A parameter compensation method, device, medium, equipment and program product of an industrial robot

Abstract

The application belongs to the technical field of industrial robot kinematics parameter calibration, and particularly relates to an industrial robot parameter compensation method, device, medium, equipment and program product. The application discloses an industrial robot parameter compensation method, which comprises the following steps: acquiring actual posture parameter groups of an operation end of a target robot when the operation end reaches each preset end position; determining theoretical end positions corresponding to each preset end position according to the actual posture parameter groups and a preset kinematics equation; determining corresponding end position errors according to the preset end positions and the corresponding theoretical end positions; and determining a posture parameter compensation strategy for the target robot according to all the actual posture parameter groups and all the end position errors. The application solves the problem that the confidence range and confidence interval of each identified parameter cannot be known in the prior art, and achieves identification of untrusted parameters, so that the calibration accuracy is improved.

Description

Technical Field

[0001] This invention belongs to the technical field of kinematic parameter calibration for industrial robots, specifically relating to a parameter compensation method, device, medium, equipment, and program product for industrial robots. Background Technology

[0002] Industrial robots are increasingly widely used in manufacturing, and their absolute positioning accuracy is a key indicator for achieving precision operations. Due to manufacturing tolerances and long-term wear and tear, there are slight errors between the actual kinematic parameters of the robot and the nominal design values, which need to be corrected through kinematic calibration.

[0003] Existing calibration methods often employ algorithms such as least squares, extended Kalman filtering, particle swarm optimization, and Levenberg-Marquardt (LM) to substitute multiple sets of end-effector pose measurement data into an error model and solve for the DH parameter correction values. These methods only output a single optimal parameter point estimate and cannot quantify the uncertainty of the calibration results, i.e., they cannot determine the confidence range and confidence interval of each identified parameter. Forcibly compensating for unreliable parameters to the controller not only fails to improve accuracy but may also introduce overfitting errors. Summary of the Invention

[0004] This application discloses a parameter compensation method for an industrial robot, comprising: acquiring actual posture parameter sets of the target robot's end effector when it reaches various preset end effector positions; determining theoretical end effector positions corresponding to each preset end effector position based on the actual posture parameter sets and preset kinematic equations; determining corresponding end effector position errors based on the preset end effector positions and the corresponding theoretical end effector positions; determining a posture parameter compensation strategy for the target robot and a covariance matrix for the posture parameter compensation strategy based on all the actual posture parameter sets and all the end effector position errors; determining usage recommendations for the posture parameter compensation strategy based on the covariance matrix and the posture parameter compensation strategy; and compensating the posture parameters of the target robot based on the posture parameter compensation strategy and the usage recommendations. This method solves the problem in the prior art where the confidence range and confidence interval of each identified parameter cannot be determined. It enables the differentiation of unreliable parameters, thereby improving calibration accuracy.

[0005] To solve the above-mentioned technical problems, the technical solution provided by the present invention includes five aspects.

[0006] In a first aspect, this application provides a parameter compensation method for an industrial robot, comprising: acquiring actual posture parameter sets when the end effector of a target robot reaches various preset end effector positions; determining theoretical end effector positions corresponding to each preset end effector position based on the actual posture parameter sets and preset kinematic equations; determining corresponding end effector position errors based on the preset end effector positions and the corresponding theoretical end effector positions; determining a posture parameter compensation strategy for the target robot and a covariance matrix for the posture parameter compensation strategy based on all the actual posture parameter sets and all the end effector position errors; determining usage recommendations for the posture parameter compensation strategy based on the covariance matrix and the posture parameter compensation strategy; and compensating the posture parameters of the target robot based on the posture parameter compensation strategy and the usage recommendations.

[0007] In some embodiments, determining the attitude parameter compensation strategy for the target robot and the covariance matrix for the attitude parameter compensation strategy based on all the actual attitude parameter sets and all the end-effector position errors includes: adding a preset perturbation amount to each attitude parameter in the actual attitude parameter sets to obtain multiple sets of perturbed attitude parameter sets; calculating the perturbed end-effector position corresponding to the perturbed attitude parameter set using the kinematic equations; organizing all the perturbed end-effector positions and the corresponding perturbed attitude parameter sets into a global perturbed position set; removing duplicates from the global perturbed position set based on all the end-effector position errors to obtain an independent parameter index set; and determining the attitude parameter compensation strategy and the covariance matrix based on each of the end-effector position errors and the independent parameter index set.

[0008] In some embodiments, determining the attitude parameter compensation strategy and the covariance matrix based on each of the end-position errors and the independent parameter index set includes: determining the weight components of each preset end position in three directions based on each of the end-position errors; and determining the attitude parameter compensation strategy and the covariance matrix based on the weight components of all preset end positions, the end-position errors, and the independent parameter index set.

[0009] In some embodiments, determining the usage recommendation for the attitude parameter compensation strategy based on the covariance matrix and the attitude parameter compensation strategy includes: constructing a proposal distribution and a prior distribution based on the attitude parameter compensation strategy and the covariance matrix; generating a posterior sample set for each parameter in the attitude parameter compensation strategy based on the proposal distribution and the prior distribution; determining a confidence interval for each parameter based on each of the posterior sample sets; and determining a usage recommendation for each parameter in the attitude parameter compensation strategy based on the confidence interval.

[0010] In some embodiments, determining the attitude parameter compensation strategy based on the weighted components of all preset end positions, the end position error, and the independent parameter index set includes: constructing a compensation strategy calculation formula including a damping coefficient based on the weighted components, the end position error, and the independent parameter index set; calculating the current compensation strategy for the attitude parameters based on the compensation strategy calculation formula; calculating trial compensation parameters based on the current compensation strategy and the independent parameter index set; constructing a gain ratio calculation formula based on the trial compensation parameters, the independent parameter index set, the weighted components of all preset end positions, and the damping coefficient; calculating the gain ratio under the current compensation strategy based on the gain ratio calculation formula; updating the damping coefficient in the compensation strategy calculation formula and the gain ratio calculation formula based on the gain ratio; and determining the attitude parameter compensation strategy based on the current compensation strategy when the current compensation strategy meets preset conditions.

