CN1356530A - In-situ calibration device for large-size 3D space measurement and its measuring method - Google Patents

Abstract

An in-situ calibrater for lage-size 3D space measurement and its measuring method is disclosed. A standard object with known reference distance is used, and more than 2 theodolites are used to observe the known standard point on said standard object at same time. A constraint equation is created on the basis of said standard distance and theodolite parameters, and then solved by optimizing method to obtain the model parameters of the odolite. Its advantages include no error caused by human factor, and high measuring precision.

Description

The in-situ calibration device of large scale three-dimensional space measurement and measuring method

Technical field

The invention belongs to fine measuring instrument and measuring method, particularly a kind of in-situ calibration device of large scale three-dimensional space measurement and measuring method.

Background technology

Demarcation is the basis of precision measurement, is the important step of modern metrology and measurement, and measuring equipment or instrument must just possess measuring accuracy through the demarcation of higher extra fine grade instrument (or device), are used for actual measurement.

In the linear measure longimetry field, medium size is Commonly Used Size, the surveying instrument kind is many, relevant calibration technique and device are more complete, the use of small size and large-scale metrology instrument (or device) is lacked relatively, relevant calibration technique and install also imperfection, especially the on-site proving of large scale 3 d space coordinate surveying instrument also lacks effective technical means.

The key problem in technology that can be implemented in on-site proving volume coordinate surveying instrument is: set up a high precision 3 d space coordinate measurement mechanism at the scene, with this device to being demarcated by calibration system.Under the current techniques condition, the on-the-spot effective scheme of setting up high precision 3 d space coordinate measurement mechanism is to adopt two (or many) high-precision electronic transits to constitute packaged type large scale volume coordinate measurement mechanisms, its measuring principle is spatial intersection's measuring principle: after supposing that two transits are fixing, relation each other (location parameter) is known, when observing a certain measured point simultaneously with two transits, by this some observation angle and the location parameter between two transits in two transits just can be in the hope of this coordinate in the space.

The three-dimensional coordinate measurement principle of being made up of two transits as shown in Figure 2.Two transits are called left transit and right transit, and the coordinate system of their correspondences is respectively O ₁X ₁Y ₁Z ₁, O ₂X ₂Y ₂Z ₂, establish measured point P at O ₁X ₁Y ₁Z ₁And O ₂X ₂Y ₂Z ₂In coordinate be respectively (x ₁, y ₁, z ₁), (x ₂, y ₂, z ₂), during measurement, left transit survey P point is at O ₁X ₁Y ₁Z ₁In horizontal angle and vertical angle be α ₁, β ₁, right transit survey P is at O ₂X ₂Y ₂Z ₂In horizontal angle and vertical angle be α ₂, β ₂, know by the space analysis relation: ${\{}_{{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="A0113650200081.png"\; state="\{\{state\}\}">y</figure-callout>}}_1={\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="A0113650200081.png"\; state="\{\{state\}\}">z</figure-callout>}}_1{\&CenterDot;}^{\mathrm{tg}{\mathrm{\&beta;}}_1}{/}_{\sin {\mathrm{\&alpha;}}_1}}^{x_1={\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="A0113650200081.png"\; state="\{\{state\}\}">z</figure-callout>}}_1\&CenterDot;{\mathrm{ctg\&alpha;}}_1}---\left(1\right)$ ${\{}_{{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="A0113650200081.png"\; state="\{\{state\}\}">y</figure-callout>}}_2={\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="A0113650200081.png"\; state="\{\{state\}\}">z</figure-callout>}}_2{\&CenterDot;}^{\mathrm{tg}{\mathrm{\&beta;}}_2}{/}_{{\sin \mathrm{\&alpha;}}_2}}^{x_2={\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="A0113650200081.png"\; state="\{\{state\}\}">z</figure-callout>}}_2\&CenterDot;\mathrm{ctg}{\mathrm{\&alpha;}}_2}---\left(2\right)$ $\left[\begin{array}{c}{x}_2\\ y_2\\ {\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="A0113650200081.png"\; state="\{\{state\}\}">z</figure-callout>}}_2\end{array}\right]=\left[\begin{array}{ccc}r1& r2& r3\\ r4& r5& r6\\ r7& r8& r9\end{array}\right]\left[\begin{array}{c}{x}_1\\ y_1\\ {\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="A0113650200081.png"\; state="\{\{state\}\}">z</figure-callout>}}_1\end{array}\right]+\left[\begin{array}{c}t1\\ t2\\ t3\end{array}\right]---\left(3\right)$ $R=\left[\begin{array}{ccc}r1& r2& r3\\ r4& r5& r6\\ r7& r8& r9\end{array}\right]T=\left[\begin{array}{c}t1\\ t2\\ t3\end{array}\right]---\left(4\right)$

