JPH0412801B2 - - Google Patents

Description

[Detailed description of the invention]

[Industrial Field of Application] The present invention is a method of measuring the distance to the placement position of the pattern by using a posture measurement mark pattern having circular marks or the like at four equal positions on one circumference. It is related to. [Prior Art] For example, an automobile wheel has bolt holes at four equal positions on one circumference of a disk portion in the rim, and the wheel is automatically attached to the wheel attachment portion of the vehicle body. In such cases, it is desirable to be able to automatically detect the array positions of the bolt holes of the wheel and to be able to measure the distance to the bolt holes. In addition, not only the wheels of the automobile mentioned above, but also various industrial parts often have some kind of mark such as a hole at four equal parts of a circumference, and it is difficult to automatically assemble the parts. , it is usually necessary to automatically detect the positions of these holes, that is, the orientation of the parts, and the distance to the parts. Furthermore, when a mobile object such as a mobile robot that moves within a space appropriately measures its own posture and position, a circular shape is placed at an appropriate position within the space at four equal positions on one circumference. By displaying a simple and characteristic pattern with marks such as , etc., and detecting that pattern on the moving body, the attitude of the moving body itself and the position to the mark can be measured. Conventionally, although it is possible to detect attitude angles and distances using mark patterns using relatively advanced pattern recognition technology, no method has been proposed using simple and inexpensive equipment. do not have. [Problems to be Solved by the Invention] An object of the present invention is to automatically detect a three-dimensional posture relative to the mark pattern using a very simple and inexpensive device, and at the same time to detect a three-dimensional posture relative to the pattern using a very simple and inexpensive device. An object of the present invention is to provide a method of automatically measuring the distance to a mark pattern using the mark pattern. [Means for Solving the Problems] In order to achieve the above object, the method of the present invention provides a method in which a pattern in which marks are placed at four equal positions on one circumference is appropriately rotated around three orthogonal axes. This mark pattern is measured through an optical system in a state in which Then, the position relative to the mark pattern is measured, and the position up to the mark pattern is measured based on the measured value of the amount of positional deviation in the x-axis or y-axis direction when the mark pattern is imaged by the above-mentioned optical system. The technical means of distance measurement is adopted. To explain the method of the present invention in more detail, the first
In a fixed xyz coordinate system in a certain space as shown in Figure A, rotate by an angle φ around the x axis,
Rotate around the y-axis by an angle ψ, then rotate around the z-axis by an angle θ, and the newly obtained rotating coordinate system is created as shown in Figure 1B.
Assuming the x′y′z′ coordinate system, from the above xyz fixed coordinate system,
Coordinate transformation to the x′y′z′ rotating coordinate system can be performed by geometric calculation using the relationships shown in Table 1.