[0011] In some embodiments, determining the covariance matrix based on the weight components of all the preset end positions, the end position error, and the set of independent parameter indices includes: determining the final residual based on the end position error when the current compensation strategy meets preset conditions; determining the robust scaling estimate of the current compensation strategy based on the final weight components and the final residual when the current compensation strategy meets preset conditions; and determining the covariance matrix based on the robust scaling estimate, the final weight components, and the set of independent parameter indices.

[0012] Secondly, this application proposes a parameter compensation device for an industrial robot, comprising: a first acquisition module for acquiring actual posture parameter sets when the end effector of a target robot reaches various preset end effector positions; a first determination module for determining theoretical end effector positions corresponding to each preset end effector position based on the actual posture parameter sets and preset kinematic equations; a second determination module for determining corresponding end effector position errors based on the preset end effector positions and the corresponding theoretical end effector positions; a third determination module for determining a posture parameter compensation strategy for the target robot and a covariance matrix for the posture parameter compensation strategy based on all the actual posture parameter sets and all the end effector position errors; a fourth determination module for determining usage recommendations for the posture parameter compensation strategy based on the covariance matrix and the posture parameter compensation strategy; and a first execution module for compensating the posture parameters of the target robot based on the posture parameter compensation strategy and the usage recommendations.

[0013] Thirdly, this application proposes a computer electronic production apparatus, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of any of the methods described in the first aspect.

[0014] Fourthly, this application proposes a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in any one of the first aspects of the claims.

[0015] Fifthly, this application proposes a computer program product comprising a computer program that, when executed by a processor, implements the steps of the method described in any of the first aspects.

[0016] This application discloses a parameter compensation method for an industrial robot, comprising: acquiring actual posture parameter sets of the target robot's end effector when it reaches various preset end effector positions; determining theoretical end effector positions corresponding to each preset end effector position based on the actual posture parameter sets and preset kinematic equations; determining corresponding end effector position errors based on the preset end effector positions and the corresponding theoretical end effector positions; determining a posture parameter compensation strategy for the target robot and a covariance matrix for the posture parameter compensation strategy based on all the actual posture parameter sets and all the end effector position errors; determining usage recommendations for the posture parameter compensation strategy based on the covariance matrix and the posture parameter compensation strategy; and compensating the posture parameters of the target robot based on the posture parameter compensation strategy and the usage recommendations. This method solves the problem in the prior art where the confidence range and confidence interval of each identified parameter cannot be determined. It enables the differentiation of unreliable parameters, thereby improving calibration accuracy. Attached Figure Description

[0017] One or more embodiments are illustrated by way of example with reference to the accompanying drawings, and these illustrative descriptions do not constitute a limitation on the embodiments.

[0018] Figure 1 The main flowchart of a parameter compensation method for an industrial robot provided in this application embodiment; Figure 2 A main structural block diagram of a parameter compensation device for an industrial robot provided in this application embodiment; Figure 3 This is a structural block diagram of a computer electronic production equipment provided in an embodiment of this application. Detailed Implementation

[0019] Industrial robots are increasingly widely used in manufacturing, and their absolute positioning accuracy is a key indicator for achieving precision operations. Due to manufacturing tolerances and long-term wear and tear, there are slight errors between the actual kinematic parameters of the robot and the nominal design values, which need to be corrected through kinematic calibration.

[0020] Existing calibration methods often employ algorithms such as least squares, extended Kalman filtering, particle swarm optimization, and Levenberg-Marquardt (LM) to substitute multiple sets of end-effector pose measurement data into an error model and solve for the DH parameter correction values. These methods only output a single optimal parameter point estimate and cannot quantify the uncertainty of the calibration results, i.e., they cannot determine the confidence range and confidence interval of each identified parameter. Forcibly compensating for unreliable parameters to the controller not only fails to improve accuracy but may also introduce overfitting errors.

[0021] Furthermore, existing calibration methods struggle to systematically analyze parameter identifiability. In practical calibration, certain parameter sets in the observation equations may exhibit approximate linear correlations, resulting in highly similar effects of these parameters on the end-effector pose, making them indistinguishable from limited measurement data. Traditional methods lack quantitative diagnostic tools for identifiability, making it difficult for engineers to determine which parameters can be reliably compensated and which should be removed from the model.

[0022] Furthermore, existing methods often fail to propagate the uncertainty of parameter identification to the end-point positioning error, making it impossible to predict the range of residual absolute positioning accuracy after calibration before implementing compensation. This restricts the quantitative decision-making of accuracy attainment and compensation strategies in engineering projects.

[0023] To address the aforementioned issues, existing research has incorporated a Bayesian framework into robot kinematic parameter identification, using Markov Chain Monte Carlo (MCMC) sampling to obtain the complete posterior distribution of parameters, thereby quantifying calibration uncertainty. However, current Bayesian calibration methods often start from broad, uninformative priors and identify a limited number of parameters. In high-dimensional parameter spaces, MCMC requires an extremely long burn-in phase to converge to the high-probability region, resulting in enormous computational costs and hindering practical engineering applications. Furthermore, existing Bayesian methods often directly sample all nominal parameters without performing parameter identifiability analysis before sampling to eliminate redundant parameters, leading to excessively high parameter space dimensionality and further exacerbating the computational burden and sampling difficulties.

[0024] To address the aforementioned technical problems, this invention proposes a parameter compensation method for industrial robots. The implementation details of this parameter compensation method for industrial robots are described below. The following content is for illustrative purposes only and is not essential for implementing this solution.

[0025] Example 1: like Figure 1 As shown, this application provides a parameter compensation method for an industrial robot. This method is applicable to electronic production equipment, which can be a server, mobile terminal, computer, cloud platform, etc. The data processing functionality of the production equipment provided in this application embodiment can be implemented by the processor of the electronic production equipment calling program code, wherein the program code can be stored in a computer storage medium. The parameter compensation method for the industrial robot includes: Step S1: Obtain the actual posture parameter set when the target robot's end effector reaches each preset end effector position.

[0026] The target robot in this application is a six-degree-of-freedom industrial robot. Since the data collected by the measuring instrument is in the instrument's own coordinate system, it needs to be transformed to the robot's base coordinate system.

