High-precision construction method for measuring network of laser tracker

Abstract

The invention relates to a high-precision construction method for a measurement network of a laser tracker. According to the method, firstly, the precision of transformation parameters between adjacent LTMSs is improved by using a weight coefficient matrix based on enhanced reference system point measurement errors and an iterative optimization algorithm; secondly, on the basis of the principle that the total measurement error of any two measurement points is minimized, the optimal number of LTMS is determined; and finally, optimizing the spatial position of each LTMS according to the principle of minimum measurement error. According to the high-precision construction method for the laser tracker measurement network, the measurement precision of the laser tracker arranged at each measurement station is improved, and the overall measurement precision of the laser tracker measurement network is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of laser tracker measurement networks, and in particular to a high-precision construction method of a laser tracker measurement network. Background Art

[0002] With the acceleration of intelligent manufacturing and the increasing demands for component size and precision in the manufacturing industry, automated digital measurement has become a driving force behind the development of intelligent manufacturing. The laser tracker is a portable three-dimensional coordinate measuring instrument widely used in aircraft assembly, large aerospace components, particle accelerators, machine tool error calibration, and other fields. It offers advantages such as a large measurement range, high accuracy, and high efficiency, enabling rapid measurement of large objects or complex features. However, using a single laser tracker deployed at a single measurement station is not sufficient to perform measurement tasks on objects with complex structures or large volumes. To address these measurement tasks, it is necessary to construct a laser tracker measurement network consisting of multiple measurement stations.

[0003] However, existing methods for constructing laser tracker measurement networks still have significant limitations, including poor versatility and low parameter accuracy when transferring between adjacent measurement stations. Furthermore, existing methods for constructing laser tracker measurement networks still lack effective strategies for determining the optimal number of measurement stations and for assigning measurement areas to each station. Currently, these methods primarily rely on the long-term operational experience of technicians, often with limited reliability. The resulting number of measurement stations and assigned measurement areas are often suboptimal, which in turn affects the overall performance of the laser tracker measurement network. Summary of the Invention

[0004] To this end, the present invention provides a high-precision construction method for a laser tracker measurement network, which improves the measurement accuracy of the laser tracker arranged at each measurement station and improves the overall measurement accuracy of the laser tracker measurement network.

[0005] To solve the above technical problems, the present invention provides a high-precision construction method for a laser tracker measurement network, comprising: using two adjacent laser trackers to measure the measurement value of each ERS point arranged between the two adjacent laser trackers; wherein a plurality of ERS points are arranged between two adjacent measurement stations, and a laser tracker is arranged at each of the measurement stations; According to the measurement values, a measurement value matrix corresponding to each laser tracker is obtained; Calculating a measurement error of each of the measurement values, constructing a weight coefficient matrix corresponding to the measurement value matrix based on the measurement error, and decentralizing the measurement value matrix based on the weight coefficient matrix to obtain a decentralized measurement value matrix; The decentralized measurement value matrix in the measurement coordinate system of one of the two adjacent laser trackers is converted to the measurement coordinate system of the other, thereby constructing an error function; and initial transfer parameters are obtained based on the error function; Constructing an accuracy optimization objective function based on the initial transfer station parameters and taking the minimum overall registration error of the measurement values ​​obtained by corresponding measurements of the two laser trackers as the goal; Based on the precision optimization objective function, the initial transfer parameters are iteratively optimized to obtain high-precision transfer parameters; Obtain all discrete points on the surface of the component being measured, designate several of them as measured points, calculate the normal vectors of each of the measured points and form a normal vector set; Obtaining overall measurement errors of any two measured points under a same-station measurement scheme and a different-station measurement scheme, respectively, and dividing the measurement area to which each measured point belongs according to the normal vector set and the overall measurement error; Arrange measurement stations of the same number as the measurement area and set corresponding initial coordinates, obtain a first measurement value without measurement error and a second measurement value with measurement error corresponding to each measured point in each measurement area, and construct a position target optimization function based on the first measurement value and the second measurement value; Based on the position target optimization function, the initial coordinates are optimized to determine the optimal spatial arrangement position of the measurement station.

[0006] In one embodiment of the present invention, a measurement value matrix corresponding to each laser tracker is obtained based on the measurement values, including: In the world coordinate system There are two laser trackers in the lower layout and ,exist and There are m nodes for calculation and ERS points for transfer parameters , ; Each ERS point By the kth laser tracker Measure the measured value ,as follows: , In the formula, c is the cosine of the trigonometric function, s is the sin of the trigonometric function, yes pass The measured distance value, is the vertical angle, is the horizontal angle; Let all the laser trackers passing through k Measured Constructing the measurement matrix , then: , in, is a The matrix of and The matrices composed of their respective measurement values ​​can be expressed as and .

