A method for mutual aiming and testing of laser trackers in hidden areas

Abstract

This invention discloses a method for mutual aiming and measurement of laser trackers in hidden areas, belonging to the field of large-space precision measurement technology. The invention deploys a reference tracker in the visible area and the tracker under test in the hidden area. The tracker under test drives a target sphere to perform spherical motion, while the reference tracker collects data from spherical sampling points. A robust Taubin sphere center fitting algorithm is used to fit the rotation center coordinates of the tracker under test, completing self-calibration. Finally, coordinate system transformation achieves measurement and coordinate unification in the hidden area. The robust Taubin sphere center fitting algorithm of this invention introduces robust estimation concepts, effectively suppressing the influence of abnormal data on the fitting results through weighted iterative optimization of the objective function. This invention completely solves the technical problems of not being able to deploy a common visible point and achieve coordinate system unification in hidden / narrow areas, significantly improving the accuracy and robustness of sphere center fitting, and meeting the collimation requirements of high-end devices such as particle accelerators.

Description

Technical Field

[0001] This invention belongs to the field of large-space precision measurement technology, and specifically relates to laser tracker joint measurement technology, specifically a method for mutual aiming and measurement of hidden areas of laser trackers and a robust Taubin sphere center fitting method. Background Technology

[0002] With the rapid development of high-end scientific facilities such as particle accelerators, the requirements for the accuracy of three-dimensional coordinate measurements over large spatial areas are constantly increasing during the construction and operation of these facilities. Laser trackers, with their advantages of high precision, wide range, and portability, have become core equipment in the field of accelerator collimation measurement.

[0003] In practical measurement scenarios, for narrow, obstructed, and hidden areas (such as accelerator cavities, narrow pipes, and blind spots inside equipment), a single laser tracker cannot complete line-of-sight measurements, requiring a multi-laser tracker joint measurement scheme. Traditional multi-laser tracker joint measurement systems require the construction of a high-precision polygonal measurement system through multiple common line-of-sight points to unify the coordinate system of multiple instruments; however, in hidden / narrow areas, it is impossible to deploy a sufficient number of common line-of-sight points, nor can the visibility of these common points be guaranteed. This results in the inability to achieve high-precision coordinate system fusion, and the measurement accuracy cannot meet the collimation requirements of high-end devices.

[0004] Meanwhile, during the mutual aiming calibration of laser trackers, the coordinates of the instrument's rotation center need to be obtained through sphere center fitting. Existing conventional sphere center fitting algorithms include conventional least squares fitting algorithm, Partt fitting algorithm, and ordinary Taubin fitting algorithm. When abnormal data (gross errors) are generated due to factors such as mechanical errors of instrument rotation and environmental interference during the measurement process, the fitting results of existing algorithms will show serious deviations, poor robustness, and cannot meet the requirements of ultra-high precision calibration. Summary of the Invention

[0005] To address the aforementioned shortcomings of existing technologies, this invention aims to solve the technical problems of laser trackers being unable to complete coordinate system alignment through common points in hidden / narrow areas, and the weak robustness and insufficient fitting accuracy of existing sphere center fitting algorithms. It provides a method for mutual aiming and measurement in hidden areas of laser trackers, along with a robust Taubin sphere center fitting method for mutual aiming calibration, thereby achieving high-precision coordinate measurement and multi-instrument coordinate system fusion in hidden areas.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] This invention provides a method for mutual aiming and testing of laser trackers in hidden areas, comprising the following steps:

[0008] S1 Measurement System Setup: The first laser tracker is deployed in the line-of-sight area as a reference tracker; the second laser tracker is deployed in the hidden / narrow area to be measured, and a target ball is fixedly installed on the probe of the second laser tracker.