[0027] Specifically, this application first sets a preset number of end-effector positions, then controls the robot to reach each preset end-effector position, at which point the robot's actual posture parameters are acquired. Since the actual posture parameters acquired at this time are based on the measuring instrument's own coordinate system, they need to be transformed to the robot's base coordinate system.

[0028] When performing attitude parameter coordinate transformation, it is necessary to first achieve axis fitting between the robot and the measuring instrument. The axis fitting process is as follows: 1. Determine the first axis line: Keep Do not move, only drive Rotate within the effective range (within the measuring range of the instrument), and record a set of data at regular intervals, for a total of... The set of points is used to fit axis 1.

[0029] 2. Determine the second axis line: Fixed at 0° Do not move, only drive Rotate within the effective range (within the measuring range of the instrument), and record a set of data at regular intervals, for a total of... The group uses these points to fit axis 2.

[0030] After fitting the axis, the actual attitude parameters corresponding to each preset end position acquired by the measuring instrument can be transformed into the robot's base coordinate system. The specific coordinate transformation process is as follows: 1. Confirm axis: Using the data collected when determining the first axis, a spatial circle is fitted, the plane containing the circle is calculated, and the center of the circle is calculated. Calculation after The plane unit normal vector That is The direction of the axis.

[0031] 2. Confirm axis: Using the data collected when determining the second axis, a spatial circle is fitted, the plane containing the circle is calculated, and the center of the circle is calculated. Calculation after The plane unit normal vector That is The direction of the axis, here The direction of the axis is not necessarily the same as They may be the same, or they may be opposite; it depends on the specific robot.

[0032] 3. Confirm axis: Using cross product, .

[0033] 4. Verification of axis pose and fitting quality: Before performing origin calculations, the two extracted axes need to be geometrically constrained to determine the quality of point cloud acquisition and fitting. Perpendicularity check: Calculate the normal vector and If the spatial angle deviates from 90° by a value greater than the preset angle threshold, it indicates a serious tilt, and the data for axis fitting needs to be re-acquired.

[0034] Intersection check (common perpendicular determination): Calculate starting from . , The first axis is the direction, and with Starting point The length of the common perpendicular segment between the first and second axes is given by the direction of the first axis. Ideally, the first and second axes of an industrial robot should intersect in space (the length of the common perpendicular should be close to 0). If the calculated length of the common perpendicular segment exceeds a preset spatial distance threshold, it is determined that a severe "skewed misalignment" has occurred between the two axes in space. This usually means that instrument drift or severe local outliers have occurred during the data acquisition process, and the axis fitting data needs to be reacquired.

[0035] 5. Calculate the origin of the base coordinate system. calculate and The midpoint of the common perpendicular is used to obtain the center of the circle in the coordinate system of joint 1. The coordinates are then used to translate the robot's base structure offset distance along the negative Z-axis. Find the origin of the base coordinate system. .

[0036] 6. Generate the homogeneous transformation matrix Through the above steps, the three axial vectors x, y, z of the robot base coordinate system and the origin coordinate p are determined in the measuring instrument coordinate system (C).

[0037] 7. Coordinate Transformation Let the measured raw data be (Actual attitude parameters), their coordinates in the robot's base coordinate system are: Then there is By transforming the measured raw data, the position coordinates of each measured pose in the robot's base coordinate system can be obtained.

[0038] 8. Outlier Handling To address outliers that may occur in complex industrial environments due to sensor obstruction, optical path interference, or mechanical vibration, this step introduces the Huber loss function for robustness processing.

[0039] Specifically, the system is based on the nominal standard deviation of the measuring equipment. Automatically calculate residual discrimination threshold , usually take Among them, the scaling factor The value ranges from 1.345 to 2.0. This applies to the position residual of a single measurement point. Its loss function The structure is as follows: when When using squared loss The property that its second derivative is constant is used to ensure fast convergence under normal measurement noise. when When switching to linear loss By limiting the maximum contribution of outliers to the gradient, the negative interference of gross errors caused by disturbances on the subsequent construction of the Jacobian matrix and the convergence direction of the LM iteration is effectively reduced.

[0040] After the coordinate transformation process described above, the actual attitude parameters in the measuring instrument coordinate system can be converted into the actual attitude parameters in the robot coordinate system. Then, the actual attitude parameters in the robot coordinate system corresponding to each preset end position are combined to form the actual attitude parameter group described in this application.

[0041] This mechanism enables the model to automatically suppress anomalous disturbances without discarding potentially valid observation data, significantly improving the practicality and robustness of the calibration scheme in non-ideal operating environments.

[0042] Step S2: Determine the theoretical end position corresponding to each of the preset end positions based on the actual attitude parameter set and the preset kinematic equations.

[0043] Step S3: Determine the corresponding end position error based on the preset end position and the corresponding theoretical end position.

[0044] To calibrate the robot's position, it is necessary to determine the robot's theoretical position under corresponding parameters. Therefore, this application adopts the modified DH (Hyperdynamic Dexterity) convention to establish the robot's forward kinematics model, i.e., the kinematic equations in this application. The corresponding theoretical end-effector position is obtained by substituting the actual posture parameter set into the kinematic equations.

[0045] The homogeneous transformation matrix between adjacent link coordinate systems in this application is as follows: in, For joint torsion angle, The length of the link. Joint angle (including zero offset). This represents the link offset. For robots with parallel joint axes (e.g., the axes of joints 2-3 and 3-4 are parallel), the standard MDH model exhibits singularities in the parallel axis case. This application introduces an additional corrected rotation angle about the Y-axis at the end of the transformation chain. The initial value is 0. For the above parallel axis pairs, respectively, introduce... and This expands the complete parameter vector from 24 dimensions in the standard MDH to 26 dimensions. Therefore, the actual attitude parameter set substituted into the kinematic equations in this application is represented as follows: Multiply the transformation matrices of each link in turn to obtain the homogeneous matrix of the end coordinate system relative to the base coordinate system. Take the first three rows of its fourth column as the theoretical end position. .

[0046] For the j-th measurement point, calculate the position error: in For the j-th preset end position, The error between the j-th preset end position and the j-th theoretical end position is the end position error.

[0047] Step S4: Determine the attitude parameter compensation strategy for the target robot and the covariance matrix for the attitude parameter compensation strategy based on all the actual attitude parameter sets and all the end position errors.

