CN112033286B - Measuring method of structure six-degree-of-freedom motion measuring system based on binocular vision - Google Patents
Measuring method of structure six-degree-of-freedom motion measuring system based on binocular vision Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/02—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness
- G01B11/028—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness by measuring lateral position of a boundary of the object
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/26—Measuring arrangements characterised by the use of optical techniques for measuring angles or tapers; for testing the alignment of axes
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/02—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness
- G01B21/04—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness by measuring coordinates of points
- G01B21/042—Calibration or calibration artifacts
Abstract
The invention discloses a binocular vision-based structural six-degree-of-freedom motion measurement system and a measurement method thereof. Step 1: pasting a round target on the surface of the structure, and arranging at least three measuring points by taking the center of the round target as the measuring points; step 2: calibrating the vision measuring system by using a checkerboard calibration method; and step 3: capturing target motion with two cameras; and 4, step 4: carrying out image point coordinate optimization on the target motion captured in the step 3; and 5: and finishing the six-degree-of-freedom measurement of the structure. The method aims to solve the problems of inconvenient technical operation, low measurement precision, higher cost, low applicability, complex operation and low engineering practicability when the traditional measurement method is used for processing six-degree-of-freedom motion measurement.
Description
Technical Field
The invention belongs to the technical field of structure six-degree-of-freedom motion measurement; in particular to a measuring method of a structure six-freedom-degree motion measuring system based on binocular vision.
Background
Currently, the measurement methods can be classified into contact measurement and non-contact measurement. The measuring methods such as the pull-wire type displacement meter, the dial indicator, the linear variable differential pressure type transducer and the like are common contact measuring methods which have high precision and high reliability, but the methods have the defects of troublesome sensor arrangement, low efficiency and great influence on fields and environment. When the measurement conditions are severe, such as severe deformation of the members, and in an environment with high temperature or severe temperature change, the accuracy of the touch sensor is difficult to ensure.
The non-contact measurement is not in direct contact with a component, has small influence on the structure, has high measurement efficiency, can stably work under complex conditions and provides higher precision, and is a hotspot concerned by students. The computer vision measurement method is an important non-contact measurement method. The vision measurement method can provide abundant measurement information, realize real-time high-precision measurement and is simple to operate. Nowadays, computer technology and camera technology are increasingly used in the field of surveying.
When a wave test is carried out, six-degree-of-freedom motion which needs to be measured, namely three-dimensional displacement and three-dimensional corner of a structure are measured. The six-degree-of-freedom motion of the structure is difficult to obtain by the traditional measuring method. In addition, in the test, the structure needs to be arranged on the water surface, and the contact type sensor is difficult to arrange.
Disclosure of Invention
The invention aims to solve the problems of inconvenient technical operation, low measurement precision, higher cost, low applicability, complex operation and low engineering practicability of the traditional measurement method when the traditional measurement method is used for processing the six-degree-of-freedom motion measurement.
The invention is realized by the following technical scheme:
a measuring method of a binocular vision-based structure six-degree-of-freedom motion measuring system comprises two cameras and a computer, wherein the two cameras are connected with the computer through a network cable, the computer is connected with a synchronous trigger, and the synchronous trigger is controlled by the computer to synchronously send acquisition signals to the cameras;
the two cameras are arranged on a tripod, so that the centers of the pictures of the two cameras are aligned with the structure to be measured.