[0009] S2 Mutual Aiming Data Acquisition: Control the probe of the second laser tracker to rotate within a preset horizontal and vertical angle range, causing the target ball to perform spherical motion; during the rotation, the first laser tracker continuously acquires the three-dimensional coordinate data of the target ball, obtaining multiple sets of spherical sampling point data;

[0010] S3 Sphere Center Fitting and Instrument Center Calibration: The robust Taubin sphere center fitting algorithm is used to fit the collected spherical sampling point data to obtain the three-dimensional coordinates of the probe rotation center of the second laser tracker in the coordinate system of the first laser tracker, thus completing the self-calibration of the second laser tracker.

[0011] S4 Coordinate System Fusion and Hidden Area Measurement: The target to be measured in the hidden area is measured by the second laser tracker to obtain the coordinates of the target to be measured in the coordinate system of the second laser tracker; based on the rotation center coordinates of the second laser tracker obtained by calibration, the transformation between the coordinate system of the second laser tracker and the reference coordinate system of the first laser tracker is completed, and the coordinates of the target to be measured in the hidden area are unified to the reference coordinate system, thus completing the high-precision measurement of the hidden area.

[0012] As a further technical solution of the present invention, in step S2, the preset horizontal angle and vertical angle range must ensure that the collected spherical sampling points cover at least 50% of the target ball's moving spherical surface, the number of sampling points is not less than 30 sets, and the sampling points are evenly distributed within the spherical surface range.

[0013] As a further technical solution of the present invention, in step S2, when collecting spherical sampling point data, the three-dimensional coordinate data of the sampling points are simultaneously corrected according to the ranging and angular measurement errors of the laser tracker.

[0014] As a further technical solution of the present invention, in step S3, the sphere center fitting and instrument center calibration adopt the robust Taubin sphere center fitting method, which includes the following steps:

[0015] T1 constructs a sphere fitting model: Based on Taubin's three-dimensional sphere fitting theory, a general equation for the sphere is constructed, the sphere center parameters and the minimization objective function are determined, and the minimum value is solved with g=1 as the constraint condition;

[0016] T2 data centering: The collected 3D coordinate data of the spherical sampling points are centered to simplify and minimize the objective function, and the objective function is transformed into matrix form;

[0017] T3 Initial parameter solution: Perform SVD singular value decomposition on the transformed matrix to obtain the initial parameters for sphere fitting, and calculate the initial sphere center coordinates and radius;

[0018] T4 Robust Weighted Iterative Optimization: Introduces a robust estimation method based on weighted iteration, constructs residual-related weight factors, weights the objective function, and optimizes the sphere fitting parameters through multiple iterations; when the parameter difference between two adjacent iterations is less than the preset convergence threshold, the iteration stops, and the final sphere center coordinates and radius are output.

[0019] As a further technical solution of the present invention, in step T1, the general equation for the Taubin three-dimensional sphere fitting is:

[0020] (1)

[0021] (2)

[0022] Where a, b, c are the coordinates of the sphere's center, and r is the radius of the sphere;

[0023] The objective function to be minimized is:

[0024] (3)

[0025] The minimum value is found using g=1 as a constraint, as shown in the following formula:

[0026] (4)

[0027] By analogy with Partt's objective function, we know that the upper part of equation (3) is the minimization objective function, and the lower part is the constraint condition.

[0028] As a further technical solution of the present invention, in step T2, the centralization process satisfies:

[0029] The sampling data are all centralized

[0030] Right now

[0031] (5)

[0032] The objective function then becomes the following formula (6):

[0033] (6)

[0034] make Substituting into (6), the minimization objective function becomes as shown in equation (7):

[0035] (7)

[0036] Similarly, (7) can be written in matrix form as shown in formula (8):

[0037] (8)

[0038] in As a parameter, = At this point, the constraints are incorporated into the objective function.

[0039] As a further technical solution of the present invention, in step T4, the weighting factor is obtained by the following formula:

[0040] (9)

[0041] To avoid the denominator being 0, a minimum value k is added to the denominator, and the weighting factor is adjusted accordingly. .

[0042] As a further technical solution of the present invention, in step T4, the preset convergence threshold is no greater than 10^-7. During the iteration process, the sphere fitting parameters obtained in the previous iteration are substituted into the objective function in matrix form to solve for the correction result of this iteration. The iteration is repeated until the convergence condition is met.

