Pipeline overall hoisting positioning error pre-control method based on digital twinning

Abstract

The present application relates to hoisting control technical field, disclose a kind of based on digital twinning pipeline overall hoisting positioning error pre-control method, comprising the following steps: step S101, extraction single frame hole ring radial error time slope;Step S102, obtain single-axis scaling angular velocity is calculated;Step S103, obtain corrected angular velocity is calculated;Step S104, extraction distortion point set characteristic parameter;Step S105, generate pre-control instruction vector;Step S106, obtain final docking target pose is calculated.This application is according to single frame hole ring radial error time slope and the geometric sensitivity analysis of digital twinning, without multiple frame data splicing can accurately eliminate swing scanning asynchronous caused point cloud distortion, through feedforward network correction angular velocity system deviation, again fusion static geometry difference and dynamic pre-control instruction, realize the integrated compensation of static size position deviation and dynamic swing deviation, substantially reduce docking positioning error.

Description

Technical Field

[0001] This invention relates to the field of hoisting control technology, and more specifically, to a method for pre-controlling the positioning error of pipeline hoisting based on digital twins. Background Technology

[0002] Pipeline hoisting is a critical construction step in energy, chemical and other fields. The accuracy of flange connection directly affects the quality of the project and the safety of operation. To achieve automated connection, the industry generally uses LiDAR to collect flange hole ring point clouds for positioning, but it faces prominent technical challenges in practical applications.

[0003] The single-frame point cloud acquired by LiDAR is a three-dimensional point set with timestamps. The single-frame data needs to be generated by scanning line by line within a non-zero duration. However, the load will continue to swing during the scanning cycle, resulting in different instantaneous postures of the flange corresponding to different sampling points in the same frame, forming motion distortion, which causes the hole ring point cloud to deviate from the true geometry. At the same time, flange manufacturing errors and installation deviations will cause static deviations between the design geometry and the measured geometry. The static deviation and the dynamic swing deviation are superimposed, further increasing the positioning difficulty.

[0004] Existing positioning methods mostly rely on multi-frame point cloud stitching or complex dynamic modeling. Multi-frame processing leads to poor real-time performance and cannot adapt to the dynamic characteristics of the hoisting process. Some methods do not effectively distinguish between static and dynamic deviations, and only perform single corrections, resulting in insufficient positioning accuracy. Other methods attempt distortion correction, but rely on complex algorithms or additional sensor data, leading to poor engineering applicability. These problems cause flange docking positioning errors to exceed the standard, which not only affects construction efficiency but may also cause safety hazards such as sealing failure and pipeline damage. There is an urgent need for a precise positioning solution that can achieve composite compensation for distortion correction and deviation within a single frame. Summary of the Invention

[0005] This invention provides a method for pre-controlling the positioning error of pipeline hoisting based on digital twins, which solves the technical problems mentioned in the background.

[0006] This invention provides a method for pre-controlling positioning errors in the overall hoisting of pipelines based on digital twins, comprising the following steps:

[0007] Step S101: Obtain the point cloud of the flange hole ring with timestamps, calculate the radial residual of each sampling point relative to the best-fit circle, establish a linear regression relationship between the radial residual and the sampling time, and extract the time-series slope of the radial error of the hole ring in a single frame.

[0008] Step S102: Apply virtual micro-rotation to each axis in the digital twin model, calculate the axial sensitivity of the radial error time-series slope of the single-frame aperture ring relative to the rotational change, select the master sensitive axis, and convert the radial error time-series slope of the single-frame aperture ring into a single-axis scaled angular velocity through the axial sensitivity of the master sensitive axis.

[0009] Step S103: The radial error temporal slope, axial sensitivity, and single-frame readout duration of the single-frame aperture ring are used as input vectors to input a preset fixed-parameter feedforward network model, and the corrected angular velocity is output.

[0010] Step S104: After correcting the angular velocity, rotate each point in a single frame in the opposite direction to the same reference time, and re-estimate the distortion-free circle center, distortion-free aperture radius, and distortion-free normal based on the distortion-free point set.

[0011] Step S105: Calculate the short-term attitude increment based on the corrected angular velocity, construct the leading edge point by using the undistorted normal and the undistorted aperture ring radius, calculate the vector product of the short-term attitude increment and the leading edge point lever arm with the reference point as the reference, and generate the pre-control command vector.

[0012] Step S106: Calculate the static geometric difference between the digital twin design geometry and the distortion-free circle center and distortion-free normal; calculate the difference between the design pitch circle radius and the distortion-free hole ring radius and convert it into a planar displacement correction amount; combine the current pose, static geometric difference, planar displacement correction amount and pre-control command vector to output the final docking target pose.

[0013] The beneficial effects of this invention are as follows: Based on the temporal slope of the radial error of the single-frame hole ring and the geometric sensitivity analysis of digital twins, this invention can accurately eliminate point cloud distortion caused by asynchronous swing scanning without multi-frame data stitching, and simultaneously acquire the distortion-free circle center radius and normal. By correcting the angular velocity system deviation through a fixed-parameter feedforward network, and then fusing static geometric difference and dynamic pre-control commands, it achieves integrated compensation for static dimensional position deviation and dynamic swing deviation, significantly reducing docking positioning error. The entire process requires no additional sensors or complex dynamic modeling, completing data processing and target pose generation within a single frame. It has strong real-time performance and good engineering applicability, effectively improving the accuracy and efficiency of flange docking, and reducing construction risks and safety hazards caused by positioning deviations. Attached Figure Description

[0014] Figure 1 This is a flowchart of a pipeline hoisting and positioning error pre-control method based on digital twins according to the present invention;

[0015] Figure 2 This is a schematic diagram comparing the point cloud distortion correction results of the present invention;

[0016] Figure 3 This is a schematic diagram of the radial residual time series analysis of the present invention;

[0017] Figure 4 This is a schematic diagram comparing the angular velocity estimation performance of the present invention;

[0018] Figure 5This is a schematic diagram comparing the final hoisting and positioning accuracy of the present invention. Detailed Implementation

[0019] The subject matter described herein will now be discussed with reference to exemplary embodiments. It should be understood that these embodiments are discussed only to enable those skilled in the art to better understand and implement the subject matter described herein, and changes may be made to the function and arrangement of the elements discussed without departing from the scope of this specification. Various processes or components may be omitted, substituted, or added as needed in the examples. Furthermore, features described in some examples may be combined in other examples.

[0020] It should be noted that, unless otherwise defined, the technical or scientific terms used in one or more embodiments of the present invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in one or more embodiments of the present invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" indicate that the element or object preceding the term encompasses the elements or objects listed following the term and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0021] like Figures 1-5 As shown, a method for pre-controlling the positioning error of pipeline hoisting based on digital twins includes the following steps:

[0022] Step S101: Obtain the point cloud of the flange hole ring with timestamps, calculate the radial residual of each sampling point relative to the best-fit circle, establish a linear regression relationship between the radial residual and the sampling time, and extract the time-series slope of the radial error of the hole ring in a single frame.

[0023] Step S102: Apply virtual micro-rotation to each axis in the digital twin model, calculate the axial sensitivity of the radial error time-series slope of the single-frame aperture ring relative to the rotational change, select the master sensitive axis, and convert the radial error time-series slope of the single-frame aperture ring into a single-axis scaled angular velocity through the axial sensitivity of the master sensitive axis.

