A high-precision construction method for laser tracker measurement network

Abstract

This invention relates to a high-precision construction method for a laser tracker measurement network. First, it uses a weighting coefficient matrix based on enhanced reference frame point measurement error and an iterative optimization algorithm to improve the accuracy of parameter transformation between adjacent laser trackers (LTMS). Second, based on the principle of minimizing the overall measurement error between any two measurement points, it determines the optimal number of LTMS. Finally, it optimizes the spatial position of each LTMS according to the principle of minimizing measurement error. This invention provides a high-precision construction method for a laser tracker measurement network, improving the measurement accuracy of laser trackers deployed at each measurement station and enhancing the overall measurement accuracy of the laser tracker measurement network.

Description

Technical Field

[0001] This invention relates to the field of laser tracker measurement network technology, and in particular to a high-precision method for constructing a laser tracker measurement network. Background Technology

[0002] With the acceleration of intelligent manufacturing, the increasing demands for component size and precision in the manufacturing industry have made automated digital measurement a driving force for the development of intelligent manufacturing. Laser trackers are portable coordinate measuring instruments widely used in aircraft assembly, large aerospace components, particle accelerators, machine tool error calibration, and other fields. They offer advantages such as a large measurement range, high precision, and high efficiency, enabling rapid measurement of large objects or complex features. However, a single laser tracker deployed at a single measurement station cannot complete the measurement task for objects with complex structures or large volumes. To address these measurement tasks, a laser tracker measurement network consisting of multiple measurement stations is needed.

[0003] However, existing methods for constructing laser tracker measurement networks still have significant limitations, including poor versatility and low accuracy of parameters when transferring between adjacent measurement stations. Furthermore, these methods lack effective strategies for determining the optimal number of measurement stations and dividing the measurement area for each station. Currently, the methods for determining the optimal number of measurement stations and dividing the measurement area for each station mainly rely on the long-term operational experience of technicians, which often has limited reliability. The determined number of measurement stations and the measurement area divided for each station are usually not optimal, thus affecting the overall performance of the laser tracker measurement network. Summary of the Invention

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

[0005] To address the aforementioned technical problems, this invention provides a high-precision method for constructing a laser tracker measurement network, comprising: measuring the measurement value of each ERS point arranged between two adjacent laser trackers using 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 measurement station;

[0006] Based on the measured values, a measurement value matrix corresponding to each laser tracker is obtained;

[0007] Calculate the measurement error of each of the measured values, construct a weight coefficient matrix corresponding to the measured value matrix based on the measurement error, and decentralize the measured value matrix based on the weight coefficient matrix to obtain a decentralized measured value matrix.

[0008] The decentralized measurement value matrix in the measurement coordinate system of one of the two adjacent laser trackers is transformed to the other measurement coordinate system to construct an error function; based on the error function, the initial relocation parameters are obtained.

[0009] Based on the initial transfer station parameters, and with the goal of minimizing the overall registration error of the measurements obtained by the two laser trackers, an accuracy optimization objective function is constructed.

[0010] Based on the accuracy optimization objective function, the initial transfer station parameters are iteratively optimized to obtain high-precision transfer station parameters;

[0011] Obtain all discrete points on the surface of the component to be measured, and designate several of them as the measured points. Calculate the normal vector of each measured point and form a set of normal vectors.

[0012] Obtain the overall measurement error 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 based on the normal vector set and the overall measurement error;

[0013] Arrange the same number of measurement stations as the measurement area, and set the corresponding initial coordinates. Obtain the first measurement value without measurement error and the second measurement value with measurement error for each measured point in each measurement area. Construct a position target optimization function based on the first measurement value and the second measurement value.

[0014] Based on the location target optimization function, the initial coordinates are optimized to determine the optimal spatial layout of the measurement station.

[0015] In one embodiment of the present invention, a measurement value matrix corresponding to each laser tracker is obtained based on the measured values, including:

[0016] In the world coordinate system Two laser trackers are arranged below. and ,exist and There are m units arranged between them for calculation and ERS points of inter-station parameters , ;

[0017] Each ERS point via the kth laser tracker The measured value was obtained. ,as follows:

[0018] ,

[0019] In the formula, c is the cosine of trigonometric functions, and s is the sinine of trigonometric functions. yes pass The measured distance value, It is a vertical angle. It is a horizontal angle;

[0020] Let all the laser trackers pass through the k-th laser tracker Measured Constructing a matrix of measured values Then we have:

[0021] ,

[0022] in, It is The matrix, then and The matrices formed by their respective measurements can be represented as follows: and .

[0023] In one embodiment of the present invention, the measurement error of each of the measured values ​​is calculated; a weight coefficient matrix corresponding to the measured value matrix is ​​constructed based on the measurement error; and the measured value matrix is ​​decentralized based on the weight coefficient matrix to obtain a decentralized measured value matrix, including:

[0024] Each ERS point Measured values Measurement errors along the x, y and z axes respectively , and as follows:

[0025] ,

[0026] In the formula, , and They are respectively , and The measurement errors can be determined separately based on... , and Calculated; where, , and They are , and The error accuracy is provided in the laser tracker's technical manual;

[0027] according to Measurement error , and The size is Set weight coefficient matrix as follows:

[0028] ,

[0029] in, It is Matrix;

[0030] According to the following formula, respectively and Decentralization yields the corresponding decentralized measurement matrix. and :

[0031] ,

[0032] in, It is the Hadamard product, which multiplies corresponding elements of two matrices. It is A matrix whose elements are all 1s, i.e. .