[0048] In some embodiments, step S4, "determining an attitude parameter compensation strategy for the target robot and a covariance matrix for the attitude parameter compensation strategy based on all the actual attitude parameter sets and all the end-effector position errors," includes: Step S41: Add a preset perturbation amount to each attitude parameter in the actual attitude parameter group to obtain multiple perturbation attitude parameter groups.

[0049] Step S42: Calculate the end position of the disturbance corresponding to the disturbance attitude parameter set using the kinematic equations.

[0050] Step S43: Organize all the disturbance end positions and the corresponding disturbance attitude parameter sets into a global disturbance position set.

[0051] Although this application states that the global perturbation position set can be obtained based on the actual attitude parameter set, in practice, this application constructs a 3×26 Jacobian matrix from the actual attitude parameter sets of each preset end position, where the Jacobian matrix corresponding to the j-th preset end position is... For ease of reference, the Jacobian matrix will be referred to here. This is called the independent Jacobian matrix. Its k-th column represents the partial derivative of the last position with respect to the k-th parameter, approximated using forward difference numerical methods. The perturbation step size It is applicable to both length parameters in mm and angle parameters in rad. Let be the k-th dimensional unit vector. By sequentially applying perturbations to the 26 parameters and calling forward kinematics to calculate the change in the end position, the perturbation end position in this application can be obtained. Of course, the perturbation end position here is generated based on the preset end position j, and it is still presented in the form of a matrix, which can be called the perturbation position matrix.

[0052] Then, the perturbation position matrices of all preset end positions are vertically concatenated into a 3N×26 global Jacobian matrix. This refers to the set of global perturbation locations in this application, which is still presented here as the location of a matrix. This matrix can be called the global perturbation location matrix.

[0053] Step S44: Deduplicate the global disturbance position set according to all the said end position errors to obtain an independent parameter index set.

[0054] Normalize each column of the global perturbation position matrix by dividing it by its 2-norm to obtain the normalized perturbation position matrix. .right Perform QR decomposition with column permutations: Where E is a column permutation matrix, such that the absolute values ​​of the diagonal elements of matrix R are... Arranged in descending order.

[0055] To achieve adaptive threshold adjustment, this step does not use a preset fixed constant, but instead establishes a redundant judgment threshold. The functional relationship between the measurement system's random error and the model's sensitivity to perturbations is established. To prevent the threshold from being amplified infinitely due to the extremely small residual at the end of the iteration, thus mistakenly eliminating key parameters, a noise lower limit threshold is introduced as a stabilizing term in the denominator. The specific formula is as follows: in, The elements on the diagonal of matrix R are... The nominal standard deviation of the external measuring equipment (reflecting the level of physical noise). Let be the norm of all end position error vectors. This is a scaling factor, whose value is automatically set based on the sampling rate at the calibration site. A residual lower limit estimate determined by measurement noise is introduced. , The safety factor is greater than 1 (e.g., 1.5 to 3.0), and N is the number of preset end positions.

[0056] The dynamic behavior of this adaptive mechanism is as follows: (1) Initial stage of iteration: At the beginning of calibration, the model error is much greater than the measurement noise. (maximum), at which point the threshold is obtained. Minimal. The system adopts a forgiving strategy, retaining most parameters in the optimization process to ensure that the gradient descent direction can quickly eliminate major geometric biases.

[0057] (2) Mid-to-late stage of iteration (dynamic tightening and prevention of false positives): As the residual The threshold continues to decrease. As the value gradually increases, the system begins to dynamically eliminate weak coupling parameters whose contribution to the residual has been submerged by noise. When the residual approaches the system's physical noise limit, the denominator is... Truncation, threshold The model is stabilized at a reasonable and constant upper limit. This not only ensures that the redundancy removal intensity matches the current signal-to-noise ratio in real time, but also effectively prevents the "false killing of important parameters" caused by threshold divergence at the end of the iteration, thus guaranteeing the convergence stability of the model in the high-precision range.

[0058] Then based on this dynamic threshold , in matrix R, the absolute value is less than The parameter columns corresponding to the diagonal elements are identified as redundant parameters and removed from the index set. Finally, a set of independent parameter indices is obtained, the number of which is denoted as . Extract the corresponding columns to form a reduced Jacobian matrix, which can be referred to here as the independent index parameter matrix. The dimension is 3N× .

[0059] Step S45: Determine the attitude parameter compensation strategy and the covariance matrix based on each of the end position errors and the set of independent parameter indices.

[0060] In some embodiments, step S45, "determining the attitude parameter compensation strategy and the covariance matrix based on each of the end-position errors and the independent parameter index set," includes: Step S451: Determine the weight components of each preset end position in three directions based on each of the end position errors.

[0061] Step S452: Determine the attitude parameter compensation strategy and the covariance matrix based on the weight components of all the preset end positions, the end position error, and the independent parameter index set.

[0062] In some embodiments, step S452, "determining the attitude parameter compensation strategy based on the weight components of all the preset end positions, the end position error, and the independent parameter index set," includes: Step S4521: Construct a compensation strategy calculation formula containing the damping coefficient based on the weighted components, the end position error, and the set of independent parameter indices.

[0063] Step S4522: Calculate the current compensation strategy for the attitude parameters according to the compensation strategy calculation formula.

[0064] Step S4523: Calculate the trial compensation parameters based on the current compensation strategy and the set of independent parameter indices.

[0065] Step S4524: Construct a gain ratio calculation formula based on the trial compensation parameters, the independent parameter index set, the weight components of all the preset end positions, and the damping coefficient.

[0066] Step S4525: Calculate the gain ratio under the current compensation strategy according to the gain ratio calculation formula.

[0067] Step S4526: Update the damping coefficient in the compensation strategy calculation formula and the gain ratio calculation formula according to the gain ratio.

[0068] Step S4527: When the current compensation strategy meets the preset conditions, determine the attitude parameter compensation strategy according to the current compensation strategy.

[0069] In some embodiments, step S452, "determining the covariance matrix based on the weight components of all the preset end positions, the end position error, and the independent parameter index set," includes: Step S45281: Determine the final residual based on the end position error when the current compensation strategy meets the preset conditions.