[0024] Step S103: The radial error temporal slope, axial sensitivity, and single-frame readout duration of the single-frame aperture ring are used as input vectors to input a preset fixed-parameter feedforward network model, and the corrected angular velocity is output.

[0025] Step S104: After correcting the angular velocity, rotate each point in a single frame in the opposite direction to the same reference time, and re-estimate the distortion-free circle center, distortion-free aperture radius, and distortion-free normal based on the distortion-free point set.

[0026] Step S105: Calculate the short-term attitude increment based on the corrected angular velocity, construct the leading edge point by using the undistorted normal and the undistorted aperture ring radius, calculate the vector product of the short-term attitude increment and the leading edge point lever arm with the reference point as the reference, and generate the pre-control command vector.

[0027] Step S106: Calculate the static geometric difference between the digital twin design geometry and the distortion-free circle center and distortion-free normal; calculate the difference between the design pitch circle radius and the distortion-free hole ring radius and convert it into a planar displacement correction amount; combine the current pose, static geometric difference, planar displacement correction amount and pre-control command vector to output the final docking target pose.

[0028] In one embodiment of the present invention, the spatial coordinates and sampling time of each sampling point in a single frame flange hole ring point cloud are obtained to construct a point cloud data set;

[0029] Calculate the centroid of all spatial coordinates in the point cloud dataset, construct a covariance matrix based on the deviation between each spatial coordinate and the centroid, select the eigenvector corresponding to the smallest eigenvalue of the covariance matrix as the plane normal, and construct the best-fit plane through the centroid and the plane normal.

[0030] Each spatial coordinate in the point cloud dataset is projected along the plane normal to the best-fit plane to obtain the projected point set; Casagrande circle fitting is performed on the projected point set to calculate the center coordinates and aperture radius of the best-fit circle.

[0031] Calculate the Euclidean distance between each projection point in the projection point set and the center coordinates of the circle, and subtract the radius of the hole ring from the Euclidean distance to obtain the radial residual corresponding to each sampling point;

[0032] Calculate the mean of the sampling time and the mean of the radial residual for all sampling points. Calculate the sum of the products of the deviations of the sampling time and the radial residual from their respective means. Divide the sum of the products of the deviations by the sum of the squares of the deviations of the sampling time from the mean of the sampling time to obtain the temporal slope of the radial error of the single-frame aperture ring.

[0033] Specifically, the formula for calculating the timing slope of the radial error of a single-frame aperture ring is as follows:

[0034] ,in Indicates the first Sampling time for each sampling point This represents the mean across all sampling times. Indicates the first The radial residual of each sampling point relative to the best-fit circle (the difference between the distance from the point to the fitting circle after projection onto the best-fit plane and the radius of the hole ring). This represents the mean of the radial residuals.

[0035] It should be noted that a single-frame flange bolt hole ring point cloud represents a dataset containing all 3D sampling points of the flange bolt hole ring area, collected by devices such as LiDAR within a single scanning cycle. This dataset corresponds to only one continuous scanning time period and does not include data from multiple scanning cycles. The spatial coordinates of the sampling points represent the position data of each sampling point in the 3D coordinate system within the single-frame flange bolt hole ring point cloud; the sampling time of the sampling points represents the specific time data corresponding to the LiDAR acquisition of each sampling point. The point cloud dataset represents the dataset formed by associating the spatial coordinates of all sampling points in the single-frame flange bolt hole ring point cloud with their corresponding sampling times. The structure of each element contains the spatial coordinates of a sampling point and the sampling time of that point. The centroid represents the average position of the spatial coordinates of all sampling points in the single-frame flange bolt hole ring point cloud; the deviation of each spatial coordinate from the centroid represents the difference between the spatial coordinates of each sampling point and the centroid coordinates in the 3D direction, used to indicate the degree of deviation of a single sampling point from the overall center of the point cloud.

[0036] It should be noted that the covariance matrix is ​​a 3x3 matrix constructed based on the 3D deviations of all sampling points from the centroid. It describes the dispersion of the point cloud along each coordinate axis in 3D space and between the coordinate axes. Specifically, constructing the covariance matrix includes:

[0037] First, calculate the sum of the squares of the deviations of all sampling points in the X-axis direction, divide by the total number of sampling points, and obtain the elements of the first row and first column of the matrix;

[0038] Calculate the sum of the products of the X-axis deviation and the Y-axis deviation of all sampling points, divide by the total number of sampling points, and obtain the element in the first row and second column of the matrix;

[0039] Calculate the sum of the products of the X-axis deviation and the Z-axis deviation of all sampling points, divide by the total number of sampling points, and obtain the element in the first row and third column of the matrix;

[0040] Calculate the sum of the products of the Y-axis deviation and the X-axis deviation of all sampling points, divide by the total number of sampling points, and obtain the element in the second row and first column of the matrix;

[0041] Calculate the sum of the squares of the Y-axis deviations of all sampling points, divide by the total number of sampling points, and obtain the element in the second row and second column of the matrix;

[0042] Calculate the sum of the products of the Y-axis deviation and the Z-axis deviation of all sampling points, divide by the total number of sampling points, and obtain the element in the second row and third column of the matrix;

[0043] Calculate the sum of the products of the Z-axis deviation and the X-axis deviation of all sampling points, divide by the total number of sampling points, and obtain the element in the third row and first column of the matrix;

[0044] Calculate the sum of the products of the Z-axis deviation and the Y-axis deviation of all sampling points, divide by the total number of sampling points, and obtain the element in the third row and second column of the matrix;

[0045] Calculate the sum of the squares of the Z-axis deviations of all sampling points, divide by the total number of sampling points, and obtain the element in the third row and third column of the matrix.

[0046] It should be noted that the three eigenvalues ​​of the covariance matrix are obtained through eigenvalue decomposition algorithms (such as the Jacobi algorithm). The smallest of these three eigenvalues ​​is selected as the minimum eigenvalue of the covariance matrix. The plane normal represents the eigenvector corresponding to the minimum eigenvalue of the covariance matrix. This vector is perpendicular to the plane containing the flange annulus and is used to represent the normal direction of the flange plane. When performing eigenvalue decomposition on the covariance matrix, the eigenvector bound to the minimum eigenvalue is obtained. This eigenvector is then normalized (i.e., each of the three components of the vector is divided by its magnitude, which is the square root of the sum of the squares of the three components). The resulting normalized vector is the eigenvector corresponding to the minimum eigenvalue of the covariance matrix. The best-fit plane represents the plane that best fits the distribution of the single-frame flange hole ring point cloud. This plane can encompass all sampling points to the maximum extent. Specifically, with the centroid as a point on the plane and the plane normal as the perpendicular direction of the plane, the plane equation satisfies: the plane normal component on the X-axis multiplied by (X coordinate of any point minus X coordinate of the centroid), plus the plane normal component on the Y-axis multiplied by (Y coordinate of any point minus Y coordinate of the centroid), plus the plane normal component on the Z-axis multiplied by (Z coordinate of any point minus Z coordinate of the centroid), the result equals 0. All points that satisfy this equation constitute the best-fit plane.

[0047] It should be noted that the projection point set represents the set of all projected points formed after the spatial coordinates of all sampling points in a single frame flange hole ring point cloud are projected perpendicularly along the plane normal direction onto the best-fit plane. Specifically, for each sampling point, the distance from the sampling point to the best-fit plane is first calculated (the distance is calculated by multiplying the plane normal component on the X-axis by (sampling point X coordinate minus centroid X coordinate), adding the plane normal component on the Y-axis by (sampling point Y coordinate minus centroid Y coordinate), adding the plane normal component on the Z-axis by (sampling point Z coordinate minus centroid Z coordinate), and taking the absolute value of the result). Then, the sampling point is moved this distance along the plane normal direction towards the best-fit plane, and the coordinates of the moved point are the projection point coordinates of the sampling point on the best-fit plane. The projection point coordinates of all sampling points constitute the projection point set.

