Method for initial calibration and optimization of rotation axis and hand-eye relationship of line laser scanning system

Abstract

The application discloses a line laser scanning system rotating shaft and hand-eye relationship initial calibration and optimization method, comprising: establishing three coordinate systems of a camera coordinate system, a moving coordinate system and a base coordinate system and conversion relations in the scanning system; introducing a joint arm coordinate system, and using a joint arm measuring machine to complete initial calibration of rotating shaft parameters and a translation vector in a hand-eye matrix; using rotating shaft initial calibration parameters and an ICP algorithm to complete initial calibration of the whole hand-eye matrix; and based on a standard cylinder and a special target, comprehensively optimizing the rotating shaft parameters and the hand-eye matrix. The method has the advantages of fast calibration speed, high efficiency, simple operation, good optimization effect, and significantly improved point cloud rotation splicing precision.

Description

Technical Field

[0001] This invention relates to the field of visual inspection system calibration technology, specifically to a method for initial calibration and optimization of the rotation axis and hand-eye relationship of a line laser scanning system. Background Technology

[0002] In recent years, with the development of science and technology, my country has achieved many innovative results in fields such as aerospace, transportation, and robotics. To improve the performance and stability of machines, the industry has increasingly higher requirements for the quality, precision, and even service life of critical components, especially aero-engine blades, gears, and bearings. Therefore, dimensional inspection, defect identification, and 3D reconstruction technologies for large or rotating parts have received widespread attention and are a research hotspot in the visual inspection industry.

[0003] Hand-eye calibration primarily aims to determine the coordinate transformation relationship between the camera and the robotic arm. Due to sensor installation errors, sensor calibration is necessary to establish this transformation. Hand-eye calibration is divided into two categories: eye-to-hand and eye-in-hand. Eye-to-hand: The camera is mounted outside the robotic arm, and the calibration plate is mounted on the end effector. In this case, we need to find the transformation relationship between the camera coordinate system and the robotic arm's base coordinate system. Eye-in-hand: The camera is mounted on the robotic arm, and the calibration plate is fixed outside the robotic arm. In this case, we need to find the coordinate transformation relationship between the camera coordinate system and the end effector of the robotic arm.

[0004] The line laser scanning system consists of a three-axis displacement stage, a rotary stage, and a laser sensor. It can achieve line structured light multidimensional scanning, allowing the sensor's field of view to fully cover any part of the workpiece. Point clouds acquired from various angles are rotated and stitched together to complete the three-dimensional reconstruction of the blade's morphology. The effectiveness of the point cloud rotation and stitching depends on the calibration accuracy of the rotation axis and the hand-eye matrix. To ensure calibration accuracy, the existing technology, as disclosed in the literature "A Novel Digital Dental Model Laser Scanning System," employs the following calibration scheme: using a high-low sphere method for rotation axis calibration; laser scanning of the sphere and fitting the scan data to obtain the sphere's center position; repeating this operation with the rotary stage to obtain multiple sphere center positions at the same height; fitting a spatial circle to obtain the circle's center position; then raising and lowering the standard sphere position and repeating the steps to obtain a sequence of circle center positions; finally, fitting the optimal straight line for all circle centers. The existing technical document "Precision Calibration Method for Non-Contact Optical Measurement of Aircraft Blades" discloses a calibration scheme as follows: A point cloud of the cross-sectional profile of a standard sphere is obtained using a translational scanning method. Data is collected multiple times by rotating the turntable. Then, the singular value decomposition method is used to fit the sphere's center, and the least squares method is used to solve the equation of the sphere's trajectory plane and the normal vector of the rotation axis. Finally, the intersection point of the rotation axis and the trajectory plane is determined; this point is the rotation axis center. Another existing technical document, "Research on Three-Dimensional Surface Scanning and Detection Method of Rotating Workpieces Based on Structured Light," discloses a calibration scheme as follows: A surface scanning and detection model of the rotating workpiece is established based on a cylindrical coordinate system, and the hand-eye relationship is calibrated using homography transformation in a line structured light measurement system. Wang Zhenyou proposed a joint calibration method for the turntable and the hand-eye relationship, using a double-sphere rod as the calibration object. After calibrating the rotation axis parameters and the hand-eye matrix, the results are substituted into the objective function for nonlinear optimization to obtain the optimal solution. All of the above-mentioned existing calibration methods for rotation axis parameters and hand-eye relationships suffer from cumbersome processes and low efficiency. Therefore, a new approach must be proposed to address the shortcomings of existing technologies. Summary of the Invention

[0005] 1. The technical problem to be solved:

[0006] To address the aforementioned technical problems, this invention provides a method for initial calibration and optimization of the rotation axis and hand-eye relationship in a line laser scanning system. This method is used to calibrate the hand-eye relationship from the camera coordinate system to the translation coordinate system. The calibration method is highly accurate and easy to operate.

[0007] 2. Technical Solution:

[0008] A method for initial calibration and optimization of the rotation axis and hand-eye relationship in a line laser scanning system. The line laser scanning system acquires the contour point cloud of the object under test through its laser sensor. An articulated arm measuring machine is used to implement the initial calibration and optimization method of the hand-eye relationship in the line laser scanning system. The initial calibration and optimization method of the hand-eye relationship specifically includes the following steps:

[0009] Step 1: In the online laser scanning system, establish the base coordinate system, the translation coordinate system where the translation stage is located, and the camera coordinate system where the line laser sensor is located. The transformation relationship from the camera coordinate system to the translation coordinate system is a hand-eye relationship. Obtain the transformation matrix from the camera coordinate system to the translation coordinate system and the transformation matrix from the translation coordinate system to the base coordinate system. The line laser scanning system is equipped with a translation stage consisting of translation axes in the X, Y, and Z directions. The line laser sensor can move in the corresponding coordinate axis directions. The line laser scanning system is equipped with a disk-shaped turntable. Driven by its rotation axis, the turntable rotates the object to be measured on the surface of the turntable, enabling the line laser sensor to collect the contour point cloud of the object on the turntable. The end of the articulated arm measuring machine is equipped with a connecting structure for fixing the probe or laser scanning head. The articulated arm measuring machine controls the movement of the end via its robotic arm structure.

