阅读说明：本技术 一种基于刚性约束的激光跟踪仪测量精度提升方法 (Laser tracker measurement accuracy improving method based on rigid constraint ) 是由 刘巍 伍嘉豪 逯永康 赵伟康 郑研 张洋 马建伟 周颖皓 于 2021-08-13 设计创作，主要内容包括：本发明属于大尺寸/数字化测量领域,涉及一种基于刚性约束的激光跟踪仪测量精度提升方法。该方法首先基于稳定性原则设置若干公共点及测试点,利用激光跟踪仪多站采集公共点与测试点的三维坐标。然后通过坐标系粗转换获取转换后公共点坐标。根据公共点粗转换前后相对于质心距离偏差大小设置权重；最后,以匹配残差加权平方和最小作为最优性条件进行坐标系转换,实现了激光跟踪仪不同站位之间的测量坐标系转换参数的高精求解。该方法充分考虑了公共点测量误差对坐标系转换精度的影响,通过公共点转换前后相对于质心距离偏差大小设置权重,有效减小测量误差的影响,提高了坐标系转换精度。(The invention belongs to the field of large-size/digital measurement, and relates to a method for improving measurement accuracy of a laser tracker based on rigid constraint. The method comprises the steps of firstly setting a plurality of common points and test points based on a stability principle, and collecting three-dimensional coordinates of the common points and the test points by utilizing a plurality of stations of a laser tracker. And then, obtaining the transformed common point coordinates through rough transformation of a coordinate system. Setting weight according to the distance deviation of the common points before and after coarse conversion relative to the centroid; and finally, the coordinate system conversion is carried out by taking the minimum weighted sum of squares of the matched residual errors as an optimality condition, so that the high-precision solution of the conversion parameters of the measurement coordinate system among different stations of the laser tracker is realized. The method fully considers the influence of the common point measurement error on the coordinate system conversion precision, and the weight is set relative to the centroid distance deviation before and after the common point conversion, so that the influence of the measurement error is effectively reduced, and the coordinate system conversion precision is improved.)

1. A method for improving the measurement precision of a laser tracker based on rigid constraint is characterized in that a plurality of common points and test points are set based on a stability principle, and the coordinates of the common points and the test points at two different station positions are collected by the laser tracker; then, coarse conversion of the measurement coordinate system under two stations is carried out by using a singular value decomposition method to obtain a coarse conversion parameter R between the two stations⁰、T⁰And according to R⁰、T⁰Calculating coordinates of the common points after conversion, and determining the weight according to the deviation of the distances of the common points before and after coarse conversion relative to the centroid; finally, based on the set weight, the coordinate system conversion is carried out by taking the minimum weighted sum of squares of the matched residual errors as a solution optimality condition, the solution of coordinate system conversion parameters of the laser tracker at different station positions is completed, and the conversion precision of the large-size range measurement coordinate system is improved; the method comprises the following specific steps:

first, common point coordinate acquisition based on multi-station laser tracker measurement

Firstly, mounting a plurality of common points and test points on a cement foundation or an assembly member of a measuring field; then, sequentially arranging the laser tracker at two different stations S1 and S2, carrying out j times of repeated measurement on n common points in a measurement field, and simultaneously collecting coordinates of the test points; the i-th common point coordinate obtained by the laser tracker in the station positions S1 and S2 for j times of repeated measurement is recorded as { P }^r,iAnd { P }^M,iTaking an average value of the obtained point set coordinates, namely the nominal values of the ith point under S1 and S2, and recording the nominal values as P_r,iAnd P_M,iNamely:

wherein, the subscript j represents the number of repetitive measurements of the laser tracker; the k test point coordinates collected by the laser tracker at the station positions S1 and S2 are respectively recorded as Q_r,k、Q_M,k；

Secondly, solving the multi-station coordinate system rough conversion parameters based on the singular value decomposition method

Setting the objective function asWhen the objective function reaches the minimum value, solving the objective function by utilizing an SVD decomposition method to obtain a coarse conversion parameter R⁰、T⁰:

