CN113916128A - Method for improving precision based on optical pen type vision measurement system - Google Patents
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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
- G01B11/002—Measuring arrangements characterised by the use of optical techniques for measuring two or more coordinates
- G01B11/005—Measuring arrangements characterised by the use of optical techniques for measuring two or more coordinates coordinate measuring machines
Abstract
The invention provides a method for improving precision based on an optical pen type vision measuring system. The method comprises the following steps: a measuring system is set up, an optical pen probe is used for contacting a measured point, and images within a threshold range are collected through a CCD camera; solving the two-dimensional coordinates of the characteristic points in an image coordinate system and the three-dimensional coordinates of the characteristic points in a light pen coordinate system; solving a rotation matrix and a translation matrix between the light pen coordinate system and the camera coordinate system; establishing an equation of each characteristic point through an R, T matrix of the picture to obtain n groups of effective data; solving the distance from the center of the measuring head to the characteristic point; and fitting an equation of the sphere in a coordinate system to obtain the actual position of the measuring head center. The invention utilizes the combination methods of spherical surface fitting, generalized inverse method of least square method, position invariant principle and the like to calculate the actual position of the optical pen measuring head within the obtained threshold range, thereby improving the measuring precision and portability of the optical pen.
Description
Technical Field
The invention relates to a method for improving precision based on an optical pen type vision measurement system, and belongs to the technical field of vision measurement.
Background
With the continuous development of the human society, industrial measurement becomes an extremely important link in the industrial development process, and with the development of automobile production and aerospace industry, the work related to workpiece measurement is more and more, and the requirement on the measurement accuracy of the workpiece is more and more strict. At present, the domestic mainstream measuring technology cannot keep up with the steps required by measurement. Traditional three-Coordinate Measuring Machines (CMMs) have not been able to meet some of the industrial field on-line measurement requirements due to their large size and limited measurement range; indoor GPS, laser radar, optical laser tracker and other common measuring equipment have the defects of low measuring efficiency, high cost, complex configuration, poor portability and the like, and influence the development of modern measuring technology. Therefore, a machine vision measuring system is developed, the vision measuring system is mainly based on computer vision, comprises a measuring technology, an electronic technology and an image processing technology, and creates a brand-new measuring structure frame, so that the measuring limitation is reduced, the measurement is more flexible and convenient, the geometric dimension of a workpiece can be measured at multiple angles, and good reverberation is caused in the modern manufacturing fields of aerospace, automobiles and the like. The optical pen type three-coordinate measuring system based on machine vision has the advantages of small volume, convenience in carrying, flexibility in assembly according to field measurement requirements, and good applicability, so that the optical pen type three-coordinate measuring system is more and more widely applied in China, and therefore, the improvement of the precision has important significance in the development of the optical pen type three-coordinate measuring system and the development of modern measuring technology.
The actual coordinates of the center of the light pen probe in the coordinate system directly affect the measurement accuracy of the three-coordinate measurement system. In practical application, the center of the stylus probe is mostly a theoretical value when the stylus is processed, and the processing error of the stylus can directly affect the measurement precision. In the measurement process, due to different measurement objects, such as a plurality of deep holes, grooves and the like, the optical pen probe needs to be replaced for measurement, even if the same optical pen probe is used, the coordinate changes slightly due to different forces during multiple installation, and therefore self-calibration of the center of the probe is important. In addition, in the working process of the three-coordinate measuring system, a reprojection error is inevitable, and the SMSF method can balance a part of errors, so that the experimental result is more accurate.
Disclosure of Invention
The invention aims to provide a method for improving the precision based on an optical pen type vision measuring system, which reduces the measuring error and improves the measuring precision.
In order to achieve the purpose, the invention is realized by the following technical scheme:
a method for improving accuracy based on an optical pen type vision measuring system is characterized by comprising the following steps:
1) a measuring system is set up, a light pen probe is used for contacting a measured point, and an image is collected through a CCD camera;
2) solving the two-dimensional coordinates of the characteristic points in an image coordinate system and the three-dimensional coordinates of the characteristic points in a light pen coordinate system;
3) solving a rotation matrix and a translation matrix between the light pen coordinate system and the camera coordinate system; establishing a camera coordinate system (u, v, w), a light pen coordinate system (X, Y, z) and a pixel coordinate system (X, Y); establishing a relation between a light pen coordinate system and a camera coordinate system:
wherein R is a rotation matrix, and T is a translation matrix, so as to complete the conversion between the light pen coordinate system and the camera coordinate system; establishing a relation between a camera coordinate system and a pixel coordinate system:
converting a camera coordinate system and a pixel coordinate system by an equation (3); wherein f is the focal length of the lens,
4) establishing an equation of each characteristic point through an R, T matrix of the picture to obtain n groups of effective data;
5) solving the distance from the center of the measuring head to the characteristic point;
6) and fitting an equation of the sphere in a coordinate system to obtain the actual position of the measuring head center.
