CN105823417A

CN105823417A - Method of improving laser tracker station moving precision based on photogrammetry

Info

Publication number: CN105823417A
Application number: CN201610160703.XA
Authority: CN
Inventors: 孙占磊; 景喜双; 张承阳; 张宇翔; 罗敏; 赵罡
Original assignee: Beihang University
Current assignee: Beihang University
Priority date: 2016-03-21
Filing date: 2016-03-21
Publication date: 2016-08-03
Anticipated expiration: 2036-03-21
Also published as: CN105823417B

Abstract

A method for improving the accuracy of a laser tracker transfer station based on photogrammetry. The steps are as follows: 1. Install equipment and fix public points; 2. Use laser trackers to measure targets and public points at two sites A and B; 3. Use Photogrammetry measures the coordinates of common points; 4. The centroids of the two point clouds coincide and coincide with the origin of the coordinate system; 5. The photogrammetry point cloud rotates around the coordinate axis until a set of corresponding vectors coincides; Rotate the axes until the specified corresponding vectors coincide; 7. Perform inverse centroid processing on the rotated photogrammetry point cloud; 8. Find multiple sets of corrected data, and calculate their average value as the correction value; Point coordinates are corrected; 10. Use the unit quaternion method to solve the conversion matrix; 11. Calculate the length and angle of the measurement target; through the above steps, the effect of improving the accuracy of the laser tracker transfer station is achieved, and the measurement of the laser tracker is solved. The problem of large errors when large-sized objects.

Description

A method of improving the accuracy of laser tracker transfer station based on photogrammetry

技术领域technical field

本发明涉及一种基于摄影测量提高激光跟踪仪转站精度的方法，属于测量技术领域。The invention relates to a method for improving the transfer station accuracy of a laser tracker based on photogrammetry, and belongs to the technical field of measurement.

背景技术Background technique

使用激光跟踪仪进行测量和摄影测量都是精密测量中的常见测量方式。摄影测量具有精度高、效率高、自动化程度高等特点，测量范围包括离散点测量、变形和运动测量、三维轮廓测量等，已经广泛应用在汽车制造、航空航天制造、机器人标定、管路测量等很多工业领域。Both surveying with laser trackers and photogrammetry are common methods of measurement in precision surveying. Photogrammetry has the characteristics of high precision, high efficiency, and high degree of automation. The measurement range includes discrete point measurement, deformation and motion measurement, three-dimensional contour measurement, etc. It has been widely used in automobile manufacturing, aerospace manufacturing, robot calibration, pipeline measurement, etc. industrial field.

激光跟踪仪是一种便携式三坐标测量系统，由于其具有测量精度高、效率快等特点，目前被广泛应用于航空、航天、汽车、船舶等工业测量的各个技术领域。在这些领域中，在测量大尺寸物体时，需要采用激光跟踪仪多站位测量技术。多站位测量转站技术与单站位测量相比，测量精度差，很难满足航空航天等领域高精度要求。因此需要一种新的技术和方法来提高对于大尺寸物体的测量精度。The laser tracker is a portable three-coordinate measurement system. Due to its high measurement accuracy and fast efficiency, it is currently widely used in various technical fields of industrial measurement such as aviation, aerospace, automobiles, and ships. In these fields, when measuring large-scale objects, laser tracker multi-site measurement technology is required. Compared with single-site measurement, multi-site measurement transfer station technology has poor measurement accuracy, and it is difficult to meet the high-precision requirements of aerospace and other fields. Therefore, a new technology and method is needed to improve the measurement accuracy of large-scale objects.

当激光跟踪仪进行转站测量时，在公共点距离激光跟踪仪较远的情况下，激光跟踪仪测量点的误差较大。而摄影测量系统具有很高的便携性，可以在距离公共点较近的情况下进行测量，从而得到较高精度的公共点测量值。When the laser tracker performs transfer station measurement, if the common point is far away from the laser tracker, the error of the measurement point of the laser tracker is relatively large. The photogrammetry system has high portability, and can be measured when the distance from the public point is relatively close, so as to obtain a high-precision measurement value of the public point.

发明内容Contents of the invention

发明目的purpose of invention

鉴于激光跟踪仪测量大尺寸物体时误差大的问题，本发明的目的是提供一种基于摄影测量提高激光跟踪仪转站精度的方法，可以在激光跟踪仪的基础上提高测量精度。In view of the problem of large errors when the laser tracker measures large-sized objects, the purpose of the present invention is to provide a method for improving the accuracy of the laser tracker's transfer station based on photogrammetry, which can improve the measurement accuracy on the basis of the laser tracker.