T⁰＝[t_x t_y t_z]^T (4)

Wherein, alpha, beta and gamma represent a measuring coordinate system of the station S1Rotation angle, t, of the measuring coordinate system relative to the station position S2_x,t_y,t_zIndicating the position of the origin of the measurement coordinate system of the station S1 in the measurement coordinate system of the station S2;

calculating the mean value and covariance matrix of the two point sets by adopting an SVD decomposition method:

in the formula, mu_r、μ_MThe mean value of the common point coordinate point sets measured by the first station and the second station is respectively, and the matrix H is a covariance matrix of the two point sets;

SVD is carried out on the covariance matrix H, so that H is UDV^TIn the formula, D is a diagonal matrix, and U and V are orthogonal matrices, and the following are obtained:

if det R⁰When is +1, then R⁰For the solved rotation matrix, if det R⁰When the result is-1, then let V⁰＝[v₁ v₂ -v₃]Substituting to obtain: r⁰＝V⁰U^T；

Thirdly, constructing a weight coefficient based on rigid constraint of common points

Rotation matrix R obtained from the coarse conversion⁰Translation vector T⁰And the formula (8),

converting the common point coordinate measured under the station position S2 to the position S1 to obtain a conversion point groupMeasuring the set of points according to the geometric invariance of the rigid body { P }_r,iAnd set of switching pointsShould have the same centroid, find the respective centroid coordinates:

the distance from the ith common point in the measurement point group and the theoretical point group to the respective centroid is as follows:

due to the effect of common point measurement errors,namely, there is a deviation:taking the deviation as an evaluation index of the coordinate precision of the point; according to the principle that the larger the deviation is, the smaller the weight is, and the smaller the deviation is, the larger the weight is, the deviation before and after the rough conversion from the common point relative to the centroid distance is the set weight:

order toThe weight is set to:after homogenization, the following steps are performed:

the fourth step, coordinate conversion with the minimum of the weighted sum of squares of the matching residuals as the optimal solution

According to the determined weight and the collected common point coordinate set { P ] under the measuring coordinate system of the two laser tracker stations S1, S2_r,iAnd { P }_M,iAnd the corresponding optimized objective function with the minimum weighted square sum of the matching residuals is as follows:when the objective function value is minimum, solving the objective function by utilizing SVD decomposition to obtain fine conversion parameters R, T;

according to the set weight, solving the weighted centroid of the common point coordinates acquired under the laser tracker stations S1 and S2:

to derive a translation vector from the formula P_r,i＝(RP_M,i+ T), simplifying the calculation and solving process, and respectively centroiding the two groups of coordinates:

the objective function for which the weighted sum of squares of the corresponding matching residuals is minimal is:

solving the objective function minimization problem to solve

In the formula:SVD decomposition is carried out on H to obtain H ═ U Λ V^TWhere Λ is a diagonal matrix, U and V are orthogonal matrices, then the rotation matrix is: r ═ VU^TAccording to the formula P_r,i＝(RP_M,i+ T) finding the translation vector T of each common point_iThen the translation vector is:

through the steps, high-precision conversion of different coordinate systems in a large-size range is achieved.

Technical Field

The invention belongs to the field of large-size/digital measurement, and relates to a method for improving measurement accuracy of a laser tracker based on rigid constraint.

Background

The core component structure of the large aerospace equipment is more and more complex, the size is larger and larger, the precision requirement is higher and higher, and higher requirements are provided for the measurement range, precision and robustness in the manufacturing process. The laser tracker is one of the most widely used large-size measuring instruments in the field of aerospace assembly measurement at present, but due to the conditions of large size, complex shape, on-site shielding and the like of an assembly object, the measurement task is difficult to complete by single-station measurement, and the complete measurement of a large-size component must be realized by adopting a multi-station cooperative measurement mode of the laser tracker. In the measurement process of large-scale components, a global coordinate system is generally established as a uniform assembly reference, partial reference points are selected on the ground, the reference unification of measurement data of the laser tracker at different stations is completed, and then the pose of the current workpiece in the global coordinate system is calculated through coordinate conversion. In the actual assembly process, the common datum point is generally arranged on the ground, a tool or a component, the measurement error of the common datum point acquired by the laser tracker under the conditions of different distances, angles, environments and the like has typical non-uniformity and anisotropy, and the overall measurement accuracy is difficult to guarantee. In the traditional method, uncertainty is measured by a theoretical analysis system, and the overall measurement precision is improved by establishing a theoretical measurement uncertainty weight, but pure theoretical analysis is difficult to be suitable for field measurement. Therefore, in order to improve the accuracy of multi-station measurement of the laser tracker, a large-scale measurement coordinate system conversion method must be studied.

