to transform the geometric error parameter to be identified at each calibration point into the system state parameter ΔX. k ,

[0021] H k =J k D -1 (5)

[0022] ΔX k =DΔX (6)

[0023] Then, iterative identification is performed according to equation (7).

[0024] ΔX k|k =ΔX k|k-1 +K k|k ΔZ k (7)

[0025] Where ΔX k|k For the iterative identification results, k|k represents the estimated value after the k-th iteration, k|k-1 represents the prior value after the k-th iteration, and K... k|k Let ΔZ be the Kalman gain matrix. k To update the residual vector;

[0026] Iterative identification begins from the first calibration point. When k is a multiple of m, it indicates that one iteration is complete. A total of several iterations are required to obtain the final iterative identification result ΔX. k|k ;

[0027] S5. The result of iterative identification ΔX k|k The error ΔX is converted from D to the actual geometric parameter. r And compensate to the robot controller.

[0028] To further elaborate, when determining the specific redundancy parameters in step S3, the W-Score transformation is used for J. m The standardization process is performed to obtain the standardization matrix W, and then the identification Jacobian matrix J is obtained by using the standardization matrix W through equation (8). m The correlation coefficient matrix W,

[0029]

[0030] To further elaborate, the Kalman gain matrix K in step S4 k|k As shown in equation (9),

[0031]

[0032] Where P k|k-1 For the prediction error covariance matrix, R k This is the covariance matrix for measuring noise.

[0033] To elaborate further, P k|k The prediction error covariance matrix P k|k-1 The updated and corrected covariance matrix is ​​shown in equation (10).

[0034] P k|k＝ γk (IK k|k H k )P k|k-1 (IK k|k H k ) T +K k|k R k K k|k T (10)

[0035] Where γ k It is a forgetting factor.

[0036] To further elaborate, step S4 updates the residual vector ΔW. k As shown in equation (11),

[0037] ΔZ k =Z k -H k ΔX k|k -1 (11)

[0038] Among them, Z k This represents the position error of the robot's end effector.

[0039] The beneficial effects of this invention are as follows:

[0040] (I) This invention proposes a kinematic calibration method for industrial robots based on a pre-calibrated base coordinate system and the MIEKF algorithm to improve the absolute positioning accuracy of the robot. This method takes into account the efficiency of data acquisition by the laser tracker, and pre-calibrates the robot's base coordinate system {b} and tool coordinate system {t} based on the acquired end position data, so as to realize the rapid conversion between the measurement coordinate system {w} and the base coordinate system {b} and reduce the calibration time.

[0041] (ii) The present invention establishes a kinematic error model based on the principle of differential transformation. The error model includes the base coordinate system, tool coordinate system, deceleration ratio and MDH parameter errors. Furthermore, based on the requirement of complete minimum continuity of the error model, redundant parameters of the Jacobian matrix are identified and removed using correlation coefficient matrix and complex collinearity analysis, thus ensuring a more accurate error model.

[0042] (III) The MIEKF algorithm used overcomes the problem of sensitivity to initial parameter conditions when identifying robot parameter errors. It can almost completely identify the preset parameter errors and has the characteristics of high identification accuracy, fast convergence speed and high robustness. It further improves the calibration accuracy and provides a new method and idea for industrial robot kinematic calibration technology. Attached Figure Description

[0043] Figure 1 This is a schematic diagram of the process of the present invention.

[0044] Figure 2 A schematic diagram of the coordinate system for robot calibration. Detailed Implementation

[0045] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings.

[0046] A kinematic calibration method for an industrial robot includes the following steps:

[0047] S1. Pre-calibrate the robot base coordinate system {b} and the robot end-effector coordinate system {t} to obtain the pose of the robot base coordinate system {b} relative to the measurement coordinate system {w}.

[0048] Before performing pre-calibration, the following principles must be clarified: robot kinematic calibration must first be performed in the robot's base coordinate system {b}, and the end-effector position data collected by the measuring instrument is based on its own measurement coordinate system {w}, which is specifically the laser tracker's measurement coordinate system. Therefore, pre-calibrating the robot's base coordinate system {b} and the robot's end-effector coordinate system {t} facilitates kinematic calibration.

[0049] Equation (12) is obtained based on the pose relationship between the measurement coordinate system {w}, the robot base coordinate system {b}, the robot end-effector coordinate system {t}, and the robot end-effector flange center coordinate system {e}.

