CN104596443A - Light plane equation fitting locating calibration method based on inherent characteristics of three-line laser - Google Patents

Abstract

A light plane equation fitting, positioning and calibration method based on the inherent characteristics of a three-line laser belongs to the field of fitting and calibration methods for accurately fitting the spatial attitude equations of three light planes emitted by a three-line laser to a camera virtual space coordinate system. , the calibration method of the present invention specifically proposes the three true inherent characteristics that the adjacent angles of the three laser planes are known, the three laser planes all intersect on the same intersection line, and the projected light bars of the three laser planes are all parallel. At the same time, as the constraints of the mathematical model of the projection characteristics of the special three-line laser, the objective function and its constraints that can reflect the three key features as a whole are obtained, and it is possible to solve the objective function. Finally, It is a set of feasible methods to simultaneously and accurately transplant a series of physical characteristics of the three-line laser projection plane in the real world to the mathematical model of the virtual camera coordinate system.

Description

Optical Plane Equation Fitting Positioning Calibration Method Based on Inherent Characteristics of Three-Line Laser

technical field

The invention belongs to the field of fitting and calibration methods for accurately fitting the spatial attitude equations of three light planes emitted by a three-line laser to a camera virtual space coordinate system, and specifically relates to a light plane equation fitting based on the inherent characteristics of a three-line laser positioning calibration method.

Background technique

Vision measurement technology can well adapt to the new standards and requirements of modern industry for the detection of workpiece shape and size. It is a non-contact shape detection method with both precision and efficiency. The basic idea of the visual measurement method is: use a laser plane with a known spatial attitude to project on the object to be detected, and use a camera to take pictures of the projection of the laser plane on the outline of the object. By detecting the image coordinates of feature points, according to the known internal parameters of the camera The three-dimensional coordinates corresponding to the feature points in the camera coordinate system are obtained with the laser plane equation, and then the three-dimensional information of the surface contour of the object is obtained. In the process of making the spatial attitude of the laser plane a known quantity, how can the laser plane projected by the laser in the real physical world be mapped in the virtual space coordinate system of the camera to become known through modeling, calibration and other processes The mathematical space equation has always been the focus of research in the field of visual measurement technology.

At present, the methods for solving and determining the spatial plane equation of a single line-structured laser have become mature, and there are various methods. Their commonality is to obtain the internal parameters of the camera and the three-dimensional information of the target through calibration. The spatial coordinates (x, y, z) corresponding to each discrete feature point are used as discrete feature points for fitting the light plane, and the space equation of any laser light plane can be obtained by using multiple non-collinear discrete feature points.

For example, in the article "Quick Calibration Method for Multi-Line Structured Light Vision Sensor" with patent application number 201310352766.1, the solution method of formula (12) includes a set of discrete feature point space coordinates (x, y, z) acquisition method.

As another example, Sun Q, Hou Y, Tan Q, Li G (2014) A Flexible Calibration Method Using the PlanarTarget with a Square Pattern for Line Structured Light Vision published by the inventor of the present invention on the academic journal Public Library of Science In the article System.PLoS ONE9(9):e106911.doi:10.1371/journal.pone.0106911, in its chapter 2.2Subpixelcenter localization of the light stripe, it is proposed to solve the pixel coordinates of the center point of the laser light stripe (x _p , y _p ) Corresponding to the extraction method of the coordinates (X _c , Y _c , Z _c ) in the camera coordinate system, according to this method, continuous and more accurate pixel coordinates of the center point of the light strip can be obtained, so it can also be used as a method to obtain all the points on the laser light strip A set of discrete feature point space coordinates (x, y, z) method is required, the above method is referred to as discrete feature point space coordinate extraction method B.

With the help of any of the above methods for obtaining the spatial coordinates (x, y, z) of the known discrete feature points, we can obtain a set of known spatial coordinates of the discrete feature points to fit and solve an approximation through these discrete points The spatial plane equation of the laser plane is thus obtained in the established camera virtual coordinate system to obtain a laser plane space attitude equation, and the laser projection plane in the real physical world is transplanted into the virtual camera coordinate system. By repeating the above process, the second, third, and even more new virtual laser space plane equations can be further obtained. Through this known method, it can be further realized that multiple laser planes projected by multi-line lasers in the real physical world are roughly combined and mapped into a calibration process of known mathematical space equations under the virtual space coordinate system of the camera.

However, this rough method of fitting multiple light planes in the same camera virtual coordinate system is far from meeting the accuracy requirements of visual measurement for coordinate positioning of the laser space plane equation. Simply fitting the laser space plane equation for a single-line laser There are obvious defects in the fitting method that the combined calibration technology is repeatedly applied to the optical plane calibration of multi-line lasers in order to achieve the alignment of multiple optical planes in the same coordinate system. The existing laser space plane equation fitted by discrete feature points is not accurate enough. Due to the unavoidable system errors such as detection error and algorithm error, the obtained laser space plane equation cannot be strictly compared with the laser projection plane in the real world. coincide. Therefore, even under the same calibration conditions of the light plane space attitude equation, if the obtained first and second laser space plane equations are first intersected in the virtual camera coordinate system, and the first intersection line is formed Then, according to the same method, when the third laser space plane equation is also fitted to the same virtual camera coordinate system, then under the error interference, the third laser space plane equation can be compared with the first two The laser plane intersects with other two new intersection lines, but does not overlap with the intersection lines of the first and second laser space plane equations.