At present, methods for resolving a coordinate system transformation matrix mainly include a quaternion method, a least square method, a singular value decomposition method and a Rodrigues matrix method. In 9.2011, beijing aerospace university chenwuyi, on the 'rigid body pose error detection method based on singular value decomposition' in 9 th volume of 'computer integrated manufacturing system', a singular value decomposition method is adopted to determine the actual pose of the moving platform, the sum of squares of position errors of measurement points after pose transformation is taken as a target function, the elimination of dead spots in actual measurement data is realized through a target function value, and the correctness of a result is ensured. The method provides good idea reference for improving the conversion precision of the coordinate system. However, since the number of common points for registration is limited, the elimination of too many unstable common points will cause the loss of registration accuracy, which is not favorable for the improvement of assembly accuracy.

Wudan et al, university of Qinghua, 12.2020 published "Construction and incertation Evaluation of Large-scale Measurement System of Laser transceivers in Aircraft Assembly" on Measurement, which proposed a multi-station beam adjustment method. And (3) constructing an integral measurement coordinate system by adjusting all the measurement stations and the enhanced reference points through light beams, and then registering the integral measurement coordinate system to the assembly coordinate system by using the stable reference enhanced points. The method unifies all laser trackers and reference enhanced point points into an overall measurement coordinate system through beam adjustment, greatly increasing the number of common points available for registration. Thus, elimination of some reinforced reference points with poor stability does not cause loss of registration accuracy. However, in the method, reference values such as a reference scale are not set, and system errors possibly caused by beam adjustment are ignored.

Disclosure of Invention

The invention overcomes the defects of the prior art, and provides a method for improving the measurement accuracy of a laser tracker based on rigid constraint aiming at the problems of large conversion error, poor robustness and the like during multi-station conversion of the laser tracker. The method comprises the steps that firstly, a certain number of common points and test points are arranged on the basis of a stability and envelopment principle, and a laser tracker respectively collects space coordinates of the key points at two stations; then, the singular value decomposition method is adopted to solve the conversion parameter R among the multiple coordinate systems in an equal weight mode⁰、T⁰(ii) a Obtaining the coordinates of each common point in the global coordinate system by using the conversion parameters; calculating the rigid distance deviation between the common point and the centroid distance before and after conversion according to the rigid distanceSetting weights from invariance constraints; and finally, converting a coordinate system by using the optimality condition with the minimum weighted sum of squares of the matched residual errors as a solution, thereby realizing the optimal solution of the conversion parameters between different stations of the laser tracker. Experiments prove that the method can effectively improve the conversion precision of the multi-station cooperative measurement of the laser tracker, avoids the complex solving process of multi-source error transfer modeling, and has the characteristics of high robustness, high precision and the like.