Preferably, the equation establishing process of the feature points in step 4 is as follows:
1) establishing a linear equation of the jth characteristic point in the image:
sj＝r7xj+r8yj+r9zj+tz＝tz(a9xj+a10yj+a11zj+1)＝tzζj (5)
wherein
Equation (5) is equivalent to:
2) a1, a2,. a11 is obtained by using a least square method, and the formula is as follows:
3) the initial value of R, T is obtained by solving the linear equation system, and the parameters of equation 6 and 7 are separated to obtain the following equation:
4) solving for an optimal solution G, R, T for the image, according to the following iterative equation;
wherein:
B＝(fa1 fb1 fa2 fb2 … faN fbN fp1 … fp6)T (14)，
in the formula rn(n ═ 1,2,3.. 9) is a parameter of the rotation matrix R, anConverting the contents of the formula for R, T, wherein
k is the number of iterations;
5) r, T, establishing a characteristic equation of each characteristic point,
wherein i is the ith image, and j is the jth characteristic point;
and the distance between the jth characteristic point of the ith image and the center of the measuring head.
Preferably, the specific steps of step 6 are:
1) calculating the actual position of the measuring head center coordinate by using 8n coordinates of n groups of pictures of the five fitted spheres to obtain a residual error formula:
2) respectively calculating partial derivatives:
3) and substituting the coordinate values, making the partial derivative result be a zero structural equation set, and solving to obtain the actual position of the center coordinate of the measuring head.
Preferably, n is more than or equal to 3 in the step 4.
The invention has the advantages that: according to the invention, by means of the spherical surface fitting, the generalized inverse method of the least square method and the position invariant principle, the low-precision measurement which only can use the theoretical value of the mechanical structure is eliminated, a part of errors in the measurement process are balanced, the precision of the measurement result is improved to 0.05mm compared with the data which is not self-calibrated after the mechanical structure is measured by a three-coordinate measuring machine, and the relative error is accurate to 0.001 mm. The measuring precision of the three-coordinate measuring system is greatly improved, high-precision measurement becomes possible, and the three-coordinate measuring system can be more widely applied to the fields of automobiles, aviation and the like which need high-precision measurement.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention.
FIG. 1 is a schematic view of the flow structure of the present invention.
FIG. 2 is a schematic diagram of characteristic point labels of the present invention.
FIG. 3 is a schematic diagram of the spherical fitting of the present invention.
FIG. 4 is a schematic view of a measurement process according to the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the 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.
1) A measuring system is set up, an optical pen probe is used for contacting a measured point, and images within a threshold range are collected through a CCD camera;
2) solving the two-dimensional coordinates of the characteristic points in an image coordinate system and the three-dimensional coordinates of the characteristic points in a light pen coordinate system;
3) solving a rotation matrix and a translation matrix between the light pen coordinate system and the camera coordinate system;
establishing a camera coordinate system (u, v, w), a light pen coordinate system (X, Y, z), a pixel coordinate system (X, Y)
And R is a rotation matrix, and T is a translation matrix, so that the conversion between the light pen coordinate system and the camera coordinate system is completed.
The camera coordinate system and the pixel coordinate system have a relationship, coordinates in the corresponding camera coordinate system can be obtained by inputting the coordinates in the pixel coordinate system, and the conversion between the camera coordinate system and the pixel coordinate system is performed by the formula (3).
4) Establishing an equation of each characteristic point through an R, T matrix of the picture to obtain n groups of effective data; the j-th feature point in an image has the following relation, wherein only R, T is a variable, and the combination of the formula (1) and the formula (3) is substituted into the formula (4)
Xj＝(Uj-Xc)dx-δx,Yj＝(Vj-Yc)dy-δy
Of which only R, T are variables, which are converted into a system of linear equations:
sj＝r7xj+r8yj+r9zj+tz＝tz(a9xj+a10yj+a11zj+1)＝tzζj
then the formula (5) is equivalent to
In the formula (6), 11 unknowns exist, and a is obtained by using the least square method by using the corresponding points of the object image obtained by more than 6 pairs1，a2，...a11Since R is orthogonal, the relationship of formula (7) exists
(6) (7) separating the parameters to calculate R, T
The solution obtained in the formula (8) is feasible in the ideal perspective imaging process, because the coordinate values of the object point and the image point in each coordinate system have no error, and the calculated R satisfies the orthogonal system constraint relation. However, in an actual environment, due to various factors, such as a camera parameter calibration error, a control point center image plane position extraction error, a coordinate value calibration error of a control point center in a light pen coordinate system, and the like, the R matrix does not satisfy the orthogonal constraint relationship, and then a large error is also generated along with the matrix T, so that the solution cannot be performed by using a linear equation set method, and an initial value of R, T can be obtained by using a linear equation set solution.