On the other hand, the latest research has found that the multi-line structured light laser shown in Figure 1 is a kind of three laser planes that can emit three adjacent angles from the same line light source, and the three laser planes can be in the same A three-line laser whose projection plane forms three parallel light strips is of extraordinary significance in some special visual measurement methods, because a three-line laser can emit three lines from the same line light source at the same angle α structure laser plane, and the included angle α between each laser plane is a real and symmetrical known quantity, therefore, if the first laser plane a, the second laser plane b and the third laser plane b emitted by the three-line laser are The space equation of the laser plane c is solved separately in the camera coordinate system and the three are accurately fitted, and finally in the virtual space coordinate system of the camera, the three virtual laser plane space equations all intersect on the same intersection line L, then it can be Transplant the inherent real physical characteristics of the aforementioned three-line laser with known angles α between the three laser planes into the camera virtual space coordinate system of the visual measurement imaging system, and use this important feature to greatly improve the subsequent visual measurement process. Measurement accuracy and efficiency. In the aforementioned invention 201310352766.1 "Quick calibration method for multi-line structured light vision sensor", a calibration method for multi-line structured light vision sensor in the camera virtual coordinate system is also introduced. Theoretically speaking, this method can directly It is used for the calibration process of a three-line laser that can emit three laser planes with the same adjacent angles from the same line light source, and whose three laser planes can form three parallel light bars on the same projection plane. However, its method does not take advantage of the real and known inherent physical property that the angles between two adjacent laser planes are the same among the three laser planes emitted by the required laser from the same line source, so it cannot be further corrected and reduce system errors. In addition, the calibration method introduced in the aforementioned invention 201310352766.1 "Quick Calibration Method for Multi-Line Structured Light Vision Sensor" must also use the principle of cross-ratio invariance between the laser projection light strip and the inherent grid lines on the directional grid target. Assist in the acquisition of the space coordinates (x, y, z) of discrete feature points and the calibration of multiple laser space plane equations in the same camera coordinate system. However, due to the limited number of inherent grid lines on the directional grid, the number of discrete feature points that can be obtained by intersecting it with the laser projection light strip is relatively small, and the small number of discrete feature points is bound to be unfavorable. The coordinate accuracy of the fitted laser space plane equation in the camera virtual system.

In addition, the inventor of the present invention published Sun Q, Hou Y, Tan Q, Li G (2014) A Flexible Calibration Method Using the PlanarTarget with a Square Pattern for Line Structured Light Vision System in the academic journal Public Library of Science. In the article PLoS ONE9(9):e106911.doi:10.1371/journal.pone.0106911, in Chapter 1, Methods, Chapter 1.Calibration of camera model also discloses a method for calibrating the internal parameters of the camera, referred to as the camera Internal parameter calibration method A.

Contents of the invention

In order to solve the existing laser space plane equation fitting and calibration technology for single-line lasers, the method of roughly fitting multiple light planes in the same camera virtual coordinate system by stitching is far from satisfying the requirements of visual measurement for laser space plane equations. Coordinate positioning accuracy requirements, while the existing laser space plane equation calibration method for multi-line structured light lasers fails to make full use of the inherent important physical characteristics of multi-line structured light lasers, and must also rely on laser projection light strips and directional gratings The cross-ratio invariance principle of the inherent grid lines on the grid target can assist in the acquisition of the spatial coordinates of discrete feature points and the calibration of multiple laser space plane equations in the same camera coordinate system. However, due to the limited number of inherent grid lines on the directional grid, the number of discrete feature points that can be obtained by intersecting the directional grid with the laser projection light strip is relatively small, so the system error cannot be corrected and reduced, which is not conducive to To further improve the technical problem of fitting and calibrating the laser space plane equation in the camera virtual coordinate system, the present invention provides a light plane equation fitting, positioning and calibrating method based on the inherent characteristics of the three-line laser.

The technical solution adopted by the present invention to solve the technical problems is as follows:

A light plane equation fitting positioning calibration method based on the inherent characteristics of three-line lasers, characterized in that the method comprises the following steps:

Step 1: Select a three-line laser that can emit three laser planes with the same adjacent angles from the same line light source, and whose three laser planes can form three parallel light stripes on the same projection plane, and use the three-line laser The angle value parameter α of the angle between two adjacent laser planes is obtained from the inherent factory performance index parameters;

Step 2: Complete the calibration of the internal parameters of the camera according to the calibration method A of the internal parameters of the camera;

Step 3: Obtain a set R of space coordinate values of N groups of discrete feature points for the first laser plane (a) in the three-line laser, which specifically includes the following sub-steps:

Step 3.1: According to the discrete feature point spatial coordinate extraction method B, perform the required first laser light strip (a-1) on the target plane (K) of the first laser plane (a) of the three-line laser described in step 1. Sampling and extraction of the spatial coordinates (x, y, z) of a group of discrete feature points, so as to obtain the laser light bar ( a-1) The spatial coordinates of the first set of discrete feature points obtained by sampling: Where i=1,2,...,n, n represents the number of discrete feature points sampled on the laser light strip (a-1), and the respective superscripts (a) of the coordinate values (x, y, z) Both indicate that the discrete feature point belongs to the first laser plane (a);