技术方案Technical solutions

为实现上述目的，本发明提供了一种基于摄影测量提高激光跟踪仪转站精度的方法，该方法使用到的设备包括：至少一台激光跟踪仪，用于目标物体和公共点的测量；至少一个激光跟踪仪控制柜，与激光跟踪仪连接；至少一个激光跟踪仪靶球，用作激光跟踪仪测量目标；一台数码摄像机，用于摄影测量，进行拍摄相片；多个摄影测量靶球，用作摄影测量目标；多个靶球座，用于固定两种靶球；多个标记点，粘贴在公共点附近；至少一个基准尺，用作摄影测量标定；至少一个工作站，与激光跟踪仪连接及处理摄影图像。In order to achieve the above object, the present invention provides a method for improving the accuracy of the laser tracker transfer station based on photogrammetry. The equipment used in the method includes: at least one laser tracker for the measurement of target objects and public points; at least A laser tracker control cabinet, connected with the laser tracker; at least one laser tracker target ball, used as the laser tracker to measure the target; a digital camera, used for photogrammetry, to take pictures; multiple photogrammetry target balls, Used as a photogrammetric target; multiple target ball mounts for holding two types of target balls; multiple marker points, glued near a common point; at least one reference ruler for photogrammetric calibration; at least one workstation, with a laser tracker Link and process photographic images.

如上所述的设备中，其中激光跟踪仪既可以只使用一台，通过移动激光跟踪仪的方式进行转站测量，又可以使用多台在不同位置进行测量。数码摄像机使用摄影测量中专用的量测摄像机。工作站中需安装包含与激光跟踪仪配套的连接、处理软件和摄影测量处理软件。摄影测量靶球为专用的与激光跟踪仪大小相等的靶球。In the above-mentioned equipment, only one laser tracker can be used to perform the transfer station measurement by moving the laser tracker, and multiple sets can be used to measure at different positions. The digital camera uses a dedicated measurement camera for photogrammetry. The workstation needs to be installed with the connection and processing software and photogrammetry processing software supporting the laser tracker. The photogrammetry target ball is a special target ball with the same size as the laser tracker.

本发明一种基于摄影测量提高激光跟踪仪转站精度的方法，其实施步骤如下：The present invention is a method for improving the accuracy of laser tracker transfer stations based on photogrammetry, and its implementation steps are as follows:

步骤一：安装相应的设备，固定公共点。使用激光跟踪仪在站点A测量目标A’与公共点。记录A’和公共点的测量结果。设n个公共点的坐标集合为：P_L1(a₁，a₂，a₃，……，a_n)。Step 1: Install corresponding equipment and fix public points. Use a laser tracker to measure target A' and common points at site A. Record the measurements of A' and the common point. Let the coordinate set of n public points be: P _L1 (a ₁ , a ₂ , a ₃ ,..., a _n ).

步骤二：使用激光跟踪仪在站点B测量目标B’与公共点。站点B需与站点A有一定距离。记录B’和公共点的测量结果。设该步骤中n个公共点的坐标集合为：P_L2(a₁，a₂，a₃，……，a_n)。Step 2: Use the laser tracker to measure the target B' and the common point at site B. Site B needs to be a certain distance from site A. Record the measurements of B' and the common point. Let the coordinate set of n common points in this step be: P _L2 (a ₁ , a ₂ , a ₃ ,..., a _n ).

步骤三：使用摄影测量测量公共点的坐标。设坐标集合为P_P(b₁，b₂，b₃，……，b_n)。Step 3: Use photogrammetry to measure the coordinates of the public points. Let the set of coordinates be P _P (b ₁ , b ₂ , b ₃ ,..., b _n ).

步骤四：由于摄影测量系统与激光跟踪仪系统都有各自独立的坐标系，无法直接修正公共点测量值。因此本发明提出一种几何图形修正的方法。Step 4: Since the photogrammetry system and the laser tracker system have their own independent coordinate systems, it is impossible to directly correct the measured values of the common points. Therefore, the present invention proposes a geometric figure correction method.

几何图形修正方法的思想大致为：将在两个不同坐标系下的公共点云测量值都视为刚体，通过一些列旋转和平移，使得两个点云的质心完全重合，两个点云中其他点大致重合。再用精度较高的公共点云测量值代替精度较低的测量值，即可完成修正。The idea of the geometric figure correction method is roughly: treat the public point cloud measurements in two different coordinate systems as rigid bodies, and through a series of rotations and translations, the centroids of the two point clouds are completely coincident. The other points roughly coincide. The correction is then completed by replacing the lower-precision measurement values with the higher-precision public point cloud measurement values.

