JPH0781859B2 - Position measurement method - Google Patents

Description

Description: TECHNICAL FIELD The present invention relates to a position measuring method for measuring a reference position of a measuring object using a plurality of optical systems.

[Conventional technology]

Conventionally, stereoscopic measurement using triangulation has been proposed, which seeks the position of a measurement target based on the reference distance between two cameras and the angle at which the measurement target is viewed from the baseline. When measuring the position of the measurement target, it is necessary to know the installation position coordinates of the optical system accurately to improve the measurement accuracy. Therefore, in order to obtain the true installation position parameter of the optical system, the installation position is measured by another measuring jig or the like, or calculated from the drawing.

[Problems to be solved by the invention]

However, in such a conventional method, since the parameters to be used are obtained as data obtained from outside the measurement system such as the installation direction and position of the optical system, the error increases as the distance between the measurement target and the optical system increases. In addition, since the measurement accuracy of this parameter requires a value equal to or higher than the accuracy obtained from the measurement target, there is a problem in that it cannot be easily installed.

[Means for solving problems]

In order to solve such a problem, the present invention uses only parameters within a measurement range, measures a measurement target with at least two optical systems, and determines each straight line passing through the measurement targets in the two optical systems as reference coordinates. The coordinates of an unknown point are determined from the intersections of these points. The specific means is as follows.

(A) First, two cameras are installed in the field of view while capturing the measurement object, and the optical system is used to measure the optical axis of each optical system without directly measuring the focal position of the optical system. Ask for.

(B) At least two planes orthogonal to the optical axis are obtained within the field of view of each optical system.

(C) The points obtained by projecting the measurement target on these surfaces are represented by three-dimensional reference coordinates.

(D) As a result, the object to be measured can be represented by the three-dimensional reference coordinates by the points projected on these surfaces. Therefore, by connecting the points projected on the above-mentioned opposing surfaces, the known A pair of straight lines including an unknown point where the measurement target exists in the reference coordinate system is obtained.

(E) The coordinate value of the unknown point can be represented by the coordinate value of the known reference coordinate system by obtaining the coordinate value of the intersection of the straight line.

[Operation] A straight line including the measurement object and represented by the reference coordinate system is obtained for each optical system, and the coordinates of the intersection are obtained as the position of the measurement object.

〔Example〕

FIG. 2 is a diagram for explaining the principle of a method for detecting the position of a measurement target by applying the present invention. In the figure, X, Y,
The known coordinate system represented by the Cartesian coordinate system of Z is the reference coordinate system,
Coordinate values of the reference coordinate system are reference coordinates (may be called coordinates when there is no risk of confusion with other coordinate systems)
It is defined as Further, the coordinates of the point A are represented as (X, Y, Z) _A (hereinafter, the same applies to other coordinate systems, the coordinate values are shown in parentheses, and the subscripts indicate the names of the points).

(X, Y, Z) _A, (X, Y, Z) known two points A represented by _B, when viewed B from (X, Y, Z) of a point P to be measured is represented by _P, the straight line If the angles formed by ▲ ▼ and ▲ ▼ and the coordinate axes are (α, β, γ) _P1 and (α, β, γ) _P2 , respectively, point P
The coordinates of are as follows.

X _P ＝ X _A ＋ D ₁ cosα _P1 ＝ X _B ＋ D ₂ cos α _P2 …… (1) Y _P ＝ Y _A ＋ D ₁ cosβ _P1 ＝ Y _B ＋ D ₂ cos β _P2 …… (2) Z _P ＝ Z _A ＋ D ₁ cos γ _P1 = Z _B + D ₂ cosγ _P2 (3) However, D ₁ and D ₂ are as follows.

D ₁ : Length of straight line ▲ ▼ D ₂ : Length of straight line ▲ ▼ 2 The coordinates of the intersection point P of straight lines are as follows from equations (1) to (3).

X _P ＝ X _B ＋ D ₂ cos α _P2 …… (1a) Y _P ＝ Y _B ＋ D ₂ cos β _P2 …… (2a) Z _P ＝ Z _B ＋ D ₂ cos γ _P2 …… (3a) where D ₂ is Desired.