Step 3.2: Change the inclination angle of the laser projection target plane (K), and repeat the process of step 3.1 to obtain the projection of the first laser plane (a) on the target plane (K') in the new attitude. The second set of discrete feature point space coordinates obtained by sampling the laser light strip (a-2): Where i=(n+1),(n+2),...,2n, n represents the number of discrete feature points sampled on the laser light strip (a-2), coordinate value (x, y, z) Each superscript (a) indicates that the discrete feature point belongs to the first laser plane (a);

Step 3.3: Change the inclination of the laser projection target plane N times (N≥3, N is a natural number) and repeat the process of step 3.2 until the first laser plane (a) for the aforementioned first laser plane (a) on the target plane (K) is obtained. The spatial coordinate values of the Nth group of discrete feature points obtained by sampling the laser light bar (aN) formed by projection on N new attitudes: Where i=((N-1)×n+1),((N-1)×n+2)...,N×n, n represents the number of discrete feature points sampled on the laser light strip (aN) The superscript (a) of each coordinate value (x, y, z) indicates that the discrete feature point belongs to the first laser plane (a);

Step 3.4: Merge a total of N sets of discrete feature points obtained from step 3.1 to step 3.3 into a set R of non-collinear discrete feature points:

$\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

In the formula (1), i=1, 2,..., N×n, N×n means that a total of N times in the laser light strip (a-1), (a-2)... (a-N) The total number of discrete feature points upsampled, and the superscripts (a) of the coordinate values (x, y, z) indicate that the discrete feature points belong to the first laser plane (a); N indicates the target plane The total number of changes in inclination;

Step 4: Using exactly the same method as Step 3, respectively obtain a set of discrete feature points for the second laser plane (b) in the three-line laser, which is unified and merged into a non-collinear discrete feature point by a total of N groups And for the third laser plane (c) in the three-line laser, a total of N sets of discrete feature points are unified into a set of non-collinear discrete feature points $T=(x_k^{\left(c\right)},{\mathrm{the\; y}}_k^{\left(c\right)},z_k^{\left(c\right)})......\left(3\right);$

In the formula (2), j=1, 2,..., N×n, N×n means that in step 3.1 to step 3.3, a total of N times in the laser light strip (b-1), (b-2)... (b-N) The total number of discrete feature points upsampled, and the superscripts (b) of the coordinate values (x, y, z) indicate that the discrete feature points belong to the first laser plane (b); N indicates the target plane The total number of changes in inclination;

In the formula (3), k=1, 2,..., N×n, N×n means that in step 3.1 to step 3.3, a total of N times in the laser light bar (c-1), (c-2)... (c-N) The total number of discrete feature points upsampled, and the superscripts (c) of the coordinate values (x, y, z) indicate that the discrete feature points belong to the first laser plane (c); N indicates the target plane The total number of changes in inclination;

Step 5: According to the mathematical equations of multiple space plane equations in the three-dimensional space coordinate system, define a mathematical equation expression that indicates that the three space planes all intersect on the same intersection line:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ {\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ <span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;D</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right.<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

In formula (4), (x, y, z) represent the spatial coordinate values of a group of discrete feature points on the three spatial planes satisfying the equation system;

The polynomial coefficients to be solved (A ₁ , B ₁ , C ₁ , D ₁ , A ₂ , B ₂ , C ₂ , D ₂ , λ) jointly define the respective Space attitude coefficient;

The first equation in the formula (4) is the laser space plane equation of the first laser plane (a) of the three-line laser fitted by the formula (1) described in step 3;

The second equation in the formula (4) is the laser space plane equation of the second laser plane (b) of the three-line laser fitted by the formula (2) described in step 4;

The third equation in the formula (4) is the laser space plane equation of the third laser plane (c) of the three-line laser fitted by the formula (3) described in step four;

The third equation in formula (4) also expresses that the third laser plane (c) strictly passes through the laser space plane equations of the first laser plane (a) and the second laser plane (b) in formula (4). intersection line;

Step 6: Use the set of space coordinates of a set of non-collinear discrete feature points for the aforementioned first laser plane (a) obtained in step 3 i=1,2,...,(N×n);

A set of space coordinates of a group of non-collinear discrete feature points for the aforementioned second laser plane (b) obtained in step 4 j=1,2,...,(N×n);

And a set of space coordinates of a group of non-collinear discrete feature points for the aforementioned third laser plane (c) obtained in step 4 k=1,2,...,(N×n) are jointly used as the fitting data, and the expression (4) of the mathematical equation set representing that the three spatial planes all intersect at the same intersection line determined by step 5 is used as the fitting function , and establish a unified objective function according to the well-known least squares method:

$\begin{array}{c}\mathrm{<span\; class="notranslate">\; Min</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ <span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;D</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Step 7: Taking the inherent factory performance index parameters of the three-line laser described in step 1: the angle value parameter α of the angle between two adjacent laser planes as a known constraint condition, for the three in the objective function (5) determined in step 6 The respective spatial attitude polynomial coefficients (A ₁ , B ₁ , C ₁ , D ₁ , A ₂ , B ₂ , C ₂ , D ₂ , λ) of each laser plane are further mathematically limited, so as to obtain the angle limit condition Constraint expression for :

$\left\{\begin{array}{c}\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\sqrt{{{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\sqrt{{{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}\\ \frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\sqrt{{{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\sqrt{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}\\ \frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\sqrt{{{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\sqrt{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}\end{array}\right.<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

Step 8: Simultaneously solve formula (5) and its conditional expression (6) through the known Lenvenberg-Marquardt nonlinear optimization algorithm, so as to solve (A ₁ , B ₁ , C ₁ , D ₁ , A ₂ , B ₂ , C ₂ , D ₂ , λ), and complete the use of three laser planes that can emit three adjacent angles from the same line light source, and the three laser planes can form three laser planes on the same projection plane. The inherent characteristics of the three-line laser of the parallel light strips accurately fit the space attitude equations of the three light planes emitted by the three-line laser to the fitting and calibration process in the virtual space coordinate system of the camera.

The beneficial effects of the present invention are: the calibration method of the present invention specifically proposes that the adjacent angles of the three laser planes are known, the three laser planes all intersect on the same intersection line, and the projected light bars of the three laser planes are all parallel. The three real intrinsic characteristics are simultaneously used as the constraints of the mathematical model of the projection characteristics of the special three-line laser, thereby obtaining an objective function and its constraints that can reflect these three key features as a whole, and bringing new benefits to the solution of the objective function. possibility. Finally, a set of feasible methods are given to accurately transplant a series of physical characteristics of the three-line laser projection plane in the real world to the mathematical model of the virtual camera coordinate system at the same time. In addition, the present invention also overcomes the problem that when multiple laser plane equations are directly combined in the same camera virtual coordinate system using the old method for solving and determining a single line-structured laser space plane equation, it is roughly in the same camera virtual coordinate system. The method of fitting multiple light planes is far from meeting the accuracy requirements of visual measurement for coordinate positioning of the laser space plane equation, and increases the error of the multi-line structured light fitting calibration method, which greatly improves the calibration accuracy.

Description of drawings

Figure 1 is a schematic diagram of the positional relationship of three laser planes of a three-line laser that can emit three adjacent laser planes with the same angle from the same line light source and can form three parallel light stripes on the same projection plane.

FIG. 2 is a schematic diagram of the parallel relationship of the three projected light stripes of the three laser planes in FIG. 1 on the same target plane.

FIG. 3 is a top view of FIG. 2 .

FIG. 4 is a schematic diagram of three laser light stripes parallel to each other formed after the three laser planes in FIG. 2 are respectively simplified and retained after the three laser planes are respectively projected on the target plane.

FIG. 5 is a schematic diagram of the positional relationship of changing the spatial attitude and inclination of the target plane and generating three new laser plane projection light bars on the basis of FIG. 2 .

FIG. 6 is a top view of FIG. 5 .

FIG. 7 is a schematic diagram of three laser light stripes parallel to each other formed by simplifying the three laser planes in FIG. 5 and retaining the three laser planes respectively projected on the target plane.

Detailed ways

The present invention will be described in further detail below in conjunction with the accompanying drawings.

The three-line laser shown in Figure 1 can emit three laser planes adjacent to the same angle from the same line source, and its first laser plane a, second laser plane b and third laser plane c can be in Three parallel light stripes are formed on the same projection target plane K, namely laser light stripe a-1, laser light stripe b-1 and laser light stripe c-1 shown in FIG. 2 . The laser is a STR-660-20-L01 three-line structured light laser manufactured by COHERENT. As shown in Figure 3, the angle value parameter α of the inherent angle between two adjacent laser planes when the laser leaves the factory is 11.7°.

Figure 4 is a schematic diagram of three laser light bars parallel to each other formed by simplifying the three laser planes in Figure 2 and only retaining the three laser planes respectively projected on the target plane, while Figure 5 is based on Figure 2 Change the spatial attitude of the target plane K, and generate three new laser plane projection light bars on the new target plane with an inclination angle of K ^' , namely: laser light bar a-2, laser light bar b-2 and laser light bar Schematic diagram of the positional relationship of item c-2. Keeping the position and attitude of the three-line laser unchanged, and continuing to change the space inclination attitude of the target plane K, it is also possible to obtain the Nth (N ≥ 3, N is a natural number) when changing the space attitude of the target plane K, by The three laser planes of the laser project three newly generated laser plane projection light strips under the current attitude of the corresponding target plane K, namely: laser light strip aN, laser light strip bN and laser light strip cN.