α in above-mentioned three formulas ₁, β ₁, α ₂, β ₂Be the transit survey value, RT is O ₁X ₁Y ₁Z ₁Coordinate system and O ₂X ₂Y ₂Z ₂Position relational matrix between the coordinate system (rotation matrix and translation matrix) is a fixed value, should determine in advance, so can solve the P point at O ₁X ₁Y ₁Z ₁Or O ₂X ₂Y ₂Z ₂Three-dimensional coordinate in the coordinate system.

By measuring principle as can be seen, remove the angle measurement accuracy (α of transit ₁, β ₁, α ₂, β ₂In the measuring error that comprises) and the P locus (x of ordering ₁, y ₁, z ₁, x ₂, y ₂, z ₂The size of value) influencing outside the measuring accuracy---they all are the unsurmountable errors of principless, have determined to measure the full accuracy that can reach.How to determine coordinate system O ₁X ₁Y ₁Z ₁And O ₂X ₂Y ₂Z ₂Between spatial relation (R, the error that comprises in the T parameter) directly influence measuring accuracy, be the main error component of actual measurement.

In current application, determine spatial relation adopts accurately adjustment more and takes aim at scheme mutually between the transit: at first with two accurate level-ofves of transit, the surface level revolving shaft (the y coordinate axis of transit coordinate system) of two transits of assurance is parallel to each other; Secondly aim at mutually with two transits, set the x coordinate axis (or z coordinate axis) of two transits in surface level with this and be parallel to each other.Coordinate system through accurate adjusted two transits is parallel to each other, and promptly rotation matrix R is unit matrix I, only has pure translation relation between two transit coordinate systems.After obtaining rotation matrix R and being unit matrix I, adopt to measure the space reference distance method, can obtain the translation matrix T between the coordinate system easily.Accurately the adjustment and the scheme of taking aim at mutually determine that rotation matrix has comprised sizable personal error factor between the transit coordinate system: at first, when adjusting the transit level, the manual adjustment precision is difficult to reach 2 " in; Secondly, when two transits are taken aim at mutually, because run-home is telescopical center, be unfavorable for that transit accurately aims at, have very big pointing error, the rotation matrix R of Que Dinging contains than mistake thus, and this error also can further pass to translation matrix T; The situation that another one must be considered is, in a lot of site of deployment, may have immovable barrier in the space between the transit, can not take aim at mutually between the transit.Therefore, the major defect of this method is: because manual intervention is certain to introduce suitable error, thereby influences measuring accuracy.

Summary of the invention

When adopting two above transits to set up high precision 3 d space coordinate measurement mechanism, how accurately to determine the spatial relation between two transits, the measuring error that overcomes the human factor introducing fully is the main contents of this patent invention.The present invention realizes with following method:

Need not manually adjust link, adopt the reference material of a known reference distance, be carved with two gauge points on the reference material, distance is known reference range between gauge point, observe known mark point on the reference material simultaneously with two transits, the reference range that utilizes reference material is as constraint condition, sets up to comprise between two transits the spatial relation parameter at interior equation of constraint, the utilization optimization method is found the solution above-mentioned equation of constraint, solves two spatial relation parameters between the transit.This reference material can be a gauge, can be carved with two cross grooves (gauge point) on the chi, and its spacing is known, and invariable.Spatial relation principle between accurately definite two transits as shown in Figure 1.