[0048] It should be noted that Casagrande circle fitting is used to find the circle that best fits the distribution of all projection points from the set of projection points (i.e., the best-fit circle). This algorithm determines the parameters of the circle by minimizing the sum of squared algebraic distances from all projection points to the fitted circle, and is suitable for parameter estimation of circular features such as flange hole rings. Specifically, firstly, let the general equation of the fitted circle be X squared plus Y squared, plus A multiplied by X, plus B multiplied by Y, plus C equal to 0 (where A, B, and C are the parameters to be determined); then, based on the two-dimensional coordinates (X coordinate, Y coordinate) of each projection point in the set of projection points, construct... Equation system: For each projection point, substitute its X and Y coordinates into the general equation above to obtain an equation. The equations corresponding to all projection points constitute an equation system. Then, solve the equation system using the least squares method to minimize the sum of squares of the results after substituting all projection points into the equation, and obtain the three parameters A, B, and C. Finally, calculate the center coordinates of the best-fit circle (A divided by 2 for negative X coordinates of the center, B divided by 2 for negative Y coordinates of the center) and the radius of the hole ring (radius is the square root of (A squared divided by 4 plus B squared divided by 4 minus C) based on A, B, and C.

[0049] It should be noted that the center coordinates of the best-fit circle represent the coordinates of the center of the circle that best fits the set of projected points, obtained through the Casarte circle fitting algorithm, in the two-dimensional coordinate system of the best-fit plane, used to represent the center position of the flange hole ring. The projection point represents a single point in the projection point set, that is, a single sampling point in a single frame of the flange hole ring point cloud projected onto the best-fit plane along the plane normal, and is represented by two-dimensional coordinates. The radial residual represents the radial deviation of a single projected point relative to the best-fit circle. If the residual is positive, it indicates that the projected point is outside the best-fit circle; if it is negative, it indicates that it is inside the circle; if it is zero, it indicates that the point is on the circle. The deviation of the sampling time from its mean represents the difference between the sampling time of a single sampling point and the mean of the sampling times of all sampling points, used to represent the degree of deviation of a single sampling time from the average sampling time. The deviation of the radial residual from its mean represents the difference between the radial residual of a single sampling point and the mean of the radial residuals of all sampling points, used to represent the degree of deviation of a single radial residual from the average residual. The temporal slope of the single-frame aperture ring radial error represents the rate at which the radial residual changes with the sampling time within a single frame, and is used to represent the rate of geometric distortion of the single-frame point cloud caused by the asynchronous movement and scanning.

[0050] In one embodiment of the present invention, three mutually orthogonal candidate rotation axes are established based on the plane normal of the flange surface, the coordinates of the center of the circle, and the projection point with the largest distance from the center of the circle. The first candidate rotation axis is a unit vector pointing from the center of the circle to the projection point with the largest distance. The third candidate rotation axis is the plane normal. The second candidate rotation axis is the vector product of the third and first candidate rotation axes.

[0051] The time derivative of the virtual micro-rotation is set. For each candidate rotation axis, the virtual rotation angle of each sampling point is calculated based on the deviation of the time derivative from the sampling time relative to the time mean. The original sampling points are rotated around the center and the corresponding candidate rotation axis using the Rodriguez rotation formula to generate the perturbation point set corresponding to each axis.

[0052] It should be noted that the first candidate rotation axis represents a unit vector obtained by normalizing the vector from the center of the fitted circle to the projection point with the largest distance from the center (making the vector magnitude 1), and it lies within the flange surface. First, the coordinates of the projection point with the largest distance from the center are calculated, and then the coordinates of the fitted circle's center are subtracted to obtain the initial vector. Next, the magnitude of the initial vector is calculated. Finally, each component of the initial vector is divided by this magnitude, and the resulting normalized vector is the first candidate rotation axis. The second candidate rotation axis represents a unit vector obtained by performing a cross product operation between the third candidate rotation axis (i.e., the flange surface plane normal) and the first candidate rotation axis. It lies within the flange surface and is perpendicular to both the first and third candidate rotation axes.

[0053] The time derivative of virtual micro-rotation represents an angular velocity constant artificially set to simulate minute rotational motion. It is used only for numerical calculations of the sensitivity of candidate rotation axes and does not affect the actual movement of the hoisting equipment. Its value typically ranges from 0.001 to 0.01 radians per millisecond. The virtual rotation angle represents the angle of virtual micro-rotation of each sampling point around a candidate rotation axis. It varies with sampling time and is used to generate a perturbation point set. For each candidate rotation axis and each sampling point, the time derivative of virtual micro-rotation is multiplied by the deviation of the sampling time of that sampling point from the time mean; the result is the virtual rotation angle of that sampling point around the candidate rotation axis. The perturbation point set represents the new point cloud set obtained after all sampling points are virtually rotated around a candidate rotation axis. Each candidate rotation axis corresponds to one perturbation point set. Specifically, for each candidate rotation axis, with the center of the fitted circle as the rotation center and the candidate rotation axis as the rotation axis, each original sampling point is rotated by the corresponding virtual rotation angle using the Rodrigues rotation formula to obtain the perturbation point of each original sampling point. The set of all perturbation points is the perturbation point set corresponding to that candidate rotation axis.

[0054] In one embodiment of the present invention, for each candidate rotation axis perturbation point set, planar projection, circle fitting and radial residual calculation are performed sequentially, and the radial residual is linearly regressed with the sampling time to obtain the perturbation slope corresponding to each candidate rotation axis.

[0055] Calculate the difference between the perturbation slope of each candidate rotation axis and the time-series slope of the radial error of the single-frame aperture ring, and divide the difference by the time derivative of the virtual micro-rotation to obtain the axial sensitivity of each candidate rotation axis;

[0056] The candidate rotation axis corresponding to the axial sensitivity with the largest absolute value is selected as the master sensing axis. The time-series slope of the single-frame aperture ring radial error is divided by the axial sensitivity of the master sensing axis to obtain the single-axis scaled angular velocity.

[0057] Specifically, Axial sensitivity of direction The calculation formula is as follows:

[0058] , Indicates the first Unit vectors of candidate rotation axes, Indicates surrounding The applied virtual micro-rotation angle, This represents the slope calculated from the original point set. This indicates that a wrapping force is applied to the point set. After virtual micro-rotation; the principal sensing axis is taken The largest one.

[0059] It should be noted that the perturbation slope represents the temporal slope of the single-frame aperture loop radial error corresponding to the perturbation point set. This is achieved by sequentially performing the plane projection, circle fitting, and radial residual calculation steps in S101 on the perturbation point set to obtain the radial residual for each perturbation point. Then, a linear regression is performed between the sampling time of the perturbation point and the corresponding radial residual, and the resulting regression slope is the perturbation slope corresponding to that candidate rotation axis. Axial sensitivity represents the degree to which the temporal slope of the single-frame aperture loop radial error is sensitive to the rotational motion of a candidate rotation axis, i.e., the change in slope caused by a unit rotational angular velocity. The principal sensitive axis represents the rotation axis with the largest absolute value of axial sensitivity among the three candidate rotation axes, i.e., the axis most sensitive to the rotational motion of the single-frame aperture loop radial error temporal slope. The single-axis scaled angular velocity represents the rotational angular velocity along the direction of the principal sensitive axis.