A light plane equation fitting positioning calibration method based on the inherent characteristics of the three-line laser of the present invention includes the following steps:

Step 1: Select a three-line laser that can emit three laser planes with the same adjacent angles from the same line light source, and whose three laser planes can form three parallel light bars on the same projection plane, such as COHERENT. For the STR-660-20-L01 three-line structured light laser, the angle value parameter α=11.7° of the angle between two adjacent laser planes is obtained from the inherent factory performance index parameters of the three-line laser;

Step 2: According to Sun Q, Hou Y, Tan Q, Li G (2014) A Flexible Calibration Method Using the Planar Target with a Square Pattern for Line Structured Light Vision System.PLoS ONE 9(9) published on the academic journal Public Library of Science ):e106911.doi:10.1371/journal.pone.0106911, in the first chapter Methods, the method described in Chapter 1.Calibrationof camera model completes the calibration of the internal parameters of the camera;

Step 3: Obtain a set R of space coordinate values of N sets of discrete feature points for the first laser plane a in the three-line laser, which specifically includes the following sub-steps:

Step 3.1: Solve the pixel coordinates (x _p , y _p ) of the center point of the laser light stripe corresponding to the coordinates in the camera coordinate system (X _c , Y _c , Z _c ), the more precise method is to carry out the required set of discrete feature points on the laser light strip (a-1) on the target plane K of the first laser plane a of the three-line laser described in step 1 Sampling and extraction of space coordinates (x, y, z), so as to obtain the laser light strip (a-1) obtained by sampling the first laser plane a projected on the target plane K at the initial attitude The first set of discrete feature point space coordinates: Where i=1,2,...,n, n represents the number of discrete feature points sampled on the laser light strip (a-1), and the respective superscripts (a) of the coordinate values (x, y, z) Both indicate that the discrete feature point belongs to the first laser plane a; here the The n value of the number of sampling points in i=1,...,n is set to 30, then a set of spatial coordinate values for the laser light strip (a-1) and containing 30 discrete feature points can be obtained A set of points with i=1,2,...,30;

Step 3.2: As shown in Figure 5 to Figure 7, change the inclination angle of the laser projection target plane K, so that the space attitude inclination angle of the laser projection target plane becomes K', repeat the process of step 3.1, so as to target the first laser projection The space coordinates of the second set of discrete feature points obtained by sampling the laser light strip (a-2) formed by the projection of plane a on the target plane K' under the new attitude: Where i=(n+1),(n+2),...,2n, n represents the number of discrete feature points sampled on the laser light strip (a-2), coordinate value (x, y, z) Each superscript a indicates that the discrete feature point belongs to the first laser plane a;

here will The n value of the number of sampling points in i=(n+1),(n+2),...,2n is still set to 30, then the target plane K in the new attitude of the aforementioned first laser plane a can be The second set of sampling and extraction of the spatial coordinate values of the laser light bar (a-2) containing 30 discrete feature points on the ' is obtained: a new set of laser light bar (a-2) containing 30 discrete feature points can be obtained Spatial coordinate values of feature points:

i=31,32...,60, the set of points;

Step 3.3: Change the inclination of the laser projection target plane N times (N≥3, N is a natural number) and repeat the process of step 3.2 until the first laser plane (a) for the aforementioned first laser plane (a) on the target plane (K) is obtained. The spatial coordinate values of the Nth group of discrete feature points obtained by sampling the laser light bar (aN) formed by projection on N new attitudes: Where i=((N-1)×n+1),((N-1)×n+2)...,N×n, n represents the number of discrete feature points sampled on the laser light strip (aN) The superscript (a) of each coordinate value (x, y, z) indicates that the discrete feature point belongs to the first laser plane (a);

here will i=((N-1)×n+1),((N-1)×n+2)..., the n value of the number of sampling points in N×n is still set to 30 and N=9, then The ninth group of sampling and extraction of the spatial coordinate values of 30 discrete feature points can be performed on the laser light bar (a-9) generated by the projection of the aforementioned first laser plane a at the ninth attitude of the target plane K: A new set of spatial coordinate values for the laser light bar (a-9) and containing 30 discrete feature points can be obtained i=(8×30+1),(8×30+2),...,(9×30) point set;

Step 3.4: Merge a total of nine sets of discrete feature points obtained from step 3.1 to step 3.3 into a set R of non-collinear discrete feature points:

$\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

In the formula (1), i=1, 2,..., N×n, N×n means that in step 3.1 to step 3.3, a total of N times in the laser light strip (a-1), (a-2)... (a-N) The total number of discrete feature points upsampled, and the superscript a of each coordinate value (x, y, z) indicates that the discrete feature point belongs to the first laser plane a; N represents the total change in the inclination angle of the target plane frequency;

That is: when the inclination attitude of the target plane K changes N=9 times successively, and the first laser plane a of the laser corresponds to the laser light bar (a-1) generated by projection after each attitude change of the target plane K, (a-2)...(aN) When the number n of sampling points on (aN) is set to 30, the obtained nine sets of discrete feature points each containing 30 discrete feature points can be merged into a non-collinear set containing 270 A collection of spatial coordinates of discrete feature points i=1,2,...,(9×30); A new set R containing 270 discrete feature points for the first laser plane a can be obtained;

Step 4: Using exactly the same method as Step 3, acquire and combine a total of nine sets of discrete feature points for the second laser plane b in the three-line laser into a unified and unified one for the second laser plane b that contains 270 non- A collection of collinear discrete feature points