对P_L1和P_P两个点云进行质心化处理：Perform centroid processing on the two point clouds of P _L1 and P _P :

$\overset{&OverBar; &OverBar;}{{P P}_{L L 11}} = = {P P}_{L L 11} - - {ρ ρ}_{L L}$

$\overset{&OverBar; &OverBar;}{{P P}_{P P}} = = {P P}_{P P} - - {ρ ρ}_{P P}$

与分别为质心化处理后的激光跟踪仪测量点云坐标和摄影测量点云坐标。其中，为激光跟踪仪测量点云坐标质心点；为摄影测量点云坐标质心点。 and Respectively, the coordinates of the laser tracker measurement point cloud and the photogrammetry point cloud coordinates after the centroid processing. in, Measure point cloud coordinate centroid point for laser tracker; Coordinate centroid point for photogrammetry point cloud.

此时两个点云质心重合，且与坐标系原点重合。质心记为ρ_LP。At this time, the centroids of the two point clouds coincide and coincide with the origin of the coordinate system. The centroid is denoted as ρ _LP .

步骤五：在两个质心化后的点云中，选择一对对应点a_i、b_i，设质心到两个点的向量分别为和将摄影测量点云绕坐标轴旋转，使得和两个向量方向重合。Step 5: In the two centroided point clouds, select a pair of corresponding points a _i and b _i , and set the vectors from the centroid to the two points as and Photogrammetric point cloud Rotate around the coordinate axis so that and The directions of the two vectors coincide.

点云绕Z轴逆时针旋转α的旋转矩阵为：The rotation matrix of the point cloud rotating α counterclockwise around the Z axis is:

${R R}_{z z} ((α α)) = = [\begin{matrix} c c o o s the s α α & s the s i i n no α α & 00 \\ - - s the s i i n no α α & c c o o s the s α α & 00 \\ 00 & 00 & 11 \end{matrix}]$

点云绕Y轴逆时针旋转β的旋转矩阵为：The rotation matrix of the point cloud rotating counterclockwise around the Y axis β is:

${R R}_{y the y} ((β β)) = = [\begin{matrix} c c o o s the s β β & 00 & - - s the s i i n no β β \\ 00 & 11 & 00 \\ s the s i i n no β β & 00 & cos cos β β \end{matrix}]$

点云绕坐标轴旋转，使得和两个向量方向重合的旋转矩阵可表示为：point cloud Rotate around the coordinate axis so that and The rotation matrix with coincident directions of two vectors can be expressed as:

${P P}_{p p}^{' '} = = {R R}_{z z}^{- - 11} ((- - {α α}_{22})) {R R}_{y the y}^{- - 11} ((- - {β β}_{22})) {R R}_{y the y} ((- - {β β}_{11})) {R R}_{z z} ((- - {α α}_{11})) \overset{&OverBar; &OverBar;}{{P P}_{P P}} - - - - - - ((11))$

P′_P为旋转后的摄影测量点云坐标。其中，α₁，α₂分别为和在xoy平面内投影与X轴夹角；β₁，β₂分别为和与Z轴夹角。P′ _P is the coordinates of the rotated photogrammetry point cloud. Among them, α ₁ , α ₂ are respectively and The angle between the projection and the X axis in the xoy plane; β ₁ and β ₂ are respectively and Angle with the Z axis.

步骤六：在变换后的点云中，选择另一对对应点a_j、b_j，设质心到两个点的向量分别为和记将摄影测量点云P′_P绕坐标轴旋转，使得和两个向量方向重合。Step 6: In the transformed point cloud, select another pair of corresponding points a _j , b _j , and set the vectors from the centroid to the two points as and remember Rotate the photogrammetry point cloud P′ _P around the coordinate axis, so that and The directions of the two vectors coincide.

${P P}_{P P}^{' '' '} = = {R R}_{y the y}^{- - 11} ((- - {β β}_{22})) {R R}_{z z}^{- - 11} ((- - {α α}_{22})) {R R}_{z z} ((θ θ)) {R R}_{y the y} ((- - {β β}_{22})) {R R}_{z z} ((- - {α α}_{22})) {P P}_{P P}^{' '} - - - - - - ((22))$

P″_P为旋转后的摄影测量点云坐标。其中，θ为和之间的夹角。P″ _P is the coordinates of the rotated photogrammetry point cloud. Among them, θ is and angle between.