The technical scheme adopted by the invention is a method for improving the measurement precision of a laser tracker based on rigid constraint, which is characterized in that the method is characterized in that a plurality of common points and test points are arranged based on a stability source and envelopment, and the laser tracker collects the coordinates of the test points under two station positions; then, the singular value decomposition method is adopted to solve the conversion parameter R among the multi-coordinate systems in an equal weight mode⁰、T⁰And solving the coordinates of the common points under the global coordinate system according to the conversion parameters; determining a weight model according to the constraint that the rigid distance between the common point and the centroid is unchanged before and after conversion; finally, based on the weight coefficients, the conversion parameters of the coordinate systems of different stations of the laser tracker are solved by taking the minimum weighted sum of squares of the matched residual errors as a condition for solving optimality, so that the conversion precision among multiple coordinate systems in a large-size range is improved; the method comprises the following specific steps:

firstly, obtaining the common point coordinate of the multi-station cooperative measurement of the laser tracker

Firstly, mounting a plurality of common points and test points on a cement foundation or an assembly member of a measuring field; then, sequentially arranging the laser tracker at two different stations S1 and S2, carrying out j times of repeated measurement on n common points in a measurement field, and simultaneously collecting coordinates of the test points; the i-th common point coordinate obtained by the laser tracker in the station positions S1 and S2 for j times of repeated measurement is recorded as { P }^r,iAnd { P }^M,iTaking an average value of the obtained point set coordinates, namely the nominal values of the ith point under S1 and S2, and recording the nominal values as P_r,iAnd P_M,iNamely:

wherein, the subscript j represents the number of repetitive measurements of the laser tracker; the k test point coordinates collected by the laser tracker at the station positions S1 and S2 are respectively recorded as Q_r,k、Q_M,k。

Secondly, solving the conversion parameters of the multi-station coordinate system by equal weight based on the singular value decomposition method

Setting the objective function asWhen the objective function reaches the minimum value, solving the objective function by utilizing an SVD decomposition method to obtain a conversion parameter R⁰、T⁰:

T⁰＝[t_x t_y t_z]^T (4)

Where α, β, γ denote the rotation angle of the measurement coordinate system of the station S1 with respect to the measurement coordinate system of the station S2, t_x,t_y,t_zIndicating that the station S1 measures the position of the coordinate system origin in the measurement coordinate system of the station S2.

Calculating the mass center and covariance matrix of the two point sets by using a singular value decomposition method:

in the formula, mu_r、μ_MThe centroid of the common point coordinate point set measured by the first station and the second station is respectively, and the matrix H is a covariance matrix of the two point sets.

SVD is carried out on the covariance matrix H, so that H is UDV^TWhere D is a diagonal matrix and U and V are orthogonal matrices, we can obtain:

if det R⁰When is +1, then R⁰For the solved rotation matrix, if det R⁰When it is 1, then let V⁰＝[v₁ v₂ -v₃]Substituting to obtain: r⁰＝V⁰U^T。

Thirdly, constructing a weight coefficient based on rigid distance constraint of common points

Rotation matrix R solved according to the second step⁰Translation vector T⁰And the formula (8),

converting the common point coordinate measured under the station position S2 to the position S1 to obtain a conversion point groupMeasuring the point group { P) according to the geometric invariance of the rigid body distance_r,iAnd set of switching pointsShould have the same centroid, find the respective centroid coordinates:

the distance from the ith common point in the measurement point group and the conversion point group to the respective centroid is as follows:

due to the effect of common point measurement errors,i.e. there is a non-ideal stiffness distance deviation:this deviation is used as an evaluation reference index for the coordinate accuracy of the point. Calculating a weight coefficient according to the non-ideal rigid distance deviation of the distance between the common point and the center of mass before and after conversion according to the principle that the deviation and the weight are negatively related:

order toThe weight is set to:after homogenization, the following steps are performed:

the fourth step, coordinate conversion with the minimum of the weighted sum of squares of the matching residuals as the optimal solution

According to the proposed weight coefficient calculation method and the collected common point coordinates { P ] under the measuring coordinate system of the two laser tracker stations S1 and S2_r,iAnd { P }_M,iAnd the corresponding optimized objective function with the minimum weighted square sum of the matching residuals is as follows:when the objective function value is minimum, the objective function is solved by using an SVD decomposition method to obtain the conversion parameters R, T.