[0033] 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 transformed to the measurement coordinate system of the other, thereby constructing an error function; based on the error function, initial transfer parameters are obtained, including:

[0034] Calculate using the following formula Measurement coordinate system Switch to Error in the measurement coordinate system :

[0035] ,

[0036] in, This is the initial rotation matrix in the initial transfer station parameters;

[0037] ,

[0038] In the formula, It is to find the sum of the elements on the main diagonal;

[0039] right Singular value decomposition yields:

[0040] ,

[0041] In the formula, It is a diagonal matrix. and It is an orthogonal identity matrix;

[0042] but for:

[0043] ;

[0044] The initial translation vector in the initial transfer station parameters is calculated using the following formula. :

[0045] .

[0046] In one embodiment of the present invention, the accuracy optimization objective function is as follows:

[0047] ,

[0048] In the formula, It is the overall registration error; when The initial rotation matrix can be obtained by taking the minimum value. and initial translation vector Optimized high-precision rotation matrix and high-precision translation vector .

[0049] In one embodiment of the present invention, based on the initial transfer station parameters and with the objective of minimizing the overall registration error of the measurements obtained by the two laser trackers, an accuracy optimization objective function is constructed, including:

[0050] Using the LM algorithm to and Perform iterative optimization:

[0051] Step 1: Set initial values; where, The initial value is , The initial value is The initial value of the iteration number k is Define the damping factor The initial value is ;

[0052] Step 2: Calculation The k-th update vector is , Solving the following equation yields:

[0053] ,

[0054] In the formula, yes The Jacobian matrix at the k-th iteration is, i.e. , It is the identity matrix;

[0055] Step 3: Update :

[0056] ,

[0057] Step 4: Calculate the objective function value after iteration. ;

[0058] Step 5: Calculate the overall registration error change. :

[0059] ,

[0060] Step 6: Judgment The size, if Then increase And return to Step 2; if Then decrease ; and make And return to Step 2;

[0061] Repeat Steps 2 through 6 until... , If the threshold is reached, then the iteration stops; at this point... That is and Optimized high-precision rotation matrix and high-precision translation vector .

[0062] In one embodiment of the present invention, all discrete points on the surface of the component to be measured are obtained, and a number of them are designated as measured points. The normal vectors of each measured point are calculated and a set of normal vectors is formed, including:

[0063] Let all discrete points on the surface of the tested component form a set. M discrete points are designated as the measured points and form a set. ,and For sets any measured point in normal vector It is synthesized by the normal vector of the triangular plane formed by it and its neighboring points in the neighborhood;

[0064] Any measured point The N neighboring points are respectively Assuming that every two adjacent neighboring points and Both can be used with the measured point Forming a planar triangle ;

[0065] make The normal vector is The center of mass is , With the measured point The distance between them is ,and With the measured point The included angle between the vertices is Among them, planar triangles normal vector included angle and distance The results can be calculated using the following formulas:

[0066] ,

[0067] ,

[0068] ,

[0069] In the formula, are neighboring points Point of view The unit direction vector; are neighboring points Point of view The unit direction vector;

[0070] Define the angle of influence factor :

[0071] ,

[0072] Define distance influence factor :

[0073] ,

[0074] Then the measured point normal vector Calculated using the following formula:

[0075] ,

[0076] Similarly, for the measured point Calculate the set The normal vectors of all other measured points within the same area.

[0077] In one embodiment of the present invention, obtaining the overall measurement error of any two measured points under the same-station measurement scheme and the different-station measurement scheme includes:

[0078] When using a co-station measurement scheme, for the set Any two measured points in and When the same laser tracker, LT0, is used to measure the points respectively and When taking measurements, the measured point The measured values ​​obtained by LT0 measurement without measurement error and the measured values ​​with measurement error are respectively and ; the measured point The measured values ​​obtained by LT0 measurement without measurement error and the measured values ​​with measurement error are respectively and ;

[0079] Define evaluation indicators To quantify the measured points and Overall measurement error when measured by LT0 The larger the value, the more likely the measured point is to be measured. and The larger the overall measurement error between them; Represented as:

[0080] ;

[0081] When using a cross-station measurement scheme, the measured point and Measurements were taken using two different laser trackers, LT1 and LT2, with g ERS points positioned between LT1 and LT2. ;ERS point The number g is greater than 3, and all ERS points Not arranged in a linear fashion;

[0082] When measured by LT1 and LT2 respectively, Measurement values ​​containing measurement errors and ; When measured with LT1, Measurement values ​​excluding measurement errors And measured values ​​containing measurement errors ; When measured with LT1, Measurement values ​​excluding measurement errors ; When measured by LT2, Measurement values ​​containing measurement errors ;

[0083] according to and Calculate the rotation matrix of the LT2 measurement coordinate system relative to the LT1 measurement coordinate system. Translation vector ;

[0084] Will Measurement values ​​obtained by LT2 measurement Transforming to the LT1 measurement coordinate system yields:

[0085] ,

[0086] definition To evaluate the measured point and The overall measurement error when measured by LT1 and LT2 respectively is expressed as:

[0087] ,

[0088] Then when At that time, the measured point and A co-station measurement scheme is adopted; when At that time, the measured point and A cross-station measurement scheme was adopted.

