CN101957175B - Three-point micro-plane-based normal detection method - Google Patents

Abstract

The invention discloses a three-point micro-plane-based normal detection method. Based on differential geometry thought, namely a method for approximately substituting a micro-plane for a micro-curved surface and due to the application of a laser displacement sensor technique and a data acquisition technique, the normal vector of a point to be measured on a curved surface can be measured by a certain algorithm. A method for calibrating relevant parameters comprises the following steps of: establishing a measuring space; formulating a spherical surface and establishing a spherical surface equation; after installing a sensor, acquiring a plurality of data points, which must meet the spherical surface equation, from the spherical surface by using the sensor so as to obtain a plurality of parameter-containing equations; and solving the equation set by a fminsearch minimum optimization method to work out the relevant parameters. The three-point micro-plane-based normal detection method has the advantages of capacity of performing non-contact measurement, high measurement precision, convenient and quick measurement and application in the fields of measurement such as normal error correction, normal posture adjustment, normal detection and the like.

Description

Based on 3 little plane formula normal direction detection methods

Technical field

The present invention relates to a kind of normal direction detection technique in the field of measurement, specifically is a kind of based on design and the correlation parameter scaling method of Surface Method 3 little planar processes, the employing non-contact measurement to measuring method.

Background technology

In commercial production, measuring technique is being brought into play very important effect, along with development of technology; The particularly development of laser technology, sensor technology; Measurement means is variation and evolution earlier more, and the measurand that requires in the production run simultaneously is also more and more, many times need measure the normal vector on a certain curved surface; Like the brill riveting in aircraft manufacturing process technology, the method vector coincidence at point to be processed place on the processing axis that just requires boring and riveting machine and the aircraft skin; Domestic technology and document about this respect is fewer at present, therefore proposes Surface Method to measurement, and designs a kind of measuring method and correlation parameter scaling method, and the field of measurement in commercial production has the significant values meaning.

Summary of the invention

The object of the present invention is to provide the scaling method of a kind of Surface Method to measurement and correlation parameter.The present invention has utilized laser sensor technology and data acquisition technology and based on the design philosophy of 3 little planar processes, can carry out the measurement of curved surface normal direction accurately, quickly and easily.

The present invention realizes that through following technical scheme implementation step is following:

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:

$\stackrel{\&RightArrow;}{P_2{\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="HDA0000026228760000011.png"\; state="\{\{state\}\}">P</figure-callout>}}_1}=(P_{x1}-P_{x2},P_{y1}-P_{y2},P_{z1}-P_{z2})$

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

$\stackrel{\&RightArrow;}{N}=\stackrel{\&RightArrow;}{P_2{\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="HDA0000026228760000011.png"\; state="\{\{state\}\}">P</figure-callout>}}_1}\&times;\stackrel{\&RightArrow;}{P_2{P}_3}$

The normal vector that calculates is applied to normal error correction, the adjustment of normal direction attitude, normal direction detection.

Described laser displacement sensor attitude parameter scaling method: implementation step is following:

1) according to step 1) in (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 (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) finds the solution the attitude parameter of other 2 sensors.

Design concept of the present invention replaces little curved surface based on differential geometric thought-little plane approximation, has adopted laser sensor technology, not only can carry out non-contact measurement, and measuring accuracy height, convenient measurement, fast; Calibration algorithm among the present invention is simple, easy in addition realizes, and when application fminsearch minimum optimization is found the solution, initial value is chosen less demanding.

Description of drawings

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

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

(a) figure is a world coordinate system 1;

(b) figure is that laser displacement sensor is arranged synoptic diagram and intermediate conversion coordinate system 2;

(c) be laser displacement sensor local coordinate system 3;

Below in conjunction with accompanying drawing content of the present invention is done further explain.

Embodiment

With reference to shown in Figure 1, be based on infinitesimal geometry thought, choosing 1 the 3 small plane of point type near certain point on the curved surface, with the approximate normal vector that replaces this some place on the curved surface of the normal vector on this small plane, resultant error receives the influence of little plane sizes.Therefore, little plane sizes is chosen according to accuracy requirement, 1 expression sensor.

With reference to shown in Figure 2,1 expression sensor, 2 expression spheres.Implementation step of the present invention is: set up measurement model---attitude parameter demarcation---, and Surface Method is to measurement, and embodiment is following:

(1) 3 laser sensors is installed on the three coordinate measuring machine, and makes 3 laser of ejaculation constitute taper, regulate the size that tapering is controlled little plane according to accuracy requirement.

(2) use three coordinate measuring machine to set up a world coordinate system 1; It is the coordinate system 1 in the accompanying drawing 2; Selecting the coordinate system of the terminal joint of three coordinate measuring machine for use is intermediate conversion coordinate system 2; Being coordinate system 2 in the accompanying drawing 2, is the Z axle along laser rays respectively in addition, is that initial point is set up 3 local coordinate systems 3 with the working sensor RP.The relation of each coordinate system is following: coordinate system 1 is the terminal pose of three coordinate measuring machine with the transformation relation of coordinate system 2, from three coordinate measuring machine software, obtains; Coordinate system 3 is that the laser displacement sensor attitude parameter is to be calibrated with the transformation relation of coordinate system 2.

(3) in world coordinate system 1, place a standard ball, use three coordinate measuring machine to demarcate sphere centre coordinate, and set up spherical equation: (x-a) according to the standard ball radius ²+ (y-b) ²+ (z-c) ²=r ², be used for parameter calibration.

(4) with the single-sensor be research object, the control three coordinate measuring machine is gathered 30 measuring points on the standard sphere, collect the shift value L of each measuring point through data acquisition equipment _i, can obtain the coordinate of measuring point under local coordinate system 3 (0,0, w _i), w _i=-L _i

(5) carry out coordinate transform: with the measuring point coordinate (0,0, w _i) transform in the world coordinate system 1, transformation for mula does

$P_i=R_0*R_i*\left(\begin{array}{c}0\\ 0\\ w_i\\ 1\end{array}\right)$ 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, each parameter is to be calibrated.Coordinate satisfies spherical equation (x after the conversion _P-a) ²+ (y _P-b) ²+ (z _P-c) ²=r ²Obtain 30 spherical equations.

(6) in matlab, use fminsearch minimum optimization method and find the solution 30 spherical equations that obtain, can solve each parameter in the coordinate transform formula.

(7) after each parametric solution comes out, then can carry out the curved surface normal direction and measure.Implementation algorithm is: through 3 sensor acquisition data; On curved surface, obtain the volume coordinate of 3 points; Can constitute 3 vectors, any 2 vectorial multiplication crosses can be tried to achieve little planar process vector, i.e. Surface Method vector; Algorithm realizes that with programming software the vector that draws is used for field of measurement such as normal error correction, the adjustment of normal direction attitude.

Bore in the riveting technology in the aircraft robotization, require cutter usually, to guarantee the crudy in hole along the normal direction feeding of covering processing stand place.Need carry out automatic posture adjustment in the automation process, must obtain the normal direction at processing stand place, then normal direction fed back to control system and carry out the attitude adjustment.Characteristics such as the present invention has just solved how to realize obtaining of normal direction, and has utilized the laser without contact measurement, and measuring accuracy is high, and is convenient can meet practical application request.

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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