[0043] As a further technical solution of the present invention, in step T4, the weighted minimization objective function is solved by introducing Lagrange multipliers to solve the minimum problem. After differentiating the matrix corresponding to the objective function, the spherical fitting parameters in the iterative process are solved by using the SVD singular value decomposition method.

[0044] As a further technical solution of the present invention, for the measurement scenario of multiple consecutive hidden areas, multiple second laser trackers are deployed in sequence in different hidden areas. Taking the first laser tracker as the reference, the cascaded coordinate system transformation of multiple instruments is completed through mutual aiming and measurement between adjacent laser trackers and sphere center fitting calibration, so as to unify the measurement results of all hidden areas under the reference coordinate system.

[0045] This technology proposes a method for mutual aiming and testing of laser trackers in hidden areas, which has the following advantages and beneficial effects:

[0046] 1. The mutual aiming and measurement method provided by this invention does not require the deployment of a common line of sight in hidden / narrow areas. It can complete the self-calibration and coordinate system fusion of the tracker in the hidden area by simply collecting mutual aiming data and fitting the center of the sphere with two trackers. This completely solves the technical problem of the inability to see through hidden / narrow areas and the inability to build a traditional polygonal measurement system. It realizes high-precision measurement of hidden areas and can be widely used in precision measurement scenarios in narrow blind areas such as particle accelerators and the interior of large industrial equipment.

[0047] 2. The robust Taubin sphere center fitting method proposed in this invention introduces a robust estimation idea based on weighted iteration on the basis of the traditional Taubin algorithm. By weighting the objective function with residual-related weight factors, the influence of measurement outliers and gross errors on the fitting results is effectively suppressed, and the accuracy and robustness of sphere center fitting are greatly improved. The calculation process is simplified by centering and SVD decomposition, which reduces the amount of computation while ensuring ultra-high fitting accuracy, and adapts to the real-time requirements of field measurement.

[0048] 3. The measurement method of the present invention has a simple operation process, requiring no complicated equipment setup and on-site operation, which greatly improves the efficiency of precision measurement in hidden areas. At the same time, the calibration accuracy and measurement accuracy can meet the collimation measurement requirements of high-end scientific devices such as particle accelerators, and have extremely strong engineering practical value. Attached Figure Description

[0049] Figure 1 This is a schematic diagram of the layout of the laser tracker hidden area mutual aiming and mutual testing system described in this invention;

[0050] Figure 2 This is a schematic diagram of the sphere center fitting simulation measurement of the hidden region described in this invention.

[0051] In the diagram: 1-Laser tracker A, 2-Laser tracker B, 3-Obstructed area, 4-Open area, 5-Target ball. Detailed Implementation

[0052] The present invention will be further described below with reference to the embodiments. It should be noted that these are merely examples and descriptions of the inventive concept. Those skilled in the art can make various modifications or additions to the specific embodiments described or use similar methods to replace them, as long as they do not deviate from the inventive concept or exceed the scope defined in the claims, they should all be considered to fall within the protection scope of the present invention.

[0053] like Figure 1 As shown, the present invention proposes a method for mutual aiming and measurement in the hidden area of ​​a laser tracker, specifically for the measurement scenario of the hidden area in the narrow cavity of a particle accelerator. The specific implementation steps are as follows:

[0054] Step 1: Deployment of the measurement system;

[0055] The first laser tracker (reference tracker, denoted as tracker A) is deployed in the visible area outside and inside the relevant equipment of the accelerator. The instrument is leveled and initialized, and a reference measurement coordinate system under the gravity coordinate system is established. The second laser tracker (tracker under test, denoted as tracker B) is deployed in the hidden area to be measured outside and inside the relevant equipment of the accelerator. The instrument is leveled, and a high-precision Leica target ball is fixedly installed on the probe of tracker B to ensure that the target ball and the probe are rigidly connected without relative displacement.

