CN101957175B - Method of normal direction detection based on three-point micro-plane - Google Patents

Abstract

The invention discloses a detection method based on three-point micro-plane normal direction, based on the idea of differential geometry—micro-plane approximation instead of the micro-curved surface method, and applying laser displacement sensor technology and data acquisition technology, through a certain algorithm can measure the The normal vector of the point to be measured. The calibration method of relevant parameters is: firstly establish a measurement space, then draw up a spherical surface in this space and establish the spherical equation, after installing the sensor, collect some data points on the spherical surface, these data points must satisfy the spherical equation, so that Get a number of equations containing parameters, and then apply the fminsearch minimum optimization method to solve the equations, and then you can solve each parameter. The invention not only can perform non-contact measurement, but also has high measurement accuracy, convenient and fast measurement, and can be applied to measurement fields such as normal direction error correction, normal direction attitude adjustment, normal direction detection and the like.

Description

Method of normal direction detection based on three-point micro-plane

technical field

The invention relates to a normal direction detection technology in the field of measurement, in particular to the design of a method for measuring the normal direction of a curved surface based on a three-point microplane method and adopting non-contact measurement and a method for calibrating related parameters.

Background technique

In industrial production, measurement technology plays a pivotal role. With the advancement of technology, especially the development of laser technology and sensor technology, the measurement methods are more diversified and advanced, and the measured objects required in the production process are also increasing. More often, it is necessary to measure the normal vector on a certain surface, such as the drilling and riveting technology in the aircraft manufacturing process, it is required that the processing axis of the drilling and riveting machine coincides with the normal vector at the point to be processed on the aircraft skin; There are relatively few technologies and literatures in this area. Therefore, it is of great value and significance in the field of measurement in industrial production to propose a surface normal measurement and design a measurement method and related parameter calibration method.

Contents of the invention

The purpose of the present invention is to provide a calibration method for measuring the normal direction of a curved surface and related parameters. The invention utilizes laser sensor technology and data acquisition technology and is based on the design idea of the three-point micro-plane method, and can accurately, quickly and conveniently measure the normal direction of the curved surface.

The present invention is realized through the following technical solutions, and the implementation steps are as follows:

1) Model establishment: 3 laser displacement sensors are evenly distributed in a ring on the head of the three-coordinate measuring machine. The spatial attitude of the sensor can make the laser beam shoot on the curved surface in a cone shape, and adjust the taper according to the accuracy requirements to control the three laser points. The size of the microfacets formed;

2) Establish a space coordinate system: first, establish a world coordinate system 1 with a three-coordinate measuring machine; then select the terminal joint coordinate system of the three-coordinate measuring machine as the intermediate conversion coordinate system 2; The direction of line emission is the negative direction of the z-axis, and the local coordinate system 3 with the working reference point of the laser displacement sensor as the coordinate origin;

3) Collect data: use the data acquisition card and LabVIEW software to collect the voltage signal of the laser displacement sensor and convert it into a displacement value L _i ;

4) Calculate the coordinates of the laser point: use the displacement measured by the laser displacement sensor to know the coordinates (0, 0, w _i ) of the laser point in the local coordinate system 3, w _i =-L _i , and convert according to the Euler coordinates The formulas are used to obtain the coordinates of the three laser points in the coordinate system 1, and the coordinate conversion formula is as follows:

$P_i=R_0*R_i*\left(\begin{array}{c}0\\ 0\\ w_i\\ 1\end{array}\right)$ i=1,2,3

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}$

$<span\; class="notranslate">\; =</span>\left[\begin{array}{cccc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]<span\; class="notranslate">\; *</span>\left[\begin{array}{cccc}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]<span\; class="notranslate">\; +</span>\left[\begin{array}{cccc}\mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right]$

