CN112050733A - Multi-station conversion precision improving method based on high-precision virtual standard device - Google Patents
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Abstract
The invention discloses a multi-station conversion precision improving method based on a high-precision virtual standard device, belongs to the field of digital measurement, and relates to a multi-station conversion precision improving method based on a high-precision virtual standard device. Firstly, acquiring an original three-dimensional coordinate of a common point through multi-station measurement of a laser tracker; and then constructing a large-size virtual standard based on a laser tracker and a multilateration method, obtaining the high-precision geometric length between the common points of the virtual meter, and correcting the error of the coordinates of the common points by taking the high-precision geometric length as a constraint. And finally, completing the conversion of the coordinate system between the measuring stations based on the corrected common point coordinates, and calculating the coordinate conversion error. The method realizes the optimization and correction of the common point coordinates based on the length constraint between the virtual standard device common points and the Levenberg-Marquardt nonlinear optimization method, reduces the error of data conversion between coordinate systems, and improves the measurement precision of the common point coordinates of each station. The method has the characteristics of simple and convenient operation, high precision and strong robustness.
Description
Technical Field
The invention belongs to the field of digital measurement, and relates to a multi-station conversion precision improving method based on a high-precision virtual standard device.
Background
With the continuous improvement of the requirements of manufacturing precision and assembling performance of high-end major engineering equipment in the fields of aerospace and energy transportation, a new technology for driving the manufacturing and assembling of an airplane by multi-source high-precision digital measurement becomes a hotspot in the current digital manufacturing field. The manufacturing accuracy of the large-scale component, which is a core component of high-end heavy assembly, is one of the key factors that restrict the overall manufacturing accuracy and assembly performance of the equipment. Therefore, it is very important to study a digital measurement method for a large-sized member. However, the large member has a complicated structure and a large size, which can reach ten meters or even tens of meters, and the measurement error of the laser tracker increases significantly with the increase of the measurement range, so that the measurement accuracy of the laser tracker is difficult to meet the accuracy requirement of manufacturing and assembling large workpieces, and thus the contradiction between the measurement range and the measurement accuracy is very prominent. To overcome this difficulty, multi-station measurement methods based on laser trackers are increasingly becoming an important method for large-scale measurement techniques. Data transfer between multi-site coordinate systems is achieved by means of a plurality of common points. Therefore, the measurement accuracy of the common point is one of the key factors that restrict the accurate data transmission among the multiple stations. However, the measurement error of the common point exists in each measurement station, and improving the measurement accuracy of the common point under each station is a key core method for solving the problem of poor accuracy of multi-station data transfer.
The research focus of data transmission among multiple stations of the laser tracker mainly focuses on a multi-station conversion method, a station space layout method, a common point layout method, an error analysis method and the like, and the research focuses only on improving the precision of data conversion among the multiple stations through the improvement of the measurement precision of common points. In volume 66 of IEEE Transactions on Instrumentation and Measurement in 2017, and An Accurate Point-Based Rigid Registration Method for Laser Tracker Registration in phase 2, Qinghua university Wan and the like, a Method for improving the repositioning accuracy of a Laser Tracker by using points on a high-precision-calibrated repositioning standard (the side length is only 500mm) and a priori Measurement value as constraints is provided. The method considers the uncertainty matrix of the laser tracker measurement, and corrects the measurement error of the measured point by establishing a Lagrange equation. The method provides good idea reference for improving the measurement accuracy of the common point, but for large-size field measurement, the standard device has limited size and high manufacturing cost, and the requirement of the field large-size measurement is difficult to meet. In 2015, Jiang university Jin et al published "Configuration Analysis of the ERS Points in Large-Volume Metrology System" in Sensors ", which proposed a new method to reduce the transformation matrix errors by optimizing the spatial layout of the enhanced reference Points (ERS Points). In order to evaluate the quality of the ERS point layout form, a series of sensitivity coefficients are provided, and finally, some ERS point recommended layouts are qualitatively provided. The text provides a good idea reference for the spatial layout of the common points, but the prior distance constraint is lacked between the common points, and the precision cannot be improved through the prior distance. In conclusion, the research of a large-scale etalon with high robustness, high precision and high stability for large-scale measurement is urgently needed to improve the multi-station conversion precision.