将公式(1)与公式(2)可以化简为：Formula (1) and formula (2) can be simplified as:

${P P}_{P P}^{' '' '} = = {R R}_{y the y}^{- - 11} ((- - {β β}_{22})) {R R}_{z z}^{- - 11} ((- - {α α}_{22})) {R R}_{z z} ((θ θ)) {R R}_{y the y} ((- - {β β}_{11})) {R R}_{z z} ((- - {α α}_{11})) \overset{&OverBar; &OverBar;}{{P P}_{P P}}$

步骤七：此时，两个点云的质心完全重合，且两个点云中其他点大致重合。用摄影测量点云P″_P中各点坐标代替激光跟踪仪点云中各点坐标。对点云P″_P进行逆质心化处理，即可得到修正后的最终点云坐标P′_L1。Step 7: At this point, the centroids of the two point clouds are completely coincident, and other points in the two point clouds are roughly coincident. Use the coordinates of each point in the photogrammetric point cloud P″ _P to replace the laser tracker point cloud The coordinates of each point in . Inverse centroid processing is performed on the point cloud P″ _P to obtain the corrected final point cloud coordinates P′ _L1 .

P′_L1＝P″_P+ρ_L1 P′ _L1 =P″ _P +ρ _L1

步骤八：为了提高几何图形修正方法的精度，可以利用两组点云中N组对应点分别进行一次修正计算，求得N组修正后的数据，计算N组数据的平均值作为最后的修正结果。Step 8: In order to improve the accuracy of the geometric figure correction method, N sets of corresponding points in the two sets of point clouds can be used to perform a correction calculation respectively to obtain N sets of corrected data, and calculate the average value of the N sets of data as the final correction result .

分别选择a_i、b_i(i＝1，2，……，n)作为对应点，使得每组质心与对应点的向量方向均进行一次重合，减小该方向上的修正误差。重复上述步骤五，得到n组变换后的点云。其中，步骤六中所述的“另一对对应点a_j、b_j”的选择有n-1种方式，如果分别选择所有对应点进行计算，将要进行n(n-1)次修正计算，计算量大且最后修正结果精度提高不大。因此，为了减小计算量，本发明选择a_i+1、b_i+1(i＝1，2，……，n)作为对应点进行计算，重复上述步骤六。再重复步骤七，进行逆质心化处理，对得到的n组逆质心化后的点云每个点取平均值。实验证明，N组数据的平均值的精度高于仅进行一组数据修正的精度。Select a _i , b _i (i=1, 2, ..., n) as corresponding points respectively, so that the vector directions of each group of centroids and corresponding points are coincident once, and the correction error in this direction is reduced. Repeat step five above to obtain n sets of transformed point clouds. Among them, there are n-1 ways to select “another pair of corresponding points a _j , b _j ” mentioned in step 6. If all corresponding points are selected for calculation, n(n-1) correction calculations will be performed, The amount of calculation is large and the accuracy of the final correction result is not greatly improved. Therefore, in order to reduce the calculation amount, the present invention selects a _i+1 , b _i+1 (i=1, 2, . . . , n) as corresponding points for calculation, and repeats the above step six. Repeat step seven again to perform inverse centroid processing, and average each point of the obtained n groups of inverse centroidized point clouds. Experiments have proved that the accuracy of the average value of N sets of data is higher than that of correcting only one set of data.

步骤九：重复步骤四至步骤八，对站位B中的公共点进行坐标修正：将步骤四至步骤八中的P_L1替换为P_L2，按照完全相同的方法进行计算，得到一组点云P′_L2。Step 9: Repeat steps 4 to 8 to correct the coordinates of the common points in station B: replace P _L1 in steps 4 to 8 with _PL2 , and perform calculations in exactly the same way to obtain a set of point clouds P′ _L2 .

步骤十：利用单位四元数法求解两个不同站位激光跟踪仪之间的转换矩阵。Step 10: Use the unit quaternion method to solve the transformation matrix between two different station laser trackers.

P′_L2＝R(q^R)P′_L1+q^T P′ _L2 ＝R(q ^R )P′ _L1 +q ^T

其中，R(q^R)与q^T为利用单位四元数法求得的旋转矩阵和平移矩阵。Among them, R(q ^R ) and q ^T are the rotation matrix and translation matrix obtained by the unit quaternion method.

$R R (({q q}^{R R})) = = [\begin{matrix} {R R}_{1111} & {R R}_{1212} & {R R}_{1313} \\ {R R}_{21 twenty one} & {R R}_{22 twenty two} & {R R}_{23 twenty three} \\ {R R}_{3131} & {R R}_{3232} & {R R}_{3333} \end{matrix}]$

其中， q₀、q₁、q₂、q₃为单位四元数。in, q ₀ , q ₁ , q ₂ , and q ₃ are unit quaternions.