[0089] In one embodiment of the present invention, the measurement region to which each of the measured points belongs is divided based on the set of normal vectors and the overall measurement error, including:

[0090] Step 1: Let set The set consists of the normal vectors corresponding to all measured points. ;

[0091] Step 2: From the set Choose any element And establish the measurement area using it as the initial point. ;

[0092] Step 3: Traverse the collection sequentially For each remaining element, if a certain element is visited... and and its corresponding measured points and If the following relationship is satisfied, then the measured point Divided into measurement areas Inside;

[0093] ,

[0094] ,

[0095] In the formula, It has already been assigned to the measurement area. Each measured point within, yes The corresponding normal vector; The point being measured and Overall measurement error when measured with the same LT0 laser tracker; The point being measured and The overall measurement error when measured by laser tracker LT1 and laser tracker LT2 respectively;

[0096] Step 4: Update the collection and set Then repeat Steps 2-3 for the remaining measured points until the measurement area to which all measured points belong is divided.

[0097] In one embodiment of the present invention, the location target optimization function is:

[0098] ,

[0099] Wherein, the known coordinates of each measured point in the world coordinate system are: Let the initial coordinates of the measurement stations within the measurement area, set according to human experience, be... , Arranged in The measured value, excluding measurement error, when measured by the laser tracker. And measured values ​​containing measurement errors .

[0100] The technical solution of the present invention has the following advantages compared with the prior art:

[0101] The present invention discloses a high-precision construction method for a laser tracker measurement network. By calculating high-precision transfer parameters between adjacent measurement stations, the optimal number of measurement stations is determined, and the optimal spatial arrangement of each measurement station is optimized. This improves the measurement accuracy of the laser trackers arranged at each measurement station and enhances the overall measurement accuracy of the laser tracker measurement network.

[0102] This invention determines the optimal number of measurement stations based on the size and shape characteristics of the component being measured. This avoids the problem of excessive measurement stations leading to data redundancy and reduced overall measurement efficiency. Simultaneously, it also avoids the problem of insufficient measurement stations resulting in incomplete coverage of the component and reduced overall measurement completeness.

[0103] This invention improves the measurement accuracy of the laser tracker placed at each measurement station by optimizing the optimal spatial arrangement for each station.

[0104] This invention improves the uniformity of measurement data from various laser trackers by calculating high-precision transfer parameters between adjacent measurement stations, thereby enhancing the overall measurement accuracy of the laser tracker measurement network. Attached Figure Description

[0105] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0106] Figure 1 This is a flowchart of the high-precision construction method for the laser tracker measurement network of the present invention.

[0107] Figure 2 This is a schematic diagram of the laser tracker measurement network.

[0108] Figure 3 This is a schematic diagram of the transfer station parameter calculation model.

[0109] Figure 4 This is a schematic diagram of the model for obtaining the normal vector of the measured point.

[0110] Figure 5 This is a schematic diagram of the same-station measurement model.

[0111] Figure 6 This is a schematic diagram of a cross-station measurement model.

[0112] Figure 7 This is a schematic diagram of the measurement area division. Detailed Implementation

[0113] 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 and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0114] In this invention, when directions (up, down, left, right, front, and back) are described, it is only for the convenience of describing the technical solution of this invention, and does not indicate or imply that the technical features referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, it should not be construed as a limitation of this invention.

[0115] In this invention, "several" means one or more, "multiple" means two or more, "greater than," "less than," "exceeding," etc., are understood to exclude the stated number; "above," "below," "within," etc., are understood to include the stated number. In the description of this invention, the terms "first" and "second" are used only to distinguish technical features and should not be construed as indicating or implying relative importance, or implicitly indicating the number of indicated technical features, or implicitly indicating the order of the indicated technical features.

[0116] In this invention, unless otherwise explicitly defined, the terms "setting," "installing," and "connecting" should be interpreted broadly. For example, they can refer to a direct connection or an indirect connection through an intermediate medium; a fixed connection, a detachable connection, or an integrally formed connection; a mechanical connection, an electrical connection, or a connection capable of mutual communication; or the internal connection of two components or the interaction between two components. Those skilled in the art can reasonably determine the specific meaning of the above terms in this invention based on the specific content of the technical solution.

[0117] The laser tracker measurement network will be introduced first below.

[0118] Reference Figure 2The diagram shows a schematic of a laser tracker measurement network. This network mainly consists of multiple measurement stations surrounding the component under test. Each measurement station is a location for placing a laser tracker (LT) (the number of stations is determined by the size and shape of the component). Several Enhanced Reference Systems (ERS) points are artificially placed between adjacent measurement stations. When using this network to measure the component, one laser tracker can be placed at each station simultaneously for full coverage measurement. However, in practice, due to the high cost of a single laser tracker, it is usually deployed in rotation at each station. Since each laser tracker's measurement data is based on its current station, it is necessary to unify the data from each station to obtain the overall measurement data for the component. This unification is achieved by rotating and translating the data from the laser trackers placed between adjacent stations. The ERS points mentioned earlier are used to calculate the transformation parameters (rotation matrix R and translation vector T) between adjacent measurement stations.