[0007] In one embodiment of the present invention, the measurement error of each of the measurement values ​​is calculated, a weight coefficient matrix corresponding to the measurement value matrix is ​​constructed based on the measurement error, and the measurement value matrix is ​​decentralized based on the weight coefficient matrix to obtain a decentralized measurement value matrix, including: Each ERS point The measured value Measurement errors along the x, y and z axes respectively , and as follows: , Where, , and They are , and The measurement errors can be calculated based on , and Calculated; among them, , and They are , and The error accuracy is provided in the technical manual of the laser tracker; according to The measurement error , and The size of Set the weight coefficient matrix as follows: , in, is a Matrix of According to the following formula, and Decentralization can obtain the corresponding decentralized measurement value matrix and : , in, It is the Hadamard product, which multiplies the corresponding elements of the two matrices performing the operation; is a A matrix with all elements set to 1, that is .

[0008] In one embodiment of the present invention, the decentralized measurement value matrix in the measurement coordinate system of one of two adjacent laser trackers is converted to the measurement coordinate system of the other, thereby constructing an error function; and based on the error function, initial transfer parameters are obtained, including: Use the following formula to calculate Measuring coordinate system Convert to Error in measurement coordinate system : , in, is the initial rotation matrix in the initial rotation parameters; , Where, It is to find the sum of the elements on the main diagonal; right Performing singular value decomposition yields: , Where, is a diagonal matrix, and is the orthogonal identity matrix; but for: ; The initial translation vector in the initial transfer parameters is calculated using the following formula: : .

[0009] In one embodiment of the present invention, the accuracy optimization objective function is as follows: , Where, is the overall registration error; when When the minimum value is taken, the initial rotation matrix can be obtained and the initial translation vector Optimized high-precision rotation matrix and high-precision translation vectors .

[0010] In one embodiment of the present invention, based on the initial transfer station parameters and with the goal of minimizing the overall registration error of the measurement values ​​obtained by corresponding measurements by two laser trackers, an accuracy optimization objective function is constructed, including: Using LM algorithm to and Perform iterative optimization: Step 1: Set the initial value; where, The initial value is , The initial value is , the initial value of the number of iterations k is , define the damping factor The initial value is ; Step 2: Calculation The kth update vector of , Solved by the following formula: , Where, yes The Jacobian matrix at the kth iteration is , is the identity matrix; Step 3: Update : , Step 4: Calculate the objective function value after iteration ; Step 5: Calculate the change in overall registration error : , Step 6: Judgement If the size , then increase , and return to Step 2; if , then reduce ; and make And return to Step 2; Repeat Step 2 to Step 6 until , Is the threshold, then stop the iteration; at this time That is and Optimized high-precision rotation matrix and high-precision translation vectors .

[0011] In one embodiment of the present invention, all discrete points on the surface of the component being measured are obtained, and several of them are designated as measured points. The normal vectors of the measured points are calculated to form a normal vector set, including: Let all the discrete points on the surface of the measured component form a set , where M discrete points are designated as measured points and constitute the set ,and ; For the collection Any measured point in Normal vector , synthesized by the normal vectors of the triangular plane formed by it and its neighboring points in the neighborhood; Any measured point The N neighbors of , assuming that every two adjacent points and Both can be connected with the measured point Forming a flat triangle ; make The normal vector is , the center of mass is , With the measured point The distance between ,and The measured point The angle between the vertices is ; Among them, the plane triangle Normal vector , angle and distance They can be calculated by the following formulas: , , , Where, It is a neighbor Pointing Point The unit direction vector of ; It is a neighbor Pointing Point The unit direction vector of ; Defining the Angle Impact Factor : , Defining distance impact factors : , The measured point Normal vector Calculated by the following formula: , The same applies to the measured point , calculate the set Normal vectors of all other measured points within.

[0012] In one embodiment of the present invention, obtaining the overall measurement errors of any two measured points under the same-site measurement scheme and the different-site measurement scheme respectively includes: When using the same-station measurement solution, for the collection Any two measured points in and , when using the same laser tracker, LT0, to measure the points and When measuring, the measured point The measurement values ​​obtained by LT0 without measurement error and the measurement values ​​with measurement error are and ;Measured point The measurement values ​​obtained by LT0 without measurement error and with measurement error are and ; Defining evaluation metrics To quantify the measured point and The overall measurement error when measured by LT0, The larger the measured point and The larger the overall measurement error between Expressed as: ; When using the off-site measurement solution, the measured point and The measurements are performed using different laser trackers, namely LT1 and LT2, with g ERS points arranged between LT1 and LT2. ERS points The number g is greater than 3, and all ERS points Not arranged linearly; When measured by LT1 and LT2 respectively, Measurement value containing measurement error and ; When measured by LT1, Measured value without measurement error and measurements with measurement errors ; When measured by LT1, Measured value without measurement error ; When measured by LT2, Measurement value containing measurement error ; according to and Calculate the rotation matrix of the LT2 measurement coordinate system relative to the LT1 measurement coordinate system and translation vectors ; Will Measurement values ​​obtained by LT2 measurement Converting to the LT1 measurement coordinate system yields: , definition To evaluate the measured point and The overall measurement error when measured by LT1 and LT2 respectively is expressed as: , Then when When the measured point and Use the same-station measurement scheme; when When the measured point and Adopt the off-site measurement scheme.