[0056] System layout structure such as Figure 1 As shown, tracker A is in the line-of-sight area and can directly observe the target ball on the probe of tracker B. Tracker B is in a hidden area inside the cavity and cannot achieve coordinate system unity with tracker A through a traditional common point.

[0057] Step 2: Mutual aiming data acquisition;

[0058] The probe of the tracker B rotates at a constant speed within a preset horizontal and vertical angle range, causing the target ball to move spherically around the rotation center of the tracker B's probe. In this embodiment, the vertical angle scanning range is 30°~150°, and the horizontal angle scanning range is 0°~180°, ensuring that the sampling points cover more than 50% of the target ball's moving spherical surface. During the rotation, the tracker A continuously collects the target ball's three-dimensional coordinate data. The number of sampling points is set to 30 sets and is evenly distributed within the spherical surface. Simultaneously, the sampling point coordinates are corrected for errors based on the trackinger A's ranging accuracy (1μm+0.5μm / m) and angle measurement accuracy (0.5″), ultimately obtaining a three-dimensional coordinate dataset of 30 sets of spherical sampling points.

[0059] Step 3: Center fitting and instrument center calibration;

[0060] The robust Taubin sphere center fitting algorithm described in this invention is used to fit the collected 30 sets of spherical sampling point data to obtain the three-dimensional coordinates of the probe rotation center of tracker B in the reference coordinate system of tracker A, thus completing the self-calibration of tracker B. The specific fitting steps are as follows:

[0061] The formula for representing a sphere in the Taubin three-dimensional method is as follows (1):

[0062] (1)

[0063] At this point, the parameters of the sphere's center are as follows (2):

[0064] (2)

[0065] The objective function for minimizing the value is given by formula (3): (3)

[0066] The minimum value is solved using g=1 as a constraint, as shown in formula (4):

[0067] (4)

[0068] By analogy with Partt's objective function, we can see that the upper part of equation (3) is the minimization objective function, and the lower part is the constraint condition. Since the calculation becomes complicated and cumbersome after deriving the ball formula, it is assumed that the sampled data are all centered. ,Right now

[0069] (5)

[0070] The objective function then becomes the following formula (6):

[0071] (6)

[0072] make Substituting into (6), the minimization objective function becomes as shown in equation (7):

[0073] (7)

[0074] Similarly, (7) can be written in matrix form as shown in formula (8):

[0075] (8)

[0076] in As a parameter, = At this point, the constraints are incorporated into the objective function. The next step will be to... Perform SVD decomposition, and obtain the following results: The third column of the matrix will be This step simplifies the calculation.

[0077] During the measurement process, the laser tracker may experience anomalies in the measurement data due to mechanical errors caused by instrument rotation. A robust estimation method based on weighted iteration can mitigate the impact of outliers on the fitting results. By substituting the initial result into equation (8), the second correction result is obtained. This process is repeated multiple times. When the difference between the current iteration result and the previous result is less than a certain value (10 is used in subsequent simulation experiments), the result is corrected. -7 If the iteration stops, the obtained corrections are substituted into the fitted sphere center and radius.

[0078] In the iterative calculation, the method of minimizing the absolute value of the residuals is selected. The weighting factor is given by the following formula (9):

[0079] (9)

[0080] To prevent errors during the calculation process In this case, the weighting factor can be: , where k takes a minimum value. Introducing robust estimation into the Taubin sphere fitting algorithm is challenging because the Taubin algorithm is not a common indirect adjustment model. Its minimization objective function needs to be weighted, as shown in the following formula (10):

[0081] (10)

[0082] make ,in Then the constraint conditions can be expressed in matrix form as follows: The minimum value problem is solved by introducing Lagrange multipliers. To solve the minimum problem, we can work on the matrix. Differentiate to obtain To solve the minimum problem, the SVD decomposition method of the matrix can also be used.