[0119] The construction of the laser tracker measurement network involves determining the number of measurement stations, the spatial coordinates of each measurement station, and the conversion parameters between adjacent measurement stations based on the size and shape characteristics of the measured parts.

[0120] This embodiment provides a method for constructing a high-precision measurement network for a laser tracker, including the following steps:

[0121] S1. Measure the value of each ERS point arranged between two adjacent laser trackers; wherein, a number of ERS points are arranged between two adjacent measurement stations, and a laser tracker is arranged at each measurement station.

[0122] Specifically, such as Figure 3 As shown, in the world coordinate system Two laser trackers are arranged below (i.e. and ).exist and There are m units arranged between them for calculation and ERS points of inter-station parameters , Each ERS point via the kth laser tracker The measured value was obtained. ,as follows:

[0123] (1),

[0124] In the formula, c is the cosine of trigonometric functions, and s is the sinine of trigonometric functions. yes pass The measured distance value. (Compared to...) similar, It is a vertical angle. It's a horizontal angle.

[0125] S2, Based on the measured value The measurement value matrix corresponding to each laser tracker is obtained. .

[0126] Specifically, let all those passing through the k-th laser tracker Measured Constructing a matrix of measured values Then we have:

[0127] (2),

[0128] in, It is The matrix, then and The matrices formed by their respective measurements can be represented as follows: and .

[0129] S3. Calculate the measurement error of each of the measured values, and construct a weight coefficient matrix corresponding to the measured value matrix based on the measurement error. Based on the weight coefficient matrix For the measured value matrix and Decentralization is performed to obtain a decentralized measurement matrix. and .

[0130] Due to all actual measured values , and All of these include measurement errors, therefore the result calculated using formula (1) is... The measured values ​​also include errors. Measured values Measurement errors along the x, y and z axes respectively , and It can be expressed as follows according to formula (3):

[0131] (3),

[0132] In the formula, , and They are respectively , and The measurement errors can be determined separately based on... , and The calculation yielded the following result. , and They are , and The error accuracy is provided in the technical manual of the laser tracker.

[0133] Taking the Leica AT960-MR laser tracker as an example, according to its technical manual, , Due to the measurement obtained If it contains measurement error, then , and The results can be calculated using formulas (4) and (5) respectively:

[0134] (4),

[0135] (5),

[0136] In the formula, , and The unit is (i.e., micrometers) The unit is m (meter). Additionally, and It can also be converted to a form in units of "''" (i.e., seconds) according to formula (6):

[0137] (6),

[0138] because It includes measurement error, and the larger the measurement error, the greater the error. The greater the deviation from its true value, the better. Therefore, according to Measurement error , and The size is Set weight coefficient matrix .

[0139] (7),

[0140] in, It is also The matrix.

[0141] According to formula (8), respectively for each of the following: and Decentralization yields the corresponding decentralized measurement matrix. and :

[0142] (8),

[0143] in, It is the Hadamard product, which performs the operation by multiplying corresponding elements of two matrices. It is A matrix whose elements are all 1s, i.e. .

[0144] S4. Transform the decentralized measurement value matrix in the measurement coordinate system of one of the two adjacent laser trackers to the other measurement coordinate system, thereby constructing an error function; based on the error function... Obtain the initial transfer station parameters and .

[0145] Specifically, Measurement coordinate system Switch to Error in the measurement coordinate system It can be expressed as follows according to formula (9):

[0146] (9),

[0147] Expanding formula (9) yields:

[0148] (10)

[0149] when When the minimum value is obtained, the solution can be found. And to make Minimum is equivalent to making Take the maximum value.

[0150] Based on existing literature, we can conclude that:

[0151] (11),

[0152] In the formula, It is to find the sum of the elements on the main diagonal.

[0153] To solve for the equation (11) to make the equality hold. ,right Singular value decomposition yields:

[0154] (12)

[0155] In the formula, It is a diagonal matrix. and It is an orthogonal identity matrix.

[0156] but It can be obtained from formula (13):

[0157] (13);

[0158] Further, It can be obtained from formula (14):

[0159] (14)

[0160] S5. Based on the initial transfer parameters and An accuracy optimization objective function is constructed with the goal of minimizing the overall registration error of the measurements obtained from the corresponding measurements by the two laser trackers.

[0161] Specifically, by making and To construct the optimization objective function by minimizing the overall registration error. :

[0162] (15)

[0163] In the formula, It is the overall registration error; when The initial rotation matrix can be obtained by taking the minimum value. and initial translation vector Optimized high-precision rotation matrix and high-precision translation vector .

[0164] S6. Based on the accuracy optimization objective function, the initial transfer station parameters are iteratively optimized to obtain high-precision transfer station parameters.

[0165] Specifically, the Levenberg-Marquardt (LM) algorithm is used to perform the following steps: and The iterative optimization process is as follows:

[0166] Step 1: Set initial values; where, The initial value is , The initial value is The initial value of the iteration number k is Damping factor The initial value is =0.1.

