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

Abstract

The invention discloses a method of improving laser tracker station moving precision based on photogrammetry. The method comprises the following steps: 1, a device is mounted and a common point is fixed; 2, a laser tracker is used for measuring a target and the common point at two stations A and B; 3, photogrammetry is used for measuring coordinates of the common point; 4, centroids of two point clouds are coincident and coincident with the original point of a coordinate system; 5, a photogrammetry point cloud rotates around a coordinate axis until a group of corresponding vectors are coincident; 6, the photogrammetry point cloud rotates around the coordinate axis to specify corresponding vectors to be coincident; 7, inverse centroid processing is carried out on the photogrammetry point cloud after rotation; 8, data after correction of multiple groups are solved, and the average value is calculated as a correction value; 9, coordinates of the common point in the station B are corrected; 10, a unit quaternion method is used for solving a conversion matrix; and 11, the length, the angle and the like of the measurement target are calculated. The effects of improving the laser tracker station moving precision are achieved, and the problem of large errors when the laser tracker measures a large-sized object can be solved.

Description

A kind of method turning station precision based on photogrammetric raising laser tracker

Technical field

The present invention relates to a kind of method turning station precision based on photogrammetric raising laser tracker, belong to field of measuring technique.

Background technology

Use laser tracker measure with photogrammetric be all the common metering system in accurate measurement.Photogrammetric have precision height, efficiency height, automaticity high, measurement scope includes that discrete point is measured, deformed and motion measurement, measuring three-dimensional profile etc., has been widely used in a lot of industrial circle such as automobile making, Aero-Space manufacture, Robot calibration, pipeline measurement.

Laser tracker is that a kind of portable three-coordinate measures system, owing to it has the features such as certainty of measurement is high, efficiency is fast, is widely used in each technical field of the commercial measurements such as Aeronautics and Astronautics, automobile, boats and ships at present.In these areas, when measuring large sized object, need to use laser tracker multi-court position measurement technology.Multi-court position measurement turns compared with station technology measures with single erect-position, and certainty of measurement is poor, is difficult to meet the field high-precision requirement such as Aero-Space.It is thus desirable to a kind of new technology and method improve the certainty of measurement for large sized object.

When laser tracker carry out turn station measure time, common point distance laser tracker farther out in the case of, laser tracker measure point error bigger.And Digital Photogrammetric System has the highest portability, can measure in the case of distance common point is relatively near, thus obtain the common point measured value of degree of precision.

Summary of the invention

Goal of the invention

In view of laser tracker measures the problem that large sized object time error is big, it is an object of the invention to provide a kind of method turning station precision based on photogrammetric raising laser tracker, certainty of measurement can be improved on the basis of laser tracker.

Technical scheme

For achieving the above object, the invention provides a kind of method turning station precision based on photogrammetric raising laser tracker, the equipment that the method uses includes: at least one laser tracker, for target object and the measurement of common point；At least one laser tracker switch board, is connected with laser tracker；At least one laser tracker target ball, measures target as laser tracker；One DV, for photogrammetric, carries out shooting photograph；Multiple photogrammetric target balls, as photogrammetry targets；Multiple target ball seats, are used for fixing two kinds of target balls；Multiple labelling points, are pasted onto near common point；At least one station meter, as photogrammetric calibration；At least one work station, is connected with laser tracker and processes photographs.

In equipment as above, wherein laser tracker both only can use one, carries out turning station and measures, multiple stage can be used again to measure at diverse location by the way of mobile laser tracker.Measurement video camera special during DV use is photogrammetric.Work station need installation kit contain connection, process software and the Photogrammetric Processing software supporting with laser tracker.Photogrammetric target ball is special target ball equal-sized with laser tracker.

A kind of method turning station precision based on photogrammetric raising laser tracker of the present invention, implementation step is as follows:

Step one: install corresponding equipment, fixing common point.Laser tracker is used to measure target A at website A ' and common point.Record A ' and the measurement result of common point.If the coordinate set of n common point is: P_L1(a₁, a₂, a₃..., a_n)。

Step 2: use laser tracker to measure target B at website B ' and common point.Website B need to have certain distance with website A.Record B ' and the measurement result of common point.If in this step, the coordinate set of n common point is: P_L2(a₁, a₂, a₃..., a_n)。

Step 3: use the coordinate of photogrammetric measurement common point.If coordinate set is P_P(b₁, b₂, b₃..., b_n)。

Step 4: owing to Digital Photogrammetric System and laser tracker system have the most independent coordinate system, it is impossible to directly revise common point measured value.Therefore a kind of method that the present invention proposes geometric figure correction.