[0060] In one embodiment of the present invention, the radial error timing slope of the single-frame aperture ring, the axial sensitivity of the main sensitive axis, and the single-frame readout duration are combined in sequence to construct a three-dimensional input vector;

[0061] The three-dimensional input vector is normalized element-wise by a preset mean vector and standard deviation vector. The difference between the three-dimensional input vector and the mean vector is calculated, and the difference is divided element-wise by the standard deviation vector to obtain the normalized input vector.

[0062] The normalized input vector is input into the first hidden layer of the fixed-parameter feedforward network model. The normalized input vector is linearly transformed by the first fixed weight matrix and the first fixed bias vector is accumulated. The first preset element-wise activation function is applied to the operation result to obtain the first hidden layer feature vector.

[0063] The first hidden layer feature vector is input into the second hidden layer of the fixed parameter feedforward network model. The first hidden layer feature vector is linearly transformed by the second fixed weight matrix and accumulated by the second fixed bias vector. The second preset element-wise activation function is applied to the result to obtain the second hidden layer feature vector.

[0064] The second hidden layer feature vector is input into the output layer of the fixed parameter feedforward network model. The second hidden layer feature vector is linearly transformed by the third fixed weight matrix and the third fixed bias scalar is accumulated to output the corrected angular velocity.

[0065] It should be noted that the preset mean vector represents a three-dimensional constant vector composed of the average values ​​of each component obtained after offline statistical analysis of multiple sets of three-dimensional input vector samples under different scenarios. At least 1000 sets of three-dimensional input vector samples covering different flange materials, measurement distances, and incident angles were collected. The average values ​​of the first component (slope), the second component (sensitivity), and the third component (readout time) of all samples were calculated respectively. The three average values ​​were then combined in the order of slope mean, sensitivity mean, and readout time mean to obtain the preset mean vector. The preset standard deviation vector represents a three-dimensional constant vector composed of the standard deviations of each component obtained after offline statistical analysis of multiple sets of three-dimensional input vector samples under different scenarios. This vector is used to eliminate dimensional and numerical scale differences among the components of the input vector. Normalization of the input vector is performed using Z-Score, which will not be elaborated here.

[0066] It should be noted that the first fixed weight matrix represents a pre-set constant matrix in the first hidden layer with a dimension equal to the number of neurons in the first hidden layer multiplied by 3. It is dimensionless, and each element represents the weight of the input vector component on the corresponding neuron in the first hidden layer. If the first hidden layer has 8 neurons, the first fixed weight matrix is ​​8 rows and 3 columns, where each row corresponds to one neuron in the first hidden layer, and each column corresponds to one component of the normalized input vector. The matrix element values ​​are obtained through offline supervised training. The first fixed bias vector represents a pre-set constant vector in the first hidden layer with a dimension consistent with the number of neurons in the first hidden layer. It is dimensionless and used to adjust the offset of the linear transformation result, avoiding feature extraction bias caused by input data distribution shifts. The first pre-set element-wise activation function uses the ReLU function. The first hidden layer feature vector represents the vector output by the first hidden layer after linear transformation, bias accumulation, and activation operation. Its dimension is the same as the number of neurons in the first hidden layer. Specifically, matrix-vector multiplication is first performed on the first fixed weight matrix and the normalized input vector (multiplying each element of the matrix with each component of the input vector and summing the results to obtain the corresponding values ​​for each row, and all values ​​form an intermediate vector). Then, the intermediate vector is added element-wise to the first fixed bias vector to obtain the linear operation result. Finally, the first preset element-wise activation function is applied to each element of the linear operation result, and the resulting vector is the first hidden layer feature vector.

[0067] It should be noted that the second fixed weight matrix represents a pre-set constant matrix in the second hidden layer with dimensions equal to the number of neurons in the second hidden layer multiplied by the number of neurons in the first hidden layer. It is dimensionless, and each element represents the weight of the influence of the corresponding component of the first hidden layer feature vector on the corresponding neuron in the second hidden layer. If the second hidden layer has 4 neurons and the first hidden layer has 8 neurons, then the second fixed weight matrix is ​​4 rows and 8 columns. The second fixed bias vector represents a pre-set constant vector in the second hidden layer with dimensions matching the number of neurons in the second hidden layer. If the second hidden layer has 4 neurons, then the second fixed bias vector is 4-dimensional. The second pre-set element-wise activation function is the ReLU function. The second hidden layer feature vector represents the vector output by the second hidden layer after linear transformation, bias accumulation, and activation operation. Its dimension is the same as the number of neurons in the second hidden layer. Specifically, first, a matrix-vector multiplication is performed between the second fixed weight matrix and the first hidden layer feature vector (multiplying each element of the matrix with each component of the first hidden layer feature vector and summing the results to obtain the corresponding values ​​for each row, with all values ​​forming an intermediate vector). Then, the intermediate vector is added element-wise to the second fixed bias vector to obtain the linear operation result. Finally, the second preset element-wise activation function is applied to each element of the linear operation result, and the resulting vector is the second hidden layer feature vector.

[0068] It should be noted that the third fixed weight matrix represents a pre-set constant matrix in the output layer with a dimension of 1 × the number of neurons in the second hidden layer. It is dimensionless, and each element represents the weight of the corresponding component of the second hidden layer feature vector on the output (corrected angular velocity). Specifically, if the second hidden layer has 4 neurons, the third fixed weight matrix will be 1 row and 4 columns. The third fixed bias scalar represents a pre-set, single constant value in the output layer. It is dimensionless and used to adjust the offset of the linear transformation result of the output layer to ensure the numerical accuracy of the corrected angular velocity. Specifically, the third fixed weight matrix is ​​first multiplied by the second hidden layer feature vector (multiplying each row element of the matrix with each component of the second hidden layer feature vector and then summing the results to obtain a single intermediate value); then this intermediate value is added to the third fixed bias scalar, and the result is the corrected angular velocity.

[0069] It should be noted that all fixed parameters are obtained through the following offline training process: 1. Construct training dataset: Collect at least 1000 sets of samples, each set containing a 3D input vector and a label (true angular velocity). The true angular velocity is synchronously measured using a high-precision gyroscope (accuracy must be better than 0.001 radians per millisecond); 2. Initialize parameters: Initialize all weight matrix elements to random values ​​between -0.1 and 0.1, and initialize the bias vector / scalar to 0; 3. Training iteration: Use the stochastic gradient descent algorithm, with the mean square error between the corrected angular velocity and the label output by the network as the loss function. Each iteration takes 16 sets of samples (batch size), calculates the gradient of the loss function with respect to each parameter, and updates the parameters according to the rule parameter = parameter - learning rate × gradient (the learning rate is initially set to 0.001 and halved every 100 iterations); 4. Stop condition: Stop training when the loss function value is less than 0.001 for 50 consecutive iterations (or the number of iterations reaches 1000), save the final weight matrix and bias as fixed parameters for online calculation, and ensure that the parameters can accurately fit the bias mapping relationship.