Since it has been proved that the coordinates of the unknown point P can be obtained by knowing the coordinates of the intersection of the two straight lines in this way, the method of obtaining the straight line will be described next.

FIG. 3 is a view showing planes H ₁ and H ₂ which are orthogonal to the optical axis and are parallel to each other when the point P is seen by the camera 1 and the point P is projected on the planes. The Cartesian coordinate system represented by x, y of the two-dimensional plane in the field of view seen by the camera is called the vision coordinate system, and the coordinate values of that coordinate system are called the vision coordinates (when there is no fear of confusion with the reference coordinates). There is)
It is defined as

Assuming that the amount of deviation of the point P from the optical axis is Δx, Δy, the coordinates of the points (X, Y, Z) _PH1 and (X, Y, Z) _PH2 projected on each surface are as follows.

However, a _{11 to} c ₁₂ are calibration coefficients, which will be described later, when converting the vision coordinates into the reference coordinates.

Point projected on _two planes H ₁ and H ₂ (X, Y, Z) _PH1 (X, Y, Z)
_{When PH2} is calculated, the coordinates of these two points are used next, and the point P
A straight line L ₁ passing through 3 points including is obtained by the following formula.

However, d ₁ is the distance between the point P and (X, Y, Z) _{PH 1} in FIG. 3, and each cosine value is obtained as follows.

A = (X _PH1 −X _PH2 ) ² + (Y _PH1 −Y _PH2 ) ² + (Z _PH1 −Z _PH2 ) ² (9) At least two cameras are used for measurement in stereoscopic view. Similarly for the camera, planes H ₃ , H ₄ and straight line L ₂
(These are not shown in FIG. 3, but are shown in FIG. 1).

However, X _PH3 , Y _PH3 , Z _PH3 , and d ₂ are the specifications obtained by the same method as described above in the optical system of the camera. Moreover, each cosine value is as follows.

B = (X _PH3 −X _PH4 ) ² + (Y _PH3 −Y _PH4 ) ² + (Z _PH3 −Z _PH4 ) ² Figure 4 shows the relationship between the straight line L ₁ thus obtained and the reference coordinate system. ing.

The above idea is explained assuming that the direction of the optical axis is given, but it is not yet known at this axial point, so a method for obtaining it will be explained next. Rows that connexion the Kiyari blade Chillon to obtain the reference coordinates of the unknown point, two lines l _b, the coordinates 1 _c intersects the plane H ₁ perpendicular to the optical axis l _a through focus f as shown in FIG. 5 To (x, y) b, (x, y)
As c, it is necessary to find the direction and starting point of the two straight lines as follows.

In FIG. 5, for example, members with circular holes are shown as X, Y, Z
Mount it on the table and position the center of the hole along the optical axis l _a as point A ₁
~ A ₂ and move to the center coordinates of the hole (X, Y,
Z) Get _{A1 and A2} . To check whether the center of the hole is on the optical axis, look at the hole with the camera and measure the center of the hole (pixels)
Should always be equal when moving through the hole. In calibration, the measured value at the center of the hole is (x,
y) Move the hole so that it becomes _a and obtain the reference coordinates (X, Y, Z) _A1 of that point. Also again, moving the hole, measurements of Bijiyon (x, y) Another point to A _{1 which a} is not changed (X, Y,
Z) Get _A2 . However, (x, y) _a is the center position of the visual field of the camera. Similarly, for straight lines l _b and l _c , do the following.

When the measurement value with the camera is (x, y) _{b in} the vision coordinates, the reference coordinates of the hole are (X, Y, Z) _B1 and (X, Y, Z) _B2 .
Further, when the measurement value by the camera is (x, y) _{c in} the vision coordinates, the reference coordinates of the hole are (X, Y, Z) _C1 and (X, Y, Z) _C2 .

The equation of line l _a is

d _a is the distance from (X, Y, Z) _A1 to (X, Y, Z) _a , and each cosine value is obtained as follows.