[0010] Step 2: Move all three translation axes of the line laser scanning system to the zero position. Connect the articulated arm measuring machine to a spherical probe of a preset diameter. Use the probe to collect the coordinate information of the origin (zero position) of the base coordinate system and multiple points on each coordinate axis in the articulated arm coordinate system. Use the RANSAC algorithm to fit points on the same coordinate axis to a straight line, obtaining the position p of each coordinate axis and the origin in the articulated arm coordinate system. B This leads to the transformation matrix from the base coordinate system to the articulated arm coordinate system;

[0011] Step 3: Control the turntable to rotate one revolution. The probe at the end of the articulated arm measuring machine moves with the control console under the control of its robotic arm structure. The probe measures a random fixed point on the surface of the turntable. When the turntable rotates 10°, the position of the probe is obtained once, thus obtaining the coordinates of the point after rotation in the articulated arm coordinate system. The multiple coordinates obtained during the rotation are fitted into a circle using the RANSAC algorithm to obtain the center position of the circle on the surface of the turntable and the normal direction of the circle passing through the center position. Using the inverse matrix of the transformation matrix from the base coordinate system to the articulated arm coordinate system obtained in Step 2, the center coordinates and the normal direction are transformed back to the base coordinate system. The center coordinates and normal direction in the base coordinate system are the coordinates of a point on the straight line where the rotation axis of the turntable is located in the base coordinate system and the direction of the rotation axis.

[0012] Step 4: Replace the probe at the end of the articulated arm measuring machine with a spherical ruby ​​probe; use the ruby ​​probe to sample points on the top, bottom, side, and front of the line laser sensor surface, and use RANSAC to fit the plane to obtain the position p of the origin of the camera coordinate system in the articulated arm coordinate system. c Using the transformation matrix obtained in step three from the base coordinate system to the articulated arm coordinate system, the coordinates p c and coordinates p BTransform from the articulated arm coordinate system to the base coordinate system, and then obtain the transformation matrix from the camera coordinate system to the translation coordinate system, which is the translation vector of the initial hand-eye matrix;

[0013] Step 5: Place the target of the preset shape on the turntable surface, and use a line laser sensor and an articulated arm measuring machine to scan the target to obtain two point clouds of the target; transform the point cloud of the target scanned by the line laser sensor to the articulated arm coordinate system, and then use the ICP algorithm to register the two point clouds in the articulated arm coordinate system to obtain the registration matrix of the point cloud scanned by the line laser sensor to the point cloud scanned by the articulated arm. This registration matrix is ​​the initial hand-eye matrix.

[0014] Step Six: Select a cylinder of a preset size as the target to replace the target in Step Five. The laser sensor scans the cylinder once every 90° rotation of the turntable to obtain a point cloud of the contour. Perform RANSAC cylinder fitting on the point cloud scanned at 0° and optimize the parameters of the rotation axis and cylinder axis.

[0015] Step 7: Transform the optimized rotation axis to the articulated arm coordinate system, use the initial hand-eye matrix as the initial value of the optimization variable, construct the objective function, use the point cloud of the target scanned by the linear laser sensor in Step 5 as the source point cloud, use the point cloud of the target scanned by the articulated arm as the target point cloud, calculate the distance between the source point cloud and the target point cloud as the error metric, minimize the sum of squared residuals of the error metric to optimize the hand-eye matrix.

[0016] Furthermore, step two uses a jumping frog cone as a reference for data collection, which specifically includes:

[0017] S21: Move the three translation axes of the system to the zero point position of the system's grating ruler. The probe of the articulated arm measuring machine is a 15mm diameter probe, which measures the position of the zero point at this time. Fix the jumping frog cone to a point on the translation axis in the Z-axis direction and collect the position of that point. Control the translation axis in the X-axis direction to move, and collect point cloud data of the jumping frog cone once at a preset distance. Stop collecting when the movement reaches the limit position, and then the translation axis returns to the zero point position. Repeat the above process to complete the acquisition of point cloud data in the Y and Z axis directions.

[0018] S22: Fit a straight line to the obtained point cloud data using the RANSAC algorithm; during the line fitting process, the spatial straight line is represented by the following parametric equation:

[0019]

[0020] In the above formula, (x0 y0 z0) represents a known point on the line; (ijk) is the direction vector of the line; and t is a parameter.

[0021] make Equation (1) is transformed into equation (2):

[0022] p=p0+t·n , t∈R (2)

[0023] Two points p are randomly selected and collected on the same coordinate axis. 1， p2, calculate p for each of the other points on this coordinate axis as follows: i The distance d to the line containing the axis i The expression is:

[0024]

[0025] A threshold is set for the distance from a point to the line corresponding to the coordinate axis. If the distance from a point to the corresponding line is less than the threshold, the point is considered an interior point of the line, and it is retained and counted. Otherwise, it is considered an exterior point of the line and the exterior points are removed. Repeat the above steps n times to find all interior points that meet the conditions of interior points after traversing all points. Substitute the obtained interior points into formula (2) to obtain the optimized line equation, which is the fitted line equation.

[0026] S23: Obtain the coordinate axis direction n of the base coordinate system based on the fitted linear equation. x n y n z The position p of the origin in the articulated arm coordinate system B The transformation matrix from the base coordinate system to the articulated arm coordinate system is obtained.

[0027] Furthermore, step three specifically includes:

[0028] S31: Remove the jumping frog cone on the Z-axis and fix a jumping frog cone on the turntable surface near its edge; collect point cloud data once every 10° rotation of the turntable, and collect point cloud data once with the probe, for a minimum of 36 point cloud data.

[0029] S32: Fitting a circle using the RANSAC algorithm; the standard equation describing the spatial circle during the spatial circle fitting process is as follows:

[0030] (xa) 2 +(yb) 2 +(zc) 2 =r 2 (4)

[0031] In the above formula, (a,b,c) represents the center of the spatial circle, and r is the radius of the spatial circle;

[0032] In step S31, three points are randomly selected from the point cloud data collected. The distance d from each of the other points to the circle is calculated using the following formula. i :

[0033]

[0034] A preset distance threshold is set for the distance from a point to a circle. If the distance from a point to a circle is less than the threshold, the point is considered an inner point of the circle, and it is retained and counted. Otherwise, it is considered an outer point and the outer point is removed. This process is repeated n times. The inner points are then substituted into formula (4) to obtain the optimized spatial circle equation, which is the fitted circle equation.