[0167] Step 2: Calculation The k-th update vector is , It can be solved by formula (16):

[0168] (16)

[0169] In the formula, yes The Jacobian matrix at the k-th iteration is, i.e. , It is an identity matrix.

[0170] Step 3: Update .

[0171] (17)

[0172] Step 4: Calculate the objective function value after iteration. .

[0173] Step 5: Calculate the overall registration error change. .

[0174] (18)

[0175] Step 6: Judgment The size, if Then increase (Right now =10 ) and return to Step 2. If Then decrease (Right now = / 10) and make Then return to Step 2.

[0176] Repeat Steps 2 through 6 until... ( If a pre-set, relatively small threshold is used, then the iteration stops. At this point... That is and Optimized precision value and .

[0177] It should be noted that the existing transfer station parameters and Typically, calculations are performed by setting up several ERS points. The process is as follows: First, several ERS points are placed between two adjacent measurement stations, and each point is individually measured using a laser tracker (LT) placed at two LTMS stations. Then, the Singular Value Decomposition (SVD) algorithm is used to calculate R and T based on the measurements from the ERS points.

[0178] However, due to measurement errors and layout structure of ERS points, the accuracy of R and T calculated directly using the existing SVD algorithm is usually low. This embodiment, through steps S1 to S6, proposes a novel method to calculate R and T, thus achieving high-precision transfer parameters between adjacent measurement stations. Specifically, based on the measurement errors of the ERS points, a different weighting coefficient matrix is ​​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 was used to... and Iterative optimization is performed to obtain more accurate transfer station parameters R and T.

[0179] The optimal number of measurement stations will now be determined. It should be noted that in a complete measurement network, each measurement station (LTMS) needs to measure all points within its measurement area (i.e., each LTMS corresponds to a specific measurement area, and the number of measurement areas equals the number of LTMS). Therefore, the optimal number of LTMS can be determined by dividing the optimal measurement areas for all measured points.

[0180] 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, based on the principle of minimizing overall measurement error, the optimal measurement scheme for any two measured points is determined. Finally, the measurement areas to which all measured points belong are divided by combining the determined optimal measurement scheme and the normal vector of each measurement point. Specifically:

[0181] S7. Obtain all discrete points on the surface of the component to be measured, and designate several of them as measured points, calculate the normal vector of each measured point and form a set of normal vectors.

[0182] For a known measured component S, all discrete points on its surface are in the world coordinate system. The coordinates of all points on the surface of S are known and can be determined based on the dimensions of the three-dimensional model of S. Let all discrete points on the surface of S form a set. M discrete points are designated as the measured points and form a set. ,and For sets any measured point in normal vector It is synthesized by the normal vector of the triangular plane formed by it and its neighboring points in the neighborhood.

[0183] like Figure 4 As shown, any measured point The N neighboring points are respectively Assuming that every two adjacent neighboring points and Both can be used with the measured point Forming a planar triangle .make The normal vector is The center of mass is , With the measured point The distance between them is ,and With the measured point The included angle between the vertices is Among them, planar triangles normal vector included angle and distance The results can be calculated using the following formulas:

[0184] (19)

[0185] (20)

[0186] (21), the following formula is obtained

[0187] In the formula, are neighboring points Point of view The unit direction vector; are neighboring points Point of view The unit direction vector.

[0188] Because at the measured point Multiple neighboring points within the neighborhood will interact with the measured point. This forms multiple different planar triangles, and the included angles of the different triangles are... They may have different values. Therefore, the normal vectors of different triangles will have different values ​​for the measured point. normal vector The composition should be based on the included angle The size of the angle contributes different degrees of weight. The larger the value, the greater the weight of the contribution should be. Therefore, the angle of influence factor should be defined. :

[0189] (twenty two),

[0190] In addition, the centroids of different triangles With the measured point Distance between They may also have different values. Therefore, the normal vectors of different triangles will have different values ​​for the measured point. normal vector The synthesis should also be based on distance The magnitude of the distance contributes different degrees of weight. The larger the value, the smaller the weight of the contribution should be. Therefore, a distance influence factor is defined. :

[0191] (twenty three),

[0192] Then the measured point normal vector Calculated using the following formula:

[0193] (twenty four),

[0194] Similarly, for the measured point Calculate the set The normal vectors of all other measured points within the same area.

[0195] S8. Obtain the overall measurement error 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.

[0196] Specifically, the process of determining the optimal measurement scheme for any two measured points is as follows.

[0197] For any two measurement points, their overall measurement error may differ depending on whether they are measured by LT measurements arranged in the same LTMS or by LT measurements arranged in two different LTMSs. Currently, the selection of the measurement scheme for any two measurement points mainly relies on the long-term experience of technicians, which has low reliability. Therefore, this paper analyzes the overall measurement error of any two measured points under two different measurement schemes (i.e., co-station measurement and inter-station measurement) and proposes an optimal measurement scheme selection method based on minimizing the overall measurement error.

[0198] Overall measurement error under the same-station measurement scheme

[0199] like Figure 5 As shown, for the set Any two measured points in and When the same LT (i.e., LT0) is used to measure the points respectively and When conducting measurements, the principle of minimizing the sum of measurement errors at all measured points can be followed, directly starting from the measured point. and Coordinate optimization yields LT0 in the world coordinate system The layout coordinates in the next simulation are: .but It can be regarded as being with and Relevant dependent variables.