A measuring method of a structure six-degree-of-freedom movement measuring system based on binocular vision comprises the following steps:
step 1: pasting a circular target on the surface of the structure, and arranging at least three measuring points by taking the center of the circular target as a measuring point; two cameras are arranged in front of the measuring point, the two cameras are respectively arranged in the left front of the measuring point and the right front of the measuring point, and the measuring point is in the visual fields of the left camera and the right camera;
and 2, step: calibrating the vision measuring system by using a checkerboard calibration method; arranging the chessboard pattern calibration plate in a view field, and selecting a plane where the chessboard pattern calibration plate is positioned as a structure reference plane when the calibration plate is tightly attached to the structure surface;
and step 3: capturing target motion with two cameras; collecting a moving image, completing the identification of the circle target in the first image, tracking and capturing the motion of the circle target in the motion process, and obtaining pixel coordinates of a measuring point on the left camera image and the right camera image;
and 4, step 4: carrying out image point coordinate optimization on the target motion captured in the step 3; calculating corresponding polar lines of matched image points of the left camera and the right camera according to the calibration result, and optimizing the coordinates of the image points by a polar line equation to obtain optimized coordinates of the image points;
and 5: completing the six-degree-of-freedom measurement of the structure; and calculating the three-dimensional displacement of the measuring points by the optimized image point coordinates, and selecting three measuring points to calculate the three-dimensional corner of the structure to finish the six-degree-of-freedom measurement of the structure.
Further, the step 2 is specifically to calculate an internal parameter matrix a of a left camera of the vision measuring system from the acquired calibration imagelInner parameter matrix A of the right-hand camerar(ii) a Left camera reference frame to right camera reference frame rotation matrix Rl2rAnd a translation vector Tl2r(ii) a Converting the structural reference surface into a rotation matrix R and a translation vector T of a left camera reference system;
Al、Ar、Rl2rand Tl2rThe expression of (a) is:
wherein the content of the first and second substances,the equivalent focal lengths of the left camera on the u and v axes of the image plane,the equivalent focal lengths of the right camera on the u and v axes respectively, (u)l,vl) And (u)r,vr) The coordinates of the left camera principal point and the right camera principal point in the image plane, ri(i 1,2.., 9) is a rotation matrix parameter from the left camera reference frame to the right camera reference frame, tx,ty,tzThe parameters of the translation matrix from the left camera reference frame to the right camera reference frame are respectively.
Further, the specific process of capturing the target motion in step 3 is as follows:
step 3.1: selecting a point area in a first image collected by a left camera, and binarizing the image by using a Niblack algorithm;
step 3.2: calculating the equivalent eccentricity of a closed area in the binary image, and comparing the equivalent eccentricity with a set threshold value;
step 3.3: extracting sub-pixel edges of the circular target by adopting a Canny-Zernike algorithm, fitting the extracted sub-pixel edges to obtain an elliptic equation, calculating by using the elliptic equation to obtain an elliptic center coordinate, and taking the elliptic center coordinate as an initial coordinate of a left camera measuring point;
step 3.4: inputting the displacement of the predicted measuring points to obtain a search subarea of each measuring point;
step 3.5: completing the time sequence matching of the images acquired by the right camera by using the same method as the steps 3.1 to 3.4, and completing the matching of the images acquired by the left camera and the right camera according to the measuring point numbers; thereby obtaining the coordinates p of the matched image points of the left camera image and the right camera imagel、pr。
Further, the specific process of step 3.5 is to acquire the internal parameter matrix a of the left cameralInner parameter matrix A of the right-hand camerarLeft camera to right camera rotation matrix Rl2rAnd a translation vector Tl2rA fundamental matrix F of the camera is calculated,
F=Ar -T[Tl2r]×Rl2rAl -1
from the basic matrix F and the coordinates p of the matching image pointsl、prSolving the equation l corresponding to the polar linel、lr:
ll=Fpr
lr=Fpl
Equation l from polar linel、lrCoordinates p with the image pointl、prDetermining the distance d from the image point to the epipolar linelAnd dr(ii) a The vertical line of the polar line is taken as the image point, and the direction vector pointing to the polar line from the image point is Dl,DrCoordinates p 'of post-optimization image points'l、p′rComprises the following steps:
further, the step 5 structure six-degree-of-freedom measurement method specifically comprises the following processes: firstly, calculating the normalized coordinate X of the optimized image pointnl=[xnl,ynl]T,Xnr=[xnr,ynr]T:
Then, three-dimensional coordinates X ═ X [ X ] of the measuring points in the reference system of the left camera are obtainedw,yw,zw]T:
To convert the coordinate system to the structural reference surface, the three-dimensional coordinates P of the final measurement point are obtained:
P=R-1(X-T)
after the three-dimensional coordinates of each measuring point are obtained, three measuring points are selected and named as measuring point 1, measuring point 2 and measuring point 3, and the initial three-dimensional coordinates of the three measuring points are obtained and are Pi(i is 1,2,3), and the three-dimensional coordinate at a certain moment in the motion process is Pi' (i-1, 2, 3); and calculating the three-dimensional displacement and the three-dimensional corner of the structure by taking the measuring point 2 as a rotation center. Three-dimensional displacement and three-dimensional rotation angles are expressed by using a rotation matrix r and a translation vector t;
this gives:
t=P′2-P2
P′i=r·Pi+t
further, the following are obtained:
[P′1-t,P′2-t,P′3-t]=r·[P1,P2,P3]
the rotation matrix r can be solved by the above formula, and the rotation matrix r is decomposed into rolling alpha, pitching beta and yawing gamma, thereby obtaining the six-degree-of-freedom measurement result of the structure.