[0013] In one embodiment of the present invention, dividing the measurement area to which each measured point belongs according to the normal vector set and the overall measurement error includes: Step 1: Let the set The normal vectors corresponding to all measured points in the ; Step 2: From the collection Take any element And use it as the initial point to establish the measurement area ; Step 3: Traverse the collection in sequence For each remaining element in , if an element is traversed and and its corresponding measured point and At the same time, the following relationship is satisfied, and the measured point Divide into measurement areas Inside; , , Where, It has been divided into the measurement area For each measured point within yes The corresponding normal vector; is the measured point and Overall measurement error when measuring with the same laser tracker LT0; is the measured point and The overall measurement error when measured by laser tracker LT1 and laser tracker LT2 respectively; Step 4: Update the collection and collection , and repeat Steps 2 to 3 for the remaining measured points until the division of the measurement area to which all measured points belong is completed.

[0014] In one embodiment of the present invention, the position target optimization function is: , Among them, the known coordinates of each measured point in the world coordinate system are , let the initial coordinates of the measurement stations set according to manual experience in the measurement area be , Arranged in The measured value without measurement error when measuring with a laser tracker and measurements with measurement errors .

[0015] The above technical solution of the present invention has the following advantages over the prior art: The high-precision construction method of a laser tracker measurement network described in the present invention calculates high-precision transfer parameters between adjacent measurement stations, determines the optimal number of measurement stations, and optimizes the optimal spatial layout position of each measurement station, thereby improving the measurement accuracy of the laser tracker arranged at each measurement station and the overall measurement accuracy of the laser tracker measurement network.

[0016] The present invention determines the optimal number of measurement stations based on the size and morphological characteristics of the component being measured. This avoids the problem of too many measurement stations, which can lead to redundant measurement data and reduce overall measurement efficiency. It also avoids the problem of too few measurement stations, which can result in incomplete measurement of the component being measured and reduce overall measurement integrity.

[0017] The present invention improves the measurement accuracy of the laser tracker arranged at each measurement station by optimizing the best spatial arrangement position for each measurement station.

[0018] The present invention improves the unified accuracy of measurement data of each laser tracker by calculating high-precision transfer parameters between adjacent measurement stations, thereby improving the overall measurement accuracy of the laser tracker measurement network. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to make the contents of the present invention more clearly understood, the present invention is further described in detail below based on specific embodiments of the present invention in conjunction with the accompanying drawings.

[0020] Figure 1 It is a flow chart of the method for constructing a high-precision measurement network using a laser tracker according to the present invention.

[0021] Figure 2 This is a schematic diagram of the laser tracker measurement network.

[0022] Figure 3 It is a schematic diagram of the transfer parameter calculation model.

[0023] Figure 4 It is a schematic diagram of the model for obtaining the normal vector of the measured point.

[0024] Figure 5 This is a schematic diagram of the same-station measurement model.

[0025] Figure 6 This is a schematic diagram of the off-site measurement model.

[0026] Figure 7 This is a schematic diagram of the division of the measurement area. DETAILED DESCRIPTION

[0027] The present invention will be further described below with reference to the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it. However, the embodiments are not intended to limit the present invention.

[0028] In the present invention, if directions (up, down, left, right, front and back) are described, it is only for the convenience of describing the technical solution of the present invention, and does not indicate or imply that the technical features referred to must have a specific orientation, be constructed and operate in a specific orientation. Therefore, it cannot be understood as a limitation of the present invention.

[0029] In the present invention, "several" means one or more, "multiple" means more than two, "greater than," "less than," "exceeds," etc. are understood to exclude the number itself; "above," "below," "within," etc. are understood to include the number itself. In the description of the present invention, the use of "first" or "second" is solely for the purpose of distinguishing technical features and is not to be construed as indicating or implying relative importance, implicitly specifying the number of the indicated technical features, or implicitly specifying the order of the indicated technical features.

[0030] In the present invention, unless otherwise expressly defined, terms such as "disposed," "installed," and "connected" should be interpreted broadly. For example, they may refer to direct connection or indirect connection through an intermediate medium; fixed connection or detachable connection or integral molding; mechanical connection or electrical connection or mutual communication; and internal connection between two components or interaction between two components. Those skilled in the art can reasonably determine the specific meanings of the above terms in the present invention based on the specific content of the technical solution.

[0031] The following first introduces the laser tracker measurement network.

[0032] Reference Figure 2 Figure 2 shows a schematic diagram of a laser tracker measurement network. A laser tracker measurement network primarily consists of multiple measurement stations surrounding the component under test. A measurement station is where a laser tracker (LT) is positioned (in principle, the number of measurement stations is determined based on the size and morphological characteristics of the component under test). Additionally, several ERS (Enhanced Reference System) points are strategically placed between adjacent measurement stations. When using a laser tracker measurement network to measure a component under test, a laser tracker can be deployed simultaneously at each measurement station, providing full coverage of the component under test. However, due to the high cost of a single laser tracker in practice, measurements are often performed by rotating a single laser tracker at each measurement station. However, the measurement data from each laser tracker is based on the current measurement station. Therefore, the data from each laser tracker at each measurement station must be unified to obtain the overall measurement data for the component under test. This unification is achieved by rotating and translating the data from the laser trackers between adjacent measurement stations. The ERS points mentioned above are used to calculate the transformation parameters (rotation matrix R and translation vector T) between adjacent measurement stations.