[Table] As shown in Figure 2A, the mark pattern used to measure relative three-dimensional posture and distance in the present invention is placed at four equal positions on the circumference of radius r ₀ , with approximately the same diameter. There are marks 1 to 4 in a circular or other arbitrary shape, and this mark pattern provides an x'y'z' arbitrary posture by giving rotation around each coordinate axis to the xyz fixed coordinate system. rotational coordinate system
It is assumed that the center of the circle in which the marks 1 to 4 are arranged is aligned with the origin of the rotating coordinate system on the x'y' plane. The pattern in the above rotating coordinate system is shown in Figure 2B.
_In order to observe from the xyz fixed coordinate system as shown in _{Fig .} , r ₀ , 0) and convert the coordinates of those marks into coordinates P ₁ and P ₂ in the xyz fixed coordinate system.The coordinate values of coordinates P ₁ and P ₂ can be calculated as follows by referring to Table 1. It can be expressed as P ₁ {(cosθ・cosψ＋sinθ・sinφ・sinψ) r ₀ ,
sinθ・cosφ・r ₀ , −(cosθ・sinψ−sinθ・sinφ・sinψ) r ₀ } P ₂ {(−sinθ・cosψ＋cosθ・sinφ・sinψ) r ₀ ,
cosθ・cosφ・r ₀ , (sinθ・sinψ+cosθ・sinφ・cosψ) r ₀ } Here, two sets of marks located opposite to the center of the circle in which the above marks 1 to 4 are arranged, namely mark 1, 3 and marks 2 and 4, respectively.
Let the positional deviation in the x-axis direction perpendicular to the viewing direction (z-axis direction) be P31 → (x) and P24 → (x), and the above z
The positional deviation in the y-axis direction perpendicular to the axis and x-axis is expressed as P
31→(y) and P42→(y), measure their positional deviations, and calculate the following γ ₁ , γ ₂ , and γ ₃ , the above can be obtained using a relatively simple formula. x-axis,
Relative attitude angles φ, ψ, and θ about the y- and z-axes can be measured. Note that the calculation formulas for the attitude angles φ, ψ, and θ shown here are merely examples, and are not limited to these. γ ₁ =P31/→(y)/P42(y)=2sinθ・cosφ・r ₀
/2cosθ・cosφ・r ₀ =tanθ ...(1) γ ₂ =P24/→(x)/P31(x)=2(sinθ・cosψ
−cosθ・sinφ・sinψ) r ₀ /2(cosθ・cosψ＋sinθ
・sinφ・sinψ) r ₀ = tanθ−sinφ・tanψ/1+tanθ
・sinφ・tanψ……(2) γ ₃ =P31/→(x)/P42(y)=2(cosθ・cosψ
+sinθ・sinφ・sinψ）r ₀ ／2cosθ・cosφ・r ₀ =cos
ψ／cosφ＋tanθ・tanφ・sinψ……(3) As can be seen from the above equation (1), z of the pattern
The attitude angle θ around the axis can be determined by the following equation, regardless of the attitude angles φ and ψ around the other y- and z-axes. θ=tan ^-1 (γ ₁ ) ...(4) Also, if the value of θ can be calculated in this way, using equations (2) and (3) as simultaneous equations, x of the above pattern
The rotation angles φ, ψ around the axis and the y-axis can be calculated. Note that the distances from the x-axis to mark 1 or mark 3 are the same, and the distances from the x-axis to mark 2 or mark 4 are also the same, so when measuring γ ₁ , γ ₂ and γ ₃ mentioned above, , instead of measuring the distance between marks, it is also possible to measure the distance from the x-axis to each desired mark. The above measurement is performed by appropriately processing an optical image obtained through an optical system, since the mark pattern is measured from a distant position. In this case, since the attitude with respect to the mark pattern is measured based on the ratio of positional deviations in the x and y axis directions for the mark located at the opposing position, measurement can be performed regardless of the distance to the mark pattern. Next, a method of measuring the distance to the posture measurement mark pattern using such a mark pattern will be described. The coordinate P ₁ when mark 1 is viewed from the xyz fixed coordinate system is given by the formula described above. Therefore, for example, if the x coordinate of mark 1 is measured and it is R, then the following The radius r ₀ of the same circumference on which the four marks are placed can be found using the formula. r ₀ =R/cos θ·cos ψ+sin θ·sin φ·sin ψ When measuring the x or y coordinate of the mark as R, the above equation needs to be changed with reference to Table 1. Of course, the value of this radius r ₀ is known at the stage of arranging the marks, but since the above radius r ₀ is large when the marks are viewed close up and small when viewed from a distance, from this relationship The distance can be found. Now, as shown in Fig. 3, when an object of length S (length corresponding to the above R) is viewed through the optical system from a position of distance L, an image generated at a position of distance b from the optical system. If the size is I, the following relationship holds true. S・b/L=I...(5) Also, in the optical system, there is a relationship of 1/L+1/b=1/f...(6), so the above equation (5) becomes I=S・It can be expressed as 1/(L/f)-1...(7). Therefore, by measuring the size I of the image, the distance L can be determined. However, the measurement can also be facilitated by the following processing. That is, when an object of known length S is viewed from a known reference distance L ^* using an optical system with a known focal length f ^* , the size of the image is I ^* (this can be measured accurately). Then, from the above equation (7), I ^* = S・1/(L ^* / f ^* ) − 1 ... (8) is obtained, and from the above equations (7) and (8), I/ I ^* = (L ^* / f ^* ) - 1 / (L / f) - 1 ... (9
) becomes. Therefore, by rearranging this equation (9), the distance L to the center of gravity of the four marks can be obtained using the following equation. In this case, distance L is independent of S. L=f[(L ^* /f ^* -1)・(I ^* /I)+1]...(1
0) In the above equation (10), if the focal length of the optical system is a constant value, L=f ^* [(L ^* /f ^* -1)・(I ^* /I) + 1]... (