The invention has the beneficial effects that:
by using the vision measurement method, the vision measurement of the six-degree-of-freedom motion of the structure is effectively completed. The initial recognition and tracking of the structure six-freedom-degree motion vision measurement system on the circular target are realized, the sub-pixel coordinates of the center of the circular target are obtained, and the high-precision measurement requirement is met.
The last step in the visual measurement is the three-dimensional reconstruction. The accuracy of the three-dimensional reconstruction directly affects the accuracy of the measurement. Because errors are accumulated in the processes of calibration, image target positioning and the like, how to reasonably eliminate the errors is the key content for improving the three-dimensional measurement precision of the space point coordinates. The invention optimizes the coordinates of the image points before three-dimensional reconstruction, and can effectively improve the measurement precision.
Drawings
FIG. 1 is a schematic diagram of the hardware architecture of the system of the present invention.
FIG. 2 is a diagram of a measurement software interface according to the present invention.
FIG. 3 is a flow chart of the measurement software of the present invention.
FIG. 4 is a graph of the recognition results of a circular target in a first image of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
A measuring method of a binocular vision-based structure six-degree-of-freedom motion measuring system comprises two cameras and a computer, wherein the two cameras are connected with the computer through a network cable, the computer is connected with a synchronous trigger, and the synchronous trigger is controlled by the computer to synchronously send acquisition signals to the cameras;
the two cameras are arranged on a tripod, and the postures of the cameras are adjusted, so that the picture centers of the two cameras are aligned to the structure to be detected.
A measuring method of a structure six-degree-of-freedom movement measuring system based on binocular vision comprises the following steps:
step 1: pasting a round target on the surface of the structure, and arranging at least three measuring points by taking the center of the round target as the measuring points; two cameras are arranged in front of the measuring point, the two cameras are respectively arranged in the left front of the measuring point and the right front of the measuring point, and the measuring point is in the visual fields of the left camera and the right camera;
step 2: calibrating the vision measuring system by using a checkerboard calibration method; arranging the checkerboard calibration plate in a view field, changing the posture of the checkerboard calibration plate, collecting a plurality of images for camera calibration by using a left camera and a right camera, and selecting a plane of the checkerboard calibration plate as a structure reference surface when the calibration plate is tightly attached to the structure surface;
and step 3: capturing target motion with two cameras; collecting a moving image, completing the identification of the circle target in the first image, tracking and capturing the motion of the circle target in the motion process, and obtaining pixel coordinates of a measuring point on the left camera image and the right camera image;
and 4, step 4: carrying out image point coordinate optimization on the target motion captured in the step 3; calculating corresponding polar lines of matched image points of the left camera and the right camera according to the calibration result, and optimizing the coordinates of the image points by a polar line equation to obtain optimized coordinates of the image points;
and 5: completing the six-degree-of-freedom measurement of the structure; and calculating the three-dimensional displacement of the measuring points by the optimized image point coordinates, and selecting three measuring points to calculate the three-dimensional corner of the structure to finish the six-degree-of-freedom measurement of the structure.