[0033] The construction of the laser tracker measurement network actually requires determining the number of measurement stations, the position coordinates of each measurement station in space, and the conversion parameters between adjacent measurement stations based on the size and morphological characteristics of the measured parts.

[0034] This embodiment provides a method for constructing a high-precision laser tracker measurement network, comprising the following steps: S1. Using two adjacent laser trackers, measure the measurement value of each ERS point arranged between the two adjacent laser trackers; wherein, several ERS points are arranged between two adjacent measurement stations, and a laser tracker is arranged at each measurement station.

[0035] Specifically, if Figure 3 As shown, in the world coordinate system There are two laser trackers arranged below (i.e. and ).exist and There are m nodes for calculation and ERS points for transfer parameters , Each ERS point By the kth laser tracker Measure the measured value ,as follows: (1), In the formula, c is the cosine of the trigonometric function, s is the sin of the trigonometric function, yes pass The distance value obtained by measurement. similar, is the vertical angle, is the horizontal angle.

[0036] S2. According to the measured value , get the measurement value matrix corresponding to each laser tracker .

[0037] Specifically, let all the laser trackers passing through the kth laser tracker Measured Constructing the measurement matrix , then: (2), in, is a The matrix of and The matrices composed of their respective measurement values ​​can be expressed as and .

[0038] S3. Calculate the measurement error of each measurement value, and construct a weight coefficient matrix corresponding to the measurement value matrix based on the measurement error. , based on the weight coefficient matrix , for the measurement value matrix and Decentralize and obtain the decentralized measurement value matrix and .

[0039] Since all actual measurements , and All contain measurement errors, so the formula (1) is used to calculate The measured value also contains errors. The measured value Measurement errors along the x, y and z axes respectively , and It can be expressed according to formula (3): (3), Where, , and They are , and The measurement errors can be calculated based on , and Calculated. Among them, , and They are , and The error accuracy is provided in the laser tracker's technical manual.

[0040] Taking the Leica AT960-MR laser tracker as an example, according to its technical manual, , Due to the measured contains measurement errors, then , and It can be calculated according to formula (4) and (5) respectively: (4), (5), Where, , and The unit is (i.e. micrometers), The unit of is m (meter). In addition, and It can also be converted into a form with "''" (i.e., seconds) as the unit according to formula (6): (6), because It contains measurement error, and the larger the measurement error, The greater the deviation from its true value. The measurement error , and The size is Set the weight coefficient matrix .

[0041] (7), in, Also a The matrix of .

[0042] According to formula (8), and Decentralization can obtain the corresponding decentralized measurement value matrix and : (8), in, Is the Hadamard product, which multiplies corresponding elements in the two matrices where the operation is performed. is a A matrix with all elements set to 1, that is .

[0043] S4, converting the decentralized measurement value matrix in the measurement coordinate system of one of the two adjacent laser trackers to the measurement coordinate system of the other, thereby constructing an error function; based on the error function , get the initial transfer parameters and .

[0044] Specifically, Measuring coordinate system Convert to Error in measurement coordinate system It can be expressed according to formula (9): (9), Expanding formula (9) yields: (10), when When the minimum value is taken, we can solve . But to make Minimum is equivalent to making Take the maximum value.

[0045] According to existing literature knowledge: (11), Where, It is to find the sum of the elements on the main diagonal.

[0046] To solve the equation (11) ,right Performing singular value decomposition yields: (12), Where, is a diagonal matrix, and is the orthogonal identity matrix.

[0047] but According to formula (13), we can get: (13); Furthermore, According to formula (14), we can get: (14), S5, according to the initial transfer parameters and The accuracy optimization objective function is constructed with the goal of minimizing the overall registration error of the measurement values ​​obtained by corresponding measurements of the two laser trackers.

[0048] Specifically, by and The overall registration error is minimized to construct the optimization objective function : (15), Where, is the overall registration error; when When the minimum value is taken, the initial rotation matrix can be obtained and the initial translation vector Optimized high-precision rotation matrix and high-precision translation vectors .

[0049] S6. Based on the precision optimization objective function, the initial transfer parameters are iteratively optimized to obtain high-precision transfer parameters.

[0050] Specifically, the Levenberg-Marquardt (LM) algorithm is used according to the following steps: and Perform iterative optimization, the process is as follows: Step 1: Set the initial value; where, The initial value is , The initial value is , the initial value of the number of iterations k is , damping factor The initial value is =0.1.

[0051] Step 2: Calculation The kth update vector of , It can be solved by formula (16): (16), Where, yes The Jacobian matrix at the kth iteration is , is the identity matrix.

[0052] Step 3: Update .

[0053] (17), Step 4: Calculate the objective function value after iteration .