In the formula, P _i represents the coordinates of the laser point; R ₀ is the end pose of the three-coordinate measuring machine, which is obtained from the software of the three-coordinate measuring machine; R _i is the homogeneous transformation matrix of the local coordinate system 3 relative to the intermediate transformation coordinate system 2, Where r _z1 and r _x2 are the rotation angles of coordinate system 3 around the z-axis and x-axis of coordinate system 2 respectively, (a _i , b _i , c _i ) are the translation vectors of coordinate system 3 to coordinate system 2, and r _z1 , r _x2 , (a _i , b _i , c _i ) for calibration;

5) Calculate the normal vector: use the coordinates of the 3 laser points obtained in step 4) to obtain 3 vectors, and then cross-multiply any 2 vectors to obtain the normal vector of the three-point microplane. The formula is as follows:

$\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="P"\; filenames="HDA0000026228760000011.png"\; state="\{\{state\}\}">P</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="y"\; filenames="HDA0000026228760000012.png"\; state="\{\{state\}\}">y</figure-callout></span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>$

$\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="y"\; filenames="HDA0000026228760000012.png"\; state="\{\{state\}\}">y</figure-callout></span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>$

$\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; =</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="P"\; filenames="HDA0000026228760000011.png"\; state="\{\{state\}\}">P</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; \&times;</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}}$

The calculated normal vector is used for normal error correction, normal attitude adjustment, and normal detection.

The attitude parameter calibration method of the laser displacement sensor: the implementation steps are as follows:

1) According to step 1 in (1), install the laser displacement sensor on the head of the three-dimensional coordinate measuring machine and establish the following measurement space: Follow step 2 in (1) to use the three-dimensional coordinate measuring machine to establish a world coordinate system 1 and establish a Transform the coordinate system 2 in the middle, and then draw up a spherical equation (xa) ² + (yb) ² + (zc) ² = r ² in the world coordinate system 1 with a standard sphere, where (a, b, c) represent the center of the sphere Coordinates, r represents the radius of the ball, the coordinates of the center of the ball are calibrated with a three-coordinate measuring machine, and the radius of the ball is known;

2) Use one of the sensors to operate the three-coordinate measuring machine to uniformly collect 30 measuring points on the spherical surface to obtain 30 displacement values;

3) Substituting the measured displacement value into the spherical equation and applying the fminsearch minimum optimization method to solve each parameter value;

4) Repeat step 2) and step 3) to solve the attitude parameters of the other two sensors.

The design principle of the present invention is based on the idea of differential geometry—the microplane approximately replaces the microcurved surface, and adopts laser sensor technology, which not only enables non-contact measurement, but also has high measurement accuracy, convenient and fast measurement; in addition, the calibration algorithm in the present invention is simple, It is easy to implement, and when using fminsearch to solve the minimum optimization, the requirements for initial value selection are not high.

Description of drawings

Fig. 1 is a principle explanatory diagram of the present invention;

Fig. 2 is a model schematic diagram of the present invention;

(a) The figure is the world coordinate system 1;

(b) The figure is a schematic diagram of the layout of the laser displacement sensor and the intermediate conversion coordinate system 2;

(c) is the local coordinate system 3 of the laser displacement sensor;

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

Detailed ways

As shown in Figure 1, based on the idea of differential geometry, a 3-point micro-plane is selected near a certain point on the surface, and the normal vector of this micro-plane is used to approximately replace the normal vector at the point on the surface. The resulting error is affected by the micro-plane The effect of size. Therefore, the size of the microplane is selected according to the accuracy requirement, and 1 represents the sensor.

Referring to Fig. 2, 1 represents a sensor, and 2 represents a spherical surface. The implementation steps of the present invention are: establishing a measurement model——attitude parameter calibration——surface normal measurement, and the specific implementation methods are as follows:

(1) Install the three laser sensors on the three-coordinate measuring machine, and make the three emitted lasers form a cone, and adjust the taper to control the size of the micro-plane according to the accuracy requirements.