[0083] Step 4: Coordinate system fusion and hidden area measurement;

[0084] The target to be measured in the hidden area inside the accelerator cavity is measured by tracker B to obtain the three-dimensional coordinates of the target in the coordinate system of tracker B. Based on the rotation center coordinates of tracker B obtained by calibration, and combined with the angle measurement data of tracker B, a coordinate transformation matrix is ​​constructed to complete the seven-parameter transformation between the coordinate system of tracker B and the reference coordinate system of tracker A. The coordinates of all targets to be measured in the hidden area are unified to the reference coordinate system, and finally the high-precision measurement of the hidden area of ​​the accelerator cavity is completed.

[0085] To verify the accuracy and robustness of the method of this invention, a simulation comparison experiment was conducted simultaneously in this embodiment. The experimental steps are as follows:

[0086] (1) The measuring station built in the same spatial rectangular coordinate system is used as the “origin tracker” (200,1000,100), and the first sphere center coordinate is used as the initial point of the “tracker to be measured” (1000,1000,0). The initial distance is 979.79 mm.

[0087] (2) The "origin tracker" measures the "tracker under test" and simultaneously calculates the initial coordinates of points on the sphere's surface. The number of measured points on the simulated moving tracker surface is 30, with a simulated coverage area of ​​approximately 50%. The vertical angle of the scan is... Horizontal angle Within the specified range, the simulated data acquisition method is uniform acquisition.

[0088] (3) Calculate the points (S,V,H) from each point on the sphere to the station. Based on the influence of the distance and angle measurement errors of the laser tracker on (x,y,z), add random errors mx, my, and mz to the sphere of the moving tracker.

[0089] (4) The simulated sphere center coordinates are calculated using the conventional sphere center fitting algorithm, Partt algorithm, Taubin algorithm and robust Taubin algorithm respectively.

[0090] (5) Calculate the distance from the measuring station to the simulated center of the sphere and compare the results.

[0091] (6) The experiment was conducted three times at different centers of the sphere. Figure 2 As shown, gross errors were also introduced to verify and demonstrate the robustness of the algorithm.

[0092] (7) The simulation experiment was conducted 10,000 times, and the results of the maximum absolute deviation, average absolute deviation and average root mean square error of the above ball fitting algorithm were compared.

[0093] The above is an exemplary description of the invention. Obviously, the specific implementation of the invention is not limited to the above-described manner. Any non-substantial improvement made using the inventive concept and technical solution of the invention, or the direct application of the inventive concept and technical solution to other situations without modification, is within the protection scope of the invention.

Claims

1. A method for laser tracker hidden zone inter-targeting and inter- measuring, characterized in that, Includes the following steps: S1 Measurement System Setup: The first laser tracker is deployed in the line-of-sight area as a reference tracker; the second laser tracker is deployed in the hidden / narrow area to be measured, and a target ball is fixedly installed on the probe of the second laser tracker. S2 Mutual Aiming Data Acquisition: Control the probe of the second laser tracker to rotate within a preset horizontal and vertical angle range, causing the target ball to perform spherical motion; during the rotation, the first laser tracker continuously acquires the three-dimensional coordinate data of the target ball, obtaining multiple sets of spherical sampling point data; S3 Sphere Center Fitting and Instrument Center Calibration: The robust Taubin sphere center fitting algorithm is used to fit the collected spherical sampling point data to obtain the three-dimensional coordinates of the probe rotation center of the second laser tracker in the coordinate system of the first laser tracker, thus completing the self-calibration of the second laser tracker. S4 Coordinate System Fusion and Hidden Area Measurement: The target to be measured in the hidden area is measured by the second laser tracker to obtain the coordinates of the target to be measured in the coordinate system of the second laser tracker; based on the rotation center coordinates of the second laser tracker obtained by calibration, the transformation between the coordinate system of the second laser tracker and the reference coordinate system of the first laser tracker is completed, and the coordinates of the target to be measured in the hidden area are unified to the reference coordinate system, thus completing the high-precision measurement of the hidden area.