The thought of geometric figure modification method is substantially: the common point cloud measured value under two different coordinates is all considered as rigid body, is rotated and translation by some row so that the barycenter of two some clouds is completely superposed, and in two some clouds, other points substantially overlap.Again with the measured value that the common point cloud measured value replacement precision that precision is higher is relatively low, can complete to revise.

To P_L1And P_PTwo some clouds carry out barycenter process:

$\stackrel{\‾}{P_{L1}}=P_{L1}-{\mathrm{\ρ}}_L$

$\stackrel{\‾}{P_P}=P_P-{\mathrm{\ρ}}_P$

WithIt is respectively the laser tracker measurement pointcloud coordinate after barycenterization processes and photogrammetric some cloud coordinate.Wherein,For laser tracker measurement pointcloud coordinate center of mass point；For photogrammetric some cloud coordinate center of mass point.

Now two some cloud barycenter overlap, and overlap with coordinate origin.Barycenter is designated as ρ_LP。

Step 5: in the some cloud after two barycenter, select a pair corresponding point a_i、b_iIf the vector of barycenter to two point is respectivelyWithBy photogrammetric some cloudRotate around coordinate axes so thatWithTwo vector direction overlap.

The spin matrix of some cloud rotation alpha counterclockwise about the z axis is:

$R_z\left(\mathrm{\α}\right)=\left[\begin{array}{ccc}cos\mathrm{\α}& sin\mathrm{\α}& 0\\ -sin\mathrm{\α}& cos\mathrm{\α}& 0\\ 0& 0& 1\end{array}\right]$

Point cloud around the spin matrix of Y-axis rotation β counterclockwise is:

$R_y\left(\mathrm{\β}\right)=\left[\begin{array}{ccc}cos\mathrm{\β}& 0& -sin\mathrm{\β}\\ 0& 1& 0\\ sin\mathrm{\β}& 0& \cos \mathrm{\β}\end{array}\right]$

Point cloudRotate around coordinate axes so thatWithThe spin matrix of two vector direction coincidences is represented by:

$P_p^{\′}=R_z^{-1}(-{\mathrm{\α}}_2)R_y^{-1}(-{\mathrm{\β}}_2)R_y(-{\mathrm{\β}}_1)R_z(-{\mathrm{\α}}_1)\stackrel{\‾}{P_P}---\left(1\right)$

P′_PFor postrotational photogrammetric some cloud coordinate.Wherein, α₁, α₂It is respectivelyWithAt xoy plane inner projection and X-axis angle；β₁, β₂It is respectivelyWithWith Z axis angle.

Step 6: in some cloud after the conversion, select another to corresponding point a_j、b_jIf the vector of barycenter to two point is respectivelyWithNoteBy photogrammetric some cloud P '_PRotate around coordinate axes so thatWithTwo vector direction overlap.

$P_P^{\′\′}=R_y^{-1}(-{\mathrm{\β}}_2)R_z^{-1}(-{\mathrm{\α}}_2)R_z\left(\mathrm{\θ}\right)R_y(-{\mathrm{\β}}_2)R_z(-{\mathrm{\α}}_2)P_P^{\′}---\left(2\right)$

P″_PFor postrotational photogrammetric some cloud coordinate.Wherein, θ isWithBetween angle.

By formula (1) with formula (2) can be with abbreviation:

$P_P^{\′\′}=R_y^{-1}(-{\mathrm{\β}}_2)R_z^{-1}(-{\mathrm{\α}}_2)R_z\left(\mathrm{\θ}\right)R_y(-{\mathrm{\β}}_1)R_z(-{\mathrm{\α}}_1)\stackrel{\‾}{P_P}$

Step 7: now, the barycenter of two some clouds is completely superposed, and in two some clouds, other points substantially overlap.With photogrammetric some cloud P "_PIn each point coordinates replace laser tracker point cloudIn each point coordinates.To a cloud P "_PCarry out inverse barycenterization to process, i.e. can get revised maximal end point cloud coordinate P '_L1。

P′_L1=P "_P+ρ_L1

Step 8: in order to improve the precision of geometric figure modification method, it is possible to use in two groups of some clouds, N group corresponding point carry out a corrected Calculation respectively, tries to achieve the revised data of N group, calculates the meansigma methods of N group data as last correction result.