Further, the step 2 is specifically to calculate an internal parameter matrix a of a left camera of the vision measuring system from the acquired calibration imagelInner parameter matrix A of the right-hand camerar(ii) a Left camera reference frame to right camera reference frame rotation matrix Rl2rAnd a translation vector Tl2r(ii) a Converting the structural reference surface into a rotation matrix R and a translation vector T of a left camera reference system;
Al、Ar、Rl2rand Tl2rThe expression of (a) is:
further, the specific process of capturing the target motion in step 3, namely realizing the circular target tracking identification, is as follows:
step 3.1: selecting a point area in a first image collected by a left camera, and binarizing the image by using a Niblack algorithm;
step 3.2: calculating the equivalent eccentricity of a closed area in the binary image, and comparing the equivalent eccentricity with a set threshold value; if the closed area has the same area distance with an ellipse, the eccentricity of the ellipse is the equivalent eccentricity of the ellipse of the closed area. If the equivalent eccentricity of the closed area is smaller than a set threshold value, rejecting the area; if the equivalent eccentricity of the closed area is greater than a set threshold value, the closed area is considered as a circular target image;
step 3.3: extracting sub-pixel edges of the circular target by adopting a Canny-Zernike algorithm, fitting the extracted sub-pixel edges to obtain an elliptic equation, calculating by using the elliptic equation to obtain an elliptic center coordinate, and taking the elliptic center coordinate as an initial coordinate of a left camera measuring point;
step 3.4: inputting the displacement of the predicted measuring points to obtain a search subarea of each measuring point; the timing sequence matching of the images collected by the left camera is completed by using an IC-GN algorithm in the search subarea;
step 3.5: completing the time sequence matching of the images acquired by the right camera by using the same method as the steps from 3.1 to 3.4, and completing the matching of the images acquired by the left camera and the right camera according to the measuring point numbers; thereby obtaining the coordinates p of the matched image points of the left camera image and the right camera imagel、pr。
Further, the specific process of step 3.5 is to acquire the internal parameter matrix a of the left cameralInner parameter matrix A of the right-hand camerarLeft camera to right camera rotation matrix Rl2rAnd a translation vector Tl2rA fundamental matrix F of the camera is calculated,
F=Ar -T[Tl2r]×Rl2rAl -1
from the basic matrix F and the coordinates p of the matching image pointsl、prSolving the equation l corresponding to the polar linel、lr:
ll=Fpr
lr=Fpl
Equation l from polar linel、lrCoordinates p with the image pointl、prDetermining the distance d from the image point to the epipolar linelAnd dr(ii) a The cross-point is taken as a perpendicular to the polar line, and the direction vector from the image point to the polar line is Dl,DrCoordinates p 'of post-optimization image points'l、p′rComprises the following steps:
further, the step 5 structure six-degree-of-freedom measurement method specifically comprises the following processes: firstly, calculating the normalized coordinate X of the optimized image pointnl=[xnl,ynl]T,Xnr=[xnr,ynr]T:
Then, three-dimensional coordinates X ═ X [ X ] of the measuring points in the reference system of the left camera is obtainedw,yw,zw]T:
To convert the coordinate system to the structural reference surface, the three-dimensional coordinates P of the final measurement point are obtained:
P=R-1(X-T)
after the three-dimensional coordinates of each measuring point are obtained, three measuring points are selected and named as measuring point 1, measuring point 2 and measuring point 3, and the initial three-dimensional coordinates of the three measuring points are obtained and are Pi(i is 1,2,3), and the three-dimensional coordinate at a certain moment in the motion process is Pi' (i-1, 2, 3); and calculating the three-dimensional displacement and the three-dimensional corner of the structure by taking the measuring point 2 as a rotation center. Three-dimensional displacement and three-dimensional rotation angles are expressed by using a rotation matrix r and a translation vector t;
this gives:
t=P′2-P2
P′i=r·Pi+t
further obtaining:
[P′1-t,P′2-t,P′3-t]=r·[P1,P2,P3]
the rotation matrix r can be solved by the above formula, and the rotation matrix r is decomposed into rolling alpha, pitching beta and yawing gamma, thereby obtaining the six-degree-of-freedom measurement result of the structure.