[0200] Then the measured point Measurement values ​​obtained by LT0 measurement without measurement error It can be represented as:

[0201] (25),

[0202] In the formula, yes The distance value measured via LT0 is theoretically free of measurement error. similar, It is a vertical angle. It's a horizontal angle. And... , and They can be expressed by formulas (26) to (28) respectively:

[0203] (26)

[0204] (27)

[0205] (28)

[0206] Measured point Measurement values ​​obtained through LT0 measurement, including measurement errors It can be represented as:

[0207] (29)

[0208] In the formula , and They are , and The measurement errors can still be determined separately based on... , and The calculation is as follows. Taking the Leica AT960-MR laser tracker as an example again, due to the current... If it is a distance value without measurement error expressed based on known coordinates, then... , and The results can be calculated using formulas (30) and (31) respectively:

[0209] (30)

[0210] (31),

[0211] In the formula , and The unit is (i.e., micrometer). The unit is m (meter). Additionally, and It can also be converted to a form in units of "''" (i.e., seconds) according to formula (32):

[0212] (32),

[0213] Similar to It can be expressed similarly according to formulas (25) to (32). Measurement values ​​excluding measurement errors And measured values ​​containing measurement errors .

[0214] Define evaluation indicators To quantify the measured points and The overall measurement error when measured by LT0. The larger the value, the more likely the measured point is to be measured. and The larger the overall measurement error between them, the greater the error. According to , , and The value is represented as:

[0215] (33);

[0216] Overall measurement error under the off-site measurement scheme

[0217] like Figure 6 As shown, the measured point and When measurements are taken using different LTs (i.e., LT1 and LT2), g ERS points are arranged between LT1 and LT2. (To simplify the analysis process, let g=4). In the world coordinate system The arrangement coordinates in the next simulation can be determined according to... and The coordinates were set to , , , Where 'a' is a specific value that can be freely set, and the ERS point... The number and overall layout can also be flexibly set. However, ERS points The quantity g needs to be greater than 3, and all ERS points They are not arranged linearly (not collinear).

[0218] Similar to LT0, it can be based on , , , and The coordinates of LT1 in the world coordinate system were optimized. The layout coordinates in the next simulation are: .according to , , , and The coordinates can be optimized to obtain LT2 in the world coordinate system. The layout coordinates in the next simulation are: Similarly, and Still with and Relevant dependent variables.

[0219] Similarly The following measurements can be expressed similarly using formulas (25) to (32): When measured by LT1 and LT2 respectively, Measurement values ​​containing measurement errors and . When measured with LT1, Measurement values ​​excluding measurement errors And measured values ​​containing measurement errors . When measured with LT1, Measurement values ​​excluding measurement errors ; When measured by LT2, Measurement values ​​containing measurement errors Additionally, it can be based on and Calculate the rotation matrix of the LT2 measurement coordinate system relative to the LT1 measurement coordinate system. Translation vector .and and Also with and Relevant dependent variables.

[0220] Will Measurement values ​​obtained by LT2 measurement Transforming to the LT1 measurement coordinate system yields:

[0221] (34),

[0222] and The definition is similar, definition 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:

[0223] (35),

[0224] Because it is used for calculation and The parameters are all related to and The relevant dependent variable. Therefore, for any two measured points... and They can be obtained directly from their coordinates. and The size relationship between them. Then when At that time, the measured point and Co-station surveying is appropriate. When At that time, the measured point and It is advisable to use off-site measurement.

[0225] Specifically, based on the set of normal vectors and the overall measurement error, the measurement areas to which each of the measured points belongs are divided, including the following steps:

[0226] Step 1: Let set The set consists of the normal vectors corresponding to all measured points. ;

[0227] Step 2: As Figure 7 As shown, from the set Choose any element And establish the measurement area using it as the initial point. ;

[0228] Step 3: Traverse the collection sequentially Each remaining element in the list. If a certain element is encountered during iteration... and and its corresponding measured points and If the relationship shown in formulas (36) and (37) is satisfied, then the measured point Divided into measurement areas Inside.

[0229] (36)

[0230] (37)

[0231] In the formula, It has already been assigned to the measurement area. Each measured point within, yes The corresponding normal vector. and The definitions are respectively with and Similar, that is The point being measured and Overall measurement error when measured with the same LT0 laser tracker; The point being measured and The overall measurement error when measured by laser tracker LT1 and laser tracker LT2 respectively.

[0232] Step 4: Update the collection and set Then repeat Steps 2-3 for the remaining measured points until the measurement area to which all measured points belong is divided.

[0233] After dividing the measurement areas to all measured points, a Lightning Measurement Station (LTMS) will be deployed in each measurement area to measure all measured points within that area. Therefore, the optimal number of LTMS is equal to the number of measurement areas.

[0234] The optimal spatial layout of the measurement station will be determined next.

[0235] S9. Arrange the same number of measurement stations as the measurement area, and set the corresponding initial coordinates. Obtain the first measurement value without measurement error and the second measurement value with measurement error for each measured point in each measurement area. Construct a position target optimization function based on the first measurement value and the second measurement value.