[0050]

[0051] in, The pose transformation of the robot's end flange center coordinate system {e} relative to the robot's base coordinate system (b) is defined as follows: For the position transformation of the robot end flange center coordinate system {e} relative to the robot base coordinate system {b}, It is a 3x3 identity matrix, that is This represents the position transformation of the robot's end-effector coordinate system {t} relative to the robot's end-effector flange center coordinate system {e}. The unknown quantity to be solved;

[0052] To measure the attitude transformation of coordinate system {w} relative to robot base coordinate system {b}. To measure the position transformation of coordinate system {w} relative to robot base coordinate system {b}. This represents the attitude transformation of the robot's end-effector coordinate system {t} relative to the measurement coordinate system {w}.

[0053] The position transformation of the robot's end-effector coordinate system {t} relative to the measurement coordinate system {w} can be obtained by acquiring data using a laser tracker.

[0054] Equation (12) is transformed to obtain equation (13):

[0055]

[0056] Subsequently via Kronek The operation and straightening operator vec() can transform equation (13) into equation (14):

[0057]

[0058] Where I3 is the third-order identity matrix;

[0059] Since the calibration of this invention measures the end-effector positions of m groups of robots, the above equation (14) can be transformed into an overdetermined system of equations (15):

[0060] E wm =pinv(H wm )*P wm (15)

[0061] Among them, H wm P is a 3m×15 matrix. wm E is a 3m×1 column vector. wm Given a 1×15 column vector to be solved, E can be obtained using the least squares (LS) algorithm. wm Thus, the part to be calibrated can be obtained.

[0062] posture Depend on Obtained by inverse, To measure the pose of coordinate system {w} relative to robot base coordinate system {b}. Solving equation (1) yields the following results:

[0063]

[0064] in, To measure the attitude transformation of coordinate system {w} relative to robot base coordinate system {b}. To measure the position transformation of coordinate system {w} relative to robot base coordinate system {b}, thereby completing the pre-calibration of robot base coordinate system {b} and robot end-effector coordinate system {t}.

[0065] S2. Establish the kinematic error model. The robot's forward kinematics is obtained by establishing MDH models for each joint and then multiplying them together. Therefore, the MDH model for the coordinate system is:

[0066]

[0067] Due to manufacturing and assembly issues, the geometric parameters of each joint in the MDH model contain errors, resulting in the actual transformation of adjacent joints becoming... in This is the differential change of coordinate system {i} relative to coordinate system {i-1}. Small errors exist in the motor, reducer, and belt-gear transmission structures of each joint in an industrial robot, causing discrepancies between the actual and theoretical rotation values ​​of the joint commands from the robot controller. Therefore, this invention introduces a reduction ratio error r. i When there is no reduction ratio error, r i =1, then the actual rotation value of the joint angle is r. i θ i Since the MDH model is established by setting six motion parameters, namely angle θ, offset d, link a, angle α, angle β, and reduction ratio r, it can be known that... It is a linear function with six motion errors. Expanding it and ignoring higher-order differential terms,

[0068]

[0069] In the above formula, Δθ i , Δd, Δa i , Δα i Δβ i Δr i These correspond to the small errors in the joint coordinate system of the MDH model, namely, angle θ, offset d, link a, angle α, angle β, and reduction ratio r.

[0070] This represents the differential error of the current joint coordinate system i relative to the previous joint coordinate system i-1, as shown in equation (16):

[0071]

[0072] in, The pose of the robot in its current joint coordinate system i relative to the previous joint coordinate system i-1; This represents the actual pose of the robot's current joint coordinate system i relative to the previous joint coordinate system i-1.

[0073] The differential error matrix between adjacent joints relative to the current coordinate system {i} is shown in equation (17):

[0074]

[0075] In equation (17) This represents the positional error between adjacent joints. This represents the attitude error of adjacent joints.

[0076] Combined with appendix Figure 2 As shown, line ① represents the relative position of the robot end-effector coordinate system {t} in the measurement coordinate system {w}; line ② represents the relative position of the theoretical base coordinate system {b′} obtained from the pre-calibrated robot base coordinate system {b} and the measurement coordinate system {w}; line ③ represents the relative position of the theoretical tool coordinate system {t′} obtained from the pre-calibrated robot end-effector coordinate system {t} and the measurement coordinate system {w}. Since the actual robot kinematic model has geometric parameter errors, both the pre-calibrated robot base coordinate system {b} and the robot end-effector coordinate system {t} have deviations. Line ④ represents the relative position of the theoretical base coordinate system {b′} and the theoretical end-effector center coordinate system {e′}; line ⑤ represents the relative position of the pre-calibrated robot base coordinate system {b} and the robot end-effector center coordinate system {e}; and line ⑥ represents the relative position of the pre-calibrated robot end-effector center coordinate system {e} and the robot end-effector coordinate system {t}.