[0035] S33: Obtain the center position of the circle based on the fitted circle equation. Normal direction passing through the center of the circle The transformation matrix obtained in step S23 is obtained as follows: Inverse matrix:

[0036]

[0037] Position of the center Normal direction Transform to the base coordinate system as follows:

[0038]

[0039] Furthermore, the translation vector of the hand-eye matrix obtained in step four

[0040] Furthermore, step five specifically includes:

[0041] S51: Fix the target of the preset shape on the turntable and face it directly towards the line laser sensor. The line laser sensor scans one side of the target along the positive Z-axis to obtain its point cloud P in the camera coordinate system. Cramera ;

[0042] S52: Replace the probe of the articulated arm measuring machine with a laser probe, rotate the turntable 180°, and scan the target with the laser probe to obtain the point cloud P of the target portion in the articulated arm coordinate system. ArmCMM ;

[0043] S53: Set the initial value of the rotation matrix for the transformation matrix from the camera coordinate system to the translation coordinate system. Based on the initial translation vector obtained in step four The initial hand-eye matrix T is as follows:

[0044]

[0045] Based on the coordinate transformation relationship from the base coordinate system to the articulated arm coordinate system in step two, P Cramera Transform to the articulated arm coordinate system, and then P ArmCMM The point cloud P is obtained by rotating it 180° around the rotation axis obtained from the initial calibration. ArmCMM ;

[0046] S54: P Cramera Set as the source point cloud, rotate the point cloud P ArmCMM Set as the target point cloud; all points in the target point cloud q i If q is formed into a set Q, then i ∈Q; Use KD-Tree to find the corresponding point set p in the source point cloud. i ∈P, such that ||p i -q i ||Minimum; obtain the matching point set P consisting of all matching points; the centroid of the matching point set in the articulated arm coordinate system is obtained as follows:

[0047]

[0048] In the above formula, Represents the centroid of the source point cloud; The centroid of the target point cloud is represented by N; N represents the number of matching point sets; then decentralization is performed.

[0049]

[0050] In the above formula, p' i ,q' i These are the decentralized points from the source point cloud and the target point cloud, respectively.

[0051] The covariance matrix H is constructed for the decentralized point sets of the source and target point clouds, as follows:

[0052]

[0053] The covariance matrix H is decomposed using SVD, and the decomposition result is as follows:

[0054] H=UΣV T (12)

[0055] In the above formula, H represents the covariance matrix; U represents the matrix representing the left singular vector of matrix H; V T The matrix representing the right singular vectors of H;

[0056] At this point, the rotation matrix R = VU T Translation vector

[0057] The calculated rotation matrix and translation vector are applied to the source point cloud P. Cramera The source point cloud at the new location is as follows:

[0058] P new =RP+t, (13)

[0059] S55: The iteration stops by calculating the mean square error after transformation; whereby the mean square error E between the two point clouds after transformation is calculated as follows:

[0060]

[0061] The iteration terminates when the mean square error change is less than the preset error threshold or when the preset maximum number of iterations is reached. The registration matrix obtained at this time is the true initial hand-eye matrix.

[0062] Furthermore, step six specifically includes the following steps:

[0063] S61: Select a standard cylinder of a preset size and fix it on the turntable. The laser sensor collects the cylinder point cloud once every 90° rotation of the turntable, and converts the collected cylinder point cloud to the base coordinate system.

[0064] S62: Perform cylindrical fitting on the point cloud scanned at 0° to obtain the axial position and orientation parameters of the fitted cylinder;

[0065] S63: Create an optimization object, given initial values ​​x0 = [abc 00d ef 00], where the first five are the initial values ​​of the turntable axis and the last five are the initial values ​​of the cylinder axis;

[0066] S64: Use the Plüuücker matrix to represent the standard cylindrical axis; construct it through two points on the straight line containing the standard cylindrical axis; assuming the line passes through points P1 and P2, the Plücker coordinates of the line can be represented as:

[0067] L=(d,m) (15)

[0068] Where d = P2 - P1 is the direction vector of the line, and m = P1 × P2 is the moment vector of the line;

[0069] The expression for the line can be obtained using the Pluücker matrix calculation formula as follows:

[0070]

[0071] In the above formula, m = (m3, m2, m1) and d = (d1, d2, d3) are the moment vector and direction vector of the line, respectively;

[0072] S65: The distance d from the points in the point cloud obtained in step S61 to the axis of the standard cylinder, traversed in random order. i ;

[0073] The sum of squares of the errors from the point to the cylindrical surface is calculated using the following formula:

[0074] err i =(d i -r)2 (17)

[0075] Where, d i is the distance from the i-th point to the axis of the cylinder; r is the standard cylinder radius;

[0076] The total error err is obtained by summing the squared errors at this point. 总 As shown in the following formula:

[0077]

[0078] The total error is calculated iteratively. With each iteration, the parameters of the rotating shaft and the cylinder axis are automatically optimized until the total error is lower than the preset threshold. The iteration stops at this point, and the parameters of the rotating shaft and the cylinder axis are the final optimized parameters.

[0079] 3. Beneficial effects:

[0080] (1) This method proposes an initial calibration and optimization method for the rotation axis and hand-eye relationship of a line laser scanning system. It uses an articulated arm measuring machine (ACM) to initially calibrate the rotation axis parameters and hand-eye matrix. A frog-shaped probe, coupled with its matching probe head, drives the end effector of the ACM to rotate, acquiring the trajectory points on a plane and fitting a circle. The center coordinates and normal of the circle are then directly calculated, achieving rapid initial calibration of the rotation axis. The calibration scheme, combined with the ACM, is simple to operate, fast to acquire data, highly efficient, and provides stable data quality. Compared to the commonly used method of acquiring trajectory points on different planes and fitting circles on multiple planes, the selected rotation axis calibration method has a simplified and efficient calculation process.

[0081] (2) The present method is a method for initial calibration and optimization of the rotation axis and hand-eye relationship of a line laser scanning system. Based on the obtained initial rotation axis parameters and initial hand-eye matrix, the rotation axis and hand-eye matrix are comprehensively optimized based on a standard cylinder and a special target, which greatly improves the calibration accuracy.

[0082] (3) The method of initial calibration and optimization of the rotation axis and hand-eye relationship of a line laser scanning system is shown in the verification experiment. It can be clearly seen that the overlapping area of ​​the point cloud after being stitched with the rotation axis parameters and hand-eye matrix before optimization has obvious layering and large deviation. However, the overlapping area of ​​the point cloud after being stitched with the rotation axis parameters and hand-eye matrix after optimization is closely intertwined and the deviation is very small. This shows that the optimized rotation axis parameters and hand-eye matrix are extremely accurate, demonstrating the significant effect of the optimization method. Attached Figure Description

[0083] Figure 1 This is a flowchart of the initial calibration and optimization method for the rotation axis and hand-eye relationship of the linear laser scanning system in this invention;

[0084] Figure 2This is a schematic diagram of the layout of the line laser scanning system and articulated arm measuring machine involved in this invention, as well as the corresponding coordinate system established.