[0070] It should be noted that the samples must cover all actual hoisting scenarios to ensure the universality of the mean and standard deviation: 1. Flange material: covering common materials such as carbon steel, stainless steel, and alloy steel (different materials have different reflectivities, affecting slope and sensitivity); 2. Measurement distance: covering 2 to 10 meters (common measurement range for LiDAR, distance affects point cloud accuracy); 3. Incident angle: covering 0 to 30 degrees (common angle range during flange hoisting, incident angle affects projection accuracy); 4. Swing rate: covering 0.001 to 0.01 radians per millisecond (the swing rate range of conventional hoisting, ensuring coverage of different dynamic scenarios); at least 50 sets of samples should be collected for each scenario, with a total sample size of no less than 1000 sets, to avoid abnormal values ​​after normalization of certain types of inputs due to missing scenarios (such as exceeding the reasonable range of -3 to 3), affecting the stability of network operations.

[0071] In one embodiment of the present invention, the median of the sampling time of a single frame is selected as the reference time, the time difference of each sampling point relative to the reference time is calculated, the time difference is multiplied by the corrected angular velocity and the negative is taken to obtain the reverse rotation angle of each sampling point.

[0072] Using the center of the best-fit circle as the rotation center and the principal sensing axis as the rotation axis, the sampling points are rotated by the corresponding reverse rotation angle using the Rodriguez rotation formula to generate a set of distortion-free points.

[0073] Calculate the centroid and covariance matrix of the distortion-free point set, select the eigenvector corresponding to the smallest eigenvalue of the covariance matrix as the distortion-free normal, construct the distortion-free best-fit plane, and project the distortion-free point set onto the distortion-free best-fit plane.

[0074] Specifically, the first The coordinates of each point at the reference time after distortion correction The calculation formula is as follows:

[0075] ,in Indicates the first The three-dimensional coordinates of the original sampling points Indicates the center of the best-fit circle. Indicates about the axis Rotation angle Rodriguez's rotation The unit vector representing the principal sensing axis. Indicates the corrected angular velocity. Indicates a reference time.

[0076] It should be noted that the reference time is used to uniformly correct points sampled at different times to the same instantaneous attitude, avoiding correction deviations caused by extreme sampling times. The reverse rotation angle represents the rotation angle used to compensate for asynchronous distortion within the frame; it is calculated by multiplying the time difference of a single sampling point by the corrected angular velocity, and the negative value of the product is the reverse rotation angle for that sampling point. The rotation center is the center of the hole ring circle obtained through Casagrande circle fitting, serving as the reference point for distortion-free rotation and ensuring that the rigid geometry of the hole ring remains unchanged after rotation. The distortion-free normal vector represents the normal vector of the distortion-free best-fit plane, perpendicular to the distortion-free plane of the flange. The distortion-free best-fit plane represents the plane that best fits the distortion-free point set. Specifically, the centroid of the distortion-free point set is taken as the point on the plane, and the distortion-free normal is taken as the perpendicular direction of the plane. The plane equation satisfies: the distortion-free normal X component multiplied by (X coordinate of any point minus X coordinate of the centroid), plus the distortion-free normal Y component multiplied by (Y coordinate of any point minus Y coordinate of the centroid), plus the distortion-free normal Z component multiplied by (Z coordinate of any point minus Z coordinate of the centroid), the result equals 0. All points that satisfy this equation constitute the distortion-free best-fit plane.

[0077] In one embodiment of the present invention, a local orthogonal coordinate system is established in the distortion-free best fitting plane, the projected distortion-free points are converted into planar coordinates, the fitting parameters are solved by the Casa circle fitting model, and the radius of the distortion-free hole ring and the coordinates of the center of the distortion-free circle in the plane are calculated based on the fitting parameters.

[0078] The coordinates of the undistorted center of a circle in a plane are transformed into the coordinates of the undistorted center of a circle in three-dimensional space by using a local orthogonal coordinate system.

[0079] It should be noted that the projected distortion-free point represents the point on the distortion-free best-fit plane that is perpendicularly projected along the distortion-free normal. Specifically, for each distortion-free point, the distance from that point to the distortion-free best-fit plane is calculated (the distance is the distortion-free normal X component multiplied by (distortion-free point X coordinate minus centroid X coordinate), plus the distortion-free normal Y component multiplied by (distortion-free point Y coordinate minus centroid Y coordinate), plus the distortion-free normal Z component multiplied by (distortion-free point Z coordinate minus centroid Z coordinate), and the absolute value is taken). The distortion-free point is then moved this distance along the distortion-free normal along the plane, and the point after the movement is the projected distortion-free point. The local orthogonal coordinate system represents a two-dimensional orthogonal coordinate system constructed within the distortion-free best-fit plane, used to convert the projected three-dimensional distortion-free points into two-dimensional planar coordinates. Specifically, the X-axis unit vector (1,0,0) is selected. If the absolute value of the dot product between this vector and the distortion-free normal is greater than 0.9 (close to parallel), then the Y-axis unit vector (0,1,0) is used instead. The cross product of the selected unit vector and the distortion-free normal is performed to obtain the first coordinate axis vector, which is normalized and used as the U-axis of the local coordinate system. The cross product of the distortion-free normal and the U-axis is performed to obtain the second coordinate axis vector, which is normalized and used as the V-axis of the local coordinate system. The U-axis and V-axis constitute a local orthogonal coordinate system in the plane.

[0080] It should be noted that the planar coordinates represent the two-dimensional coordinates (U-axis coordinates and V-axis coordinates) of the projected distortion-free points in the local orthogonal coordinate system. Specifically, for each projected distortion-free point, the deviation vector between that point and the centroid of the distortion-free point set is calculated. The deviation vector is multiplied by the U-axis of the local orthogonal coordinate system to obtain the U-axis coordinate of that point. The deviation vector is also multiplied by the V-axis of the local orthogonal coordinate system to obtain the V-axis coordinate of that point. The U-axis coordinate and V-axis coordinate together constitute the planar coordinates. The fitting parameters of the Casagrande circle fitting model include three parameters. Specifically, let the general equation of the Casagrande circle fitting model be: planar coordinates U² + V², plus A multiplied by U, plus B multiplied by V, plus C equals 0, where A, B, and C are the fitting parameters. Based on the planar coordinates of all projected distortion-free points, a system of equations is constructed (substituting each point into the equation yields an equation). The system of equations is solved using the normal equation method (calculating the product of the transpose and coefficient matrix of the coefficient matrix, then inverting it and multiplying it by the product of the transpose and dependent variable vector of the coefficient matrix) to obtain the fitting parameters A, B, and C. The radius of the distortion-free orifice ring represents the actual radius of the flange orifice ring under distortion-free conditions. Specifically, the square root of the difference obtained by dividing the square of the fitting parameter A by 4, adding the square of the fitting parameter B by 4, and then subtracting the fitting parameter C, is the radius of the distortion-free orifice ring. The coordinates of the distortion-free center in the plane represent the two-dimensional coordinates (U-axis and V-axis coordinates) of the center of the distortion-free orifice ring in a locally orthogonal coordinate system. Specifically, the U-axis coordinate of the center is equal to the negative of the fitting parameter A divided by 2, and the V-axis coordinate of the center is equal to the negative of the fitting parameter B divided by 2. These two coordinates together constitute the coordinates of the distortion-free center in the plane. The three-dimensional distortion-free center represents the actual coordinates of the center of the distortion-free orifice ring in three-dimensional space. Specifically, the result of multiplying the U-axis coordinate of the center in the plane by the U-axis vector of the locally orthogonal coordinate system by the centroid of the distorted point set, and then multiplying the V-axis coordinate of the center in the plane by the V-axis vector of the locally orthogonal coordinate system, is the three-dimensional distortion-free center.