According to the set weight, solving the weighted centroid of the common point coordinates acquired under the laser tracker stations S1 and S2:

to translate a vector from P_r,i＝(RP_M,i+ T), simplifying the calculation and solving process, and respectively centroiding the two groups of coordinates:

the objective function for which the weighted sum of squares of the corresponding matching residuals is minimal is:

solving the objective function minimization problem to solve

In the formula:SVD decomposition is carried out on H to obtain H ═ U Λ V^TWhere Λ is a diagonal matrix, U and V are orthogonal matrices, then the rotation matrix is: r ═ VU^TThe translation vector is:

through the steps, high-precision conversion of different coordinate systems in a large-size range can be realized.

The method has the advantages that the target function is constructed by using the optimality condition of the minimum solution of the weighted square sum of the matching residuals, the weight is determined by using the deviation of the distance between the common points before and after the rough conversion relative to the centroid, the high-precision solution of R, T for measuring the conversion parameters between coordinate systems under different station positions of the laser tracker is realized, the coordinate conversion of the common points is completed, the conversion precision between the coordinate systems is improved, and the influence of the matching residuals on the conversion result is reduced. Practice proves that: the method has the advantages of good practicability and universality, good robustness, high precision and high stability. The method can be used for the assembly process of large mechanical products such as airplanes in the aerospace field, can effectively reduce the influence of common point measurement errors in the installation process, and has wide application prospect.

Drawings

FIG. 1 is a flow chart of a method for improving measurement accuracy of a laser tracker based on rigid constraint;

FIG. 2 is a schematic view of a laser tracker multi-site measurement; wherein S1 and S2 are respectively different station positions of the laser tracker; p₁～P₅The black dots are common dots; q₁～Q₃The black triangle is a test point; O-X_rY_rZ_rFor the measuring coordinate system of the laser tracker station S1, O-X_MY_MZ_MIs the measurement coordinate system of the laser tracker station S2.

FIG. 3 is a diagram of common point coordinate weight construction. Wherein P is₁～P₅Measuring a common point of the laser tracker under a coordinate system at a station position S1; the black rhombus is the centroid of the common point group; d₁～d₅Distance of the common point to its centroid; p'₁～P′₅Is a common point, d 'in the measurement coordinate system converted to the station site S2 after the rough conversion of the coordinate system'₁～d′₅Is the distance of the common point to the centroid after the coarse transformation.

Detailed Description

The following detailed description of the invention refers to the accompanying drawings.

The laser tracker selected by the embodiment is of a type of Leica AT960MR, and the maximum allowable measurement error MPE is ± (15 μm +6 μm/m); the target ball and the target ball holder used as the measurement point were 0.5 inches in size.

As shown in the attached figure 1, the method comprises the steps of firstly setting a plurality of common points and test points based on a stability principle, and repeatedly measuring the coordinates of the common points at two different station positions by using a laser tracker; then, coarse conversion of the measurement coordinate system under the two stations is carried out based on a singular value decomposition method to obtain a conversion parameter R between the two stations⁰、T⁰(ii) a Using the obtained coarse transformation parameter R⁰、T⁰Calculating the transformed common point coordinate set,determining the weight according to the deviation of the distance between the common points and the centroid before and after the rough transformation, as shown in figure 3; finally, according to the set weight coefficient, the coordinate system conversion is carried out by taking the minimum weighted sum of squares of the matched residual errors as a solution optimality condition, so that the solution of coordinate system conversion parameters of the laser tracker at different stations is realized, and the conversion precision of the coordinate system measured in a large-size range is improved; in order to meet the processing and measurement requirements of large-size aerospace core components, a laser tracker needs to be adopted for multi-station cooperative measurement. In order to realize the reference unification of the measurement data of the laser tracker under different station positions, the station position s1 is set as a reference station position, and the coordinates of a common point are collected by adopting multiple stations of the laser tracker; theoretically, the coordinates of the common point acquired by the laser tracker at different stations should be matched with each other after coordinate system conversion, but due to the influence of common point measurement error and random error, the coordinates of the common point acquired at station s2 are not matched with the coordinates of the common point acquired at station s1 after coordinate conversion. As shown in the third figure, based on the principle that the common point centroid is not changed before and after conversion, P₄After the point is subjected to coordinate transformation, the distance of the point obviously changes relative to the centroid, and then P₄The point is a point with a larger error, and the discovery is utilized to firstly set a coarse conversion, and the weight is set according to the deviation of the distance of the center of mass before and after the coarse conversion of the common point, so that the high-precision solution of the coordinate system conversion parameters of the laser tracker at different station positions is realized.