Select a respectively_i、b_i(i=1,2 ..., n) as corresponding point so that often group barycenter the most once overlaps with the vector direction of corresponding point, reduces the round-off error in the direction.Repeat the above steps five, obtains the some cloud after the conversion of n group.Wherein, described in step 6 " another is to corresponding point a_j、b_j" selection have n-1 kind mode, if selecting all corresponding point to calculate respectively, n (n-1) secondary corrected Calculation will be carried out, computationally intensive and last correction result precision improves little.Therefore, in order to reduce amount of calculation, the present invention selects a_i+1、b_i+1(i=1,2 ..., n) calculate as corresponding point, repeat the above steps six.Repeating step 7, carry out inverse barycenterization and process, each point of some cloud after barycenter inverse to the n group obtained is averaged.It is demonstrated experimentally that the precision of the meansigma methods of N group data is higher than the precision only carrying out one group of data correction.

Step 9: repetition step 4, to step 8, carries out coordinate modification: by the P in step 4 to step 8 to the common point in erect-position B_L1Replace with P_L2, calculate according to identical method, obtain one group of some cloud P '_L2。

Step 10: utilize unit quaternion method to solve the transition matrix between two different erect-position laser trackers.

P′_L2=R (q^R)P′_L1+q^T

Wherein, R (q^R) and q^TFor utilizing the spin matrix and translation matrix that unit quaternion method tries to achieve.

$R\left(q^R\right)=\left[\begin{array}{ccc}{R}_{11}& R_{12}& R_{13}\\ R_{21}& R_{22}& R_{23}\\ R_{31}& R_{32}& R_{33}\end{array}\right]$

Wherein, q₀、q₁、q₂、q₃For unit quaternary number.

Step 11: so far, A, B two on erect-position Coordinate Conversion to the same coordinate system, can calculate according to formula such as general length, angles.

By above step, reach to improve laser tracker and turned the effect of station precision, solved laser tracker and measure the problem that large sized object time error is big.

Advantage

The present invention is directed to laser tracker multi-court position and turn the problem that when large-sized object is measured at station, precision is relatively low, it is proposed that the method turning station precision based on laser tracker in photogrammetric raising large scale space measurement.Due to portability and the high precision of Digital Photogrammetric System, there is higher precision relative to laser tracker in remotely measurement when close-in measurement common reference point.A kind of geometric figure coordinates compensation method is proposed simultaneously, the common point coordinate that the common point coordinate modification laser tracker measured by Digital Photogrammetric System is measured, calculating, by revised coordinate, the transformation matrix that precision is of a relatively high, improving so that turning station precision.The present invention, by turning station measuring basis chi and the plane of scanning motion, demonstrates the feasibility of the method.Test result indicate that, the method that the present invention proposes can improve the laser tracker precision when multi-court position turns station measurement larger object.

Accompanying drawing explanation

Fig. 1 is the result (as a example by five common points) after two common point point cloud barycenterization process, wherein a₁-a₅Represent the common point that laser tracker measurement obtains, b₁-b₅Represent the common point that laser tracker measurement obtains, ρ_LPRepresent the barycenter of two groups of common points.

Fig. 2 (a), (b) are corresponding point a_i、b_iSelection, andWithResult after the coincidence of direction, the same Fig. 1 of each point implication.

Fig. 3 (a), (b) are corresponding point a_j、b_jSelection, andWithThe result that two vectors overlap,Represent Representθ representsWithBetween angle, the same Fig. 1 of remaining each point implication.

Fig. 4 is common point cloud against the result after barycenter, ρ_LRepresent barycenter, the same Fig. 3 of remaining each point implication.

Fig. 5 (a), (b), (c), (d), (e) are to utilize N group corresponding point in two groups of some clouds to carry out the process of a corrected Calculation, the same Fig. 3 of each point implication respectively.

Fig. 6 the method for the invention flow chart.