[0070] Step S45282: Determine the robust scaling estimate of the current compensation strategy based on the final weight components and the final residual when the current compensation strategy meets the preset conditions.

[0071] Step S45283: Determine the covariance matrix based on the robust scaling estimate, the final weight components, and the set of independent parameter indices.

[0072] This step replaces the conventional residual sum of squares with the corresponding Huber loss, enabling the parameter identification stage to also suppress gross errors.

[0073] For a single measurement point Define the magnitude of its position error ,in The Huber loss function, identical to that used in S102, is adopted: threshold , scaling factor The value range is the same as in S102 (1.345~2.0). The nominal standard deviation of the measuring equipment is given. The total loss of all measurements is... The calibration problem is transformed into minimizing this loss.

[0074] An Iterative Reweighted Least Squares (IRLS) strategy is employed to embed the problem into the LM framework. For the current parameters... ( This represents the numerical estimate of the vector consisting of all independent kinematic parameters at the current iteration step after redundant parameters have been removed; its dimension is... ), calculate the error modulus for each measurement point and its Huber weight: Assign weights to the three coordinate components of the point to construct... diagonal weight matrix Construct the weighted normal equation and introduce a damping term: in The damping coefficient is initially set to... I is the identity matrix; Stacked for the position errors of all measurement points dimensional vector; This is the reduced Jacobian matrix, which is the matrix composed of the independent parameter columns remaining after the global Jacobian matrix has been decomposed by QR and the redundant parameter columns of linear dependence have been removed. for Transpose of; This is the normalized parameter update amount, which is the target unknown vector for solving this system of linear equations.

[0075] The normalized parameter update amount is obtained by solving the problem. Then, the physical parameter update amount is restored by using the corresponding column norm. This refers to the current compensation strategy in this application. Although it is called a compensation strategy in this application, it is actually a set of updates for each parameter.

[0076] Let the compensation parameters be tested That is, at a predetermined end position, the ratio of the actual decrease in Huber loss to the decrease predicted by the weighted quadratic model is calculated—the gain ratio. : The judgment logic of this indicator is consistent with the original steps: like Accept updates and according to Value dynamically adjusted (For example Time shrink It is 1 / 3 of the original value; Increase appropriately ); like Refuse to update, retain the original parameters, and amplify with a penalty factor of 2 to 10 times. This enhances the gradient descent component and reduces the search step size.

[0077] The iteration termination condition is also... or The relative change is lower than The solution obtained upon convergence is the maximum a posteriori estimate in the Huber robust sense. .

[0078] Using the final iteration, i.e., the weight matrix when the current compensation strategy satisfies the preset conditions. (Final weighted components) and residuals (final residuals) are used to calculate robust scaling estimates. : The approximate posterior covariance matrix is: The square root of the diagonal elements provides a robust estimate of the standard deviation of each independent parameter. This allows for a second "physical reliability filtering" process, identical to the original step (e.g., removing or fixing parameters with a standard deviation > 50 mm for length parameters or > 0.5 rad for angle parameters). This yields a high signal-to-noise ratio, a parameter starting point resistant to anomalous disturbances, providing more reliable initial values ​​and covariance structures for subsequent MCMC sampling.

[0079] Step S5: Determine usage recommendations for the attitude parameter compensation strategy based on the covariance matrix and the attitude parameter compensation strategy.

[0080] In some embodiments, step S5, "determining usage recommendations for the attitude parameter compensation strategy based on the covariance matrix and the attitude parameter compensation strategy," includes: Step S51: The attitude parameter compensation strategy and the covariance matrix are used to construct the proposed distribution and the prior distribution.

[0081] Step S52: Generate a posterior sample set for each parameter in the attitude parameter compensation strategy based on the proposed distribution and the prior distribution.

[0082] Step S53: Determine the confidence interval of each parameter based on each of the posterior sample sets.

[0083] Step S54: Determine the usage recommendations for each parameter in the attitude parameter compensation strategy based on the confidence interval.

[0084] Set the initial point of MCMC sampling to the maximum posterior point obtained in the LM stage: .

[0085] The proposal distribution is used to generate candidate parameters during the sampling process, and is constructed to use the current parameters. A multivariate Gaussian distribution with mean as the approximate posterior covariance matrix and scaled approximate posterior covariance matrix as the covariance: Where the step size scaling factor Initial value .

[0086] It should be noted that the approximate posterior covariance matrix obtained in the LM stage From residual variance and Multiplying yields the result. This is due to the reduced Jacobian matrix. There may be an approximate linear correlation between the columns, or the measured pose may not be sufficiently excited in a specific direction. It may exhibit pathological or even bizarre numerical characteristics, leading to The eigenvalues ​​are either non-positive definite or contain extremely small eigenvalues. This can cause the Cholesky decomposition required for subsequent MCMC sampling to be unstable.

[0087] Therefore, before constructing the proposal distribution and the prior distribution, we need to... Perform the following regularization operations in sequence: (1) Symmetry treatment: Update it to the arithmetic mean of itself and its transpose, that is, let This eliminates the slight asymmetry accumulated from floating-point operations, ensuring that the matrix is ​​strictly symmetric in numerical terms.

[0088] (2) Positive definiteness correction: Perform eigenvalue decomposition on the symmetric matrix and check for the smallest eigenvalue. .like If the matrix is ​​not positive definite, then a positive definite correction is applied, letting... ,in Take a pre-defined small positive value (e.g.) ), The identity matrix is ​​used. This operation ensures that all eigenvalues ​​are strictly greater than zero by diagonal loading, guaranteeing that the covariance matrix is ​​invertible and can be stably decomposed using the Cholesky method.

[0089] After the above treatment, It satisfies symmetric positive definiteness and can be used to construct the proposed and prior distributions of MCMC. At the same time, regularization only applies a slight expansion to the direction of the smallest variance, and the principal directions and magnitudes of the covariance matrix are preserved, without substantially changing the shape of the posterior distribution.