[0054] Step 5: Calculate the change in overall registration error .

[0055] (18), Step 6: Judgement If the size , then increase (Right now =10 ) and return to Step 2. If , then reduce (Right now = / 10) and make And return to Step 2.

[0056] Repeat Step 2 to Step 6 until ( is a smaller threshold set in advance), the iteration stops. That is and Optimized exact value and .

[0057] It should be noted that the existing transfer parameters and Typically, several ERS points are placed between two adjacent measurement stations and individually measured using laser trackers (LTs) at two LTMSs. R and T are then calculated from the measured values ​​of the ERS points using the singular value decomposition (SVD) algorithm.

[0058] However, due to the measurement errors and layout structure of the ERS points, the accuracy of R and T directly calculated using the existing SVD algorithm is usually low. However, this embodiment uses a new method to calculate R and T in steps S1 to S6, completing the calculation of high-precision transfer parameters between adjacent measurement stations. That is, based on the measurement errors of the ERS points, different weight coefficient matrices are assigned to the measurement values ​​of each ERS point, and the initial values ​​of R and T are calculated accordingly. and Then, the Levenberg-Marquardt (LM) algorithm is used to and Iterative optimization is performed to obtain the transfer parameters R and T with higher accuracy.

[0059] Next, we'll determine the optimal number of measurement stations. It's important to note that in a complete measurement network, each LTMS deployed on the LTMS must measure all measured points within its measurement area (that is, each LTMS corresponds to a specific measurement area, and the number of measurement areas is equal to the number of LTMSs). Therefore, the optimal number of LTMSs can be determined by dividing the optimal measurement areas for all measured points.

[0060] Based on the above analysis, the following steps propose a method for determining the optimal number of measurement stations based on measurement area division. First, the normal vectors of all measured points are calculated. Second, the optimal measurement scheme for any two measured points is determined based on the principle of minimizing overall measurement error. Finally, the measurement area to which all measured points belong is divided, combining the determined optimal measurement scheme and the normal vectors of each measured point. The details are as follows: S7. Obtain all discrete points on the surface of the component to be measured, designate several of them as measured points, calculate the normal vector of each of the measured points and form a normal vector set.

[0061] For a known component S to be measured, all discrete points on its surface are in the world coordinate system The coordinates under are all known, which can be determined according to the size of the three-dimensional model of S. Let all the discrete points on the surface of S form the set , where M discrete points are designated as measured points and constitute the set ,and ; For the collection Any measured point in Normal vector , synthesized by the normal vectors of the triangular plane formed by it and its neighboring points in the neighborhood.

[0062] like Figure 4 As shown, any measured point The N neighbors of , assuming that every two adjacent points and Both can be connected with the measured point Forming a flat triangle .make The normal vector is , the center of mass is , With the measured point The distance between ,and The measured point The angle between the vertices is ; Among them, the plane triangle Normal vector , angle and distance They can be calculated by the following formulas: (19), (20), (21), the following formula is obtained Where, It is a neighbor Pointing Point The unit direction vector of ; It is a neighbor Pointing Point The unit direction vector of .

[0063] Since at the measured point Multiple neighboring points in the neighborhood will be Constitute multiple different plane triangles, and the angles corresponding to different triangles May have different values. Therefore, the normal vectors of different triangles to the measured point Normal vector The synthesis should be based on the angle The size of contributes different degrees of weight. The larger the value, the greater the contribution weight should be. Therefore, the angle influence factor is defined as : (twenty two), In addition, the centroids of different triangles With the measured point The distance between It may also have different values. Therefore, the normal vectors of different triangles to the measured point Normal vector The synthesis should also be based on the distance The size of contributes different degrees of weight. The larger the value is, the smaller the contribution weight should be. Therefore, the distance influence factor is defined as : (twenty three), The measured point Normal vector Calculated by the following formula: (twenty four), The same applies to the measured point , calculate the set Normal vectors of all other measured points within.

[0064] S8. Obtain the overall measurement errors of any two measured points under the same-station measurement scheme and the different-station measurement scheme, and divide the measurement area to which each measured point belongs according to the normal vector set and the overall measurement error.

[0065] Specifically, the process of determining the best measurement solution for any two measured points is as follows.

[0066] The overall measurement error between any two measurement points may differ depending on whether the measurement is performed by LTs deployed in the same LTMS or by LTs deployed in two different LTMSs. Currently, the selection of a measurement plan for any two measurement points relies primarily on the long-term experience of technicians, which is less reliable. Therefore, the following analysis analyzes the overall measurement error between any two measured points under two different measurement plans (i.e., co-station measurement and off-station measurement) and proposes a method for selecting the optimal measurement plan based on minimizing the overall measurement error.

[0067] The overall measurement error under the same-station measurement scheme, like Figure 5 As shown, for the set Any two measured points in and , when the same LT (ie LT0) is used to measure the points and When measuring, the measured point can be directly measured according to the principle of minimum measurement error of all measured points. and The coordinate optimization of LT0 in the world coordinate system The layout coordinates of the simulation are .but Can be regarded as and Related dependent variables.