Specific embodiments

Below in conjunction with accompanying drawing and example, the present invention is described in further detail.

For achieving the above object, the invention provides a kind of method turning station precision based on photogrammetric raising laser tracker, the equipment that the method uses includes: at least one laser tracker, for target object and the measurement of common point；At least one laser tracker switch board, is connected with laser tracker；At least one laser tracker target ball, measures target as laser tracker；One DV, for photogrammetric, carries out shooting photograph；Multiple photogrammetric target balls, as photogrammetry targets；Multiple target ball seats, are used for fixing two kinds of target balls；Multiple labelling points, are pasted onto near common point；At least one station meter, as photogrammetric calibration；At least one work station, is connected with laser tracker and processes photographs.

In equipment as above, wherein laser tracker both only can use one, carries out turning station and measures, multiple stage can be used again to measure at diverse location by the way of mobile laser tracker.Measurement video camera special during DV use is photogrammetric.Work station need installation kit contain connection, process software and the Photogrammetric Processing software supporting with laser tracker.Photogrammetric target ball is special target ball equal-sized with laser tracker.

A kind of method turning station precision based on photogrammetric raising laser tracker of the present invention, as shown in Figure 6, it is as follows that it is embodied as step:

Step one: install corresponding equipment, fixing common point.Laser tracker is used to measure target A at website A ' and common point.Record A ' and the measurement result of common point.If the coordinate set of n common point is: P_L1(a₁, a₂, a₃..., a_n).Target A ' any number of point can be comprised, put cloud, or the shape gone out by point, point-cloud fitting.Common point number have to be larger than three, and for ensureing accuracy, common point is distributed in multiple plane as far as possible, and each plane comprises the common point of some.

Step 2: use laser tracker to measure target B at website B ' and common point.Website B need to have certain distance with website A.Record B ' and the measurement result of common point.Target B ' any number of point can be comprised, put cloud, or the shape gone out by point, point-cloud fitting.If in this step, the coordinate set of n common point is: P_L2(a₁, a₂, a₃..., a_n)。

Step 3: use the coordinate of photogrammetric measurement common point.If coordinate set is P_P(b₁, b₂, b₃..., b_n)。

Step 4: owing to Digital Photogrammetric System and laser tracker system have the most independent coordinate system, it is impossible to directly revise common point measured value.Therefore a kind of method that the present invention proposes geometric figure correction.

The thought of geometric figure modification method is substantially: the common point cloud measured value under two different coordinates is all considered as rigid body, is rotated and translation by some row so that the barycenter of two some clouds is completely superposed, and in two some clouds, other points substantially overlap.Again with the measured value that the common point cloud measured value replacement precision that precision is higher is relatively low, can complete to revise.

To P_L1And P_PTwo some clouds carry out barycenter process:

$\stackrel{\‾}{P_{L1}}=P_{L1}-{\mathrm{\ρ}}_L$

$\stackrel{\‾}{P_P}=P_P-{\mathrm{\ρ}}_P$

WithIt is respectively the laser tracker measurement pointcloud coordinate after barycenterization processes and photogrammetric some cloud coordinate.Wherein,For laser tracker measurement pointcloud coordinate center of mass point；For photogrammetric some cloud coordinate center of mass point.

Now two some cloud barycenter overlap, and overlap with coordinate origin.Barycenter is designated as ρ_LP.Fig. 1 is as a example by five common points, it is shown that the result after two some cloud barycenterization process.

Step 5: in the some cloud after two barycenter, select a pair corresponding point a_i、b_iIf the vector of barycenter to two point is respectivelyWithBy photogrammetric some cloudRotate around coordinate axes so thatWithTwo vector direction overlap.