[0085] Figure 3 This is a schematic diagram of the shaft calibration principle in step three of this invention, wherein (a) is a schematic diagram of the prior art; and (b) is a schematic diagram of this solution.

[0086] Figure 4 The diagram shows the details of the shaft calibration process in step three of the present invention; (a) shows the change in position of the jumping frog as the turntable rotates; (b) shows the position between the jumping frog and the probe.

[0087] Figure 5 This is a diagram showing the effect of RANSAC fitting of the base coordinate system coordinate axes in step two of this invention.

[0088] Figure 6 This is a diagram showing the effect of RANSAC fitting the circle in step three of this invention;

[0089] Figure 7 To verify the deviation map of the overlapping area of ​​the cylindrical point cloud before and after optimization in the example;

[0090] Figure 8 To verify the diameter of the cylinder fitted to the point cloud before and after optimization in the example;

[0091] Figure 9 To verify the external view of the blade in the scanned blade scene in the example;

[0092] Figure 10 This is a magnified view of the overlapping area of ​​the point cloud before and after optimization in the example of the scanned blade scene.

[0093] Figure labels: 1. Line laser sensor; 2. X-axis translation stage; 3. Y-axis translation stage; 4. Z-axis translation stage; 5. Turntable; 6. Articulated arm measuring machine; 7. Frog-jump cone; 8. Probe; 9. Blade. Detailed Implementation

[0094] The present invention will now be described in detail with reference to the accompanying drawings.

[0095] As attached Figure 1 The diagram shows the initial calibration and parameter optimization of the axis and hand-eye matrix of the line structured light multidimensional scanning system of this invention. A schematic diagram of the layout of the line laser scanning system and the articulated arm measuring machine, and the corresponding coordinate system established in this method, is attached. Figure 2 As shown in the figure, 1 is a line laser sensor, 2 is an X-axis translation stage, 3 is a Y-axis translation stage, 4 is a Z-axis translation stage, 5 is a turntable, and 6 is an articulated arm measuring machine.

[0096] A method for initial calibration and optimization of the rotation axis and hand-eye relationship in a line laser scanning system. The line laser scanning system acquires the contour point cloud of the object under test through its laser sensor. An articulated arm measuring machine is used to implement the initial calibration and optimization method of the hand-eye relationship in the line laser scanning system. The initial calibration and optimization method of the hand-eye relationship specifically includes the following steps:

[0097] Step 1: In the online laser scanning system, establish the base coordinate system, the translation coordinate system where the translation stage is located, and the camera coordinate system where the line laser sensor is located. The transformation relationship from the camera coordinate system to the translation coordinate system is a hand-eye relationship. Obtain the transformation matrix from the camera coordinate system to the translation coordinate system and the transformation matrix from the translation coordinate system to the base coordinate system. The line laser scanning system is equipped with a translation stage consisting of translation axes in the X, Y, and Z directions. The line laser sensor can move in the corresponding coordinate axis directions. The line laser scanning system is equipped with a disk-shaped turntable. Driven by its rotation axis, the turntable rotates the object to be measured on the surface of the turntable, enabling the line laser sensor to collect the contour point cloud of the object on the turntable. The end of the articulated arm measuring machine is equipped with a connecting structure for fixing the probe or laser scanning head. The articulated arm measuring machine controls the movement of the end via its robotic arm structure.

[0098] Step 2: Move all three translation axes of the line laser scanning system to the zero position. Connect the articulated arm measuring machine to a spherical probe of a preset diameter. Use the probe to collect the coordinate information of the origin (zero position) of the base coordinate system and multiple points on each coordinate axis in the articulated arm coordinate system. Use the RANSAC algorithm to fit points on the same coordinate axis to a straight line, obtaining the position p of each coordinate axis and the origin in the articulated arm coordinate system. B This leads to the transformation matrix from the base coordinate system to the articulated arm coordinate system;

[0099] Step 3: Control the turntable to rotate one revolution. The probe at the end of the articulated arm measuring machine moves with the control console under the control of its robotic arm structure. The probe measures a random fixed point on the surface of the turntable. When the turntable rotates 10°, the position of the probe is obtained once, thus obtaining the coordinates of the point after rotation in the articulated arm coordinate system. The multiple coordinates obtained during the rotation are fitted into a circle using the RANSAC algorithm to obtain the center position of the circle on the surface of the turntable and the normal direction of the circle passing through the center position. Using the inverse matrix of the transformation matrix from the base coordinate system to the articulated arm coordinate system obtained in Step 2, the center coordinates and the normal direction are transformed back to the base coordinate system. The center coordinates and normal direction in the base coordinate system are the coordinates of a point on the straight line where the rotation axis of the turntable is located in the base coordinate system and the direction of the rotation axis.

[0100] Step 4: Replace the probe at the end of the articulated arm measuring machine with a spherical ruby ​​probe; use the ruby ​​probe to sample points on the top, bottom, side, and front of the line laser sensor surface, and use RANSAC to fit the plane to obtain the position p of the origin of the camera coordinate system in the articulated arm coordinate system. c Using the transformation matrix obtained in step three from the base coordinate system to the articulated arm coordinate system, the coordinates p c and coordinates p B Transform from the articulated arm coordinate system to the base coordinate system, and then obtain the transformation matrix from the camera coordinate system to the translation coordinate system, which is the translation vector of the initial hand-eye matrix;

[0101] Step 5: Place the target of the preset shape on the turntable surface, and use a line laser sensor and an articulated arm measuring machine to scan the target to obtain two point clouds of the target; initially transform the point cloud of the target scanned by the line laser sensor to the articulated arm coordinate system, and then use the ICP algorithm to register the two point clouds in the articulated arm coordinate system to obtain the registration matrix of the point cloud scanned by the line laser sensor to the point cloud scanned by the articulated arm. This registration matrix is ​​the initial hand-eye matrix.

[0102] In this step, the target of the preset shape preferably has a metal target with an additional square protrusion on its surface. The square protrusions are arranged in an array, and the target as a whole is long and narrow.

[0103] Step Six: Select a cylinder of a preset size as the target to replace the target in Step Five. The laser sensor scans the cylinder once every 90° rotation of the turntable to obtain a point cloud of the contour. Perform RANSAC cylinder fitting on the point cloud scanned at 0° and optimize the parameters of the rotation axis and cylinder axis.