[0081] It should be noted that when calculating the distance from the distortion-removed point to the distortion-free best-fit plane, the sign of the distance is retained (rather than just the absolute value). That is, if the distance is positive, it means that the point is on the side of the plane's positive normal direction, and the distance needs to be moved along the negative normal direction; if the distance is negative, it means that the point is on the side of the plane's negative normal direction, and the absolute value needs to be moved along the positive normal direction. After moving, the point satisfies the plane equation, ensuring that the projected point falls accurately on the distortion-free best-fit plane and avoiding projection deviation due to incorrect direction.

[0082] In one embodiment of the present invention, a short-time prediction time window is set, the corrected angular velocity is multiplied by the short-time prediction time window to obtain the rotation angle increment, and the main sensitive axis is multiplied by the rotation angle increment to obtain the short field of view attitude increment vector.

[0083] Calculate the dot product of the main sensing axis and the distortion-free normal, multiply the distortion-free normal by the dot product to obtain the normal component, and subtract the normal component from the main sensing axis to obtain the projection component of the main axis in the flange surface.

[0084] Calculate the vector product of the distortion-free normal and the projected component, normalize the vector product to obtain the leading edge direction vector, multiply the leading edge direction vector by the radius of the distortion-free aperture ring to obtain the radius vector, and add the distortion-free circle center to the radius vector to obtain the leading edge point.

[0085] It should be noted that the short-time prediction window represents a short time interval preset before docking, used to predict the attitude changes of the flange within this interval. It is typically set between 50 and 200 milliseconds, adjusted according to the response delay of the hoisting system. The rotation angle increment represents the angle by which the flange rotates around the main sensitive axis within the short-time prediction window, reflecting the magnitude of the attitude change; the rotation angle increment is obtained by multiplying the corrected angular velocity by the short-time prediction window. The direction of the short-view attitude increment vector is the rotation axis (main sensitive axis), and the magnitude is the rotation angle (rotation angle increment), intuitively reflecting the attitude change trend of the flange within a short time. The dot product of the main sensitive axis and the undistorted normal represents the dot product of the main sensitive axis (unit vector) and the undistorted normal (unit vector), reflecting the cosine of the angle between the two vectors. The normal component represents the component of the main sensitive axis parallel to the undistorted normal. The projection component of the main axis onto the flange surface represents the effective rotation component of the main sensitive axis located within the flange surface, eliminating redundant normal components.

[0086] It should be noted that if the system response delay (the time from the issuance of the instruction to its completion) is 30 milliseconds, the short-term prediction time window must be greater than the delay (preferably 50 to 80 milliseconds) to ensure that the oscillation is exactly offset within the prediction time window after the compensation instruction is issued; if the delay is 100 milliseconds, a value of 120 to 150 milliseconds is preferred; it is forbidden to take a value less than the response delay (the oscillation has occurred before the compensation instruction is executed) or greater than 3 times the delay (the prediction error exceeds 10%), which will not be elaborated here.

[0087] It should be noted that the vector product of the distortion-free normal and the projected component represents the cross product of the distortion-free normal and the projected component. The direction is perpendicular to both and lies within the flange surface; it is the original vector of the leading edge direction. The leading edge direction vector; the X-axis component of the vector product equals the Y-axis component of the distortion-free normal multiplied by the Z-axis component of the projected component, minus the Z-axis component of the distortion-free normal multiplied by the Y-axis component of the projected component; the Y-axis component of the vector product equals the Z-axis component of the distortion-free normal multiplied by the X-axis component of the projected component, minus the X-axis component of the distortion-free normal multiplied by the Z-axis component of the projected component; the Z-axis component of the vector product equals the X-axis component of the distortion-free normal multiplied by the Y-axis component of the projected component, minus the Y-axis component of the distortion-free normal multiplied by the X-axis component of the projected component; these three together constitute the vector product of the distortion-free normal and the projected component. The leading edge direction vector represents the direction vector within the flange surface most sensitive to rotational displacement. The radius vector represents the vector pointing from the center of the undistorted circle to the leading edge point, with a length equal to the radius of the undistorted flange ring and a direction corresponding to the leading edge. The leading edge point represents the point on the flange ring with the largest rotational displacement.

[0088] In one embodiment of the present invention, a reference point is set in the digital twin coordinate system, the difference between the leading edge point and the reference point is calculated to obtain the lever arm vector, and the vector product of the short horizon attitude increment vector and the lever arm vector is calculated to obtain the feedforward translation compensation component.

[0089] The feedforward translation compensation component and the short-viewpoint attitude increment vector are combined sequentially to generate the pre-control command vector.

[0090] Specifically, feedforward translation compensation components The calculation formula is as follows:

[0091] ,in This represents the short field of view pose increment vector. Indicates the frontier point, This represents the reference point in the digital twin coordinate system. This represents the cross product of vectors.

[0092] It should be noted that the reference point in the digital twin coordinate system is selected from the fixed reference point of the hoisting system (such as the hoisting point or the origin of the docking target); the lever arm vector represents the vector pointing from the reference point to the leading edge point, reflecting the distance and direction from the reference point to the leading edge point. The feedforward translation compensation component represents the equivalent translation compensation amount of the leading edge point, which is used to offset the displacement of the leading edge point caused by rotation. The pre-control command vector represents a six-dimensional command vector containing translation compensation and rotation compensation, which is directly used for subsequent docking pose synthesis.

[0093] It should be noted that when calculating the vector product of the distortion-free normal and the projected component, the four fingers of the right hand bend from the distortion-free normal towards the projected component, and the thumb points in the direction of the vector product (ensuring the direction is the direction of the maximum rotational displacement within the flange plane). When calculating the vector product of the short-field attitude increment vector and the lever arm vector, the four fingers of the right hand bend from the short-field attitude increment vector (rotation axis) towards the lever arm vector (lever arm), and the thumb points in the direction of the translational compensation (ensuring the direction is opposite to the actual displacement direction of the leading edge point to achieve cancellation); for example, if the short-field attitude increment vector is upward (the main sensing axis is upward) and the lever arm vector is forward, the vector product direction is to the right, which exactly cancels the rotational displacement of the leading edge point to the left; in actual calculations, this can be verified using the right-hand screw rule: if the rotation is counterclockwise (viewed from the axis end), the translational compensation direction must be consistent with the rotation direction to ensure effective compensation.

[0094] In one embodiment of the present invention, the difference between the center of the digital twin design circle and the center of the distortion-free circle is calculated to obtain the translation difference vector;

[0095] Calculate the magnitude and dot product of the vector product of the distortion-free normal and the digital twin design normal, calculate the rotation angle using the four-quadrant arctangent function, normalize the vector product to obtain the rotation axis, and multiply the rotation angle by the rotation axis to obtain the rotation difference vector.

[0096] Calculate the algebraic difference between the pitch circle radius and the radius of the distortion-free orifice ring in the digital twin design, and multiply the algebraic difference by the leading edge direction vector in the flange face to obtain the planar displacement correction vector;

[0097] The planar displacement correction vector is added to the translation difference vector to obtain the corrected translation difference component. The corrected translation difference component is combined with the rotation difference vector to form the static pose increment.

[0098] The current pose, static pose increment, and pre-control command vector are superimposed according to the small pose increment composite rule to output the final docking target pose.