In the formula (2), j=1, 2,..., N×n, N×n means that in the laser light bars (b-1), (b-2)... ...(bN) The total number of discrete feature points upsampled, and the superscripts (b) of the coordinate values (x, y, z) indicate that the discrete feature points belong to the first laser plane (b); N indicates the target The total number of changes in the plane inclination; that is: when the inclination attitude of the target plane K changes N=9 times successively, and the first laser plane b of the laser corresponds to the laser light generated by projection after each attitude change of the target plane K When the number of sampling points n on the bars (b-1), (b-2)...(bN) is set to 30, the obtained nine sets containing 30 discrete feature points can be combined into one A collection of 270 discrete feature point spatial coordinates that are non-collinear: j=1,2,...,(9×30);

That is: when the inclination attitude of the target plane K changes N=9 times successively, and the second laser plane b of the laser corresponds to the laser light bar (b-1) generated by projection after each attitude change of the target plane K, (b-2)...(b-N) When the number of sampling points n is set to 30, a new set S containing 270 discrete feature points for the second laser plane b can be obtained;

Using exactly the same method as Step 3, it is also possible to obtain and merge a total of nine sets of discrete feature points for the third laser plane c in the three-line laser into a single set of 270 non-common feature points for the third laser plane c. A collection of discrete feature points of a line k=1,2...,(9×30)...(3);

In the formula (3), k=1, 2,..., N×n, N×n means that in step 3.1 to step 3.3, a total of nine times in the laser light bar (c-1), (c-2)... (c-N) The total number of discrete feature points upsampled, and the superscripts (c) of the coordinate values (x, y, z) indicate that the discrete feature points belong to the first laser plane (c); N indicates the target plane The total number of changes in the inclination angle; that is: when the inclination attitude of the target plane K changes N=9 times successively, and the third laser plane c of the laser corresponds to the laser light bar generated by projection after each attitude change of the target plane K When the number n of sampling points on (c-1), (c-2)...(c-N) is set to 30, a new set T containing 270 discrete feature points for the third laser plane c can be obtained;

Step 5: According to the mathematical equations of multiple space plane equations in the three-dimensional space coordinate system, define a mathematical equation expression that indicates that the three space planes all intersect on the same intersection line:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ {\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ <span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;D</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right.<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

In formula (4), (x, y, z) represent the spatial coordinate values of a group of discrete feature points on the three spatial planes satisfying the equation system;

The polynomial coefficients to be solved (A ₁ , B ₁ , C ₁ , D ₁ , A ₂ , B ₂ , C ₂ , D ₂ , λ) jointly define the respective Space attitude coefficient;

The first equation in the formula (4) is the laser space plane equation of the first laser plane a of the three-line laser fitted by the formula (1) described in step 3;

The second equation in the formula (4) is the laser space plane equation of the second laser plane b of the three-line laser fitted by the formula (2) described in step 4;

The third equation in formula (4) is the laser space plane equation of the third laser plane c of the three-line laser fitted by formula (3) described in step 4;

The third equation in formula (4) represents simultaneously that the third laser plane c strictly passes through the intersection line of the laser space plane equation of the first laser plane a and the second laser plane b in formula (4);

Step 6: Simultaneously use a set of non-collinear discrete feature point space coordinate sets for the first laser plane a obtained in step 3 i=1,...,(9×30) and a set of non-collinear discrete feature point space coordinates set for the second laser plane b obtained in step 4 j=1,...,(9×30) and a set of non-collinear discrete feature point space coordinates obtained in step 4 for the aforementioned third laser plane c k=1,...,(9×30) are jointly used as the fitting data, and the expression (4) of the mathematical equation system that represents that the three spatial planes all intersect at the same intersection line determined by step 5 is used as the fitting function, and Establish a unified objective function according to the well-known least squares method:

$\begin{array}{c}\mathrm{<span\; class="notranslate">\; Min</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 30</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 30</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ <span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 30</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;D</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Step 7: The inherent factory performance index parameter of the three-line laser described in step 1: the angle value parameter α=11.7° of the angle between two adjacent laser planes is used as a known constraint condition, and the objective function (5) determined in step 6 The respective spatial attitude polynomial coefficients (A ₁ , B ₁ , C ₁ , D ₁ , A ₂ , B ₂ , C ₂ , D ₂ , λ) of the three laser planes in , are further defined mathematically, so as to obtain the Constraint expression for angle qualification:

$\left\{\begin{array}{c}\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\sqrt{{{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\sqrt{{{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}\\ \frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\sqrt{{{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\sqrt{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}\\ \frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\sqrt{{{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\sqrt{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}\end{array}\right.<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

Step 8: Simultaneously solve formula (5) and its conditional expression (6) through the known Lenvenberg-Marquardt nonlinear optimization algorithm, so as to solve (A ₁ , B ₁ , C ₁ , D ₁ , A ₂ , B ₂ , C ₂ , D ₂ , λ), and complete the use of three laser planes that can emit three adjacent angles from the same line light source, and the three laser planes can form three laser planes on the same projection plane. The inherent characteristics of the three-line laser of the parallel light strips accurately fit the space attitude equations of the three light planes emitted by the three-line laser to the fitting and calibration process in the virtual space coordinate system of the camera.