Before discuss, the key that improves measuring accuracy is the spatial relation parameter of accurately determining between the transit: rotation matrix R and translation matrix T.Get by (3) formula

(T ₁-X ₂t ₃)[Y ₂(r ₇X ₁+r ₈Y ₁+r ₉)-(r ₄X ₁+r ₅Y ₁+r ₆)]＝ (5)

(t ₁-Y ₂t ₃) [X ₂(r ₇X ₁+ r ₈Y ₁+ r ₉)-(r ₁X ₁+ r ₂Y ₁+ r ₃)] in the formula: ${\{}_{{\mathrm{<figure-callout\; id="1"\; label="Y"\; filenames="A0113650200081.png"\; state="\{\{state\}\}">Y</figure-callout>}}_1=\mathrm{tg}{\mathrm{\&beta;}}_1/{\sin \mathrm{\&alpha;}}_1}^{{\mathrm{<figure-callout\; id="1"\; label="X"\; filenames="A0113650200081.png"\; state="\{\{state\}\}">X</figure-callout>}}_1=\mathrm{ctg}{\mathrm{\&alpha;}}_1}{\{}_{{\mathrm{<figure-callout\; id="2"\; label="Y"\; filenames="A0113650200081.png"\; state="\{\{state\}\}">Y</figure-callout>}}_2=\mathrm{tg}{\mathrm{\&beta;}}_2/\sin {\mathrm{\&alpha;}}_2}^{{\mathrm{<figure-callout\; id="2"\; label="X"\; filenames="A0113650200081.png"\; state="\{\{state\}\}">X</figure-callout>}}_2=\mathrm{ctg}{\mathrm{\&alpha;}}_2}$ α ₁, β ₁, α ₂, β ₂Be respectively two transits and record the horizontal angle and the vertical angle of impact point.

(5) the formula correspondence is nonlinear equation, wherein contain 12 all in rotation matrix R and translation matrix T parameters to be asked, and this equation is for variable t ₁, t ₂, t ₃Be homogeneous.

Allow two transits aim at the different n in a space impact point P simultaneously _i(i=1 ..., n) obtain n equation, promptly

(t ₁-X _2it ₃)[Y _2i(r ₇X _1i+r ₈Y _1i+r ₉)-(r ₄X _1i+r ₅Y _1i+r ₆)]＝ (6)

(t ₁-Y _2it ₃)[X _2i(r ₇X _1i+r ₈Y _1i+r ₉)-(r ₁X _1i+r ₂Y _1i+r ₃)] ${\{}_{Y_{1i}=\mathrm{tg}{\mathrm{\&beta;}}_{1i}/\sin {\mathrm{\&alpha;}}_{1i}}^{X_{1i}=\mathrm{ctg}{\mathrm{\&alpha;}}_{1i}}{\{}_{Y_{2i}=\mathrm{tg}{\mathrm{\&beta;}}_{2i}/\sin {\mathrm{\&alpha;}}_{2i}}^{X_{2i}=\mathrm{ctg}{\mathrm{\&alpha;}}_{2i}}$ I=1 in the formula ..., n.In addition, the element among the rotation matrix R satisfies the quadrature constraint:

Simultaneous (6) (7) adopts non-linear optimized Algorithm (as the Gauss-Newton method), and (this equation is for variable t can to calculate all elements among the rotation matrix R and two elements among the T ₁, t ₂, t ₃Be homogeneous).

After obtaining two elements among rotation matrix R and the T, with two gauge points (reference range is D therebetween) on two transit aiming space criteria things, can obtain the 3 d space coordinate (wherein comprising the another one unknown element among the T) of two gauge points by (1) (2) (3), equal this constraint condition of reference range D by distance between two points, obtain all elements among the translation matrix T easily.During practical application, can will find the solution rotation matrix R and the translation matrix T combines, that is: aim at gauge point on the reference material that is positioned at the space diverse location simultaneously with two transits, obtain equation (6) and reference range D, calculate rotation matrix R and translation matrix T simultaneously.

Above-mentioned finding the solution in rotation matrix R and the translation matrix T process eliminated accurate adjustment and taken aim at link mutually, overcome the measuring error that human factor is introduced from principle, improved measuring accuracy effectively, and avoided the influence of spatial obstacle thing.

Experimental results show that: the combined type transit three-dimensional coordinate measurement device that adopts this measurement model, " transit of angle measurement accuracy can be realized the linear measure longimetry precision of 3 μ m in the 1m scope can to realize the pairing linear measure longimetry precision of transit self angle measurement accuracy fully: 0.5.

Description of drawings

Fig. 1: accurately determine spatial relation schematic diagram between two transits

Fig. 2: transit three-dimensional coordinate measurement schematic diagram;

Embodiment

As shown in Figure 1: the gauge 3 of a known reference apart from d is placed in the measurement space, with two transits 1,2 observe the cross groove (gauge point) on the gauge simultaneously, utilize on the gauge gauge point and reference range as constraint condition, set up and comprise two transit spatial relation parameters at interior equation of constraint.Change the position of gauge in measurement space more than 6 times, obtain a plurality of equation of constraint groups altogether, the equation of constraint group of utilizing optimization method to find the solution to obtain obtains two transit spatial relation parameters R, T.In model parameter substitution transit survey model, precision measurement that just can implementation space point three-dimensional coordinate need not manually participate in the adjustment of transit and aiming mutually during measurement.