The system uses a CCD camera, model AVTGX1050, using the GigEVision interface protocol. In order to be suitable for different measuring ranges, an M3Z1228C-MP series zoom lens and an LM5JCM series fixed focus lens are adopted. The image data of the camera is connected with a gigabit network card through an RJ-45 network cable interface, and the model of the gigabit network card is PCIe-PoE 74. The PCIe-PoE74 acquisition card manufacturer is a company of Leishachi technology, and can be connected with 4 gigabit network cables simultaneously to meet the bandwidth of data acquired by two cameras at high speed. The computer model is a Daire OptiPlex7070 commercial desktop computer, the CPU dominant frequency of the computer is 3GHz, and the memory size is 32G. The image acquisition card is connected with the computer through a PCIe interface on a computer mainboard.
The software interface for measuring the six-degree-of-freedom movement of the structure is shown in figure 2. And controlling the camera to complete six-freedom-degree motion measurement by using measurement software. The structure six-freedom motion vision measurement software can realize the functions of image acquisition, image real-time display and storage, structure six-freedom motion analysis, calculation result output and the like.
The structure six-degree-of-freedom motion vision measurement flow is shown in figure 3. According to the measurement requirement, the structure six-freedom-degree motion vision measurement software is mainly divided into four modules which are respectively image acquisition, camera calibration, target tracking and result output. Corresponding operation buttons and input boxes are arranged under each module, and a user can input corresponding parameters according to actual conditions to obtain a six-freedom-movement measuring result.
Claims (4)
1. A measuring method of a structure six-degree-of-freedom motion measuring system based on binocular vision is characterized in that the measuring system comprises two cameras and a computer, the two cameras are connected with the computer through a network cable, the computer is connected with a synchronous trigger, and the synchronous trigger is controlled by the computer to synchronously send acquisition signals to the cameras;
the two cameras are arranged on a tripod, so that the picture centers of the two cameras are aligned to the structure to be detected;
the configuration method of the measuring system comprises the following steps:
step 1: pasting a round target on the surface of the structure, and arranging at least three measuring points by taking the center of the round target as the measuring points; two cameras are arranged in front of the measuring point, the two cameras are respectively arranged in the left front of the measuring point and the right front of the measuring point, and the measuring point is in the visual fields of the left camera and the right camera;
step 2: calibrating the vision measuring system by using a checkerboard calibration method; arranging the chessboard pattern calibration plate in a view field, and selecting a plane where the chessboard pattern calibration plate is positioned as a structure reference surface when the calibration plate is tightly attached to the structure surface;
and step 3: capturing target motion with two cameras; collecting a moving image, completing the identification of the circle target in the first image, tracking and capturing the motion of the circle target in the motion process, and obtaining pixel coordinates of a measuring point on the left camera image and the right camera image;
and 4, step 4: carrying out image point coordinate optimization on the target motion captured in the step 3; calculating corresponding polar lines of matched image points of the left camera and the right camera according to the calibration result, and optimizing the coordinates of the image points by a polar line equation to obtain optimized coordinates of the image points;
the specific process of the step 4 is that an internal parameter matrix A of the left camera is acquiredlInner parameter matrix A of the right-hand camerarLeft-hand camera to right-hand camera rotation matrix Rl2rAnd a translation vector Tl2rCalculating to obtain a basic matrix F, F ═ A of the camerar -T[Tl2r]×Rl2rAl -1
From the basic matrix F and the coordinates p of the matching image pointsl、prSolving the equation l corresponding to the polar linel、lr:
ll=Fpr
lr=Fpl
Equation l from polar linel、lrCoordinates p with the image pointl、prDetermining the distance d from the image point to the epipolar linelAnd dr(ii) a The left camera and the right camera cross the image point to be taken as the vertical line of the polar line, and the direction vector pointing to the polar line from the image point is Dl,DrCoordinates p 'of post-optimization image points'l、p′rComprises the following steps:
and 5: completing the six-degree-of-freedom measurement of the structure; and calculating the three-dimensional displacement of the measuring points by the optimized image point coordinates, and selecting three measuring points to calculate the three-dimensional corner of the structure to finish the six-degree-of-freedom measurement of the structure.