By simultaneously solving formula (5) and its limiting condition expression (6), the solution of the obtained equation must express the following meanings precisely and simultaneously:

First: the three known planes represented by the plane equations after the solution must be able to form three rays a, b, and c as shown in Figure 3 or Figure 6; three rays on the same target plane The projected line segments must be parallel to each other;

Second: The three known planes represented by the plane equations after the solution must intersect precisely at the same intersection line L at the same time;

Third: For the three known planes represented by the plane equations after the solution is obtained, the angle between two adjacent planes must be equal to the known quantity α;

It can be seen from this that the three known planes represented by the plane equations after the solution must be the aforementioned three laser planes with the same adjacent angles that can be emitted from the same line light source, and the three laser planes can be projected on the same plane. The ideal mathematical model of a three-line laser that forms three parallel light strips on a plane, that is, a series of physical characteristics of the three-line laser projection plane in the real world are simultaneously and accurately transplanted to the mathematical model of the virtual camera coordinate system.

The optical plane equation fitting positioning calibration method of the present invention is directly according to the inventor's disclosure on the academic journal Public Library of Science to solve the pixel coordinates (x _p , y _p ) of the center point of the laser light bar corresponding to the coordinates in the camera coordinate system ( The more accurate method of X _c , Y _c , Z _c ) extracts the pixel coordinates of the center point of the projected light strip pattern of the laser plane in the camera photo, and the obtained light strip center is each pixel point on the continuous light strip pattern The data volume and accuracy of the discrete feature points obtained by this mature method are much higher than those obtained by using the directional grid method with a very limited number of inherent grid lines. Coordinate accuracy, thus providing a reliable guarantee for further correction and reduction of system errors from the perspective of data sources.

On the other hand, the present invention makes full use of the inherent characteristics of a three-line laser that can emit three adjacent laser planes with the same included angle from the same line light source, and whose three laser planes can form three parallel light bars on the same projection plane. Features: Its high-precision adjacent laser plane angle is a known quantity given by its factory index, and the three laser planes emitted by the laser are actually projected from the same precise line light source.

The most important thing is that the calibration method of the present invention specifically proposes that the adjacent angles of the three laser planes are known, the three laser planes all intersect on the same intersection line, and the projection light bars of the three laser planes are all parallel. The real inherent characteristics are also used as the constraints of the mathematical model of the projection characteristics of the special three-line laser, so that the objective function and its constraints that can reflect these three key features as a whole can be obtained, and it is possible to solve the objective function sex. Finally, a set of feasible methods are given to accurately transplant a series of physical characteristics of the three-line laser projection plane in the real world to the mathematical model of the virtual camera coordinate system at the same time.

In addition, the present invention also overcomes the problem that when multiple laser plane equations are directly combined in the same camera virtual coordinate system using the old method for solving and determining a single line-structured laser space plane equation, it is roughly in the same camera virtual coordinate system. The method of fitting multiple light planes is far from meeting the accuracy requirements of visual measurement for coordinate positioning of the laser space plane equation, and increases the error of the multi-line structured light fitting calibration method, which greatly improves the calibration accuracy.

Claims (1)