Claims (3)

1. the in-situ calibration device of a large scale three-dimensional space measurement, this device is based on the 3 d space coordinate measuring principle of being made up of two transits at least, it is characterized by the reference material that adopts a known reference distance, put the spatial relation of calibrating between (orientation) two transits with the known standard on the transit may observe reference material.

2. the in-situ calibration device of a kind of large scale three-dimensional space measurement as claimed in claim 1, the reference material that it is characterized by the known reference distance can be a gauge, can be carved with two cross grooves on the chi, its spacing is known, and invariable.

3. the measuring method of the in-situ calibration device of a large scale three-dimensional space measurement is characterized by the method that position relation between two transits of a kind of accurate calibration (orientation) is provided:

1 P of two transit while observation spaces has

(t ₁-X ₂t ₃)[Y ₂(r ₇X ₁+r ₈Y ₁+r ₉)-(r ₄X ₁+r ₅Y ₁+r ₆)]＝

(t ₁-Y ₂t ₃) [X ₂(r ₇X ₁+ r ₈Y ₁+ r ₉)-(r ₁X ₁+ r ₂Y ₁+ r ₃)] in (5) formula: ${\{}_{Y_1=\mathrm{tg}{\mathrm{\&beta;}}_1/\sin {\mathrm{\&alpha;}}_1}^{X_1=\mathrm{ctg}{\mathrm{\&alpha;}}_1}{\{}_{Y_2=\mathrm{tg}{\mathrm{\&beta;}}_2/\sin {\mathrm{\&alpha;}}_2}^{X_2=\mathrm{ctg}{\mathrm{\&alpha;}}_2}$ α ₁, β ₁, α ₂, β ₂Be respectively two transits and record the horizontal angle and the vertical angle of impact point.r ₁～r ₉Be two elements among the spatial relation rotation matrix R between the transit, t ₁, t ₂, t ₃Be the element among the translation matrix T

(5) the formula correspondence is nonlinear equation, wherein contain 12 all in rotation matrix R and translation matrix T parameters to be asked, and this equation is for variable t ₁, t ₂, t ₃Be homogeneous.

Allow two transits aim at the different n in a space impact point P simultaneously _i(i=1 ..., n) obtain n equation, promptly

(t ₁-X _2it ₃)[Y _2i(r ₇X _1i+r ₈Y _1i+r ₉)-(r ₄X _1i+r ₅Y _1i+r ₆)]＝ (6)

(t ₁-Y _2it ₃)[X _2i(r ₇X _1i+r ₈Y _1i+r ₉)-(r ₁X _1i+r ₂Y _i1+r ₃)] ${\{}_{Y_{1i}=\mathrm{tg}{\mathrm{\&beta;}}_{1i}/\sin {\mathrm{\&alpha;}}_{1i}}^{X_{1i}=\mathrm{ctg}{\mathrm{\&alpha;}}_{1i}}{\{}_{Y_{2i}=\mathrm{tg}{\mathrm{\&beta;}}_{2i}/\sin {\mathrm{\&alpha;}}_{2i}}^{X_{2i}=\mathrm{ctg}{\mathrm{\&alpha;}}_{2i}}$ I=l in the formula ..., n.In addition, the element among the rotation matrix R satisfies the quadrature constraint:

Simultaneous (6) (7) adopts non-linear optimized Algorithm (as the Gauss-Newton method), can calculate all elements among the rotation matrix R and two elements among the T.

After obtaining two elements among rotation matrix R and the T, with two gauge points (reference range is D therebetween) on two transit aiming space criteria things, can obtain the 3 d space coordinate (wherein comprising the another one unknown element among the T) of two gauge points by (1) (2) (3) formula, equal this constraint condition of reference range D by distance between two points, obtain all elements among the translation matrix T easily.During practical application, can will find the solution rotation matrix R and the translation matrix T combines, that is: aim at gauge point on the reference material that is positioned at the space diverse location simultaneously with two transits, obtain equation (6) and reference range D, calculate rotation matrix R and translation matrix T simultaneously.

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