(2) Use a three-coordinate measuring machine to establish a world coordinate system 1, that is, the coordinate system 1 in Figure 2, and select the coordinate system at the end joint of the three-coordinate measuring machine as the intermediate conversion coordinate system 2, that is, the coordinate system in Figure 2 2. In addition, three local coordinate systems are established along the laser line as the Z axis and the sensor working reference point as the origin. The relationship of each coordinate system is as follows: the transformation relationship between coordinate system 1 and coordinate system 2 is the end pose of the three-coordinate measuring machine, which is obtained from the software of the three-coordinate measuring machine; the transformation relationship between coordinate system 3 and coordinate system 2 is the laser displacement sensor The attitude parameters are to be calibrated.

(3) Place a standard sphere in the world coordinate system 1, use a three-coordinate measuring machine to calibrate the coordinates of the center of the sphere, and establish a spherical equation according to the radius of the standard sphere: (xa) ² +(yb) ² +(zc) ² ＝r ² , for parameter calibration.

(4) Take a single sensor as the research object, control the three-coordinate measuring machine to collect 30 measuring points on the standard spherical surface, and collect the displacement value L _i of each measuring point through the data acquisition equipment, and the measuring point can be obtained under the local coordinate system 3 The coordinates (0, 0, w _i ), w _i =-L _i .

(5) Coordinate transformation: transform the measuring point coordinates (0, 0, w _i ) into the world coordinate system 1, and the transformation formula is

$P_i=R_0*R_i*\left(\begin{array}{c}0\\ 0\\ w_i\\ 1\end{array}\right)$ i=1,2,3

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}$

$<span\; class="notranslate">\; =</span>\left[\begin{array}{cccc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]<span\; class="notranslate">\; *</span>\left[\begin{array}{cccc}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]<span\; class="notranslate">\; +</span>\left[\begin{array}{cccc}\mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right]$

In the formula, P _i represents the coordinates of the laser point; R ₀ is the end pose of the three-coordinate measuring machine, which is obtained from the software of the three-coordinate measuring machine; R _i is the homogeneous transformation matrix of the local coordinate system 3 relative to the intermediate transformation coordinate system 2, Among them, r _z1 and r _x2 are the z-axis and x-axis rotation angles of coordinate system 3 around coordinate system 2 respectively, (a _i , b _i , c _i ) are the translation vectors of coordinate system 3 to coordinate system 2, and each parameter is to be calibrated . After transformation, the coordinates satisfy the spherical equation (x _P -a) ² +(y _P -b) ² +(z _P -c) ² =r ² ; 30 spherical equations are obtained.

(6) The 30 spherical equations obtained by using the fminsearch minimum optimization method in matlab can be solved for each parameter in the coordinate transformation formula.

(7) After the parameters are solved, the surface normal measurement can be carried out. The implementation algorithm is: collect data through 3 sensors, and obtain the spatial coordinates of 3 points on the surface, which can form 3 vectors. The cross product of any 2 vectors can obtain the normal vector of the microplane, that is, the normal vector of the surface. The algorithm uses programming It is realized by software, and the obtained vector is used in measurement fields such as normal error correction and normal attitude adjustment.

In aircraft automatic drilling and riveting technology, the tool is usually required to feed along the normal direction of the skin processing point to ensure the processing quality of the hole. Automatic attitude adjustment is required in the automation process, and the normal direction at the processing point must be obtained, and then the normal direction is fed back to the control system for attitude adjustment. The invention just solves how to realize the acquisition of the normal direction, and utilizes laser non-contact measurement, high measurement accuracy, convenience and other characteristics, and can meet the actual application requirements.

Claims (2)

1. One kind based on 3 little planar processes to detection method, it is characterized in that: carry out as follows:

   1) set up model: 3 laser displacement sensor annulars are distributed in the head of three coordinate measuring machine, and the spatial attitude of sensor can make that laser is tapered to be penetrated on curved surface, controls 3 formed little plane sizes of laser point according to accuracy requirement adjustment tapering;

   2) set up space coordinates: at first, set up a world coordinate system 1 with three coordinate measuring machine; Select for use the terminal joint coordinate system of three coordinate measuring machine as intermediate conversion coordinate system 2 then; On each laser displacement sensor, setting up one in addition penetrates direction with laser rays and is z axle negative sense, is the local coordinate system 3 of true origin with laser displacement sensor work RP;