[0104] Step 7: Transform the optimized rotation axis to the articulated arm coordinate system, use the initial hand-eye matrix as the initial value of the optimization variable, construct the objective function, use the point cloud of the target scanned by the linear laser sensor in Step 5 as the source point cloud, use the point cloud of the target scanned by the articulated arm as the target point cloud, calculate the distance between the source point cloud and the target point cloud as the error metric, minimize the sum of squared residuals of the error metric to optimize the hand-eye matrix.

[0105] Furthermore, step two uses a jumping frog cone as a reference for data collection, which specifically includes:

[0106] S21: Move the three translation axes of the system to the zero point position of the system's grating ruler. The probe of the articulated arm measuring machine is a 15mm diameter probe, which measures the position of the zero point at this time. Fix the jumping frog cone to a point on the translation axis in the Z-axis direction and collect the position of that point. Control the translation axis in the X-axis direction to move, and collect point cloud data of the jumping frog cone once at a preset distance. Stop collecting when the movement reaches the limit position, and then the translation axis returns to the zero point position. Repeat the above process to complete the acquisition of point cloud data in the Y and Z axis directions.

[0107] S22: Fit a straight line to the obtained point cloud data using the RANSAC algorithm; during the line fitting process, the spatial straight line is represented by the following parametric equation:

[0108]

[0109] In the above formula, (x0 y0 z0) represents a known point on the line; (ijk) is the direction vector of the line; and t is a parameter.

[0110] make Equation (1) is transformed into equation (2):

[0111] p=p0+t·n , t∈R (2)

[0112] Two points p are randomly selected and collected on the same coordinate axis. 1， p2, calculate p for each of the other points on this coordinate axis as follows: i The distance d to the line containing the axis i The expression is:

[0113]

[0114] A threshold is set for the distance from a point to the line corresponding to the coordinate axis. If the distance from a point to the corresponding line is less than the threshold, the point is considered an interior point of the line, and it is retained and counted. Otherwise, it is considered an exterior point of the line and the exterior points are removed. Repeat the above steps n times to find all interior points that meet the conditions of interior points after traversing all points. Substitute the obtained interior points into formula (2) to obtain the optimized line equation, which is the fitted line equation.

[0115] S23: Obtain the coordinate axis direction n of the base coordinate system based on the fitted linear equation. x n y n z The position p of the origin in the articulated arm coordinate system B The transformation matrix from the base coordinate system to the articulated arm coordinate system is obtained.

[0116] Furthermore, step three specifically includes:

[0117] S31: Remove the jumping frog cone on the Z-axis and fix a jumping frog cone on the turntable surface near its edge; collect point cloud data once every 10° rotation of the turntable, and collect point cloud data once with the probe, for a minimum of 36 point cloud data.

[0118] S32: Fitting a circle using the RANSAC algorithm; the standard equation describing the spatial circle during the spatial circle fitting process is as follows:

[0119] (xa) 2 +(yb) 2 +(zc) 2 =r 2 (4)

[0120] In the above formula, (a,b,c) represents the center of the spatial circle, and r is the radius of the spatial circle;

[0121] In step S31, three points are randomly selected from the point cloud data collected. The distance d from each of the other points to the circle is calculated using the following formula. i :

[0122]

[0123] A preset distance threshold is set for the distance from a point to a circle. If the distance from a point to a circle is less than the threshold, the point is considered an inner point of the circle, and it is retained and counted. Otherwise, it is considered an outer point and the outer point is removed. This process is repeated n times. The inner points are then substituted into formula (4) to obtain the optimized spatial circle equation, which is the fitted circle equation.

[0124] S33: Obtain the center position of the circle based on the fitted circle equation. Normal direction passing through the center of the circle The transformation matrix obtained in step S23 is obtained as follows: Inverse matrix:

[0125]

[0126] Position of the center Normal direction Transform to the base coordinate system as follows:

[0127]

[0128] Furthermore, the translation vector of the hand-eye matrix obtained in step four

[0129] Furthermore, step five specifically includes:

[0130] S51: Fix the target on the turntable and face it directly towards the line laser sensor. The line laser sensor scans one side of the target along the positive Z-axis to obtain its point cloud P in the camera coordinate system. Cramera ;

[0131] S52: Replace the probe of the articulated arm measuring machine with a laser probe, rotate the turntable 180°, and scan the target with the laser probe to obtain the point cloud P of the target portion in the articulated arm coordinate system. ArmCMM ;

[0132] S53: Set the initial value of the rotation matrix for the transformation matrix from the camera coordinate system to the translation coordinate system. Based on the initial translation vector obtained in step four The initial hand-eye matrix T is as follows:

[0133]

[0134] Based on the coordinate transformation relationship from the base coordinate system to the articulated arm coordinate system in step two, P Cramera Transform to the articulated arm coordinate system, and then P ArmCMM The point cloud P is obtained by rotating it 180° around the rotation axis obtained from the initial calibration. ArmCMM ;

[0135] S54: P Cramera Set as the source point cloud, rotate the point cloud P ArmCMM Set as the target point cloud; all points in the target point cloud q i If q is formed into a set Q, then i ∈Q; Use KD-Tree to find the corresponding point set p in the source point cloud. i ∈P, such that ||p i -q i ||Minimum; obtain the matching point set P consisting of all matching points; the centroid of the matching point set in the articulated arm coordinate system is obtained as follows:

[0136]

[0137] In the above formula, Represents the centroid of the source point cloud; The centroid of the target point cloud is represented by N; N represents the number of matching point sets; then decentralization is performed.

[0138]

[0139] In the above formula, p' i ,q' i These are the decentralized points from the source point cloud and the target point cloud, respectively.

[0140] The covariance matrix H is constructed for the decentralized point sets of the source and target point clouds, as follows:

[0141]

[0142] The covariance matrix H is decomposed using SVD, and the decomposition result is as follows:

[0143] H=UΣV T (12)

[0144] In the above formula, H represents the covariance matrix; U represents the matrix representing the left singular vector of matrix H; VT The matrix representing the right singular vectors of H;

[0145] At this point, the rotation matrix R = VU T Translation vector

[0146] The calculated rotation matrix and translation vector are applied to the source point cloud P. Cramera The source point cloud at the new location is as follows:

[0147] P new =RP+t (13)

[0148] S55: The iteration stops by calculating the mean square error after transformation; whereby the mean square error E between the two point clouds after transformation is calculated as follows:

[0149]

[0150] The iteration terminates when the mean square error change is less than the preset error threshold or when the preset maximum number of iterations is reached. The registration matrix obtained at this time is the true initial hand-eye matrix.