[0068] The measured point The measurement value obtained by LT0 measurement without measurement error can be expressed as: (25), Where, yes When measuring with LT0, there is theoretically no measurement error in the distance value. similar, is the vertical angle, is the horizontal angle. And , and They can be expressed by formulas (26) to (28) respectively: (26), (27), (28), Measured point Measurement value including measurement error obtained by LT0 measurement can be expressed as: (29), In the formula , and They are , and The measurement errors can still be calculated based on , and Calculated. Still taking the laser tracker model Leica AT960-MR as an example, since is the distance value without measurement error expressed based on the known coordinates, then , and It can be calculated according to formula (30) and (31) respectively: (30), (31), In the formula , and The unit is (i.e. micrometer), The unit of is m (meter). In addition, and It can also be converted into a form with "''" (i.e., seconds) as the unit according to formula (32): (32), Similar to , can be expressed similarly according to formulas (25) to (32) Measured value without measurement error and measurements with measurement errors .

[0069] Defining evaluation metrics To quantify the measured point and Overall measurement error when measured by LT0. The larger the measured point and The larger the overall measurement error between According to 、 、 and The value of is expressed as: (33); The overall measurement error under the different-station measurement scheme is like Figure 6 As shown, the measured point and When measuring with different LTs (i.e., LT1 and LT2), g ERS points are arranged between LT1 and LT2. (In order to simplify the analysis process, assume g=4). In the world coordinate system The layout coordinates of the following simulation can be respectively based on and The coordinates are set to , , , . Among them, a is a specific value that can be set freely, and the ERS point The number and overall layout of the ERS points can also be set flexibly. The number g needs to be greater than 3, and all ERS points Not linearly arranged (not collinear).

[0070] Similar to LT0, it can be based on , , , and The coordinates of LT1 are optimized in the world coordinate system The layout coordinates of the simulation are .according to , , , and The coordinates of LT2 can be optimized in the world coordinate system The layout coordinates of the simulation are . Similarly, and Still with and Related dependent variables.

[0071] Also similar to , the following measurement values ​​can be expressed similarly according to formulas (25) to (32): When measured by LT1 and LT2 respectively, Measurement value containing measurement error and . When measured by LT1, Measured value without measurement error and measurements with measurement errors . When measured by LT1, Measured value without measurement error ; When measured by LT2, Measurement value containing measurement error In addition, you can and Calculate the rotation matrix of the LT2 measurement coordinate system relative to the LT1 measurement coordinate system and translation vectors .and and Also with and Related dependent variables.

[0072] Will Measurement values ​​obtained by LT2 measurement Converting to the LT1 measurement coordinate system yields: (34), and The definition is similar to To evaluate the measured point and The overall measurement error when measured by LT1 and LT2 respectively. According to , , and The measured value is expressed as: (35), Because it is used to calculate and The parameters are the same as and Therefore, for any two measured points and , we can directly get and The size relationship between them. Then when When the measured point and It is appropriate to use the same-station measurement. When the measured point and It is advisable to use off-site measurement.

[0073] Specifically, dividing the measurement area to which each measured point belongs according to the normal vector set and the overall measurement error includes the following steps: Step 1: Let the set The normal vectors corresponding to all measured points in the ; Step 2: Figure 7As shown, from the collection Take any element And use it as the initial point to establish the measurement area ; Step 3: Traverse the collection in sequence Each remaining element in . If an element is traversed and and its corresponding measured point and If the relationship shown in formulas (36) and (37) is satisfied at the same time, the measured point Divide into measurement areas Inside.

[0074] (36), (37), Where, It has been divided into the measurement area For each measured point within yes The corresponding normal vector. and The definitions of and Similar, that is is the measured point and Overall measurement error when measuring with the same laser tracker LT0; is the measured point and The overall measurement error when measured by laser tracker LT1 and laser tracker LT2 respectively.

[0075] Step 4: Update the collection and collection , and repeat Steps 2 to 3 for the remaining measured points until the division of the measurement area to which all measured points belong is completed.

[0076] After all measurement areas are divided, one LTMS is deployed in each measurement area to measure all the measurement points within the area. The optimal number of LTMSs is equal to the number of measurement areas divided.

[0077] Next, the optimal spatial arrangement of the measurement stations is determined.

[0078] S9. Arrange the same number of measurement stations as the measurement area and set corresponding initial coordinates, obtain a first measurement value without measurement error and a second measurement value with measurement error corresponding to each measured point in each measurement area, and construct a position target optimization function based on the first measurement value and the second measurement value.

[0079] Set any measurement area shared within measured points , the known coordinates of each measured point in the world coordinate system are Assume that the initial coordinates of LTMS set according to manual experience in the measurement area are . Similar to the above , can be expressed similarly according to formulas (25) to (32) Arranged in When measuring LT, the measured value does not include measurement error. That is, the first measurement value and the measurement value containing the measurement error That is, the second measurement value. Then the optimization objective function H shown in formula (38) can be constructed to optimize the initial coordinates of LTMS : (38), S10. Based on the position target optimization function, the initial coordinates are optimized to determine the optimal spatial arrangement position of the measurement station.