The spin matrix of some cloud rotation alpha counterclockwise about the z axis is:

$R_z\left(\mathrm{\α}\right)=\left[\begin{array}{ccc}cos\mathrm{\α}& sin\mathrm{\α}& 0\\ -sin\mathrm{\α}& cos\mathrm{\α}& 0\\ 0& 0& 1\end{array}\right]$

Point cloud around the spin matrix of Y-axis rotation β counterclockwise is:

$R_y\left(\mathrm{\β}\right)=\left[\begin{array}{ccc}cos\mathrm{\β}& 0& -sin\mathrm{\β}\\ 0& 1& 0\\ sin\mathrm{\β}& 0& \cos \mathrm{\β}\end{array}\right]$

Point cloudRotate around coordinate axes so thatWithThe spin matrix of two vector direction coincidences is represented by:

$P_p^{\′}=R_z^{-1}(-{\mathrm{\α}}_2)R_y^{-1}(-{\mathrm{\β}}_2)R_y(-{\mathrm{\β}}_1)R_z(-{\mathrm{\α}}_1)\stackrel{\‾}{P_P}---\left(1\right)$

P′_PFor postrotational photogrammetric some cloud coordinate.Wherein, α₁, α₂It is respectivelyWithAt xoy plane inner projection and X-axis angle；β₁, β₂It is respectivelyWithWith Z axis angle.

Fig. 2 is corresponding point a_i、b_iSelection, andWithResult after two vector direction coincidences.

Step 6: in some cloud after the conversion, select another to corresponding point a_j、b_jIf the vector of barycenter to two point is respectivelyWithNoteBy photogrammetric some cloud P '_PRotate around coordinate axes so thatWithTwo vector direction overlap.

$P_P^{\′\′}=R_y^{-1}(-{\mathrm{\β}}_2)R_z^{-1}(-{\mathrm{\α}}_2)R_z\left(\mathrm{\θ}\right)R_y(-{\mathrm{\β}}_2)R_z(-{\mathrm{\α}}_2)P_P^{\′}---\left(2\right)$

P″_PFor postrotational photogrammetric some cloud coordinate.Wherein, θ isWithBetween angle.

Fig. 3 shows corresponding point a_j、b_jSelection, andWithThe result that two vectors overlap.

By formula (1) with formula (2) can be with abbreviation:

$P_P^{\′\′}=R_y^{-1}(-{\mathrm{\β}}_2)R_z^{-1}(-{\mathrm{\α}}_2)R_z\left(\mathrm{\θ}\right)R_y(-{\mathrm{\β}}_1)R_z(-{\mathrm{\α}}_1)\stackrel{\‾}{P_P}$

Step 7: now, the barycenter of two some clouds is completely superposed, and in two some clouds, other points substantially overlap.With photogrammetric some cloud P "_PIn each point coordinates replace laser tracker point cloudIn each point coordinates.To a cloud P "_PCarry out inverse barycenterization to process, i.e. can get revised maximal end point cloud coordinate P '_L1.Inverse barycenter process is as shown in Figure 4.

P′_L1=P "_P+ρ_L1

Step 8: in order to improve the precision of geometric figure modification method, it is possible to use in two groups of some clouds, N group corresponding point carry out a corrected Calculation respectively, tries to achieve the revised data of N group, calculates the meansigma methods of N group data as last correction result.

Select a respectively_i、b_i(i=1,2 ..., n) as corresponding point so that often group barycenter the most once overlaps with the vector direction of corresponding point, reduces the round-off error in the direction.Repeat the above steps five, obtains the some cloud after the conversion of n group.Wherein, described in step 6 " another is to corresponding point a_j、b_j" selection have n-1 kind mode, if selecting all corresponding point to calculate respectively, n (n-1) secondary corrected Calculation will be carried out, computationally intensive and last correction result precision improves little.Therefore, in order to reduce amount of calculation, the present invention selects a_i+1、b_i+1(i=1,2 ..., n) calculate as corresponding point, repeat the above steps six.Repeating step 7, carry out inverse barycenterization and process, each point of some cloud after barycenter inverse to the n group obtained is averaged.It is demonstrated experimentally that the precision of the meansigma methods of N group data is higher than the precision only carrying out one group of data correction.

Fig. 5 is to utilize N group corresponding point in two groups of some clouds to carry out the process of a corrected Calculation respectively.

Step 9: repetition step 4, to step 8, carries out coordinate modification: by the P in step 4 to step 8 to the common point in erect-position B_L1Replace with P_L2, calculate according to identical method, obtain one group of some cloud P '_L2。

Step 10: utilize unit quaternion method to solve the transition matrix between two different erect-position laser trackers.

P′_L2=R (q^R)P′_L1+q^T

Wherein, R (q^R) and q^TFor utilizing the spin matrix and translation matrix that unit quaternion method tries to achieve.