1. The optical plane equation fitting positioning calibration method based on the inherent characteristics of the three-line laser is characterized in that the method comprises the following steps: Step 1: Select a three-line laser that can emit three laser planes with the same adjacent angles from the same line light source, and whose three laser planes can form three parallel light stripes on the same projection plane, and use the three-line laser The angle value parameter α of the angle between two adjacent laser planes is obtained from the inherent factory performance index parameters; Step 2: Complete the calibration of the internal parameters of the camera according to the calibration method A of the internal parameters of the camera; Step 3: Obtain a set R of space coordinate values of N groups of discrete feature points for the first laser plane (a) in the three-line laser, which specifically includes the following sub-steps: Step 3.1: According to the discrete feature point spatial coordinate extraction method B, perform the required first laser light strip (a-1) on the target plane (K) of the first laser plane (a) of the three-line laser described in step 1. Sampling and extraction of the spatial coordinates (x, y, z) of a group of discrete feature points, so as to obtain the laser light bar ( a-1) The spatial coordinates of the first set of discrete feature points obtained by sampling: Where i=1,2,...,n, n represents the number of discrete feature points sampled on the laser light strip (a-1), and the respective superscripts (a) of the coordinate values (x, y, z) Both indicate that the discrete feature point belongs to the first laser plane (a); Step 3.2: Change the inclination angle of the laser projection target plane (K), and repeat the process of step 3.1 to obtain the projection of the first laser plane (a) on the target plane (K') in the new attitude. The second set of discrete feature point space coordinates obtained by sampling the laser light strip (a-2): Where i=(n+1),(n+2),...,2n, n represents the number of discrete feature points sampled on the laser light strip (a-2), coordinate value (x, y, z) Each superscript (a) indicates that the discrete feature point belongs to the first laser plane (a); Step 3.3: Change the inclination of the laser projection target plane N times (N≥3, N is a natural number) and repeat the process of step 3.2 until the first laser plane (a) for the aforementioned first laser plane (a) on the target plane (K) is obtained. The spatial coordinate values of the Nth group of discrete feature points obtained by sampling the laser light bar (aN) formed by projection on N new attitudes: Where i=((N-1)×n+1),((N-1)×n+2)...,N×n, n represents the number of discrete feature points sampled on the laser light strip (aN) The superscript (a) of each coordinate value (x, y, z) indicates that the discrete feature point belongs to the first laser plane (a); Step 3.4: Merge a total of N sets of discrete feature points obtained from step 3.1 to step 3.3 into a set R of non-collinear discrete feature points: $\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$ In the formula (1), i=1, 2,..., N×n, N×n means that a total of N times in the laser light strip (a-1), (a-2)... (a-N) The total number of discrete feature points upsampled, and the superscripts (a) of the coordinate values (x, y, z) indicate that the discrete feature points belong to the first laser plane (a); N indicates the target plane The total number of changes in inclination; Step 4: Using exactly the same method as Step 3, respectively obtain a set of discrete feature points for the second laser plane (b) in the three-line laser, which is unified and merged into a non-collinear discrete feature point by a total of N groups And for the third laser plane (c) in the three-line laser, a total of N sets of discrete feature points are unified into a set of non-collinear discrete feature points $T=(x_k^{\left(c\right)},{\mathrm{the\; y}}_k^{\left(c\right)},z_k^{\left(c\right)})......\left(3\right);$ In the formula (2), j=1, 2,..., N×n, N×n means that in step 3.1 to step 3.3, a total of N times in the laser light strip (b-1), (b-2)... (b-N) The total number of discrete feature points upsampled, and the superscripts (b) of the coordinate values (x, y, z) indicate that the discrete feature points belong to the first laser plane (b); N indicates the target plane The total number of changes in inclination; In the formula (3), k=1, 2,..., N×n, N×n means that in step 3.1 to step 3.3, a total of N times in the laser light bar (c-1), (c-2)... (c-N) The total number of discrete feature points upsampled, and the superscripts (c) of the coordinate values (x, y, z) indicate that the discrete feature points belong to the first laser plane (c); N indicates the target plane The total number of changes in inclination; Step 5: According to the mathematical equations of multiple space plane equations in the three-dimensional space coordinate system, define a mathematical equation expression that indicates that the three space planes all intersect on the same intersection line: $\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ {\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ <span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right.<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$ In formula (4), (x, y, z) represent the spatial coordinate values of a group of discrete feature points on the three spatial planes satisfying the equation system; The polynomial coefficients to be solved (A ₁ , B ₁ , C ₁ , D ₁ , A ₂ , B ₂ , C ₂ , D ₂ , λ) jointly define the respective Space attitude coefficient; The first equation in the formula (4) is the laser space plane equation of the first laser plane (a) of the three-line laser fitted by the formula (1) described in step 3; The second equation in the formula (4) is the laser space plane equation of the second laser plane (b) of the three-line laser fitted by the formula (2) described in step 4; The third equation in the formula (4) is the laser space plane equation of the third laser plane (c) of the three-line laser fitted by the formula (3) described in step four; The third equation in formula (4) also expresses that the third laser plane (c) strictly passes through the laser space plane equations of the first laser plane (a) and the second laser plane (b) in formula (4). intersection line; Step 6: Use the set of space coordinates of a set of non-collinear discrete feature points for the aforementioned first laser plane (a) obtained in step 3 i=1,2,...,(N×n); A set of space coordinates of a group of non-collinear discrete feature points for the aforementioned second laser plane (b) obtained in step 4 j=1,2,...,(N×n); And a set of space coordinates of a group of non-collinear discrete feature points for the aforementioned third laser plane (c) obtained in step 4 k=1,2,...,(N×n) are jointly used as the fitting data, and the expression (4) of the mathematical equation set representing that the three spatial planes all intersect at the same intersection line determined by step 5 is used as the fitting function , and establish a unified objective function according to the well-known least squares method: $\begin{array}{c}\mathrm{<span\; class="notranslate">\; Min</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ <span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$ Step 7: Taking the inherent factory performance index parameters of the three-line laser described in step 1: the angle value parameter α of the angle between two adjacent laser planes as a known constraint condition, for the three in the objective function (5) determined in step 6 The respective spatial attitude polynomial coefficients (A ₁ , B ₁ , C ₁ , D ₁ , A ₂ , B ₂ , C ₂ , D ₂ , λ) of each laser plane are further mathematically limited, so as to obtain the angle limit condition Constraint expression for : $\left\{\begin{array}{c}\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\sqrt{{{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\sqrt{{{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}\\ \frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\sqrt{{{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\sqrt{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}\\ \frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\sqrt{{{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\sqrt{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}\end{array}\right.<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$ Step 8: Simultaneously solve formula (5) and its conditional expression (6) through the known Lenvenberg-Marquardt nonlinear optimization algorithm, so as to solve (A ₁ , B ₁ , C ₁ , D ₁ , A ₂ , B ₂ , C ₂ , D ₂ , λ), and complete the use of three laser planes that can emit three adjacent angles from the same line light source, and the three laser planes can form three laser planes on the same projection plane. The inherent characteristics of the three-line laser of the parallel light strips accurately fit the space attitude equations of the three light planes emitted by the three-line laser to the fitting and calibration process in the virtual space coordinate system of the camera.