2. The measurement method according to claim 1, wherein step 2 is to calculate an intrinsic parameter matrix A of a left camera of the vision measurement system from the acquired calibration imagelInner parameter matrix A of the right-hand camerar(ii) a Left camera reference frame rotationRotation matrix R transformed to the reference frame of the right cameral2rAnd a translation vector Tl2r(ii) a Converting the structural reference surface into a rotation matrix R and a translation vector T of a left camera reference system;
Al、Ar、Rl2rand Tl2rThe expression of (c) is:
wherein the content of the first and second substances,respectively equivalent focal lengths of the left camera on the u and v axes of an image plane,the equivalent focal lengths of the right camera on the u and v axes respectively, (u)l,vl) And (u)r,vr) The coordinates of the left camera principal point and the right camera principal point in the image plane, ri(i 1,2.., 9) is a rotation matrix parameter from the left camera reference frame to the right camera reference frame, tx,ty,tzThe parameters of the translation matrix from the left camera reference frame to the right camera reference frame are respectively.
3. The measurement method according to claim 1, wherein the step 3 of capturing the target motion comprises the following specific processes:
step 3.1: selecting a point area in a first image collected by a left camera, and binarizing the image by using a Niblack algorithm;
step 3.2: calculating the equivalent eccentricity of a closed area in the binary image, and comparing the equivalent eccentricity with a set threshold value;
step 3.3: extracting sub-pixel edges of the circular target by adopting a Canny-Zernike algorithm, fitting the extracted sub-pixel edges to obtain an elliptic equation, calculating by using the elliptic equation to obtain an elliptic center coordinate, and taking the elliptic center coordinate as an initial coordinate of a left camera measuring point;
step 3.4: inputting the displacement of the predicted measuring points to obtain a search subarea of each measuring point;
step 3.5: completing the time sequence matching of the images acquired by the right camera by using the same method as the steps from 3.1 to 3.4, and completing the matching of the images acquired by the left camera and the right camera according to the measuring point numbers; thereby obtaining the coordinates p of the matched image points of the left camera image and the right camera imagel、pr。
4. The measurement method according to claim 1, wherein the step 5 structure six-degree-of-freedom measurement method comprises the following specific processes: firstly, calculating the normalized coordinate X of the optimized image pointnl=[xnl,ynl]T,Xnr=[xnr,ynr]T:
Then, three-dimensional coordinates X ═ X [ X ] of the measuring points in the reference system of the left camera is obtainedw,yw,zw]T:
To convert the coordinate system to the structural reference surface, the three-dimensional coordinates P of the final measurement point are obtained:
P=R-1(X-T)
after the three-dimensional coordinates of each measuring point are obtained, three measuring points are selected and named as measuring point 1, measuring point 2 and measuring point 3, and the initial three-dimensional coordinates of the three measuring points are obtained and are Pi(i is 1,2,3), and the three-dimensional coordinate at a certain moment in the motion process is Pi' (i ═ 1,2, 3); to be provided withMeasuring point 2 is a rotation center, three-dimensional displacement and three-dimensional rotation angle of the structure are calculated by the three measuring points, and the three-dimensional displacement and the three-dimensional rotation angle are expressed by using a rotation matrix r and a translation vector t;
this gives:
t=P′2-P2
P′i=r·Pi+t
further obtaining:
[P′1-t,P′2-t,P′3-t]=r·[P1,P2,P3]
the rotation matrix r can be solved by the above formula, and the rotation matrix r is decomposed into rolling alpha, pitching beta and yawing gamma, thereby obtaining the six-degree-of-freedom measurement result of the structure.
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