$R\left(q^R\right)=\left[\begin{array}{ccc}{R}_{11}& R_{12}& R_{13}\\ R_{21}& R_{22}& R_{23}\\ R_{31}& R_{32}& R_{33}\end{array}\right]$

Wherein, q₀、q₁、q₂、q₃For unit quaternary number.

Step 11: so far, A, B two on erect-position Coordinate Conversion to the same coordinate system, can calculate according to formula such as general length, angles.

By above step, reach to improve laser tracker and turned the effect of station precision, solved laser tracker and measure the problem that large sized object time error is big.

Claims (1)

1. the method turning station precision based on photogrammetric raising laser tracker, it is characterised in that: implementation step is as follows:

Step one: install corresponding equipment, fixing common point；Laser tracker is used to measure target A at website A ' and common point, record A ' and the measurement result of common point；If the coordinate set of n common point is: P_L1(a₁, a₂, a₃..., a_n)；

Step 2: use laser tracker to measure target B at website B ' and common point；Website B need to have certain distance, record B ' and the measurement result of common point with website A；If in this step, the coordinate set of n common point is: P_L2(a₁, a₂, a₃..., a_n)；

Step 3: use the coordinate of photogrammetric measurement common point；If coordinate set is P_P(b₁, b₂, b₃..., b_n)；

Step 4: owing to Digital Photogrammetric System and laser tracker system have the most independent coordinate system, it is impossible to directly revise common point measured value, a kind of method that therefore present invention proposes geometric figure correction；

Geometric figure modification method is: the common point cloud measured value under two different coordinates is all considered as rigid body, is rotated and translation by some row so that the barycenter of two some clouds is completely superposed, and in two some clouds, other points overlap；Replace, with the common point cloud measured value that precision is high, the measured value that precision is low again, i.e. complete to revise；

To P_L1And P_PTwo some clouds carry out barycenter process:

$\stackrel{\‾}{P_{L1}}=P_{L1}-{\mathrm{\ρ}}_L$

$\stackrel{\‾}{P_P}=P_P-{\mathrm{\ρ}}_P$

WithIt is respectively the laser tracker measurement pointcloud coordinate after barycenterization processes and photogrammetric some cloud coordinate；Wherein,For laser tracker measurement pointcloud coordinate center of mass point；For photogrammetric some cloud coordinate center of mass point；

Now two some cloud barycenter overlap, and overlap with coordinate origin, and barycenter is designated as ρ_LP；

Step 5: in the some cloud after two barycenter, select a pair corresponding point a_i、b_iIf the vector of barycenter to two point is respectivelyWithBy photogrammetric some cloudRotate around coordinate axes so thatWithTwo vector direction overlap；

The spin matrix of some cloud rotation alpha counterclockwise about the z axis is:

$R_z\left(\mathrm{\α}\right)=\left[\begin{array}{ccc}\cos \mathrm{\α}& \sin \mathrm{\α}& 0\\ -\sin \mathrm{\α}& \cos \mathrm{\α}& 0\\ 0& 0& 1\end{array}\right]$

Point cloud around the spin matrix of Y-axis rotation β counterclockwise is:

$R_y\left(\mathrm{\β}\right)=\left[\begin{array}{ccc}\cos \mathrm{\β}& 0& -\sin \mathrm{\β}\\ 0& 1& 0\\ \sin \mathrm{\β}& 0& \cos \mathrm{\β}\end{array}\right]$

Point cloudRotate around coordinate axes so thatWithThe spin matrix of two vector direction coincidences is expressed as:

$P_p^{\′}=R_z^{-1}(-{\mathrm{\α}}_2)R_y^{-1}\left(-{\mathrm{\β}}_2\right)R_y(-{\mathrm{\β}}_1)R_z(-{\mathrm{\α}}_1)\stackrel{\‾}{P_p}---\left(1\right)$

P′_PFor postrotational photogrammetric some cloud coordinate, wherein, α₁, α₂It is respectivelyWithAt xoy plane inner projection and X-axis angle；β₁, β₂It is respectivelyWithWith Z axis angle；

Step 6: in some cloud after the conversion, select another to corresponding point a_j、b_jIf the vector of barycenter to two point is respectivelyWithNoteBy photogrammetric some cloud P '_PRotate around coordinate axes so thatWithTwo vector direction overlap；