[0236] Let any measurement area shared within Each measured point The known coordinates of each measured point in the world coordinate system are: Let the initial LTMS coordinates within the measurement area, set based on manual experience, be... Similar to the aforementioned It can be expressed similarly according to formulas (25) to (32). Arranged in LT measurement, the measured value excluding measurement error. That is, the first measured value and the measured value containing measurement error. That is, the second measured value. Then, an optimization objective function H, as shown in formula (38), can be constructed to optimize the initial coordinates of the LTMS. :

[0237] (38)

[0238] S10. Based on the location target optimization function, optimize the initial coordinates to determine the optimal spatial layout of the measurement station.

[0239] According to formulas (25)~(32) and (38), the objective function H is also The dependent variable is H. Similarly, the optimal spatial arrangement of the LTMS can be obtained by iteratively optimizing the objective function H using the aforementioned LM algorithm. Based on the optimal spatial arrangement of the LTMS at the measurement stations and the high-precision transfer station parameters, the high-precision construction of the laser tracker measurement network can be completed.

[0240] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0241] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations 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, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations 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.

[0242] 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.

[0243] 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.

[0244] Finally, it should be noted that the above specific embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to examples, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for high-precision construction of a laser tracker measurement network, characterized in that, include: The measurement values ​​of each ERS point arranged between two adjacent laser trackers are measured using two adjacent laser trackers; wherein, a number of ERS points are arranged between two adjacent measurement stations, and a laser tracker is arranged at each measurement station. Based on the measured values, a measurement value matrix corresponding to each laser tracker is obtained; Calculate the measurement error of each of the measured values, construct a weight coefficient matrix corresponding to the measured value matrix based on the measurement error, and decentralize the measured value matrix based on the weight coefficient matrix to obtain a decentralized measured value matrix. The decentralized measurement value matrix in the measurement coordinate system of one of the two adjacent laser trackers is transformed to the other measurement coordinate system to construct an error function; based on the error function, the initial relocation parameters are obtained. Based on the initial transfer station parameters, and with the goal of minimizing the overall registration error of the measurements obtained by the two laser trackers, an accuracy optimization objective function is constructed. Based on the accuracy optimization objective function, the initial transfer station parameters are iteratively optimized to obtain high-precision transfer station parameters; Obtain all discrete points on the surface of the component to be measured, and designate several of them as the measured points. Calculate the normal vector of each measured point and form a set of normal vectors. Obtain the overall measurement error 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 based on the normal vector set and the overall measurement error; Arrange the same number of measurement stations as the measurement area, and set the corresponding initial coordinates. Obtain the first measurement value without measurement error and the second measurement value with measurement error for each measured point in each measurement area. Construct a position target optimization function based on the first measurement value and the second measurement value. Based on the location target optimization function, the initial coordinates are optimized to determine the optimal spatial layout of the measurement station. The accuracy optimization objective function is as follows: ； In the formula, It is the overall registration error; when The initial rotation matrix can be obtained by taking the minimum value. and initial translation vector Optimized high-precision rotation matrix and high-precision translation vector ; Based on the accuracy optimization objective function, the initial transfer station parameters are iteratively optimized to obtain high-precision transfer station parameters; including: Using the LM algorithm to and Perform iterative optimization: Step 1: Set initial values; where, The initial value is , The initial value is The initial value of the iteration number k is Define the damping factor The initial value is ; Step 2: Calculation The k-th update vector is , Solving the following equation yields: ； In the formula, yes The Jacobian matrix at the k-th iteration is, i.e. , It is the identity matrix; Step 3: Update : ； Step 4: Calculate the objective function value after iteration. ; Step 5: Calculate the overall registration error change. : ； Step 6: Judgment The size, if Then increase And return to Step 2; if Then decrease ; and make And return to Step 2; Repeat Steps 2 through 6 until... , If the threshold is reached, then the iteration stops; at this point... That is and Optimized high-precision rotation matrix and high-precision translation vector .

2. The method for high-precision construction of a laser tracker measurement network according to claim 1, characterized in that, Based on the measured values, a measurement value matrix corresponding to each laser tracker is obtained, including: In the world coordinate system Two laser trackers are arranged below. and ,exist and There are m units arranged between them for calculation and ERS points of inter-station parameters , ; Each ERS point via the kth laser tracker The measured value was obtained. ,as follows: ； In the formula, c is the cosine of trigonometric functions, and s is the sinine of trigonometric functions. yes pass The measured distance value, It is a vertical angle. It is a horizontal angle; Let all the laser trackers pass through the k-th laser tracker Measured Constructing a matrix of measured values Then we have: ； in, It is The matrix, then and The matrices formed by their respective measurements can be represented as follows: and .

3. The method for high-precision construction of a laser tracker measurement network according to claim 2, characterized in that, Calculate the measurement error for each of the measured values; construct a weight coefficient matrix corresponding to the measured value matrix based on the measurement error; and decentralize the measured value matrix based on the weight coefficient matrix to obtain a decentralized measured value matrix, including: Each ERS point Measured values Measurement errors along the x, y and z axes respectively , and as follows: ； In the formula, , and They are respectively , and The measurement errors can be determined separately based on... , and Calculated; where, , and They are , and The error accuracy is provided in the laser tracker's technical manual; according to Measurement error , and The size is Set weight coefficient matrix as follows: ； in, It is Matrix; According to the following formula, respectively and Decentralization yields the corresponding decentralized measurement matrix. and : ； in, It is the Hadamard product, which multiplies corresponding elements of two matrices. It is A matrix whose elements are all 1s, i.e. .