步骤十一：至此，A,B两站位上坐标转换到同一坐标系，可根据一般长度、角度等公式进行计算。Step 11: At this point, the coordinates of the two stations A and B are converted to the same coordinate system, which can be calculated according to the general length, angle and other formulas.

通过以上步骤，达到了提高激光跟踪仪转站精度的效果，解决了激光跟踪仪测量大尺寸物体时误差大的问题。Through the above steps, the effect of improving the accuracy of the laser tracker transfer station is achieved, and the problem of large errors when the laser tracker measures large-sized objects is solved.

优点advantage

本发明针对激光跟踪仪多站位转站测量大型物体时精度较低的问题，提出了基于摄影测量提高大尺寸空间测量中激光跟踪仪转站精度的方法。由于摄影测量系统的便携性和高精度性，在近距离测量公共基准点时相对于激光跟踪仪在较远处测量有较高的精度。同时提出一种几何图形坐标修正方法，用摄影测量系统测量的公共点坐标修正激光跟踪仪测量的公共点坐标，通过修正后的坐标计算出精度相对较高的变换矩阵，从而使转站精度提高。本发明通过转站测量基准尺和扫描平面，验证了该方法的可行性。实验结果表明，本发明提出的方法可以提高激光跟踪仪在多站位转站测量较大物体时的精度。The invention aims at the problem of low accuracy when the laser tracker multi-station transfer station measures large objects, and proposes a method for improving the accuracy of the laser tracker transfer station in large-scale space measurement based on photogrammetry. Due to the portability and high precision of the photogrammetry system, it has higher accuracy when measuring the common reference point at a short distance than the laser tracker at a long distance. At the same time, a geometric figure coordinate correction method is proposed, which uses the common point coordinates measured by the photogrammetry system to correct the common point coordinates measured by the laser tracker, and calculates a relatively high-precision transformation matrix through the corrected coordinates, thereby improving the accuracy of the transfer station . The present invention verifies the feasibility of the method by measuring the reference ruler and the scanning plane at the transfer station. Experimental results show that the method proposed by the invention can improve the accuracy of the laser tracker when measuring larger objects at multiple stations.

附图说明Description of drawings

图1是两个公共点点云质心化处理后的结果(以五个公共点为例)，其中a₁-a₅表示激光跟踪仪测量得到的公共点，b₁-b₅表示激光跟踪仪测量得到的公共点，ρ_LP表示两组公共点的质心。Figure 1 is the result of point cloud centroid processing of two public points (taking five public points as an example), where a ₁ -a ₅ represent the common points measured by the laser tracker, and b ₁ -b ₅ represent the measurement by the laser tracker The obtained common point, ρ _LP represents the centroid of two sets of common points.

图2(a)、(b)是对应点a_i、b_i的选择，以及和方向重合后的结果，各点含义同图1。Figure 2 (a), (b) is the selection of corresponding points a _i , b _i , and and The result after the directions overlap, the meaning of each point is the same as that in Figure 1.

图3(a)、(b)是对应点a_j、b_j的选择，以及和两个向量重合的结果，表示表示θ表示和之间的夹角，其余各点含义同图1。Figure 3 (a), (b) is the selection of corresponding points a _j , b _j , and and The result of the coincidence of two vectors, express express θ means and The angle between them, and the meanings of other points are the same as those in Figure 1.

图4是公共点云逆质心化后的结果，ρ_L表示质心，其余各点含义同图3。Figure 4 is the result of the inverse centroid of the public point cloud, ρ _L represents the centroid, and the meanings of other points are the same as those in Figure 3.

图5(a)、(b)、(c)、(d)、(e)是利用两组点云中N组对应点分别进行一次修正计算的过程，各点含义同图3。Figure 5 (a), (b), (c), (d), (e) is the process of performing a correction calculation using N sets of corresponding points in the two sets of point clouds, and the meaning of each point is the same as that in Figure 3.

图6本发明所述方法流程图。Fig. 6 is a flowchart of the method of the present invention.

具体实施方案specific implementation plan

下面将结合附图和实例对本发明作进一步的详细说明。The present invention will be further described in detail below in conjunction with accompanying drawings and examples.