[0077] Therefore, when establishing the differential error model, it is necessary to consider the deviations of the base coordinate system and the tool coordinate system, as well as the actual end-effector pose of the robot caused by the errors of each joint parameter. and the nominal pose of the robot The relationship is shown in equation (18):

[0078]

[0079] Combining equations (16) and (18), we can obtain equation (19):

[0080]

[0081] in, It is the error matrix of position and orientation obtained by the differential transformation of the robot's end-effector pose relative to the measurement coordinate system; let ΔP = [d x n d y n d z n ] T ΔP is the total position deviation of the robot's end effector relative to the base coordinates. Combining equations (17) and (19), we can obtain equation (20):

[0082]

[0083] Since the model was set with 40 parameters,

[0084] ΔX in formula (20)=[Δθ Δd Δa Δα Δβ Δr Δb Δt]T The column vector of errors for each parameter is 40×1; Δt=[dt x dt y dt z ] T Differential errors are generated when pre-calibrating the tool coordinate system, where dt x dt y dt z Δb is the differential error of the pre-calibrated robot end-effector coordinate system {t} relative to the robot end-effector flange center coordinate system {e}; J is the differential error generated when calibrating the base coordinate system; J is the 3×40 identification Jacobian matrix.

[0085] Specifically, Δb = [db] x db y db z δb x δb y δb z ] T db x db y db z δb x δb y δb z It is the differential error of the pre-calibrated base coordinates relative to the measurement coordinate system w.

[0086] Since the established complete kinematic error model has redundant parameters, this invention removes redundant parameters through correlation coefficient and multicollinearity analysis. The number of redundant parameters needs to be determined first.

[0087] Measure the motion poses of m groups of robots, and identify the Jacobian matrix J in equation (2). m Singular value decomposition is performed to calculate the number of redundant parameters in the solution disturbance model:

[0088] ΔP m =J m ΔX (2)

[0089] Where, ΔP m Let denot be the total positional deviation of the motion poses of m groups of robots, and Δx be the column vector of errors for each parameter.

[0090] The identification Jacobian matrix J in equation (2) m Singular value decomposition yields equation (21):

[0091]

[0092] In equation (21), ∑=diag(σ1,σ2,…,σ r ), σ is J mThe eigenvalues ​​of the matrix, r (r≤40), are J. m The rank, set σ r >10 -5 That's J m The effective rank. Since there are a total of 40 parameters when building the model, and 33 eigenvalues ​​are obtained, i.e., r = 33, then 40 - 3 = 7 can be obtained as 7 redundant parameters.

[0093] In addition, U in equation (21) 3m V 40 It is obtained based on singular value decomposition, i.e., svd(J m ) = U*S*V, where the parameters of USV correspond to those above. This invention only uses eigenvalues.

[0094] S3. Combine the number of redundant parameters obtained in step S2, and determine the specific redundant parameters through correlation and multicollinearity analysis, and then remove the specific redundant parameters.

[0095] When determining specific redundancy parameters, the W-Score transform is used for J. m The standardization process is performed to obtain the standardization matrix W, and then the identification Jacobian matrix J is obtained by using the standardization matrix W through equation (8). m The correlation coefficient matrix W,

[0096]

[0097] The specific expression for z in equation (8) is shown in equation (22):

[0098]

[0099] The matrix elements in equation (22) are specifically obtained through the following equations (23), (24), and (25):

[0100]

[0101]

[0102]

[0103] According to equation (8), db z and d1, δb z and Δθ1, dt z and Δd6, d2 and d3, dt x The correlation coefficients between Δθ1 and Δa6 are both 1, so there is a correlation between each of them. Therefore, the correlation parameters d1, Δθ1, Δd6, d2 and Δa6 are selected for removal.

[0104] In addition, the identification Jacobian matrix columns corresponding to Δθ6 and Δα6 are respectively related to the tool coordinate system deviation dt. x dt y dt z The corresponding identification Jacobian matrix columns exhibit multicollinearity, i.e.:

[0105] J m (Δθ6)=-t y J m (dt x )+t x J m (dt y (26)

[0106] J m (Δα6)=-t z J m (dt y )+t x K m (dt z (27)

[0107] t in equations (26) and (27) x t y and t z Since Δθ6 and Δα6 are the xyz components of the tool coordinate system position, they are also redundant parameters.