[0099] Specifically, the rotational difference vector is obtained by multiplying the angle by the unit axis. The calculation formula is as follows:

[0100] ,in Represents a unit vector with an undistorted normal. The unit vector representing the normal to the digital twin design. Indicates the arctangent of the four quadrants. Represents the product of two normal vectors. Indicates the modulus length. It represents the dot product of the two normal directions.

[0101] It should be noted that the digital twin design center represents the ideal three-dimensional coordinates of the center of the flange joint circle after the flange is assembled in the digital twin model, serving as the reference for static position. The translation difference vector represents the positional deviation vector between the ideal design center and the currently measured undistorted center, reflecting the static translational deviation of the flange in three-dimensional space. The digital twin design normal represents the ideal normal unit vector of the flange plane after the flange is assembled in the digital twin model, serving as the reference for static attitude. The rotation angle represents the angle between the undistorted normal and the design normal, reflecting the magnitude of the flange's static attitude deviation; specifically, the four-quadrant arctangent function is called, with the magnitude of the vector product of the undistorted normal and the design normal as the numerator input and the dot product of the two normals as the denominator input. The angle value output by the function is the rotation angle (the angle range is from -π to π radians, ensuring the direction is consistent with the actual rotation). The rotation axis represents the unit vector of the axis of attitude adjustment between the two normals, reflecting the direction around which the flange needs to rotate to align with the design attitude.

[0102] It should be noted that the pitch circle radius of the digital twin design represents the ideal radius of the flange bore ring in the digital twin model, serving as the benchmark for static dimensions. The algebraic difference represents the dimensional deviation between the ideal design radius and the currently measured undistorted radius, reflecting the static dimensional deviation of the flange bore ring; the algebraic difference is obtained by subtracting the undistorted bore ring radius from the digital twin design pitch circle radius (a positive value indicates the measured radius is too small, and a negative value indicates the measured radius is too large). The planar displacement correction vector represents the displacement compensation amount in the sensitive direction within the flange surface, used to offset the influence of dimensional deviations on the docking position. The static pose increment represents a six-dimensional increment vector integrating static translation correction and static attitude correction; the first three dimensions represent translation (millimeters), and the last three dimensions represent rotation (radians), used to eliminate static deviations of the flange. The current pose represents the real-time three-dimensional translation and three-dimensional rotation state of the hoisting equipment. The small pose increment composite rule represents a simplified pose superposition rule under small pose increments (translation ≤ 10 mm, rotation ≤ 0.1 radians). Specifically, the composite translation = the translation component of the previous pose + the translation component of the increment (direct algebraic addition); the composite rotation = the rotation component of the previous pose + the rotation component of the increment (direct algebraic addition). No complex rotation transformation is needed because the nonlinear coupling error at small angles is < 0.1 mm / 0.001 radians. The pre-control command vector represents the six-dimensional vector generated in step S105, which includes dynamic translation compensation and rotation compensation. The final docking target pose represents the final executable command integrating static deviation correction and dynamic feedforward compensation; that is, first, the current pose and the static pose increment are composited according to the small pose composite rule (translation addition, rotation addition); then, the result of the first step is composited again with the pre-control command vector (translation addition, rotation addition); the final six-dimensional vector is the final docking target pose.

[0103] Specifically, the final docking target pose The calculation formula is as follows:

[0104] ,in Indicates the current pose. Indicates small pose increment compounding. Represents the translation difference vector. Represents the plane displacement correction vector. Represents the rotational difference vector. This represents the pre-control command vector.

[0105] It should be noted that, as Figure 2 As shown, the swaying of the pipeline during hoisting causes the sampling points to shift in space, resulting in spiral or non-closed geometric deformations in the scanning results. After processing by this invention, the geometric distortion caused by time asynchrony is eliminated, and the standard circular characteristics of the flange hole ring are restored. This verifies the effectiveness of this invention in removing dynamic distortion of the point cloud by using timestamps and angular velocity correction, and provides a high-quality data foundation for the accurate estimation of the circle center and normal in the future.

[0106] It should be noted that, as Figure 3 As shown, the blue scatter plots represent the radial residuals of the original data, which exhibit a clear linear upward or downward trend over time. The solid blue line represents the temporal slope of the extracted single-frame aperture ring radial error, indicating significant rotational motion during sampling, leading to systematic bias in the point cloud data. The red scatter plots and red line represent the radial residual distribution after correction using the method of this invention. By calculating the axial sensitivity and using a neural network model to output the corrected angular velocity, the original data undergoes distortion correction. The slope of the trend line for the red data is approximately zero, and the residual values ​​are uniformly distributed near zero. Therefore, this invention can effectively identify and eliminate systematic measurement errors caused by dynamic shaking, restoring the point cloud data to a quasi-static level and ensuring the reliability of subsequent feature extraction.

[0107] It should be noted that, as Figure 4 As shown, the red curve closely follows the black true curve, smoothly and accurately reflecting the actual oscillation state of the pipe. The results demonstrate that the neural network model used in this invention can effectively suppress noise interference.

[0108] It should be noted that, as Figure 5 As shown, by combining static pose increments with dynamic pre-control commands, the system can proactively offset sway displacements within the prediction time window. Results indicate that, using the method of this invention, the mean error of the final docking target pose is significantly reduced, and the error fluctuation range is greatly narrowed, significantly improving the success rate and safety of automated pipeline hoisting and docking.

[0109] It should be noted that the interval and threshold sizes are set for ease of comparison. The size of the threshold depends on the amount of sample data and the base number set by those skilled in the art for each set of sample data, as long as it does not affect the proportional relationship between the parameter and the quantized value. Furthermore, the above formulas are all dimensionless calculations, and the formulas are derived from software simulations using a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0110] The embodiments of this example have been described above. However, this example is not limited to the specific implementation methods described above. The specific implementation methods described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms based on the guidance of this example, and all of them are within the protection scope of this example.

Claims

1. A method for pre-controlling positioning errors in the overall hoisting of pipelines based on digital twins, characterized in that, Includes the following steps: Step S101: Obtain the flange hole ring point cloud to extract the time-series slope of the radial error of the single-frame hole ring; Step S102: Apply virtual micro-rotation to each axis, calculate the axial sensitivity of the radial error time-series slope of the single-frame aperture ring relative to the rotational change, select the master sensitive axis, and convert the radial error time-series slope of the single-frame aperture ring into a single-axis scaled angular velocity through the axial sensitivity of the master sensitive axis. Step S103: The radial error temporal slope, axial sensitivity, and single-frame readout duration of the single-frame aperture ring are used as input vectors to input the feedforward network model, and the corrected angular velocity is output. Step S104: After correcting the angular velocity, rotate each point in a single frame in the opposite direction to the same reference time, and re-estimate the distortion-free center, radius and normal based on the distortion-free point set; Step S105: Generate a pre-control command vector based on the corrected angular velocity, the distortion-free normal, and the distortion-free hole ring radius; Step S106: Calculate the static geometric difference, calculate the difference between the design pitch circle radius and the radius of the distortion-free hole ring and convert it into a planar displacement correction amount, combine the current pose, static geometric difference, planar displacement correction amount and pre-control command vector to form a pose composite, and output the final docking target pose.