C = (X _A1 −X _A2 ) ² + (Y _A1 −Y _A2 ) ² + (Z _A1 −Z _A2 ) ²
(14) In this way, by finding the direction of the optical axis and the starting point, the installation direction of the camera can be known.

Reference coordinates where the optical axis intersects the surface, reference coordinates for the point where the straight line l _b intersects the vision coordinates (x, y) _b on the surface, and reference points where the straight line l _c intersects the top surface vision coordinates (x, y) _c By obtaining the coordinates, the coordinates on the surface can be represented by the reference coordinates.

Next, a method for determining the plane orthogonal to the optical axis will be described with reference to FIG. A plane can be determined by knowing the coordinates of the three points contained on that plane. Points in Figure 6
As one point out of three points to determine the surface H ₁ orthogonal to B ₁ in the through connexion optical axis l _a is a point B _1, obtaining the other two points. Face H ₁
And the distance d ₁₀ between the point A ₁ on the optical axis and the point A ₁ on the optical axis are expressed by the equation of the plane as

d ₁₀ = (B ₁ −A ₁ ) _X cosα ₁ + (B ₁ −A ₁ ) _Y cosβ ₁ + (B ₁ −A ₁ ) _Z cosγ ₁ where cosα ₁ , cosβ ₁ and cosγ ₁ are the direction cosine of the optical axis. Is.
Then, the reference coordinates of point I in FIG. 6 are expressed as follows.

Then another straight line l _c and the point is to determine the point of intersection of the plane _{H 1 (X, Y, Z} ) C1, (X, Y, Z) in the same manner as C ₁ point and the above-described the _C2 as measurement points point of intersection with the plane perpendicular to the street light axis l _a and the optical axis l _a
The distance d ₁₁ from XI to the point A1 is obtained. Further the distance d ₁₂ from the surface and the optical axis l ₁ and intersecting point XII perpendicular point C ₂ and as optical axis l ₁ to the point A ₁ be determined in a similar manner. Here, the orthographic projection lengths a, b, c, and d for each axis have the following relationships.

The coordinate X ₆ of the intersection point VI between the straight line l _c and the surface H ₁ is obtained as follows.

Similarly by obtaining the coordinates of Y _6, Z _6, the optical axis l _a including the point B ₁
The coordinate values of three points on the plane orthogonal to can be determined.

Next, a method of converting the vision coordinates on the surface into the reference coordinates will be described. In Fig. 7, in order to express the points on the surface from the vision coordinates on the surface H ₁ using the reference coordinates, the coordinates on the surface (x, y) and the reference coordinates (X, Y, Z) The relationship is that the points where the optical axis and the plane are orthogonal are (x ₀ , y ₀ ), (X,
Y, Z) ₁ , and at point B ₁ (x ₁ , y ₁ ), (X, Y,
Z) _B1 , and at point VI, they are expressed as (x ₂ , y ₂ ), (X, Y, Z) ₆ , so that the following relationship holds.

[(X, Y, Z) _B1 − (X, Y, Z) ₁ ] ∝ [x ₁ , y ₁ ) − (x ₀ , y ₀ )] (18) [(X, Y, Z) ₆ − (X, Y, Z) ₁ ] ∝ [x ₂ , y ₂ ) − (x ₀ , y ₀ )] …… (19) The following relation between two orthogonal coordinate systems sharing the origin in space. There is.

Since the surface H ₁ is two-dimensional, the term of z becomes zero, and (18),
Equation (19) is as follows.

Where a ₁₁ and a ₁₂ are calibration coefficients, Δx ₁ and Δx ₂ ,
Δy ₁ and Δy ₂ are obtained from the following equations.

Δx ₁ = x ₁ −x ₀ Δy ₂ = y ₁ −y ₀ Δx ₂ = x ₂ −x ₀ Δy ₂ = y ₂ −y _{0 From} equation (21), a ₁₁ and a ₁₂ can be obtained. Also b ₁₁ , b
_{The same} can be obtained for ₁₂ , c ₁₁ and c ₁₂ .