[0151] Furthermore, step six specifically includes the following steps:

[0152] S61: Select a standard cylinder of a preset size and fix it on the turntable. The laser sensor collects the cylinder point cloud once every 90° rotation of the turntable, and converts the collected cylinder point cloud to the base coordinate system.

[0153] S62: Perform cylindrical fitting on the point cloud scanned at 0° to obtain the axial position and orientation parameters of the fitted cylinder;

[0154] S63: Create an optimization object, given initial values ​​x0 = [abc 00d ef 00], where the first five are the initial values ​​of the turntable axis and the last five are the initial values ​​of the cylinder axis;

[0155] S64: Use the Plücker matrix to represent the standard cylindrical axis; construct it through two points on the straight line containing the standard cylindrical axis; assuming the line passes through points P1 and P2, the Plücker coordinates of the line can be represented as:

[0156] L=(d,m) (15)

[0157] Where d = P2 - P1 is the direction vector of the line, and m = P1 × P2 is the moment vector of the line;

[0158] The expression for the line can be obtained using the Plücker matrix calculation formula as follows:

[0159]

[0160] In the above formula, m = (m3, m2, m1) and d = (d1, d2, d3) are the moment vector and direction vector of the line, respectively;

[0161] S65: The distance d from the points in the point cloud obtained in step S61 to the axis of the standard cylinder, traversed in random order. i ;

[0162] The sum of squares of the errors from the point to the cylindrical surface is calculated using the following formula:

[0163] err i =(d i -r) 2 (17)

[0164] Where, d i is the distance from the i-th point to the axis of the cylinder; r is the standard cylinder radius;

[0165] The total error err is obtained by summing the squared errors at this point. 总 As shown in the following formula:

[0166]

[0167] The total error is calculated iteratively. With each iteration, the parameters of the rotating shaft and the cylinder axis are automatically optimized until the total error is lower than the preset threshold. The iteration stops at this point, and the parameters of the rotating shaft and the cylinder axis are the final optimized parameters. Specific implementation examples:

[0169] As attached Figure 3 As shown, Figure 3 (a) The principle of calibrating the rotation axis commonly used in this method, as shown in the figure, involves fitting the trajectory points collected on different planes into circles, obtaining the centers of all the circles, and then fitting these centers into straight lines to obtain the rotation axis parameters. This method requires too much data and the calibration process is cumbersome. This method utilizes... Figure 3 The principle shown in (b) is used to collect the trajectory points (C1, C2...C1) on a plane. n By fitting a circle, the coordinates of the circle's center O' and the circle's normal O'R are directly obtained, thus achieving rapid initial calibration of the rotation axis. Figure 4 This is a calibration diagram of the rotating shaft. In the diagram, 7 represents the frog-jumping cone; 8 represents a 15mm diameter probe. (For example...) Figure 4 (a) shows the frog jumping cone fixed to the turntable, P1, P2, P3...P 36 This indicates the position of the frog jumping cone, rotating 10° each time, and then... Figure 4 (b) shows that the probe is lightly placed on the upper end of the frog jumping cone. The frog jumping cone drives the probe to move, thereby completing the acquisition of each position point. The acquisition method of points in the three motion axis directions is the same.

[0170] Verification example:

[0171] To verify the calibration effect of this method, step two in this verification example uses a 15mm spherical frog-jumping cone probe: the first frog-jumping cone is fixed to the Z-axis of the scanning system, the probe collects the current point once, then moves along the X-axis, collecting data points every 10mm, stopping at the limit position, and then returning to the zero position. This process is repeated to collect data points along the Y and Z axes. The RANSAC algorithm is used to fit a straight line, with a preset distance threshold of 0.02mm from the point to the corresponding line on that coordinate axis. All points are iterated through, and those points whose distance to the corresponding line is less than the 0.02mm threshold are classified as interior points. The resulting fitting effect is shown in the attached figure. Figure 5 As shown.

[0172] Figure 6 The image shows the result of fitting a circle to the turntable axis in step three. During this fitting process, the threshold for the circle was preset to 0.02 mm. The resulting image is shown in the attached figure. Figure 6 As shown.

[0173] In the RANSAC fitting process described above, the algorithm replaces the entire dataset with a randomly sampled subset, which effectively handles the presence of outliers. This random sampling method makes the algorithm robust to outliers and reduces their impact on model fitting, resulting in higher fitting accuracy.

[0174] In this method, steps six and seven are both processes for optimizing the initially obtained hand-eye matrix.

[0175] Figure 7 This involves creating color images of the point cloud deviation before and after optimization. During the verification process, a standard cylinder with a diameter of 19.970 mm and a length of approximately 150 mm was used as the target. The point cloud data of the cylinder was collected by a linear laser sensor every 60° rotation of the turntable. Figure 7 (a) It can be seen that in this verification example, the error of the overlapping area of ​​the two point clouds scanned by the linear laser sensor when the turntable is located at 0° and 60° before optimization is relatively large, ranging from 0.07 (corresponding to 0.077 in the figure) mm to 0.1 mm. Figure 7 (b) shows the error in the overlapping area of ​​the two point clouds after optimization. As can be seen from the figure, the deviation of the point cloud stitching is within 0.02mm (the minimum is 0.016mm in the figure). Figure 8 The values ​​represent the diameters of the cylinders fitted from the point cloud before and after optimization. Before optimization, the diameter of the fitted cylinder was 19.939 mm, which differed from the standard diameter by 0.031 mm. After optimization, the diameter of the fitted cylinder was 19.968 mm, which differed from the standard diameter by only 0.002 mm.

[0176] Figure 9 , 10For application scenarios where the hand-eye matrix calibrated using this method is used to scan blades, where... Figure 9 This is an external view of blade 9; the overlapping area of ​​the blade and the point cloud before and after optimization is locally magnified, according to... Figure 10 The blades are scanned in sections, and the point clouds of different regions are then stitched together by rotating them in the opposite direction according to the turntable angle, resulting in an effect as shown below. Figure 10 As shown in (a). Figure 10 (b) It can be seen that the overlapping area of ​​the point cloud stitching before optimization has obvious layering after being magnified, and Figure 10 (c) shows that after optimization, the overlapping area of ​​the point cloud, when magnified, shows no obvious layering; the two point clouds are tightly interwoven and stitched together. Figure 7 , Figure 8 as well as Figure 10 The experimental comparison data before and after optimization shown in the figure demonstrates that the optimization effect is very significant.