[0090] The prior distribution is used in the calculation of the posterior probability density to constrain the search range of the parameters, and is constructed as follows: Multivariate Gaussian distribution centered at 1, with amplified covariance: Amplification factor A value of 3 to 5 is recommended, with this range determined based on the typical kinematic error magnitude of a six-DOF industrial robot. After long-term use or accumulation of assembly errors, the deviation of the DH parameter in an industrial robot is typically on the sub-millimeter to millimeter scale. The typical magnitude of the square root of the diagonal elements of the approximate covariance matrix obtained in the LM stage (i.e., the parameter standard deviation estimate) is... mm or rad. If The deviation from the true optimal value is approximately If the standard deviation is one, then take This allows the prior to be agreed upon The probability of covering this bias; when the measurement noise is high or the number of calibration poses is less than 80, use Further broaden the priors to provide MCMC with more exploratory tolerance.

[0091] Since this application uses the maximum a posteriori estimate of the LM stage as the starting point of MCMC, the initial position of the chain is already near the high probability region of the posterior, and the required number of warm-up steps is significantly less than that of the scheme starting from a broad prior. In practice, for industrial robot calibration problems with 20 to 26 independent parameters, a number of warm-up steps of 1,000 to 10,000 steps and a number of formal sampling steps of 10,000 to 50,000 steps can meet the convergence requirements. In this embodiment, 5,000 steps and 30,000 steps are used respectively.

[0092] In each step, candidate points are first generated. The proposed covariance matrix is ​​then analyzed. Cholesky decomposition yields the lower triangular matrix. ,satisfy Extract standard normal random vectors ,calculate: in For each candidate point, calculate the log-posterior probability of the candidate point and the current point (the point corresponding to the current parameter). The log-posterior probability consists of the log-likelihood and the log-prior probability. Calculate the logarithmic acceptance probability: Draw uniformly random numbers .like Then accept the candidate point and let Otherwise, leave the original position unchanged.

[0093] During the warm-up phase, the cumulative acceptance rate is calculated every 100 steps. If the acceptance rate is higher than 0.40, it indicates that the step size is too small, and the step size scaling factor is adjusted. Multiply by 1.2; if the acceptance rate is below 0.10, it indicates the step size is too large, and... Multiply by 0.8. When the acceptance rate meets the preset threshold, formal sampling is performed centered on the candidate points of the target acceptance rate, obtaining 30,000 samples to form the posterior sample set. .

[0094] Regarding the above attitude parameter compensation strategy For the k-th independent parameter, calculate the posterior mean based on the posterior sample set. and posterior standard deviation : The 2.5% and 97.5% quantiles of the sample are used as the 95% confidence interval for this parameter. This interval does not assume a normal posterior distribution and directly reflects the shape of the actual distribution. Furthermore, if the 95% confidence interval of a parameter crosses zero, it indicates that the positive or negative direction of the parameter cannot be reliably determined, and it is considered an unreliable parameter. It is recommended to set it aside or assign it to zero during the compensation stage to avoid overfitting, which is the usage recommendation in this application.

[0095] Step S6: Compensate the attitude parameters of the target robot according to the attitude parameter compensation strategy and the usage suggestions.

[0096] Different robots employ different compensation methods during the compensation process. For robot controllers with modification permissions, the DH parameters stored in the robot controller are directly modified to the compensated DH parameters based on the attitude parameter compensation strategy and usage recommendations.

[0097] For robot controllers without modification permissions, an offline compensation method based on numerical iterative inverse solution is proposed, and its specific implementation is as follows: (1) Calculate the theoretical target pose For each set of nominal joint angles in the validation set or job path Substitute the robot's nominal MDH parameters and nominal parallel axis correction angle The theoretical homogeneous transformation matrix of the robot's end effector under ideal conditions is calculated using a forward kinematics algorithm. : This matrix contains the three-dimensional position coordinates that the robot should achieve, ignoring geometric errors. and the end attitude matrix.

[0098] (2) Perform numerical inverse solution under the true parameter model Using the real kinematic parameters obtained in the first stage A realistic kinematic model of the robot is constructed, and based on this model, the theoretical target pose can be generated by inverse calculation using a numerical iterative method. Compensating joint angle The specific iteration logic is as follows: Initial value assignment: Set the initial value for iteration to the nominal joint angle. This is done to shorten the search path and ensure the continuity of the solution.

[0099] Error vector construction: In each iteration, calculate the current end-effector pose and the target pose in the real model. Deviation vector between This vector is composed of position error and attitude rotation error Together they constitute. Here. Taken as the difference between the Cartesian coordinates of the target position and the current position; attitude rotation error An equivalent rotation vector representation of relative rotation is used. Specifically, the rotation matrices of the target pose and the current pose are extracted (denoted as ). and ), calculate the relative rotation matrix .Will Transform it into the form of an equivalent rotation axis unit vector n and an equivalent rotation angle θ, let .at this time norm Physically, it is directly equivalent to the shortest spatial angle of rotation around the axis required to reach the target posture from the current posture.

[0100] Damped Incremental Updates: Constructing a Realistic Model Using the Forward Difference Method Kinematic Jacobian Matrix And introduce a damping factor (like To ensure computational stability near singular robot poses (on the order of magnitude), joint angles are iteratively updated using the following formula: (3) Convergence determination and precision control Set a stringent convergence threshold when the location residual norm Less than mm and attitude residual norm Less than When the current joint angle reaches rad, stop iteration and output the current joint angle as the compensated joint angle. If convergence is not achieved within the preset maximum number of iterations, an alarm signal will be output to indicate that the point may be located at the workspace boundary or pose a singular risk.

[0101] (4) Offline saving and path correction of results The calculated compensated joint angle sequence ( The theoretical position coordinates and point numbers are saved offline in a preset format (such as JSON or CSV). During actual operation, the original nominal joint commands are replaced with the compensated joint commands and sent to the robot controller. This allows the robot to accurately reproduce the theoretical trajectory on a physical entity with geometric errors through pre-correction of joint dimensions, thereby achieving closed-loop compensation for absolute positioning accuracy.

[0102] This application addresses the problems of conventional calibration methods being unable to quantify uncertainty, systematically analyze parameter identifiability, or propagate end-point accuracy. By constructing the starting point, proposal distribution, and prior information of MCMC using the maximum a posteriori estimate and approximate covariance output from the LM stage, it achieves the technical effect of significantly shortening the warm-up time and making the quantification of uncertainty in high-dimensional parameter spaces computationally feasible.