The method comprises the following specific steps:

first, common point coordinate acquisition based on multi-station laser tracker measurement

Firstly, mounting 8 common points and 3 test points at a position with better rigidity of a cement foundation or an assembly member of a measuring field; the laser trackers are then positioned at two different stations S1, S2 in sequence, with 8 common points P in the field of view₁～P₈Repeat measurement 100 times and simultaneously collecting test point Q₁～Q₃The coordinates of (a); defining a point set obtained by respectively carrying out 100 times of repeated measurement on the ith common point coordinate by the laser tracker at station positions S1 and S2 as P^r,iAnd { P }^M,iIts average value is defined asNominal values of point i at S1, S2, denoted as P_r,iAnd P_M,i：

The k test point coordinates collected by the laser tracker at the station positions S1 and S2 are respectively recorded as Q_r,k、Q_M,k：

Secondly, solving the multi-station coordinate system rough conversion parameters based on the singular value decomposition method

And (3) calculating the mean value and covariance matrix of the common point coordinates under the two stations according to the formula (5) and the formula (6) by using an SVD decomposition method:

SVD is carried out on the covariance matrix H, so that H is UDV^TFrom equation (7), we can obtain:

T⁰＝μ_M-R⁰μ_r＝(11863.4159 3933.2543 -139.3727)

thirdly, constructing a weight coefficient based on rigid constraint of common points

Using the rotation matrix obtained in the second stepR⁰Translation vector T⁰Converting the coordinates of the common point measured at the station position S2 to the position S1 according to the formula (8) to obtain a conversion point groupMeasurement point set { P_r,iAnd set of switching pointsShould have the same centroid, the respective centroid coordinates are found according to equation (9):

calculating the distances from the common points in the measurement point group and the theoretical point group to the respective centroids according to the formula (10) as follows:

the deviation exists:

this deviation is used as an evaluation index of the coordinate accuracy of the point. Order toThe weight coefficient is set by equation (11):

W＝(w₁,w₂,w₃,w₄,w₅,w₆,w₇,w₈)

＝(0.1444 0.0261 0.0178 0.1100 0.0985 0.2270 0.0799 0.2963)

the fourth step, coordinate conversion with the minimum of the weighted sum of squares of the matching residuals as the optimal solution

According to the determined weight and the common point coordinate set { P } measured by the laser tracker under the station S1, S2 measurement coordinate system_r,iAnd { P }_M,iGet the corresponding matching residual weighted averageThe minimum and the square optimization objective function is:when the objective function reaches a minimum, the conversion parameters R, T are obtained using SVD decomposition.

According to the set weight, solving the weighted centroid of the common point coordinates acquired under the laser tracker stations S1 and S2:

to translate a vector from P_r,i＝(RP_M,i+ T), simplifying the calculation and solving process, and respectively centroiding the two groups of coordinates:

the objective function can be rewritten as:

solving the objective function minimization translates to solving:

in the formula:SVD of HSolution, i.e. H ═ U Λ V^TThe rotation matrix can be obtained:

the translation vector is:

through the steps, high-precision conversion of different measurement coordinate systems in a large-size range can be realized.

According to the invention, the target function is constructed by matching the optimality condition of the minimum solution of the weighted sum of squares of the residual errors, and the weight is determined by using the deviation of the distance relative to the centroid before and after the rough conversion of the common point, so that the R, T high-precision solution of the conversion parameters between the measurement coordinate systems of the laser tracker at different stations is realized, and the influence of the measurement error of the common point of the laser tracker is reduced. The method has guiding significance for improving the conversion precision of the multi-station coordinate system of the laser tracker, and has the characteristics of good robustness, high precision, high stability and higher application value.