本发明一种基于摄影测量提高激光跟踪仪转站精度的方法，见图6所示，其具体实施步骤如下：A method of improving the accuracy of the laser tracker transfer station based on photogrammetry of the present invention is shown in Figure 6, and its specific implementation steps are as follows:

步骤一：安装相应的设备，固定公共点。使用激光跟踪仪在站点A测量目标A’与公共点。记录A’和公共点的测量结果。设n个公共点的坐标集合为：P_L1(a₁，a₂，a₃，……，a_n)。目标A’可以包含任意数量的点，点云，或者通过点、点云拟合出的形状。公共点数目必须大于三个，为保证准确度，公共点尽量分布于多个平面，每个平面包含一定数目的公共点。Step 1: Install corresponding equipment and fix public points. Use a laser tracker to measure target A' and common points at site A. Record the measurements of A' and the common point. Let the coordinate set of n public points be: P _L1 (a ₁ , a ₂ , a ₃ ,..., a _n ). The target A' can contain any number of points, point clouds, or shapes fitted by points and point clouds. The number of common points must be greater than three. To ensure accuracy, the common points should be distributed on multiple planes as much as possible, and each plane contains a certain number of common points.

步骤二：使用激光跟踪仪在站点B测量目标B’与公共点。站点B需与站点A有一定距离。记录B’和公共点的测量结果。目标B’可以包含任意数量的点，点云，或者通过点、点云拟合出的形状。设该步骤中n个公共点的坐标集合为：P_L2(a₁，a₂，a₃，……，a_n)。Step 2: Use the laser tracker to measure the target B' and the common point at site B. Site B needs to be a certain distance from site A. Record the measurements of B' and the common point. The target B' can contain any number of points, point clouds, or shapes fitted by points and point clouds. Let the coordinate set of n common points in this step be: P _L2 (a ₁ , a ₂ , a ₃ ,..., a _n ).

几何图形修正方法的思想大致为：将在两个不同坐标系下的公共点云测量值都视为刚体，通过一些列旋转和平移，使得两个点云的质心完全重合，两个点云中其他点大致重合。再用精度较高的公共点云测量值代替精度较低的测量值，即可完成修正。The idea of the geometric figure correction method is roughly as follows: treat the public point cloud measurements in two different coordinate systems as rigid bodies, and through a series of rotations and translations, the centroids of the two point clouds are completely coincident. The other points roughly coincide. The correction is then completed by replacing the lower-precision measurement values with the higher-precision public point cloud measurement values.

$\overset{&OverBar; &OverBar;}{{P P}_{P P}} = = {P P}_{P P} - - {ρ ρ}_{P P}$

此时两个点云质心重合，且与坐标系原点重合。质心记为ρ_LP。图1以五个公共点为例，显示了两个点云质心化处理后的结果。At this time, the centroids of the two point clouds coincide and coincide with the origin of the coordinate system. The centroid is denoted as ρ _LP . Figure 1 shows the results of two point cloud centroids, taking five common points as an example.

图2为对应点a_i、b_i的选择，以及和两个向量方向重合后的结果。Fig. 2 is the selection of corresponding points a _i , b _i , and and The result after the direction of the two vectors coincides.

图3显示了对应点a_j、b_j的选择，以及和两个向量重合的结果。Figure 3 shows the selection of corresponding points a _j , b _j , and and The result of the coincidence of two vectors.

步骤七：此时，两个点云的质心完全重合，且两个点云中其他点大致重合。用摄影测量点云P″_P中各点坐标代替激光跟踪仪点云中各点坐标。对点云P″_P进行逆质心化处理，即可得到修正后的最终点云坐标P′_L1。逆质心化过程如图4所示。Step 7: At this point, the centroids of the two point clouds are completely coincident, and other points in the two point clouds are roughly coincident. Use the coordinates of each point in the photogrammetric point cloud P″ _P to replace the laser tracker point cloud The coordinates of each point in . Perform inverse centroid processing on the point cloud P″ _P to obtain the corrected final point cloud coordinates P′ _L1 . The inverse centroid process is shown in Figure 4.