2. The method of claim 1, wherein, In step S2, the preset horizontal and vertical angle ranges must ensure that the collected spherical sampling points cover at least 50% of the target ball's moving surface, the number of sampling points is no less than 30 sets, and the sampling points are evenly distributed within the spherical range.

3. The method for mutual aiming and testing of a laser tracker in a hidden area according to claim 1, characterized in that, In step S2, when collecting data of spherical sampling points, the three-dimensional coordinate data of the sampling points are simultaneously corrected based on the ranging and angular measurement errors of the laser tracker.

4. The method for mutual aiming and testing of a laser tracker in a hidden area according to claim 1, characterized in that, In step S3, the sphere center fitting and instrument center calibration adopt the robust Taubin sphere center fitting method, which includes the following steps: T1 constructs a sphere fitting model: Based on Taubin's three-dimensional sphere fitting theory, a general equation for the sphere is constructed, the sphere center parameters and the minimization objective function are determined, and the minimum value is solved with g=1 as the constraint condition; T2 data centering: The collected 3D coordinate data of the spherical sampling points are centered to simplify and minimize the objective function, and the objective function is transformed into matrix form; T3 Initial parameter solution: Perform SVD singular value decomposition on the transformed matrix to obtain the initial parameters for sphere fitting, and calculate the initial sphere center coordinates and radius; T4 Robust Weighted Iterative Optimization: Introduces a robust estimation method based on weighted iteration, constructs residual-related weight factors, weights the objective function, and optimizes the sphere fitting parameters through multiple iterations; when the parameter difference between two adjacent iterations is less than the preset convergence threshold, the iteration stops, and the final sphere center coordinates and radius are output.

5. The method for mutual aiming and testing of laser trackers in hidden areas according to claim 4, characterized in that, In step T1, the general equation for the Taubin 3D sphere fitting is: （1） （2） Where a, b, c are the coordinates of the sphere's center, and r is the radius of the sphere; The objective function to be minimized is: （3） The minimum value is found using g=1 as a constraint, as shown in the following formula: (4) By analogy with Partt's objective function, we know that the upper part of equation (3) is the minimization objective function, and the lower part is the constraint condition.

6. The method for mutual aiming and testing of a laser tracker in a hidden area according to claim 4, characterized in that, In step T2, the centralized processing satisfies: The sampling data are all centralized ; Right now (5) The objective function then becomes the following formula (6): (6) make Substituting into (6), the minimization objective function becomes as shown in equation (7): (7) Similarly, (7) can be written in matrix form as shown in formula (8): (8) in As a parameter, = At this point, the constraints are incorporated into the objective function.

7. The method for mutual aiming and testing of a laser tracker in a hidden area according to claim 1, characterized in that, In step T4, the weighting factors are obtained using the following formula: （9） To avoid the denominator being 0, a minimum value k is added to the denominator, and the weighting factor is adjusted accordingly. .

8. The method for mutual aiming and testing of a laser tracker in a hidden area according to claim 4, characterized in that, In step T4, the preset convergence threshold is no greater than 10^-7. During the iteration process, the sphere fitting parameters obtained in the previous iteration are substituted into the objective function in matrix form to solve for the correction result of this iteration. The iteration is repeated until the convergence condition is met.

9. The method for mutual aiming and testing of a laser tracker in a hidden area according to claim 4, characterized in that, In step T4, the weighted minimization objective function is solved by introducing Lagrange multipliers to solve the minimum problem. After differentiating the matrix corresponding to the objective function, the spherical fitting parameters in the iterative process are solved by the SVD singular value decomposition method.

10. The method for mutual aiming and testing of a laser tracker in a hidden area according to claim 4, characterized in that, For measurement scenarios involving multiple consecutive hidden regions, multiple second laser trackers are deployed sequentially in different hidden regions. Using the first laser tracker as a reference, the cascaded coordinate system transformation of multiple instruments is completed through mutual aiming and measurement between adjacent laser trackers and sphere center fitting calibration, unifying the measurement results of all hidden regions to the reference coordinate system.

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