2. The method for pre-controlling the positioning error of pipeline hoisting based on digital twin as described in claim 1, characterized in that, Obtain the spatial coordinates and sampling time of each sampling point in a single frame flange hole ring point cloud, and construct a point cloud data set; Calculate the centroid of all spatial coordinates in the point cloud dataset, construct a covariance matrix based on the deviation between each spatial coordinate and the centroid, select the eigenvector corresponding to the smallest eigenvalue of the covariance matrix as the plane normal, and construct the best-fit plane through the centroid and the plane normal. Each spatial coordinate in the point cloud dataset is projected along the plane normal to the best-fit plane to obtain the projected point set; Casagrande circle fitting is performed on the projected point set to calculate the center coordinates and aperture radius of the best-fit circle. Calculate the Euclidean distance between each projection point in the projection point set and the center coordinates of the circle, and subtract the radius of the hole ring from the Euclidean distance to obtain the radial residual corresponding to each sampling point; Calculate the mean of the sampling time and the mean of the radial residual for all sampling points. Calculate the sum of the products of the deviations of the sampling time and the radial residual from their respective means. Divide the sum of the products of the deviations by the sum of the squares of the deviations of the sampling time from the mean of the sampling time to obtain the temporal slope of the radial error of the single-frame aperture ring.

3. The method for pre-controlling the positioning error of pipeline hoisting based on digital twin as described in claim 1, characterized in that, Based on the plane normal of the flange face, the coordinates of the center of the circle, and the projection point with the largest distance from the center of the circle, three mutually orthogonal candidate rotation axes are established. The first candidate rotation axis is the unit vector pointing from the center of the circle to the projection point with the largest distance. The third candidate rotation axis is the plane normal. The second candidate rotation axis is the vector product of the third and first candidate rotation axes. The time derivative of the virtual micro-rotation is set. For each candidate rotation axis, the virtual rotation angle of each sampling point is calculated based on the deviation of the time derivative from the sampling time relative to the time mean. The original sampling points are rotated around the center and the corresponding candidate rotation axis using the Rodriguez rotation formula to generate the perturbation point set corresponding to each axis.

4. The method for pre-controlling the positioning error of pipeline hoisting based on digital twin as described in claim 3, characterized in that, For each candidate rotation axis perturbation point set, planar projection, circle fitting, and radial residual calculation are performed sequentially, and linear regression is performed on the radial residual and sampling time to obtain the perturbation slope corresponding to each candidate rotation axis. Calculate the difference between the perturbation slope of each candidate rotation axis and the time-series slope of the radial error of the single-frame aperture ring, and divide the difference by the time derivative of the virtual micro-rotation to obtain the axial sensitivity of each candidate rotation axis; The candidate rotation axis corresponding to the axial sensitivity with the largest absolute value is selected as the master sensing axis. The time-series slope of the single-frame aperture ring radial error is divided by the axial sensitivity of the master sensing axis to obtain the single-axis scaled angular velocity.

5. The method for pre-controlling the positioning error of pipeline hoisting based on digital twin as described in claim 1, characterized in that, The three-dimensional input vector is constructed by sequentially combining the radial error timing slope of the single-frame aperture ring, the axial sensitivity of the main sensitive axis, and the single-frame readout duration. The three-dimensional input vector is normalized element-wise by a preset mean vector and standard deviation vector. The difference between the three-dimensional input vector and the mean vector is calculated, and the difference is divided element-wise by the standard deviation vector to obtain the normalized input vector. The normalized input vector is input into the first hidden layer of the fixed-parameter feedforward network model. The normalized input vector is linearly transformed by the first fixed weight matrix and the first fixed bias vector is accumulated. The first preset element-wise activation function is applied to the operation result to obtain the first hidden layer feature vector. The first hidden layer feature vector is input into the second hidden layer of the fixed parameter feedforward network model. The first hidden layer feature vector is linearly transformed by the second fixed weight matrix and accumulated by the second fixed bias vector. The second preset element-wise activation function is applied to the result to obtain the second hidden layer feature vector. The second hidden layer feature vector is input into the output layer of the fixed parameter feedforward network model. The second hidden layer feature vector is linearly transformed by the third fixed weight matrix and the third fixed bias scalar is accumulated to output the corrected angular velocity.

6. The method for pre-controlling the positioning error of pipeline hoisting based on digital twin as described in claim 1, characterized in that, The median of the single-frame sampling time is selected as the reference time. The time difference of each sampling point relative to the reference time is calculated. The time difference is multiplied by the corrected angular velocity and the negative value is taken to obtain the reverse rotation angle of each sampling point. Using the center of the best-fit circle as the rotation center and the principal sensing axis as the rotation axis, the sampling points are rotated by the corresponding reverse rotation angle using the Rodriguez rotation formula to generate a set of distortion-free points. Calculate the centroid and covariance matrix of the distortion-free point set, select the eigenvector corresponding to the smallest eigenvalue of the covariance matrix as the distortion-free normal, construct the distortion-free best-fit plane, and project the distortion-free point set onto the distortion-free best-fit plane.

7. The method for pre-controlling the positioning error of pipeline hoisting based on digital twin as described in claim 6, characterized in that, A local orthogonal coordinate system is established in the distortion-free best-fit plane. The projected distortion-free points are converted into planar coordinates. The fitting parameters are solved by the Casa circle fitting model. The radius of the distortion-free hole ring and the coordinates of the center of the distortion-free circle in the plane are calculated based on the fitting parameters. The coordinates of the undistorted center of a circle in a plane are transformed into the coordinates of the undistorted center of a circle in three-dimensional space by using a local orthogonal coordinate system.

8. The method for pre-controlling the positioning error of pipeline hoisting based on digital twin according to claim 1, characterized in that, Set a short-time prediction window, multiply the corrected angular velocity by the short-time prediction window to obtain the rotation angle increment, and multiply the main sensing axis by the rotation angle increment to obtain the short-view attitude increment vector; Calculate the dot product of the main sensing axis and the distortion-free normal, multiply the distortion-free normal by the dot product to obtain the normal component, and subtract the normal component from the main sensing axis to obtain the projection component of the main axis in the flange surface. Calculate the vector product of the distortion-free normal and the projected component, normalize the vector product to obtain the leading edge direction vector, multiply the leading edge direction vector by the radius of the distortion-free aperture ring to obtain the radius vector, and add the distortion-free circle center to the radius vector to obtain the leading edge point.

9. A method for pre-controlling the positioning error of pipeline hoisting based on digital twins according to claim 8, characterized in that, Set a reference point in the digital twin coordinate system, calculate the difference between the leading edge point and the reference point to obtain the lever arm vector, calculate the vector product of the short horizon attitude increment vector and the lever arm vector to obtain the feedforward translation compensation component. The feedforward translation compensation component and the short-viewpoint attitude increment vector are combined sequentially to generate the pre-control command vector.

10. The method for pre-controlling the positioning error of pipeline hoisting based on digital twin according to claim 1, characterized in that, The difference between the center of the digital twin design circle and the center of the distortion-free circle is calculated to obtain the translation difference vector; Calculate the magnitude and dot product of the vector product of the distortion-free normal and the digital twin design normal, calculate the rotation angle using the four-quadrant arctangent function, normalize the vector product to obtain the rotation axis, and multiply the rotation angle by the rotation axis to obtain the rotation difference vector. Calculate the algebraic difference between the pitch circle radius and the radius of the distortion-free orifice ring in the digital twin design, and multiply the algebraic difference by the leading edge direction vector in the flange face to obtain the planar displacement correction vector; The planar displacement correction vector is added to the translation difference vector to obtain the corrected translation difference component. The corrected translation difference component is combined with the rotation difference vector to form the static pose increment. The current pose, static pose increment, and pre-control command vector are superimposed according to the small pose increment composite rule to output the final docking target pose.

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