P′_L1＝P″_P+ρ_L1 P′ _L1 =P″ _P +ρ _L1

分别选择a_i、b_i(i＝1，2，……，n)作为对应点，使得每组质心与对应点的向量方向均进行一次重合，减小该方向上的修正误差。重复上述步骤五，得到n组变换后的点云。其中，步骤六中所述的“另一对对应点a_j、b_j”的选择有n-1种方式，如果分别选择所有对应点进行计算，将要进行n(n-1)次修正计算，计算量大且最后修正结果精度提高不大。因此，为了减小计算量，本发明选择a_i+1、b_i+1(i＝1，2，……，n)作为对应点进行计算，重复上述步骤六。再重复步骤七，进行逆质心化处理，对得到的n组逆质心化后的点云每个点取平均值。实验证明，N组数据的平均值的精度高于仅进行一组数据修正的精度。Respectively select a _i , b _i (i=1, 2, ..., n) as corresponding points, so that the vector directions of each group of centroids and corresponding points are coincident once, and the correction error in this direction is reduced. Repeat step five above to obtain n sets of transformed point clouds. Among them, there are n-1 ways to select “another pair of corresponding points a _j , b _j ” mentioned in step 6. If all corresponding points are selected for calculation, n(n-1) correction calculations will be performed, The amount of calculation is large and the accuracy of the final correction result is not greatly improved. Therefore, in order to reduce the calculation amount, the present invention selects a _i+1 , b _i+1 (i=1, 2, . . . , n) as corresponding points for calculation, and repeats the above step six. Repeat step seven again to perform inverse centroid processing, and average each point of the obtained n groups of inverse centroidized point clouds. Experiments have proved that the accuracy of the average value of N sets of data is higher than that of correcting only one set of data.

图5为利用两组点云中N组对应点分别进行一次修正计算的过程。Figure 5 shows the process of performing a correction calculation using N sets of corresponding points in the two sets of point clouds.

P′_L2＝R(q^R)P′_L1+q^T P′ _L2 ＝R(q ^R )P′ _L1 +q ^T

Claims

1. A method for improving the station transferring precision of a laser tracker based on photogrammetry is characterized by comprising the following steps: the implementation steps are as follows:

the method comprises the following steps: installing corresponding equipment and fixing the common point; measuring a target A 'and a common point at a site A by using a laser tracker, and recording the measurement results of the A' and the common point; let the coordinate set of n common points be: p_L1(a₁，a₂，a₃，……，a_n)；

Step two: measuring a target B' and a common point at site B using a laser tracker; siteB, recording the measurement results of B' and the common point when the distance between B and the site A is a certain distance; the coordinate set of n common points in this step is set as: p_L2(a₁，a₂，a₃，……，a_n)；

Step three: measuring the coordinates of the common points using photogrammetry; let the set of coordinates be P_P(b₁，b₂，b₃，……，b_n)；

Step four: the photogrammetric system and the laser tracker system have independent coordinate systems respectively, and common point measurement values cannot be directly corrected, so that the invention provides a method for correcting geometric figures;

the geometric figure correction method comprises the following steps: the common point cloud measured values under two different coordinate systems are regarded as rigid bodies, the centroids of the two point clouds are completely overlapped through a certain series of rotation and translation, and other points in the two point clouds are overlapped; replacing the low-precision measured value with the high-precision common point cloud measured value to finish correction;

to P_L1And P_PTwo point clouds were centrolized:

\overset{&OverBar;}{P_{L 1}} = P_{L 1} - ρ_{L}

\overset{&OverBar;}{P_{P}} = P_{P} - ρ_{P}

andrespectively measuring point cloud coordinates and photogrammetric point cloud coordinates of the laser tracker after barycenter processing; wherein,measuring a point cloud coordinate centroid point for a laser tracker;coordinate centroid points for photogrammetry point clouds;

at the moment, the mass centers of the two point clouds are superposed and are superposed with the origin of the coordinate system, and the mass center is recorded as rho_LP；

Step five: selecting a pair of corresponding points a from the two centrolized point clouds_i、b_iLet the vectors from the centroid to the two points beAndcloud of photogrammetric pointsRotate about a coordinate axis such thatAndthe two vector directions coincide;

the rotation matrix of the point cloud counterclockwise rotation alpha around the Z axis is as follows:

R_{z} (α) = [\begin{matrix} \cos α & \sin α & 0 \\ - \sin α & \cos α & 0 \\ 0 & 0 & 1 \end{matrix}]

the rotation matrix of the point cloud counterclockwise rotation beta around the Y axis is:

R_{y} (β) = [\begin{matrix} \cos β & 0 & - \sin β \\ 0 & 1 & 0 \\ \sin β & 0 & \cos β \end{matrix}]

point cloudRotate about a coordinate axis such thatAndthe rotation matrix where the two vector directions coincide is represented as:

P_{p}^{'} = R_{z}^{- 1} (- α_{2}) R_{y}^{- 1} (- β_{2}) R_{y} (- β_{1}) R_{z} (- α_{1}) \overset{&OverBar;}{P_{p}} - - - (1)