[0177] Although the present invention has been disclosed above with reference to preferred embodiments, these are not intended to limit the present invention. Any person skilled in the art can make various changes or modifications without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention should be defined by the scope of the claims of this application.

Claims

1. A method for initial calibration and optimization of the rotation axis and hand-eye relationship in a line laser scanning system, characterized in that: The line laser scanning system acquires the contour point cloud of the object under test through its laser sensor. An articulated arm measuring machine is provided to implement the initial calibration and optimization method for the hand-eye relationship of the line laser scanning system. The initial calibration and optimization method for the hand-eye relationship specifically includes the following steps: Step 1: In the online laser scanning system, establish the base coordinate system, the translation coordinate system where the translation stage is located, and the camera coordinate system where the line laser sensor is located. The transformation relationship from the camera coordinate system to the translation coordinate system is a hand-eye relationship. Obtain the transformation matrix from the camera coordinate system to the translation coordinate system and the transformation matrix from the translation coordinate system to the base coordinate system. The line laser scanning system is equipped with a translation stage consisting of translation axes in the X, Y, and Z directions. The line laser sensor can move in the corresponding coordinate axis directions. The line laser scanning system is equipped with a disk-shaped turntable. Driven by its rotation axis, the turntable rotates the object to be measured on the surface of the turntable, enabling the line laser sensor to collect the contour point cloud of the object on the turntable. The end of the articulated arm measuring machine is equipped with a connecting structure for fixing the probe or laser scanning head. The articulated arm measuring machine controls the movement of the end via its robotic arm structure. Step 2: Move all three translation axes of the line laser scanning system to the zero position. Connect the articulated arm measuring machine to a spherical probe of a preset diameter. Use the probe to collect the coordinate information of the origin (zero position) of the base coordinate system and multiple points on each coordinate axis in the articulated arm coordinate system. Use the RANSAC algorithm to fit points on the same coordinate axis to a straight line, obtaining the position p of each coordinate axis and the origin in the articulated arm coordinate system. B This leads to the transformation matrix from the base coordinate system to the articulated arm coordinate system; Step 3: Control the turntable to rotate one revolution. The probe at the end of the articulated arm measuring machine moves with the control console under the control of its robotic arm structure. The probe measures a random fixed point on the surface of the turntable. When the turntable rotates 10°, the position of the probe is obtained once, thus obtaining the coordinates of the point after rotation in the articulated arm coordinate system. The multiple coordinates obtained during the rotation are fitted into a circle using the RANSAC algorithm to obtain the center position of the circle on the surface of the turntable and the normal direction of the circle passing through the center position. Using the inverse matrix of the transformation matrix from the base coordinate system to the articulated arm coordinate system obtained in Step 2, the center coordinates and the normal direction are transformed back to the base coordinate system. The center coordinates and normal direction in the base coordinate system are the coordinates of a point on the straight line where the rotation axis of the turntable is located in the base coordinate system and the direction of the rotation axis. Step 4: Replace the probe at the end of the articulated arm measuring machine with a spherical ruby ​​probe; use the ruby ​​probe to sample points on the top, bottom, side, and front of the line laser sensor surface, and use RANSAC to fit the plane to obtain the position p of the origin of the camera coordinate system in the articulated arm coordinate system. c Using the transformation matrix obtained in step three from the base coordinate system to the articulated arm coordinate system, the coordinates p c and coordinates p B Transform from the articulated arm coordinate system to the base coordinate system, and then obtain the transformation matrix from the camera coordinate system to the translation coordinate system, which is the translation vector of the initial hand-eye matrix; Step 5: Place the target of the preset shape on the turntable surface, and use a line laser sensor and an articulated arm measuring machine to scan the target to obtain two point clouds of the target; transform the point cloud of the target scanned by the line laser sensor to the articulated arm coordinate system, and then use the ICP algorithm to register the two point clouds in the articulated arm coordinate system to obtain the registration matrix of the point cloud scanned by the line laser sensor to the point cloud scanned by the articulated arm. This registration matrix is ​​the initial hand-eye matrix. Step Six: Select a cylinder of a preset size as the target to replace the target in Step Five. The laser sensor scans the cylinder once every 90° rotation of the turntable to obtain a point cloud of the contour. Perform RANSAC cylinder fitting on the point cloud scanned at 0° and optimize the parameters of the rotation axis and cylinder axis. Step 7: Transform the optimized rotation axis to the articulated arm coordinate system, use the initial hand-eye matrix as the initial value of the optimization variable, construct the objective function, use the point cloud of the target scanned by the linear laser sensor in Step 5 as the source point cloud, use the point cloud of the target scanned by the articulated arm as the target point cloud, calculate the distance between the source point cloud and the target point cloud as the error metric, minimize the sum of squared residuals of the error metric to optimize the hand-eye matrix.

2. The method for initial calibration and optimization of the rotation axis and hand-eye relationship of the line laser scanning system according to claim 1, characterized in that: Step two uses a jumping frog cone as a reference for data collection, which specifically includes: S21: Move the three translation axes of the system to the zero point position of the system's grating ruler. The probe of the articulated arm measuring machine is a 15mm diameter probe, which measures the position of the zero point at this time. Fix the jumping frog cone to a point on the translation axis in the Z-axis direction and collect the position of that point. Control the translation axis in the X-axis direction to move, and collect point cloud data of the jumping frog cone once at a preset distance. Stop collecting when the movement reaches the limit position, and then the translation axis returns to the zero point position. Repeat the above process to complete the acquisition of point cloud data in the Y and Z axis directions. S22: Fit a straight line to the obtained point cloud data using the RANSAC algorithm; during the line fitting process, the spatial straight line is represented by the following parametric equation: In the above formula, (x0 y0 z0) represents a known point on the line; (ijk) is the direction vector of the line; and t is a parameter. make Equation (1) is transformed into equation (2): p=p0+t·n,t∈R (2) Two points p are randomly selected and collected on the same coordinate axis. 1， p2, calculate p for each of the other points on this coordinate axis as follows: i The distance d to the line containing the axis i The expression is: A threshold is set for the distance from a point to the line corresponding to the coordinate axis. If the distance from a point to the corresponding line is less than the threshold, the point is considered an interior point of the line, and it is retained and counted. Otherwise, it is considered an exterior point of the line and the exterior points are removed. Repeat the above steps n times to find all interior points that meet the conditions of interior points after traversing all points. Substitute the obtained interior points into formula (2) to obtain the optimized line equation, which is the fitted line equation. S23: Obtain the coordinate axis direction n of the base coordinate system based on the fitted linear equation. x n y n z The position p of the origin in the articulated arm coordinate system B The transformation matrix from the base coordinate system to the articulated arm coordinate system is obtained.