11) becomes. Furthermore, by using a zoom system, the focal length of the optical system can be varied depending on the distance to the object, and if the size of the image is always constant, then L = f / f ^* L ^* , and the distance L can be easily calculated. You can ask for it. In addition, with a fixed focus system, the size of the image changes when the distance L changes, resulting in a measurement error depending on the size of the image, but as described above, by making the focal length of the optical system variable, If the size is always constant, the measurement error will not change depending on the distance. Next, the measurement error when detecting the distance to such a pattern will be considered. From the above-mentioned equation (7), the distance L can be determined as follows: L=f·(S/I+1) (11). Differentiating this equation (11) yields ∂L=(S/I+1)∂f+f(1/I∂S−S/I ² ∂I) (12). In this equation (12), since S is constant, if ∂S=0, ∂L=L[(∂f/f)−f/b(∂I/I)]...
…(13) becomes. In the above equation, ∂f/f is the focal length setting error, and ∂I/I is the image size setting error. The results of error calculations according to such calculation examples are shown in FIGS. 4 to 9. Figure 4 shows the case of a fixed focus with a constant focal length, L = 710 mm, f = 20 mm, ∂I/I =
0.05, ∂f/f is changed in several steps, and the relative accuracy with respect to the distance L on the horizontal axis is shown as ∂L/L. Note that this figure is in the form of a line graph, but this is because the portions that appear on the minus side are displayed on the plus side. According to FIG. 4, a relatively large error is expected, but in FIGS. 5 and 6, under the same conditions as in FIG. 4, ∂I/I=0.025, or ∂I/I=
When shown as 0.0125, the error is considerably smaller. On the other hand, if you use a zoom system to maintain a variable focus and keep the image size constant,
As can be seen from FIG. 7, an excellent accuracy of 5% or less can be obtained. Moreover, in the case of a fixed focus, the image becomes smaller as the distance increases and the error increases, but in the case of a variable focus, the size of the image is constant, so the image is always constant regardless of the distance. Accuracy can be obtained. Figure 8 shows a comparison of the measurement accuracy in the fixed focus case and the variable focus case under the conditions of ∂I/I=0.05 and ∂f/f=0, and the image size curve is also shown in the figure. It is also listed. Each curve showing the image size in the case of a fixed focus shows the case where the focal length f of the optical system is set to the specified value at the distance L specified in the figure in order to keep the size of the image constant. It is something. According to FIG. 8, the measurement accuracy in the variable focus case is superior to that in the fixed focus case, and moreover, the accuracy is constant. FIG. 9 shows the actual size of the error ∂L instead of the relative accuracy ∂L/L of the distance L shown in FIG. The above-mentioned device for detecting attitude angle and measuring distance converts the above-mentioned pattern into an image using an ITV camera or other image input device, and uses an arithmetic device connected to the image input device to detect opposing positions in the above-mentioned pattern. What is necessary is to measure the positional deviation of the two sets of marks and perform the above calculation, and at the same time calculate the distance, thereby measuring the attitude angle and distance in real time. be able to. [Example] Display a figure as shown in FIG. 2A on a flat plate,
The flat plate is rotated by the pointing arm at an angle φ around the horizontal axis.
and the support arm is rotatably supported by an angle ψ around a vertical axis, and the flat plate is rotated around a horizontal axis and a vertical axis while fixed at θ = 0°, I measured the distance. The preset distance L is 710 mm. FIG. 10 shows the measurement error during the measurement. This shows that measurement can be performed within the theoretical error value described above. [Effects of the Invention] According to the method of the present invention, it is possible to measure the relative posture to the mark pattern as well as the distance to the mark pattern using a very simple and inexpensive device. Distance measurement can be performed regardless of the situation. Since the above-mentioned attitude and distance measurements can be carried out in a short time using a relatively simple device, it is advantageous for use in cases where real-time processing is required, such as when measuring the attitude and position of a moving object. It is.

[Brief explanation of drawings]

1A and 1B are explanatory diagrams regarding a fixed coordinate system and a rotating coordinate system for explaining the attitude angle detection method of the present invention, and FIGS. 2A and 2B are explanatory diagrams regarding the coordinate transformation of a pattern between the above two coordinate systems. Figure, 3rd
The figure is an explanatory diagram for distance measurement, FIGS. 4 to 9 are explanatory diagrams for measuring distance according to the present invention, and FIG. 10 is a graph showing experimental results regarding the present invention. 1 to 4...mark.

Claims (1)

[Claims] 1 In a state where a pattern with marks at four equal positions on one circumference assumes an appropriately rotated attitude around three orthogonal axes, this mark pattern is measured through an optical system and relative to the center of the circle. The relative posture with respect to the mark pattern is measured based on the ratio of the positional deviation in the x and y axis directions, which are orthogonal to the line of sight direction and orthogonal to each other, for the mark at the opposing position. A distance measurement method using a mark pattern for posture measurement, characterized in that the distance to the mark pattern is measured based on the measured value of the amount of positional deviation in the x-axis or y-axis direction when an image is formed.