[0103] Furthermore, by unifying the outlier handling strategy in the two stages of data preprocessing and parameter identification through the Huber robust loss function, the interference of gross errors on the iterative convergence direction and covariance estimation is automatically suppressed without discarding potentially valid observation data, thereby improving the robustness of the calibration scheme in non-ideal operating environments.

[0104] Furthermore, by automatically identifying and eliminating redundant parameters with linear correlation in the observation equation through column normalization and QR decomposition, a systematic quantitative analysis of parameter identifiability was achieved, reducing the dimension of the parameter space and improving the sampling efficiency of subsequent MCMC.

[0105] Furthermore, the posterior standard deviation and confidence interval of each output parameter provide quantitative criteria for screening compensation parameters. If the confidence interval crosses zero, it indicates that the parameter is unreliable, which can avoid blind compensation leading to parameter compensation divergence.

[0106] Example 2: Based on the foregoing embodiments, this application provides a parameter compensation device for an industrial robot. The various modules and units included in the device can be implemented by a processor in a computer device; of course, they can also be implemented by specific logic circuits. In the implementation process, the processor can be a central processing unit (CPU), a microprocessor (MPU), a digital signal processor (DSP), or a field programmable gate array (FPGA), etc.

[0107] like Figure 2 As shown, a parameter compensation device for an industrial robot includes: a first acquisition module 1, a first determination module 2, a second determination module 3, a third determination module 4, a fourth determination module 5, and a first execution module 6.

[0108] The first acquisition module 1 is used to acquire the actual attitude parameter sets of the target robot's end effector when it reaches each preset end effector position. The first determination module 2 is used to determine the theoretical end effector position corresponding to each preset end effector position based on the actual attitude parameter sets and preset kinematic equations. The second determination module 3 is used to determine the corresponding end effector position error based on the preset end effector position and the corresponding theoretical end effector position. The third determination module 4 is used to determine an attitude parameter compensation strategy for the target robot and a covariance matrix for the attitude parameter compensation strategy based on all the actual attitude parameter sets and all the end effector position errors. The fourth determination module 5 is used to determine a usage suggestion for the attitude parameter compensation strategy based on the covariance matrix and the attitude parameter compensation strategy. The first execution module 6 is used to compensate the attitude parameters of the target robot according to the attitude parameter compensation strategy and the usage suggestion.

[0109] The various modules in the parameter compensation device for the aforementioned industrial robot can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in the processor of the device in hardware form or independently of it, or stored in the memory of the processing device in software form, so that the processor can call and execute the operations corresponding to each module. It should be noted that the module division in this embodiment is illustrative and only represents a logical functional division; in actual implementation, there may be other division methods.

[0110] Example 3: Thirdly, this application provides a computer electronic production device, such as... Figure 3 As shown, it includes: at least one processor 901; and a memory 902 communicatively connected to the at least one processor 901; wherein the memory 902 stores instructions executable by the at least one processor 901, the instructions being executed by the at least one processor 901 to enable the at least one processor 901 to perform a parameter compensation method for an industrial robot in the above embodiments.

[0111] The memory and processor are connected via a bus, which can include any number of interconnecting buses and bridges, connecting various circuits of one or more processors and memories. The bus can also connect various other circuits, such as peripheral devices, voltage regulators, and power management circuits, which are well known in the art and will not be described further herein. The bus interface provides an interface between the bus and the transceiver. The transceiver can be a single element or multiple elements, such as multiple receivers and transmitters, providing a unit for communicating with various other devices over a transmission medium. Data processed by the processor is transmitted over the wireless medium via an antenna, which further receives data and transmits it to the processor.

[0112] The processor manages the bus and general processing, and also provides various functions, including timing, peripheral interfaces, voltage regulation, power management, and other control functions. Memory is used to store data used by the processor during operation.

[0113] In addition, the computer device may include (but is not limited to) a data bus, an input / output (I / O) bus, a display, and input / output devices (e.g., keyboard, mouse, speakers, etc.).

[0114] The processor can communicate with external devices via the I / O bus through wired or wireless networks.

[0115] In one embodiment, the at least one computer-executable instruction may also be compiled into or comprise a software product / computer program product, wherein one or more computer-executable instructions are executed by a processor to perform the steps of the various functions and / or methods in the embodiments described herein.

[0116] Example 4: Fourthly, this application proposes a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in any of the first aspects.

[0117] Computer-readable storage media can be implemented by any type of volatile or non-volatile storage device or a combination thereof. Computer-readable storage media may include, but are not limited to, random access memory (RAM), read-only memory (ROM), flash memory, EPROM memory, EEPROM memory, registers, and computer storage media (e.g., hard disks, floppy disks, solid-state drives, removable disks, CD-ROMs, DVD-ROMs, Blu-ray discs, etc.).

[0118] Computer-readable storage media may also store at least one computer-executable program / instruction, such as computer-readable instructions. Computer-readable storage media include, but are not limited to, volatile memory and / or non-volatile memory. Volatile memory may include, for example, random access memory (RAM) and / or cache memory. Computer-readable storage media may include, for example, read-only memory (ROM), hard disk, flash memory, etc. For example, a non-transitory computer-readable storage medium may be connected to a computing device such as a computer, and then, when the computing device executes the computer-readable instructions stored on the computer-readable storage medium, the various methods described above can be performed.

[0119] Example 5: Fifthly, this application proposes a computer program product comprising a computer program / instructions that, when executed by a processor, implement the steps of the method described in any of the first aspects.

[0120] Those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. This program is stored in a storage medium and includes several instructions to cause a device (which may be a microcontroller, chip, etc.) or processor to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0121] It should be understood that the phrase "one embodiment" or "an embodiment" throughout the specification means that a specific feature, structure, or characteristic related to the embodiment is included in at least one embodiment of this application. Therefore, "in one embodiment" or "in an embodiment" appearing throughout the specification does not necessarily refer to the same embodiment. Furthermore, these specific features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. It should be understood that in the various embodiments of this application, the sequence numbers of the above-described processes do not imply a sequential order of execution; the execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application. The sequence numbers of the above-described embodiments are merely descriptive and do not represent the superiority or inferiority of the embodiments.