[0080] According to formulas (25) to (32) and (38), the objective function H is also The dependent variable is . Similarly, the LM algorithm described above is used to iteratively optimize the objective function H to obtain the optimal spatial layout of the LTMS. Based on the optimal spatial layout of the LTMS measurement stations and the high-precision transfer station parameters, a high-precision laser tracker measurement network can be constructed.

[0081] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0082] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0083] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0084] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0085] Finally, it should be noted that the above specific implementation methods are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to examples, those skilled in the art should understand that the technical solutions of the present invention can be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A method for constructing a high-precision laser tracker measurement network, characterized in that: include: Using two adjacent laser trackers, respectively measure the measurement value of each ERS point arranged between the two adjacent laser trackers; wherein a plurality of ERS points are arranged between two adjacent measurement stations, and a laser tracker is arranged at each of the measurement stations; According to the measurement values, a measurement value matrix corresponding to each laser tracker is obtained; Calculating a measurement error of each of the measurement values, constructing a weight coefficient matrix corresponding to the measurement value matrix based on the measurement error, and decentralizing the measurement value matrix based on the weight coefficient matrix to obtain a decentralized measurement value matrix; The decentralized measurement value matrix in the measurement coordinate system of one of the two adjacent laser trackers is converted to the measurement coordinate system of the other, thereby constructing an error function; and initial transfer parameters are obtained based on the error function; Constructing an accuracy optimization objective function based on the initial transfer station parameters and taking the minimum overall registration error of the measurement values ​​obtained by corresponding measurements of the two laser trackers as the goal; Based on the precision optimization objective function, the initial transfer parameters are iteratively optimized to obtain high-precision transfer parameters; Obtain all discrete points on the surface of the component being measured, designate several of them as measured points, calculate the normal vectors of each of the measured points and form a normal vector set; Obtaining overall measurement errors of any two measured points under a same-station measurement scheme and a different-station measurement scheme, respectively, and dividing the measurement area to which each measured point belongs according to the normal vector set and the overall measurement error; Arrange measurement stations of the same number as the measurement area and set corresponding initial coordinates, obtain a first measurement value without measurement error and a second measurement value with measurement error corresponding to each measured point in each measurement area, and construct a position target optimization function based on the first measurement value and the second measurement value; Based on the position target optimization function, the initial coordinates are optimized to determine the optimal spatial arrangement position of the measurement station.

2. The method for constructing a high-precision laser tracker measurement network according to claim 1, characterized in that: According to the measurement values, a measurement value matrix corresponding to each laser tracker is obtained, including: In the world coordinate system There are two laser trackers in the lower layout and ,exist and There are m nodes for calculation and ERS points for transfer parameters , ; Each ERS point By the kth laser tracker Measure the measured value ,as follows: ， In the formula, c is the cosine of the trigonometric function, s is the sin of the trigonometric function, yes pass The measured distance value, is the vertical angle, is the horizontal angle; Let all the laser trackers passing through k Measured Constructing the measurement matrix , then: ， in, is a The matrix of and The matrices composed of their respective measurement values ​​can be expressed as and .

3. The method for constructing a high-precision laser tracker measurement network according to claim 2, wherein: Calculating the measurement error of each of the measurement values, constructing a weight coefficient matrix corresponding to the measurement value matrix based on the measurement error, and decentralizing the measurement value matrix based on the weight coefficient matrix to obtain a decentralized measurement value matrix, including: Each ERS point The measured value Measurement errors along the x, y and z axes respectively , and as follows: ， Where, , and They are , and The measurement errors can be calculated based on , and Calculated; among them, , and They are , and The error accuracy is provided in the technical manual of the laser tracker; according to The measurement error , and The size of Set the weight coefficient matrix as follows: ， in, is a Matrix of According to the following formula, and Decentralization can obtain the corresponding decentralized measurement value matrix and : ， in, It is the Hadamard product, which multiplies the corresponding elements of the two matrices performing the operation; is a A matrix with all elements set to 1, that is .

4. The method for constructing a high-precision laser tracker measurement network according to claim 3, wherein: Converting the decentralized measurement value matrix in the measurement coordinate system of one of the two adjacent laser trackers to the measurement coordinate system of the other one, thereby constructing an error function; Based on the error function, initial transfer parameters are obtained, including: Calculate using the following formula Measuring coordinate system Convert to Error in measurement coordinate system : ， in, is the initial rotation matrix in the initial rotation parameters; ， Where, It is to find the sum of the elements on the main diagonal; right Performing singular value decomposition yields: ， Where, is a diagonal matrix, and is the orthogonal identity matrix; but for: ； The initial translation vector in the initial transfer parameters is calculated using the following formula: : 。 5. The method for constructing a high-precision laser tracker measurement network according to claim 1, wherein: The precision optimization objective function is as follows: ， Where, is the overall registration error; when When the minimum value is taken, the initial rotation matrix can be obtained and the initial translation vector Optimized high-precision rotation matrix and high-precision translation vectors .