[0108] In summary, Δθ1, Δθ6, Δd1, Δd2, Δd6, Δa6, and Δα6 are redundant parameters. After removing the redundant parameters from the interference model, the number of geometric error parameters to be identified becomes 33. Therefore, J m It becomes 3m×33, ΔX is a column vector of 33×1, ΔP m It is a column vector of 3m×1.

[0109] S4. Iteratively identify the remaining geometric error parameters to be identified after removing redundant parameters;

[0110] The Modified Iterated Extended Kalman Filter (MIEKF) algorithm is an improved form of the EKF algorithm. Its principle addresses the issue of different dimensions in the identification Jacobian matrix parameters of the position error model by making the parameters dimensionless. This is achieved through column scaling of the identification Jacobian matrix to normalize the parameters, ensuring that the influence of each column on the error of each parameter is consistent, thus improving the robustness of the identified state parameters. Furthermore, a forgetting factor is proposed to optimize the covariance matrix to prevent it from becoming ill-formed, thereby ensuring rapid convergence of the state parameters. Finally, it utilizes observation-based estimation iterations, keeping the measurement position unchanged in each iteration and updating the state parameters only through the residual vector, thus updating the observation equation and finding the optimal state parameter estimate.

[0111] Since the robot's motion pose is measured in m sets, the Jacobian matrix J is identified. m Composed of m calibration points, the Jacobian matrix J is identified by solving equation (3). m The scaling factor for each column after compression is l j Then, the diagonal variance matrix D formed by the scaling factors of each column is solved by equation (4);

[0112]

[0113] Where j is the number of geometric error parameters to be identified, i.e., j = 33;

[0114] D = diag(l1, l2, ..., l) 33 (4)

[0115] Substitute the obtained diagonal variance matrix D into equation (5) to transform the identification Jacobian matrix of each calibration point into the system observation matrix H. k Substitute the obtained diagonal variance matrix D into equation (6) to transform the geometric error parameter to be identified at each calibration point into the system state parameter ΔX. k ,

[0116] H k =J k D -1 (5)

[0117] ΔX k =DΔX (6)

[0118] J in equation (5) k It is the identification Jacobian matrix of a single calibration point, where k represents the k-th point, and there are a total of m points;

[0119] The system state equation of equation (6) is shown in equation (28).

[0120] ΔX k|k-1 =A k-1 ΔX k-1|k-1 +w k-1 (28)

[0121] A in equation (28) k-1 Let A be the state transition matrix. Since the geometric parameter error does not change with the robot's spatial position, then A... k-1 =I;w k-1 This is the noise vector of the system's random process;

[0122] Z k The robot's end-effector position error, ΔP, is related to ΔX. k|k-1 The specific relationship is shown in equation (29).

[0123] Z k =H k ΔX k|k-1 +V k (29)

[0124] V in equation (29) k For measuring noise;

[0125] Then, iterative identification is performed according to equation (7). The improved iterative extended Kalman filter steps are as follows:

[0126] Prediction of geometric parameter errors: ΔX k|k-1 =ΔX k-1|k-1

[0127] Prediction error covariance matrix: P k|k-1 =P k-1|k-1 +Q k-1 (30)

[0128] In equation (30) Q k-1 It is the covariance, Q = 10 -5 I 33×33 P 0|0 =I 33×33 ;

[0129] Kalman gain matrix:

[0130] In equation (9), P k|k-1 For the prediction error covariance matrix, R k To measure the covariance matrix of the noise, R k =10 -3 I 3×3 ;

[0131] Update residual vector: ΔZ k =Z k -H k ΔXk|k-1 (11)

[0132] Z in equation (11) k This refers to the position error of the robot's end effector.

[0133] Update the geometric error state equation: ΔX k|k =ΔX k|k-1 +K k|k ΔZ k (7)

[0134] ΔX in equation (7) k|k For the iterative identification results, k|k represents the estimated value after the k-th iteration, k|k-1 represents the prior value after the k-th iteration, and K... k|k Let ΔZ be the Kalman gain matrix. k To update the residual vector;

[0135] For equation (30), P k|k The prediction error covariance matrix P k|k-1 The updated and corrected covariance matrix is ​​shown in equation (10).