From the above, when the measurement target is viewed with a camera, the point projected on the surface is
The values when the coordinates on ₁ are converted to the standard coordinates are as follows.

Similarly, when the coordinates on the other surface H ₂ are converted into the reference coordinates, the values are as follows.

X _PH2 = X ₂ + a ₂₁ (x-x ₀ ) + a ₂₂ (y-y ₀ ) Y _PH2 = Y ₂ + b ₂₁ (x-x ₀ ) + b ₂₂ (y-y ₀ ) Z _PH2 = Z ₂ + c ₂₁ ( x−x ₀ ) + c ₂₂ (y−y ₀ ), where a ₂₁ , a ₂₂ , b ₂₁ , b ₂₂ , c ₂₁ , c ₂₂ are calibration coefficients, which convert the vision coordinates to the reference coordinates. Is a coefficient for. Further, X _1,2 , Y _1,2 and Z _1,2 represent coordinates of points where the respective planes and the optical axis are orthogonal to each other.

FIG. 1 is a diagram showing an optical system that obtains information for performing the above-described calculation, and shows surfaces H ₁ and H formed by the camera 1.
If the straight line is found to contain the two points on the measurement object and the space in the I connexion reference coordinate system _2, since the obtained straight even surface H _3, H ₄ made similarly by the camera 2, the intersection of the two straight lines By obtaining the coordinates, the spatial position coordinates of the measurement target in the reference coordinate system can be obtained. Therefore, the position of the measurement target can be obtained without directly measuring the focal position of the optical system.

In the above embodiment, one camera is assumed to have two surfaces, but if three or more surfaces are used and a straight line connecting points on those surfaces is obtained by the least square method, more accurate measurement can be performed. It

〔The invention's effect〕

As described above, according to the present invention, by forming a plurality of surfaces in the measurement field of view, it is possible to determine the straight line connecting the focal point of the optical system and the measurement target only with the data obtained from the measurement range. Installation data obtained from outside the range is unnecessary. Therefore, the measurement result is not governed by the accuracy of the installation data, and the optical system can be easily installed.
In addition, since the calculation parameters such as the optical axis are calculated using the optical system of our own, the detection accuracy of the calculation parameters and the measurement accuracy of the optical system can be treated as the same standard, and the measurement accuracy can be improved simply by improving the resolution of the optical system. It has the effect of being able to.

[Brief description of drawings]

FIG. 1 is a diagram showing an optical system for obtaining data for carrying out the present invention, FIG. 2 is a diagram for explaining a method for detecting the position of a measuring object by applying the present invention, and FIG. FIG. 4 is a diagram showing a state in which the point P is projected when the point P is viewed by a camera, FIG. 4 is a diagram showing a relationship between a straight line L and Cartesian coordinates, and FIG.
FIG. 6 is a diagram for explaining the direction of two straight lines and how to find the starting point, FIG. 6 is a diagram for explaining how to find a plane orthogonal to the optical axis, and FIG. 7 is a diagram showing the obtained vision coordinates as reference coordinates. It is a figure for demonstrating the method of converting into. 1,2 …… Camera, P …… Measurement target, H ₁ , H ₂ , H ₃ , H ₄ …… Face,
A, B …… observation point, l _a …… optical axis, l _b , l _c …… straight line, X, Y, Z…
... reference coordinates, x, y ... vision coordinates, f ... focus of optical system.

Claims (1)

[Claims] 1. A position measuring method in which position data of a measuring object is obtained by a plurality of optical systems, and the position of the measuring object in a reference coordinate system arbitrarily set from the obtained data is measured. The equation of the first straight line expressed by the reference coordinates connecting the projection points of the measurement target projected on at least two surfaces which are orthogonal and parallel to each other and which are expressed by the reference coordinates respectively, and other optical systems And an equation of a second straight line represented by the reference coordinates connecting the projection points of the measurement target projected on at least two surfaces which are orthogonal to the optical axis and are parallel to each other and are represented by the reference coordinates, respectively, A position measuring method characterized by finding the reference coordinates of the intersection of straight lines based on the equation of each straight line.