6. The method for constructing a high-precision laser tracker measurement network according to claim 5, characterized in that: According to the initial transfer parameters, and with the goal of minimizing the overall registration error of the measurement values ​​obtained by corresponding measurements of the two laser trackers, an accuracy optimization objective function is constructed, including: Using LM algorithm to and Perform iterative optimization: Step 1: Set the initial value; where, The initial value is , The initial value is , the initial value of the number of iterations k is , define the damping factor The initial value is ; Step 2: Calculation The kth update vector is , Solved by the following formula: ， Where, yes The Jacobian matrix at the kth iteration is , is the identity matrix; Step 3: Update : ， Step 4: Calculate the objective function value after iteration ; Step 5: Calculate the change in overall registration error : ， Step 6: Judgement If the size , then increase , and return to Step 2; if , then reduce ; and make And return to Step 2; Repeat Step 2 to Step 6 until , Is the threshold, then stop the iteration; at this time That is and Optimized high-precision rotation matrix and high-precision translation vectors .

7. The method for constructing a high-precision laser tracker measurement network according to claim 1, characterized in that: Obtain all discrete points on the surface of the component being measured, designate several of them as measured points, calculate the normal vectors of each of the measured points and form a normal vector set, including: Let all the discrete points on the surface of the measured component form a set , where M discrete points are designated as measured points and constitute the set ,and ; For the collection Any measured point in Normal vector , synthesized by the normal vectors of the triangular plane formed by it and its neighboring points in the neighborhood; Any measured point The N neighbors of , assuming that every two adjacent points and Both can be connected with the measured point Forming a flat triangle ; make The normal vector is , the center of mass is , With the measured point The distance between ,and The measured point The angle between the vertices is ; Among them, the plane triangle Normal vector , angle and distance They can be calculated by the following formulas: ， ， ， Where, It is a neighbor Pointing Point The unit direction vector of ; It is a neighbor Pointing Point The unit direction vector of ; Defining the Angle Impact Factor : ， Defining distance impact factors : ， The measured point Normal vector Calculated by the following formula: ， The same applies to the measured point , calculate the set Normal vectors of all other measured points within.

8. The method for constructing a high-precision laser tracker measurement network according to claim 7, characterized in that: Obtaining the overall measurement errors of any two measured points under the same-station measurement scheme and the different-station measurement scheme, including: When using the same-station measurement solution, for the collection Any two measured points in and , when using the same laser tracker, LT0, to measure the points and When measuring, the measured point The measurement values ​​obtained by LT0 without measurement error and with measurement error are and ;Measured point The measurement values ​​obtained by LT0 without measurement error and with measurement error are and ; Defining evaluation metrics To quantify the measured point and The overall measurement error when measured by LT0, The larger the measured point and The larger the overall measurement error between Expressed as: ； When using the off-site measurement solution, the measured point and The measurements are performed using different laser trackers, namely LT1 and LT2, with g ERS points arranged between LT1 and LT2. ERS points The number g is greater than 3, and all ERS points Not arranged linearly; When measured by LT1 and LT2 respectively, Measurement value containing measurement error and ; When measured by LT1, Measured value without measurement error and measurements with measurement errors ; When measured by LT1, Measured value without measurement error ; When measured by LT2, Measurement value containing measurement error ; according to and Calculate the rotation matrix of the LT2 measurement coordinate system relative to the LT1 measurement coordinate system and translation vectors ; Will Measurement values ​​obtained by LT2 measurement Converting to the LT1 measurement coordinate system yields: ， definition To evaluate the measured point and The overall measurement error when measured by LT1 and LT2 respectively is expressed as: ， Then when When the measured point and Use the same-station measurement scheme; when When the measured point and Adopt the off-site measurement scheme.

9. The method for constructing a high-precision laser tracker measurement network according to claim 8, characterized in that: Dividing the measurement area to which each measured point belongs according to the normal vector set and the overall measurement error includes: Step 1: Let the set The normal vectors corresponding to all measured points in the ; Step 2: From the collection Take any element And use it as the initial point to establish the measurement area ; Step 3: Traverse the collection in sequence For each remaining element in , if an element is traversed and and its corresponding measured point and At the same time, the following relationship is satisfied, and the measured point Divide into measurement areas Inside; ， ， Where, It has been divided into the measurement area For each measured point within yes The corresponding normal vector; is the measured point and Overall measurement error when measuring with the same laser tracker LT0; is the measured point and The overall measurement error when measured by laser tracker LT1 and laser tracker LT2 respectively; Step 4: Update the collection and collection , and repeat Steps 2 to 3 for the remaining measured points until the division of the measurement area to which all measured points belong is completed.

10. The method for constructing a high-precision laser tracker measurement network according to claim 1, characterized in that: The position target optimization function is: ， Among them, the known coordinates of each measured point in the world coordinate system are , let the initial coordinates of the measurement stations set according to manual experience in the measurement area be , Arranged in The measured value without measurement error when measuring with a laser tracker and measurements with measurement errors .

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