[0136] P k|k =γ k (IK k|k H k )P k|k-1 (IK k|k H k ) T +K k|k R k K k|k T (10)

[0137] Where γ k The forgetting factor is determined by equation (31):

[0138]

[0139] In equation (31), tr() is the trace of the matrix, N k L k All of these are known parameters for determining the forgetting factor;

[0140] Initialization error ΔX 0|0 =0; k|k-1 represents the prior value of the k-th iteration, and k|k represents the estimated value after the k-th iteration; when k is a multiple of m, it indicates that one round of iteration is completed, and it is necessary to restart the iteration from the first calibration point. The iteration stops after 4 rounds of updates, and the final iterative identification result ΔX is obtained. k|k ;

[0141] S5. The result of iterative identification ΔX k|kThe D is converted into the actual geometric parameter error ΔX using equation (32). r And compensate to the robot controller.

[0142] ΔX r =D -1 ΔX k|k (32)

[0143] The above description is not intended to limit the scope of the present invention. Any modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention shall still fall within the scope of the present invention.

Claims

1. A kinematic calibration method for an industrial robot, characterized in that, Includes the following steps: S1. Pre-calibrate the robot base coordinate system {b} and the robot end-effector coordinate system {t} to obtain the pose of the robot base coordinate system {b} relative to the measurement coordinate system {w}. ; posture Depend on Obtained by inverse, For measuring coordinate system Relative to the robot's base coordinate system The position, Solving equation (1) yields the following: （1） in, For measuring coordinate system Relative to the robot's base coordinate system attitude transformation, For measuring coordinate system Relative to the robot's base coordinate system Position transformation; S2. Establish a kinematic error model, measure the motion poses of m groups of robots, and identify the Jacobian matrix in equation (2). Singular value decomposition is performed to calculate the number of redundant parameters in solving the interference model; （2） in, Let be the total positional deviation of the motion pose of the m groups of robots. This is a column vector of errors for each parameter; S3. Combine the number of redundant parameters obtained in step S2, and determine the specific redundant parameters through correlation and multicollinearity analysis, and then remove the specific redundant parameters. S4. Iteratively identify the remaining geometric error parameters to be identified after removing redundant parameters; Since the robot's motion pose is measured in m sets, the Jacobian matrix needs to be identified. Composed of m calibration points, the Jacobian matrix is ​​identified by solving equation (3). The scaling factor for each column after compression is Then, the diagonal variance matrix D formed by the scaling factors of each column is solved by equation (4); （3） Among them The number of geometric error parameters to be identified. （4） Substitute the obtained diagonal variance matrix D into equation (5) to transform the identification Jacobian matrix of each calibration point into the system observation matrix. Substitute the obtained diagonal variance matrix D into equation (6) to transform the geometric error parameters to be identified at each calibration point into system state parameters. , , where J is the identification Jacobian matrix, and k represents the k-th iteration (5) , where ∆X is the column vector of errors for each parameter (6) Then, iterative identification is performed according to equation (7). （7） in For the iterative identification results, Indicates the first The estimated value after the next iteration Indicates the first Prior values ​​for the next iteration Here is the Kalman gain matrix. To update the residual vector; Iterative identification begins from the first calibration point, and... When the time is reached, it indicates that one iteration is complete. A total of several iterations are required to obtain the final iteration identification result. ; S5. The results of iterative identification pass Converted to actual geometric parameter error And compensate to the robot controller.

2. The kinematic calibration method for an industrial robot according to claim 1, characterized in that: When determining the specific redundancy parameters in step S3, the Z-Score transformation is used. Perform standardization to obtain a standardized matrix. Then, the normalized matrix is ​​used through equation (8). Find the identification Jacobian matrix Correlation coefficient matrix , （8）。 3. The kinematic calibration method for an industrial robot according to claim 1, characterized in that: Kalman gain matrix in step S4 As shown in equation (9), （9） in For the prediction error covariance matrix, This is the covariance matrix for measuring noise.

4. The kinematic calibration method for an industrial robot according to claim 3, characterized in that: It is the prediction error covariance matrix The updated and corrected covariance matrix is ​​shown in equation (10). （10） in It is a forgetting factor.

5. The kinematic calibration method for an industrial robot according to claim 1, characterized in that: Step S4: Update the residual vector As shown in equation (11), （11） in, This represents the position error of the robot's end effector.

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