The following equation is written using newton-gaussian iteration to search R, T for the optimal solution according to equation (4):
an objective function can be obtained that minimizes the sum of squared spatial coordinate errors:
since R is an orthogonal matrix, the following penalty function can be constructed from the orthogonality of the R matrix:
converting the constrained optimization objective function of (6) into an unconstrained optimization objective function:
penalty factor M in equation (12)1、M2...M6The method can be used for controlling the orthogonality error of the matrix R, and the larger the penalty factor is, the better the orthogonality of R is. And establishing a Newton-Gaussian optimization solving model, and searching an optimal value by using a Newton-Gaussian method. The solution model is as follows
B＝(fa1 fb1 fa2 fb2 … faN fbN fp1 … fp6)T (14)
Then the following iterative equation is present:
solving for the optimal solution G, which is R, T of the image
5) Solving the distance from the center of the measuring head to the characteristic point; r, T, the distance between the characteristic point of the light pen and the actual position of the center coordinate of the measuring head is constant according to the principle of constant position, so that it can be used to measure the distance between the characteristic point of the light pen and the actual position of the center coordinate of the measuring head
i is the ith image, j is the jth feature point, and the feature point labels are as shown in FIG. 2
And taking n groups of effective pictures, wherein the coordinate position of each picture in the light pen coordinate system is different, but the distance between the picture and the actual position of the measuring head center coordinate is the same, so that the same characteristic point of the n groups of pictures is on a sphere taking the actual position of the measuring head center coordinate as the spherical center and the constant distance between the characteristic point and the measuring head center as the radius in the same space coordinate system. And because the- (c), (c) and (c) are symmetrical in structure, the positions of the- (c), (c) and (c) are the same sphere.
6) And fitting an equation of the sphere in a coordinate system to obtain the actual position of the measuring head center. The actual position of the center coordinates of the measuring head is calculated by using 8n coordinates of n groups of pictures of the fitted five spheres.
Get the formula of residual error
Separate derivation of the deviation
And substituting the coordinate values, making the partial derivative result be a zero structural equation set, and solving to obtain the actual position of the center coordinate of the measuring head.
Claims (4)
1. A method for improving accuracy based on an optical pen type vision measuring system is characterized by comprising the following steps:
1) a measuring system is set up, a light pen probe is used for contacting a measured point, and an image is collected through a CCD camera;
2) solving the two-dimensional coordinates of the characteristic points in an image coordinate system and the three-dimensional coordinates of the characteristic points in a light pen coordinate system;
3) solving a rotation matrix and a translation matrix between the light pen coordinate system and the camera coordinate system; establishing a camera coordinate system (u, v, w), a light pen coordinate system (X, Y, z) and a pixel coordinate system (X, Y); establishing a relation between a light pen coordinate system and a camera coordinate system:
wherein R is a rotation matrix, and T is a translation matrix, so as to complete the conversion between the light pen coordinate system and the camera coordinate system; establishing a relation between a camera coordinate system and a pixel coordinate system:
converting a camera coordinate system and a pixel coordinate system by an equation (3); wherein f is the focal length of the lens,
4) establishing an equation of each characteristic point through an R, T matrix of the picture to obtain n groups of effective data;
5) solving the distance from the center of the measuring head to the characteristic point;
6) and fitting an equation of the sphere in a coordinate system to obtain the actual position of the measuring head center.
2. The method for improving accuracy of an optical pen-based vision measuring system according to claim 1, wherein the equation establishing process of the feature points in the step 4 is as follows:
1) establishing a linear equation of the jth characteristic point in the image:
sj＝r7xj+r8yj+r9zj+tz＝tz(a9xj+a10yj+a11zj+1)＝tzζj (5)
wherein
Equation (5) is equivalent to:
2) a1, a2,. a11 is obtained by using a least square method, and the formula is as follows:
3) the initial value of R, T is obtained by solving the linear equation system, and the parameters of equation 6 and 7 are separated to obtain the following equation:
4) solving for an optimal solution G, R, T for the image, according to the following iterative equation;
wherein:
B＝(fa1 fb1 fa2 fb2…faN fbN fp1…fp6)T (14)，
in the formula rn(n ═ 1,2,3.. 9) is a parameter of the rotation matrix R, anConverting the contents of the formula for R, T, wherein
k is the number of iterations;
5) r, T, establishing a characteristic equation of each characteristic point,
wherein i is the ith image, and j is the jth characteristic point;
and the distance between the jth characteristic point of the ith image and the center of the measuring head.
3. The method for improving accuracy of an optical pen-based vision measuring system according to claim 2, wherein the specific steps of the step 6 are:
1) calculating the actual position of the measuring head center coordinate by using 8n coordinates of n groups of pictures of the five fitted spheres to obtain a residual error formula:
2) respectively calculating partial derivatives:
3) and substituting the coordinate values, making the partial derivative result be a zero structural equation set, and solving to obtain the actual position of the center coordinate of the measuring head.
4. The method for improving accuracy of an optical pen-based vision measuring system according to claim 1, wherein n.gtoreq.3 in the step 4.
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