4. The method for high-precision construction of a laser tracker measurement network according to claim 3, characterized in that, The decentralized measurement value matrix in the measurement coordinate system of one of the two adjacent laser trackers is transformed to the other measurement coordinate system to construct the error function; Based on the error function, the initial transfer station parameters are obtained, including: Calculate using the following formula Measurement coordinate system Switch to Error in the measurement coordinate system : ； in, This is the initial rotation matrix in the initial transfer station parameters; ； In the formula, It is to find the sum of the elements on the main diagonal; right Singular value decomposition yields: ； In the formula, It is a diagonal matrix. and It is an orthogonal identity matrix; but for: ； The initial translation vector in the initial transfer station parameters is calculated using the following formula. : 。 5. The method for high-precision construction of a laser tracker measurement network according to claim 1, characterized in that, Obtain all discrete points on the surface of the component to be measured, and designate several of them as the measured points. Calculate the normal vector of each measured point and construct a set of normal vectors, including: Let all discrete points on the surface of the tested component form a set. M discrete points are designated as the measured points and form a set. ,and For sets any measured point in normal vector It is synthesized by the normal vector of the triangular plane formed by it and its neighboring points in the neighborhood; Any measured point The N neighboring points are respectively Assuming that every two adjacent neighboring points and Both can be used with the measured point Forming a planar triangle ; make The normal vector is The center of mass is , With the measured point The distance between them is ,and With the measured point The included angle between the vertices is Among them, planar triangles normal vector included angle and distance The results can be calculated using the following formulas: ； ； ； In the formula, are neighboring points Point of view The unit direction vector; are neighboring points Point of view The unit direction vector; Define the angle of influence factor : ； Define distance influence factor : ； Then the measured point normal vector Calculated using the following formula: ； Similarly, for the measured point Calculate the set The normal vectors of all other measured points within the same area.

6. The method for high-precision construction of a laser tracker measurement network according to claim 5, characterized in that, Obtain the overall measurement error of any two measured points under the same-station measurement scheme and the different-station measurement scheme, respectively, including: When using a co-station measurement scheme, for the set Any two measured points in and When the same laser tracker, LT0, is used to measure the points respectively and When taking measurements, the measured point The measured values ​​obtained by LT0 measurement without measurement error and the measured values ​​with measurement error are respectively and ; the measured point The measured values ​​obtained by LT0 measurement without measurement error and the measured values ​​with measurement error are respectively and ; Define evaluation indicators To quantify the measured points and Overall measurement error when measured by LT0 The larger the value, the more likely the measured point is to be measured. and The larger the overall measurement error between them; Represented as: ； When using a cross-station measurement scheme, the measured point and Measurements were taken using two different laser trackers, LT1 and LT2, with g ERS points positioned between LT1 and LT2. ;ERS point The number g is greater than 3, and all ERS points Not arranged in a linear fashion; When measured by LT1 and LT2 respectively, Measurement values ​​containing measurement errors and ; When measured with LT1, Measurement values ​​excluding measurement errors And measured values ​​containing measurement errors ; When measured with LT1, Measurement values ​​excluding measurement errors ; When measured by LT2, Measurement values ​​containing measurement errors ; according to and Calculate the rotation matrix of the LT2 measurement coordinate system relative to the LT1 measurement coordinate system. Translation vector ; Will Measurement values ​​obtained by LT2 measurement Transforming 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 At that time, the measured point and A co-station measurement scheme is adopted; when At that time, the measured point and A cross-station measurement scheme was adopted.

7. The method for high-precision construction of a laser tracker measurement network according to claim 6, characterized in that, Based on the set of normal vectors and the overall measurement error, the measurement areas to which each of the measured points belongs are divided, including: Step 1: Let set The set consists of the normal vectors corresponding to all measured points. ; Step 2: From the set Choose any element And establish the measurement area using it as the initial point. ; Step 3: Traverse the collection sequentially For each remaining element, if a certain element is visited... and and its corresponding measured points and If the following relationship is satisfied, then the measured point Divided into measurement areas Inside; ； In the formula, It has already been assigned to the measurement area. Each measured point within, yes The corresponding normal vector; The point being measured and Overall measurement error when measured with the same LT0 laser tracker; The point being measured and The overall measurement error when measured by laser tracker LT1 and laser tracker LT2 respectively; Step 4: Update the collection and set Then repeat Steps 2-3 for the remaining measured points until the measurement area to which all measured points belong is divided.

8. The method for high-precision construction of a laser tracker measurement network according to claim 1, characterized in that, The location objective optimization function is: ； Wherein, the known coordinates of each measured point in the world coordinate system are: Let the initial coordinates of the measurement stations within the measurement area, set according to human experience, be... , Arranged in The measured value, excluding measurement error, when measured by the laser tracker. And measured values ​​containing measurement errors .

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