   3) image data: utilize data collecting card and LabVIEW software collection laser displacement sensor voltage signal and convert shift value L into _i

   4) calculate the coordinate of laser point: the displacement that utilizes laser displacement sensor to record promptly know the coordinate of laser point under local coordinate system 3 (0,0, w _i), w _i=-L _i, according to the Eulerian coordinates conversion formula, try to achieve the coordinate of 3 laser point under coordinate system 1 respectively, the coordinate conversion formula is following:

   $P_i=R_0*R_i*\left(\begin{array}{c}0\\ 0\\ w_i\\ 1\end{array}\right),$ i＝1，2，3

   $R_i=R_{z1}*R_{x2}+T_i$

   $=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& \cos \left(r_{z1}\right)& \sin \left(r_{z1}\right)& 0\\ 0& -\sin \left(r_{z1}\right)& \cos \left(r_{z1}\right)& 0\\ 0& 0& 0& 1\end{array}\right]*\left[\begin{array}{cccc}\cos \left(r_{x2}\right)& \sin \left(r_{x2}\right)& 0& 0\\ -\sin \left(r_{x2}\right)& \cos \left(r_{x2}\right)& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right]+\left[\begin{array}{cccc}0& 0& 0& a_i\\ 0& 0& 0& b_i\\ 0& 0& 0& c_i\\ 0& 0& 0& 0\end{array}\right]$

   P in the formula _iThe coordinate of expression laser point; R ₀Be the terminal pose of three coordinate measuring machine, from three coordinate measuring machine software, obtain; R _iBe the homogeneous transformation matrix of local coordinate system 3 with respect to intermediate conversion coordinate system 2, wherein r _Z1, r _X2Be respectively coordinate system 3 around the z of coordinate system 2 axle, the x axle anglec of rotation, (a _i, b _i, c _i) be the translation vector of 3 pairs of coordinate systems 2 of coordinate system, to r _Z1, r _X2, (a _i, b _i, c _i) demarcate;

   5) computing method vector: 3 laser point coordinates of trying to achieve with step 4) can solve 3 vectors, and wherein any 2 vectorial multiplication crosses get final product to such an extent that 3 little planar processes are vectorial again, and formula is following:

   $\stackrel{\&RightArrow;}{P_2{P}_1}=(P_{x1}-P_{x2},P_{y1}-P_{y2},P_{z1}-P_{z2})$

   $\stackrel{\&RightArrow;}{P_2{P}_3}=(P_{x3}-P_{x2},P_{y3}-P_{y2},P_{z3}-P_{z2})$

   $\stackrel{\&RightArrow;}{N}=\stackrel{\&RightArrow;}{P_2{P}_1}\&times;\stackrel{\&RightArrow;}{P_2{P}_3}$

   The normal vector that calculates is applied to normal error correction, the adjustment of normal direction attitude, normal direction detection.
2. 2. method according to claim 1 is characterized in that, described laser displacement sensor attitude parameter scaling method: implementation step is following:

   (1) according to step 1) in the claim 1 laser displacement sensor is installed on the three dimensional coordinate measuring machine head and sets up following measurement space: according to step 2 in the claim 1) use three coordinate measuring machine to set up a world coordinate system 1 and set up an intermediate conversion coordinate system 2, in world coordinate system 1, draft a spherical equation (x-a) then with standard ball ²+ (y-b) ²+ (z-c) ²=r ², wherein, (a, b, c) expression sphere centre coordinate, r representes the radius of a ball, and sphere centre coordinate is demarcated with three coordinate measuring machine, and the radius of a ball is known;

   (2) on sphere, evenly gather 30 measuring points with one of them sensor operated three coordinate measuring machine, obtain 30 shift values;

   (3) the shift value substitution spherical equation that records is used fminsearch minimum optimization method and find the solution each parameter value;

   (4) repeating step (2), step (3) are found the solution the attitude parameter of other 2 sensors.

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