[0122] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0123] In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. The device embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods, such as: multiple units or components can be combined, or integrated into another system, or some features can be ignored or not executed. In addition, the coupling, direct coupling, or communication connection between the various components shown or discussed can be through some interfaces, and the indirect coupling or communication connection between devices or units can be electrical, mechanical, or other forms.

[0124] In the embodiments provided in this disclosure, it should be understood that the disclosed apparatus and methods can also be implemented in other ways. The apparatus embodiments described above are merely illustrative; for example, the flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of apparatus, methods, and computer program products according to various embodiments of this disclosure. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than those marked in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram and / or flowchart, and combinations of blocks in block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0125] Alternatively, if the integrated units described above are implemented as software functional modules and sold or used as independent products, they can also be stored in a computer-readable storage medium. Based on this understanding, the technical solutions of the embodiments of this application, or the parts that contribute to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a controller to execute all or part of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, ROMs, magnetic disks, or optical disks.

[0126] It should be noted that the terms "first," "second," etc., used in the specification, claims, and accompanying drawings of this disclosure are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this disclosure described herein can be implemented in orders other than those illustrated or described herein.

[0127] Those skilled in the art will understand that the above embodiments are specific embodiments for implementing this application, and in practical applications, various changes can be made to them in form and detail without departing from the spirit and scope of this application.

Claims

1. A parameter compensation method of an industrial robot, characterized by, include: Obtain the actual attitude parameter set of the target robot when the end effector reaches each preset end position; The theoretical end position corresponding to each preset end position is determined based on the actual attitude parameter set and the preset kinematic equations. The corresponding end position error is determined based on the preset end position and the corresponding theoretical end position; Based on all the actual attitude parameter sets and all the end-effector position errors, determine the attitude parameter compensation strategy for the target robot and the covariance matrix for the attitude parameter compensation strategy; Based on the covariance matrix and the attitude parameter compensation strategy, a usage recommendation for the attitude parameter compensation strategy is determined; The attitude parameters of the target robot are compensated according to the attitude parameter compensation strategy and the usage recommendations.

2. The method of claim 1, wherein, The step of determining the attitude parameter compensation strategy for the target robot based on all the actual attitude parameter sets and all the end-effector position errors, and the covariance matrix for the attitude parameter compensation strategy, includes: Each attitude parameter in the actual attitude parameter set is given a preset perturbation amount to obtain multiple sets of perturbed attitude parameter sets. The position of the disturbance end point corresponding to the disturbance attitude parameter set is calculated using the kinematic equations. All the aforementioned disturbance end positions and corresponding disturbance attitude parameter sets are organized into a global disturbance position set; The global disturbance position set is deduplicated based on all the described end position errors to obtain an independent parameter index set; The attitude parameter compensation strategy and the covariance matrix are determined based on each of the end position errors and the set of independent parameter indices.

3. The method of claim 2, wherein, The step of determining the attitude parameter compensation strategy and the covariance matrix based on each of the end-position errors and the independent parameter index set includes: The weight components of each preset end position in the three directions are determined based on each of the end position errors; The attitude parameter compensation strategy and the covariance matrix are determined based on the weighted components of all the preset end positions, the end position error, and the set of independent parameter indices.

4. The method of claim 1, wherein, The step of determining usage recommendations for the attitude parameter compensation strategy based on the covariance matrix and the attitude parameter compensation strategy includes: Based on the attitude parameter compensation strategy and the covariance matrix, construct the proposal distribution and the prior distribution; Generate a posterior sample set for each parameter in the attitude parameter compensation strategy based on the proposed distribution and the prior distribution; The confidence intervals for each parameter are determined based on each of the aforementioned posterior sample sets; Based on the confidence interval, recommendations for the use of each parameter in the attitude parameter compensation strategy are determined.

5. The method of claim 3, wherein, The step of determining the attitude parameter compensation strategy based on the weighted components of all the preset end positions, the end position error, and the independent parameter index set includes: A compensation strategy calculation formula containing the damping coefficient is constructed based on the weighted components, the end position error, and the set of independent parameter indices. The current compensation strategy for attitude parameters is calculated based on the compensation strategy calculation formula. Calculate the trial compensation parameters based on the current compensation strategy and the set of independent parameter indices; A gain ratio calculation formula is constructed based on the trial compensation parameters, the independent parameter index set, the weight components of all the preset end positions, and the damping coefficient; Calculate the gain ratio under the current compensation strategy according to the gain ratio calculation formula; The compensation strategy calculation formula and the damping coefficient in the gain ratio calculation formula are updated according to the gain ratio. When the current compensation strategy meets the preset conditions, the attitude parameter compensation strategy is determined according to the current compensation strategy.

6. The method of claim 5, wherein, Determining the covariance matrix based on the weight components of all the preset end positions, the end position error, and the set of independent parameter indices includes: The final residual is determined based on the end position error when the current compensation strategy meets the preset conditions. The robust scaling estimate of the current compensation strategy is determined based on the final weight components and the final residual when the current compensation strategy meets the preset conditions. The covariance matrix is ​​determined based on the robust scaling estimate, the final weight components, and the set of independent parameter indices.

7. A parameter compensation device of an industrial robot, characterized by, include: The first acquisition module is used to acquire the actual attitude parameter set of the target robot when the operating end of the robot reaches each preset end position; The first determining module is used to determine the theoretical end position corresponding to each of the preset end positions based on the actual attitude parameter set and the preset kinematic equations. The second determining module is used to determine the corresponding end position error based on the preset end position and the corresponding theoretical end position; The third determining module is used to determine the attitude parameter compensation strategy for the target robot and the covariance matrix for the attitude parameter compensation strategy based on all the actual attitude parameter sets and all the end position errors. The fourth determining module is used to determine a usage recommendation for the attitude parameter compensation strategy based on the covariance matrix and the attitude parameter compensation strategy. The first execution module is used to compensate the attitude parameters of the target robot according to the attitude parameter compensation strategy and the usage suggestions.

8. A computerized electronic production device, characterized by, The method includes a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method according to any one of claims 1 to 6.

9. A computer readable storage medium having stored thereon a computer program, characterized in that, When executed by a processor, the computer program implements the steps of the method according to any one of claims 1 to 6.

10. A computer program product, characterised in that, Includes a computer program that, when executed by a processor, implements the steps of the method according to any one of claims 1-6.

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