P′_Pmeasuring point cloud coordinates for the rotated camera, wherein α₁，α₂Are respectively asAndangle of included angle of projection with X-axis in xoy plane β₁，β₂Are respectively asAndincluded angle with the Z axis;

step six: selecting another pair of corresponding points a in the transformed point cloud_j、b_jLet the vectors from the centroid to the two points beAndnote the bookPhotogrammetry point cloud P'_PRotate about a coordinate axis such thatAndthe two vector directions coincide;

P_{p}^{''} = R_{y}^{- 1} (- β_{2}) R_{z}^{- 1} (- α_{2}) R_{z} (θ) R_{y} (- β_{2}) R_{z} (- α_{2}) P_{p}^{'} - - - (2)

P″_Pmeasuring point cloud coordinates for the rotated photograph, wherein theta isAndthe included angle between them;

the formula (1) and the formula (2) are simplified as follows:

P_{p}^{''} = R_{y}^{- 1} (- β_{2}) R_{z}^{- 1} (- α_{2}) R_{z} (θ) R_{y} (- β_{1}) R_{z} (- α_{1}) \overset{&OverBar;}{P_{p}}

step seven: at the moment, the centroids of the two point clouds are completely overlapped, and other points in the two point clouds are overlapped; photogrammetry of a point cloud P_PPoint cloud of middle points substituting laser trackerCoordinates of points in the center, point cloud P_PCarrying out reverse centroid processing to obtain a corrected final point cloud coordinate P'_L1；

P′_L1＝P″_P+ρ_L1；

Step eight: in order to improve the precision of the geometric figure correction method, N groups of corresponding points in two groups of point clouds are utilized to respectively carry out correction calculation once, N groups of corrected data are obtained, and the average value of the N groups of data is calculated to be used as the final correction result;

respectively select a_i、b_iI ═ 1, 2, … …, n; as corresponding points, the vector directions of each group of centroids and corresponding points are coincided once, so that the correction error in the direction is reduced; repeating the fifth step to obtain n groups of converted point clouds; wherein, the other pair of corresponding points a stated in the sixth step_j、b_j"there are n-1 modes to select, if all corresponding points are selected to calculate separately, n (n-1) correction calculations will be performed, the calculation amount is large and the accuracy of the final correction result is not improved much, therefore, in order to reduce the calculation amount, the invention selects a_i+1、b_i+1I ═ 1, 2, … …, n; calculating as corresponding points, repeating the sixth step, repeating the seventh step, performing inverse barycenter processing, and averaging each point of the n groups of point clouds subjected to inverse barycenter processing; experiments prove that the precision of the average value of the N groups of data is higher than that of only one group of data correction;

step nine: repeating the fourth step to the eighth step, and carrying out coordinate correction on the common point in the station B: p in the fourth step to the eighth step_L1Replacement by P_L2Are calculated according to the same method to obtain a group of point clouds P'_L2；

Step ten: solving a conversion matrix between two laser trackers at different station positions by using a unit quaternion method;

P_{L 2}^{'} = R (q^{R}) P_{L 1}^{'} + q^{T}

wherein R (q)^R) And q is^TThe rotation matrix and the translation matrix are obtained by using a unit quaternion method;

R (q^{R}) = [\begin{matrix} R_{11} & R_{12} & R_{13} \\ R_{21} & R_{22} & R_{23} \\ R_{31} & R_{32} & R_{33} \end{matrix}]

wherein,

\begin{matrix} R_{11} = q_{0}^{2} + q_{1}^{2} - q_{2}^{2} - q_{3}^{2}; R_{12} = 2 (q_{1} q_{2} - q_{0} q_{3}); R_{13} = 2 (q_{1} q_{3} + q_{0} q_{2}); R_{21} = \\ 2 (q_{1} q_{2} + q_{0} q_{3}); R_{22} = q_{0}^{2} - q_{1}^{2} + q_{2}^{2} - q_{3}^{2}; R_{23} = 2 (q_{2} q_{3} - q_{0} q_{1}); R_{31} = 2 (q_{1} q_{3} - \\ q_{0} q_{2}); R_{32} = 2 (q_{2} q_{3} + q_{0} q_{1}); R_{33} = q_{0}^{2} - q_{1}^{2} - q_{2}^{2} + q_{3}^{2} \end{matrix}

q₀、q₁、q₂、q₃is a unit quaternion;

step eleven: at this moment, coordinates on the A and B station positions are converted into the same coordinate system, and calculation is carried out according to a general length and angle formula;

through the steps, the effect of improving the station transferring precision of the laser tracker is achieved, and the problem of large error when the laser tracker measures large-size objects is solved.