Disclosure of Invention
The invention discloses a multi-station conversion precision improving method based on a high-precision virtual standard, which aims at solving the problems of large multi-station data transmission error, poor stability and the like caused by large common point measurement error among multiple stations of a laser tracker. The method comprises the steps of firstly, respectively acquiring common point coordinates at two stations by using a laser tracker; then, based on a multilateral measurement method, a multilateral measurement coordinate system is established by using a four-station laser tracker, and calibration work is completed; acquiring the coordinates of each common point by using a four-station laser tracker under a multilateral measurement coordinate system, and establishing a large-size virtual standard; and correcting the original measurement error of the common point by taking the common point distance measurement value of the virtual standard device as constraint, and performing coordinate conversion by using the corrected coordinate value of the common point. The method has better practicability in engineering application, and has the characteristics of simple and convenient operation, high precision and strong robustness.
The technical scheme adopted by the invention is a multi-station conversion precision improving method based on a high-precision virtual standard device, which is characterized in that firstly, a laser tracker is utilized to respectively collect common point coordinates at two station positions; constructing a large-size virtual standard device through the multi-station laser tracker and the common point, and performing error correction on the common point between the stations by using the high-precision geometric length in the large-size virtual standard device as constraint; finally, based on a typical coordinate system conversion method, coordinate conversion among multi-station coordinate systems is completed, and overall high-precision measurement of the laser tracker in a large-size range is realized; the method comprises the following specific steps:
first, laser tracker multi-station measurement
Firstly, two laser trackers are sequentially placed on No. 1 and No. 2 laser tracker station positions LT1 and LT 2; then, respectively observing a measuring point and a common point which are positioned in a field range; setting (x, y, z) as coordinates of all measuring points; alpha, beta and l are respectively a horizontal angle measurement, a vertical angle measurement and a measurement length of the laser tracker, and comprise:
the measurement point and the common point collected by the laser tracker station position LT1 No. 1 are respectively defined as PMAnd PCThe measurement point and the common point collected by the laser tracker station position LT2 No. 2 are respectively defined as QMAnd QCAnd then:
in the formula, subscripts m1 and m2 are the number of measurement points acquired by laser tracker station positions LT1 and LT2 of numbers 1 and 2, respectively; c is the number of common points;
secondly, constructing a large virtual standard device based on a multilateral measurement method;
removing the laser tracker, and sequentially placing 4 laser trackers at the measuring stations of No. 1, 2, 3 and 4 laser trackersS1, S2, S3 and S4, constructing a large-size virtual standard device through a multi-station laser tracker and a common point; then, h is more than or equal to 6 calibration points are measured, and h high-precision measurement distances are obtained at each laser tracker station; setting the coordinate of the index point as (x)1,y1,z1;x2,y2,z2;……;xh,yh,zh) The coordinates of the measuring stations of the 4 laser trackers are sequentially (X)1,Y1,Z1;X2,Y2,Z2;X3,Y3,Z3;X4,Y4,Z4) (ii) a In order to fix the coordinate system in space, the laser tracker stations S1-S4 of No. 1, 2, 3, 4 are respectively set as (0,0,0), (X)2,0,0)、(X3,Y3,0)、(X4,Y4,Z4) (ii) a Based on the multilateral length measurement principle, h calibration points are measured, and 4 laser tracker station position calibrations are completed;
wherein (x)h,yh,zh) For indexing point three-dimensional coordinates, (X)i,Yi,Zi) For three-dimensional coordinates of the laser tracker station, |11~l4hThe distance between 4 laser trackers and the calibration point;
iteratively solving the laser tracker station position coordinate (X) in the formula (3) by a Levenberg-Marquardt nonlinear optimization method2,X3,Y3,X4,Y4,Z4) Completing the calibration of the measuring station position of the laser tracker;
the calibration result of the formula (3) is utilized to carry out on-site calibration measurement on all common points, if each laser tracker can realize full coverage measurement of the common points, each common point will correspond to 4 measurement distances, namely the distance between the laser tracker and the common points, and the calculation formula of the three-dimensional coordinate of the common points is as follows:
wherein (x)u,yu,zu) Three-dimensional coordinates of a common point of a virtual etalon,/1~l4The distance between the virtual standard device public point and the laser tracker station is obtained;
simplifying the formula (4) into a formula (5) to solve the three-dimensional coordinate of the common point of each virtual standard device under the calibration coordinate system;
calculating the distance between the common points based on the three-dimensional coordinates of the virtual standard device common points:
wherein d isuvIs the length between the common points, u, v are the common point labels, and u ≠ v;