3. The method for initial calibration and optimization of the rotation axis and hand-eye relationship of the line laser scanning system according to claim 2, characterized in that: Step three specifically includes: S31: Remove the jumping frog cone on the Z-axis and fix a jumping frog cone on the turntable surface near its edge; collect point cloud data once every 10° rotation of the turntable, and collect point cloud data once with the probe, for a minimum of 36 point cloud data. S32: Fitting a circle using the RANSAC algorithm; the standard equation describing the spatial circle during the spatial circle fitting process is as follows: (x-a) 2 +(y-b) 2 +(z-c) 2 =r 2 (4) In the above formula, (a,b,c) represents the center of the spatial circle, and r is the radius of the spatial circle; In step S31, three points are randomly selected from the point cloud data collected. The distance d from each of the other points to the circle is calculated using the following formula. i : A preset distance threshold is set for the distance from a point to a circle. If the distance from a point to a circle is less than the threshold, the point is considered an inner point of the circle, and it is retained and counted. Otherwise, it is considered an outer point and the outer point is removed. This process is repeated n times. The inner points are then substituted into formula (4) to obtain the optimized spatial circle equation, which is the fitted circle equation. S33: Obtain the center position of the circle based on the fitted circle equation. Normal direction passing through the center of the circle The transformation matrix obtained in step S23 is obtained as follows: Inverse matrix: Position of the center Normal direction Transform to the base coordinate system as follows:

4. The method for initial calibration and optimization of the rotation axis and hand-eye relationship of the line laser scanning system according to claim 3, characterized in that: The translation vector of the hand-eye matrix obtained in step four 5. The method for initial calibration and optimization of the rotation axis and hand-eye relationship of the line laser scanning system according to claim 4, characterized in that: Step five specifically includes: S51: Fix the target on the turntable and face it directly towards the line laser sensor. The line laser sensor scans one side of the target along the positive Z-axis to obtain its point cloud P in the camera coordinate system. Cramera ; S52: Replace the probe of the articulated arm measuring machine with a laser probe, rotate the turntable 180°, and scan the target with the laser probe to obtain the point cloud P of the target portion in the articulated arm coordinate system. ArmCMM ; S53: Set the initial value of the rotation matrix for the transformation matrix from the camera coordinate system to the translation coordinate system. Based on the initial translation vector obtained in step four The initial hand-eye matrix T is as follows: Based on the coordinate transformation relationship from the base coordinate system to the articulated arm coordinate system in step two, P... Cramera Transform to the articulated arm coordinate system, and then P ArmCMM The point cloud P is obtained by rotating it 180° around the rotation axis obtained from the initial calibration. ArmCMM ; S54: P Cramera Set as the source point cloud, rotate the point cloud P ArmCMM Set as the target point cloud; all points in the target point cloud q i If q is formed into a set Q, then i ∈Q; Use KD-Tree to find the corresponding point set p in the source point cloud. i ∈P, such that ||p i -q i ||Minimum; obtain the matching point set P consisting of all matching points; the centroid of the matching point set in the articulated arm coordinate system is obtained as follows: In the above formula, Represents the centroid of the source point cloud; The centroid of the target point cloud is represented by N; N represents the number of matching point sets. Decentralization In the above formula, p' i ,q' i These are the decentralized points from the source point cloud and the target point cloud, respectively. The covariance matrix H is constructed for the decentralized point sets of the source and target point clouds, as follows: The covariance matrix H is decomposed using SVD, and the decomposition result is as follows: H=UΣV T (12) In the above formula, H represents the covariance matrix; U represents the matrix representing the left singular vector of matrix H; V T The matrix representing the right singular vectors of H; At this point, the rotation matrix R = VU T Translation vector The calculated rotation matrix and translation vector are applied to the source point cloud P. Cramera The source point cloud at the new location is as follows: P new =RP+t (13) S55: The iteration stops by calculating the mean square error after transformation; whereby the mean square error E between the two point clouds after transformation is calculated as follows: The iteration terminates when the mean square error change is less than the preset error threshold or when the preset maximum number of iterations is reached. The registration matrix obtained at this time is the true initial hand-eye matrix.

6. The method for initial calibration and optimization of the rotation axis and hand-eye relationship of the line laser scanning system according to claim 5, characterized in that: Step six specifically includes the following steps: S61: Select a standard cylinder of a preset size and fix it on the turntable. The laser sensor collects the cylinder point cloud once every 90° rotation of the turntable, and converts the collected cylinder point cloud to the base coordinate system. S62: Perform cylindrical fitting on the point cloud scanned at 0° to obtain the axial position and orientation parameters of the fitted cylinder; S63: Create an optimization object, given initial values ​​x0 = [abc 0 0 def 0 0], where the first five are the initial values ​​of the turntable axis and the last five are the initial values ​​of the cylinder axis; S64: The standard cylindrical axis is represented using a Plücker matrix; constructed from two points on the straight line containing the standard cylindrical axis. Assuming the line passes through points P1 and P2, the Plücker coordinates of the line can be expressed as: L=(d,m) (15) Where d = P2 - P1 is the direction vector of the line, and m = P1 × P2 is the moment vector of the line; The expression for the line can be obtained using the Plüuücker matrix calculation formula as follows: In the above formula, m = (m3, m2, m1) and d = (d1, d2, d3) are the moment vector and direction vector of the line, respectively; S65: The distance d from the points in the point cloud obtained in step S61 to the axis of the standard cylinder, traversed in random order. i ; The sum of squares of the errors from the point to the cylindrical surface is calculated using the following formula: err i =(d i -r) 2 (17) Where, d i is the distance from the i-th point to the axis of the cylinder; r is the radius of the standard cylinder; The total error err is obtained by summing the squared errors at this point. 总 As shown in the following formula: The total error is calculated iteratively. With each iteration, the parameters of the rotating shaft and the cylinder axis are automatically optimized until the total error is lower than the preset threshold. The iteration stops at this point, and the parameters of the rotating shaft and the cylinder axis are the final optimized parameters.

Images