$P_p^{\′\′}=R_y^{-1}(-{\mathrm{\β}}_2)R_z^{-1}\left(-{\mathrm{\α}}_2\right)R_z\left(\mathrm{\θ}\right)R_y(-{\mathrm{\β}}_2)R_z(-{\mathrm{\α}}_2)P_p^{\′}---\left(2\right)$

P″_PFor postrotational photogrammetric some cloud coordinate, wherein, θ isWithBetween angle；

By formula (1) with formula (2) abbreviation it is:

$P_p^{\′\′}=R_y^{-1}(-{\mathrm{\β}}_2)R_z^{-1}(-{\mathrm{\α}}_2)R_z\left(\mathrm{\θ}\right)R_y(-{\mathrm{\β}}_1)R_z(-{\mathrm{\α}}_1)\stackrel{\‾}{P_p}$

Step 7: now, the barycenter of two some clouds is completely superposed, and in two some clouds, other points overlap；With photogrammetric some cloud P "_PIn each point coordinates replace laser tracker point cloudIn each point coordinates, to a cloud P "_PCarry out inverse barycenterization to process, i.e. obtain revised maximal end point cloud coordinate P '_L1；

P′_L1=P "_P+ρ_L1；

Step 8: in order to improve the precision of geometric figure modification method, utilizes N group corresponding point in two groups of some clouds to carry out a corrected Calculation respectively, tries to achieve the revised data of N group, calculates the meansigma methods of N group data as last correction result；

Select a respectively_i、b_i, i=1,2 ..., n；As corresponding point so that often group barycenter the most once overlaps with the vector direction of corresponding point, reduces the round-off error in the direction；Repeat the above steps five, obtains the some cloud after the conversion of n group；Wherein, described in step 6 " another is to corresponding point a_j、b_j" selection have n-1 kind mode, if selecting all corresponding point to calculate respectively, n (n-1) secondary corrected Calculation will be carried out, computationally intensive and last correction result precision improves little, and therefore, in order to reduce amount of calculation, the present invention selects a_i+1、b_i+1, i=1,2 ..., n；Calculating as corresponding point, repeat the above steps six, repeat step 7, carry out inverse barycenterization and process, the point each point of cloud after barycenter inverse to the n group obtained is averaged；It is demonstrated experimentally that the precision of the meansigma methods of N group data is higher than the precision only carrying out one group of data correction；

Step 9: repetition step 4, to step 8, carries out coordinate modification: by the P in step 4 to step 8 to the common point in erect-position B_L1Replace with P_L2, calculate according to identical method, obtain one group of some cloud P '_L2；

Step 10: utilize unit quaternion method to solve the transition matrix between two different erect-position laser trackers；

$P_{L2}^{\′}=R\left(q^R\right)P_{L1}^{\′}+q^T$

Wherein, R (q^R) and q^TFor utilizing the spin matrix and translation matrix that unit quaternion method tries to achieve；

$R\left(q^R\right)=\left[\begin{array}{ccc}{R}_{11}& R_{12}& R_{13}\\ R_{21}& R_{22}& R_{23}\\ R_{31}& R_{32}& R_{33}\end{array}\right]$

Wherein,

$\begin{array}{c}{R}_{11}=q_0^2+q_1^2-q_2^2-q_3^2;R_{12}=2\left(q_1{q}_2-q_0{q}_3\right);R_{13}=2\left(q_1{q}_3+q_0{q}_2\right);R_{21}=\\ 2\left(q_1{q}_2+q_0{q}_3\right);R_{22}=q_0^2-q_1^2+q_2^2-q_3^2;R_{23}=2\left(q_2{q}_3-q_0{q}_1\right);R_{31}=2(q_1{q}_3-\\ q_0{q}_2);R_{32}=2(q_2{q}_3+q_0{q}_1);R_{33}=q_0^2-q_1^2-q_2^2+q_3^2\end{array}$

q₀、q₁、q₂、q₃For unit quaternary number；

Step 11: so far, A, B two on erect-position Coordinate Conversion to the same coordinate system, calculate according to general length, angle formula；

By above step, reach to improve laser tracker and turned the effect of station precision, solved laser tracker and measure the problem that large sized object time error is big.