thirdly, correcting the measurement error of the space common point coordinate;
the coordinate system O-X of the laser tracker station LT1 No. 1 is obtained through the formulas (1) and (2)PYPZPLower common point three-dimensional coordinate set PCLaser tracker station LT2 coordinate system O-X No. 2QYQZQLower common point three-dimensional coordinate set QC(ii) a Correcting the coordinates of the common point under the station coordinate systems of the two laser trackers, wherein the target function is as follows:
wherein c is the total number of common points among the laser tracker stations, u and v are the common point labels of the virtual standard device, and u is not equal to v;
the method comprises the following steps of taking original measurement coordinates of common points as initial values of nonlinear optimization under two laser tracker station coordinate systems, wherein parameters to be optimized are as follows:
(x1,y1,z1;x2,y2,z2;…;xu,yu,zu;…;xc,yc,zc) Optimizing the parameters to be optimized by a Levenberg-Marquardt nonlinear optimization method to respectively obtain an optimized point set P of a common point coordinate under two laser tracker station coordinate systemsC+And QC+Therefore, the coordinate optimization based on the length constraint of the virtual standard device is completed, and the original measurement error is corrected;
fourthly, converting a multi-coordinate system based on common point correction;
the data conversion between the coordinate systems of the measuring stations of the two laser trackers is carried out through the corrected common point PC+And QC+After completion, the coordinate transformation objective function is as follows:
in the formula (I), the compound is shown in the specification,is a matrix of rotations of the optical system,is a translation matrix;
then, solving the coordinate system transformation error e of each common pointu:
Therefore, the overall coordinate conversion error E is:
through the steps, the global high-precision measurement of the laser tracker in a large-size range is realized.
The invention has the advantages that a high-precision virtual standard device is constructed by using the multi-station laser tracker, the optimization and correction of the coordinates of the common points between the station coordinate systems are realized based on the length constraint between the common points of the virtual standard device and the Levenberg-Marquardt nonlinear optimization method, the measurement precision of the coordinates of the common points of each station is improved, and the error of data conversion between the coordinate systems is reduced. The method has better practicability in engineering application, and has the characteristics of simple and convenient operation, high precision and strong robustness. The method can be used for digital measurement of large components in the fields of aerospace, energy traffic and the like, provides support for high-performance manufacture of high-end heavy equipment, and has wide application prospect.
Drawings
FIG. 1 is a flow chart of a multi-station conversion accuracy improving method based on a high-accuracy virtual standard device.
FIG. 2 is a schematic view of a laser tracker multi-station measurement; wherein, the LT1-1 laser tracker station position; LT2-2 laser tracker station position; O-XPYPZPLaser tracker station LT1 coordinate system No. 1; O-XQYQZQ-laser tracker station LT2 coordinate system No. 2; C1-C5-black circle common point; M1-M5-triangle measuring points.
FIG. 3 is a schematic diagram of a high precision virtual meter build; wherein, the laser tracker stations of No. S1-S4-1, No. 2, No. 3, No. 4; C1-C5-black circle common point; T1-T7-index point; l15-distance of S1 from T5; l25-distance of S2 from T5; l35-distance of S3 from T5; l45-distance of S4 from T5; l1-distance of S1 from C1; l2-distance of S2 from C1; l3-distance of S3 from C1; l4-distance of S4 from C1; d34Distance of C3 from C4.
Detailed Description
The following detailed description of the invention refers to the accompanying drawings.
In this example, a laser tracker manufactured by Etalon corporation and having a length measurement uncertainty U (k 2) of 0.2 μm +0.3 μm/m was used; a laser tracker of the Leica AT960MR type was used, with a maximum measurement error of ± (15 μm +6 μm/m).
FIG. 1 is a flow chart of a precision improvement method, which comprises the steps of firstly constructing a large-size virtual standard at a proper position between stations by a laser tracker, and then correcting errors of common points between the stations by using a high-precision geometric distance in the standard; and finally, based on a typical coordinate conversion method, the coordinate conversion precision among multiple stations is improved, and the overall high-precision measurement of the laser tracker in a large-size range is realized. The method comprises the following specific steps:
first, laser tracker multi-station survey
As shown in the attached figure 2, the laser tracker is sequentially placed at a station LT1 and a station LT2, three triangular measuring points M1-M3 and five black circle common points C1-C5 in the visual field range are measured under the station LT1, and two triangular measuring points M4 and M5 and five black circle common points C1-C5 are measured under the station LT 2. Defining the measurement point and common point data collected by the laser tracker station LT1 as PMAnd PCThe measurement point and common point data collected by the laser tracker station LT2 are defined as QMAnd QCCalculated by equation (2).
And secondly, constructing a virtual standard device based on the multilateration method.
The laser trackers were removed and 4 laser trackers were placed in sequence at laser tracker measuring stations nos. 1, 2, 3, 4, S1, S2, S3 and S4, see fig. 3. Then, 7 calibration points T1-T7 are measured, and 7 high precision measurement distances are obtained for each laser tracker station. Under a calibration coordinate system X-Y-Z, the S1 coordinate of the laser tracker station No. 1 is (0,0,0), and the S2 coordinate of the laser tracker station No. 2 is (X)20,0) and 3 laser tracker station position S3 coordinate is (X)3,Y30), laser tracker station position No. 4S 4 coordinate is (X)4,Y4,Z4)。
With index point T5 (x)T5,yT5,zT5) For example, the calibration equation of the station positions of the 4 laser trackers is as follows:
in the formula I15、l25、l35And l45Is a known quantity, and the rest is an unknown quantity; 7 sets of equations shown in the above formula can be listed using 7 calibration points T1-T7, thereby forming a large system of equations as shown in formula (3). Through a Levenberg-Marquardt nonlinear optimization method, the laser tracker station position coordinate (X) substituted into the formula (3) is solved in an iterative manner2,X3,Y3,X4,Y4,Z4) So as to finish the station position calibration of the four laser trackers;
based on four laser tracker station coordinates (X)2,X3,Y3,X4,Y4,Z4) And solving the three-dimensional coordinates of the common points C1-C5 of the five black circles according to the formula (4) and the formula (5).
Taking the common point C1 of the black circle as an example, let its coordinate be (x)1,y1,z1) Then the coordinate calculation equation is:
in the formula x1、y1And z1Is unknown quantity, and the rest is known quantity; the coordinates of the common point C1 of the black circle can be obtained by solving the above formula, and the coordinates of the common points C2-C5 of the rest black circles can be obtained by the same method.
According to equation (6), the length between the common points of any two black circles, such as the length d between C3 and C4, can be obtained34Comprises the following steps:
and thirdly, correcting the measurement error of the spatial common point coordinate.
The laser tracker station LT1 coordinate system O-X can be obtained through the formulas (1) and (2)PYPZPLower black circleCommon point three-dimensional coordinate set PCLaser tracker station LT2 coordinate system O-XQYQZQThree-dimensional coordinate set Q of common point of lower black circleC。
Taking a formula (7) as an objective function, taking the original measurement coordinates of the common point of the black circles under the station coordinate systems of the two laser trackers as initial values of nonlinear optimization, and taking the parameter to be optimized as (x)1,y1,z1;x2,y2,z2;…;x5,y5,z5) Optimizing the parameters to be optimized by a Levenberg-Marquardt nonlinear optimization method to respectively obtain an optimized point set P of a common point coordinate under two laser tracker station coordinate systemsC+And QC+Therefore, the coordinate optimization based on the length constraint of the virtual standard is completed, and the original measurement error is corrected.
Fourthly, multi-coordinate system conversion based on common point correction
The data conversion between the coordinate systems of the measuring stations of the two laser trackers is carried out through the corrected common point PC+And QC+To accomplish this, according to equation (8), the coordinate transformation objective function is as follows:
two laser tracker station coordinate systems O-X can be obtained by solvingPYPZPAnd O-XQYQZQA rotation matrix ofAnd translation matrix
Then, the coordinate system transformation error of the common point of each black circle can be solved according to the formula (9); according to the formula (10), the overall coordinate transformation error of the black circle common points C1-C5 is:
through the steps, the global high-precision measurement of the laser tracker in a large-size range is realized.
Claims (1)
1. A multi-station conversion precision improving method based on a high-precision virtual standard device is characterized in that firstly, a laser tracker is used for respectively collecting common point coordinates at two station positions; constructing a large-size virtual standard device through the multi-station laser tracker and the common point, and performing error correction on the common point between the stations by using the high-precision geometric length in the large-size virtual standard device as constraint; finally, based on a typical coordinate system conversion method, coordinate conversion among multi-station coordinate systems is completed, and overall high-precision measurement of the laser tracker in a large-size range is realized; the method comprises the following specific steps:
first, laser tracker multi-station measurement
Firstly, two laser trackers are sequentially placed on No. 1 and No. 2 laser tracker station positions LT1 and LT 2; then, respectively observing a measuring point and a common point which are positioned in a field range; setting (x, y, z) as coordinates of all measuring points; alpha, beta and l are respectively a horizontal angle measurement, a vertical angle measurement and a measurement length of the laser tracker, and comprise:
the measurement point and the common point collected by the laser tracker station position LT1 No. 1 are respectively defined as PMAnd PCThe measurement point and the common point collected by the laser tracker station position LT2 No. 2 are respectively defined as QMAnd QCAnd then:
in the formula, subscripts m1 and m2 are the number of measurement points acquired by laser tracker station positions LT1 and LT2 of numbers 1 and 2, respectively; c is the number of common points;
secondly, constructing a large virtual standard device based on a multilateral measurement method;
removing the laser tracker, sequentially placing 4 laser trackers on measuring stations S1, S2, S3 and S4 of No. 1, 2, 3 and 4 laser trackers, and constructing a large-size virtual standard through the multi-station laser tracker and the common point; then, h is more than or equal to 6 calibration points are measured, and h high-precision measurement distances are obtained at each laser tracker station; setting the coordinate of the index point as (x)1,y1,z1;x2,y2,z2;……;xh,yh,zh) The coordinates of the measuring stations of the 4 laser trackers are sequentially (X)1,Y1,Z1;X2,Y2,Z2;X3,Y3,Z3;X4,Y4,Z4) (ii) a In order to fix the coordinate system in space, the laser tracker stations S1-S4 of No. 1, 2, 3, 4 are respectively set as (0,0,0), (X)2,0,0)、(X3,Y3,0)、(X4,Y4,Z4) (ii) a Based on the multilateral length measurement principle, h calibration points are measured, and 4 laser tracker station position calibrations are completed;
wherein (x)h,yh,zh) For indexing point three-dimensional coordinates, (X)i,Yi,Zi) For three-dimensional coordinates of the laser tracker station, |11~l4hThe distance between 4 laser trackers and the calibration point;
iteratively solving the laser tracker station position coordinate (X) in the formula (3) by a Levenberg-Marquardt nonlinear optimization method2,X3,Y3,X4,Y4,Z4) Completing the calibration of the measuring station position of the laser tracker;
the calibration result of the formula (3) is utilized to carry out on-site calibration measurement on all common points, if each laser tracker can realize full coverage measurement of the common points, each common point will correspond to 4 measurement distances, namely the distance between the laser tracker and the common points, and the calculation formula of the three-dimensional coordinate of the common points is as follows:
wherein (x)u,yu,zu) Three-dimensional coordinates of a common point of a virtual etalon,/1~l4The distance between the virtual standard device public point and the laser tracker station is obtained;
simplifying the formula (4) into a formula (5) to solve the three-dimensional coordinate of the common point of each virtual standard device under the calibration coordinate system;
calculating the distance between the common points based on the three-dimensional coordinates of the virtual standard device common points:
wherein d isuvIs the length between the common points, u, v are the common point labels, and u ≠ v;
thirdly, correcting the measurement error of the space common point coordinate;
the coordinate system O-X of the laser tracker station LT1 No. 1 is obtained through the formulas (1) and (2)PYPZPLower common point three-dimensional coordinate set PCLaser tracker station LT2 coordinate system O-X No. 2QYQZQLower common point three-dimensional coordinate set QC(ii) a Correcting the coordinates of the common point under the station coordinate systems of the two laser trackers, wherein the target function is as follows:
wherein c is the total number of common points among the station positions of the laser tracker, u and v are the common point labels of the virtual standard device, and u is not equal to v;
the method comprises the following steps of taking original measurement coordinates of common points as initial values of nonlinear optimization under two laser tracker station coordinate systems, wherein parameters to be optimized are as follows: (x)1,y1,z1;x2,y2,z2;…;xu,yu,zu;…;xc,yc,zc) Optimizing the parameters to be optimized by a Levenberg-Marquardt nonlinear optimization method to respectively obtain an optimized point set P of a common point coordinate under two laser tracker station coordinate systemsC+And QC+Completing the coordinate optimization based on the length constraint of the virtual standard device, and correcting the original measurement error;
fourthly, converting a multi-coordinate system based on common point correction;
the data conversion between the coordinate systems of the measuring stations of the two laser trackers is carried out through the corrected common point PC+And QC+After completion, the coordinate transformation objective function is as follows:
in the formula (I), the compound is shown in the specification,is a matrix of rotations of the optical system,is a translation matrix;
then, solving the coordinate system transformation error e of each common pointu:
Therefore, the overall coordinate conversion error E is:
through the steps, the global high-precision measurement of the laser tracker in a large-size range is realized.
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