JPH0370168B2 - - Google Patents

Description

[Detailed description of the invention]

[Industrial Field of Application] The present invention relates to a method of detecting a three-dimensional attitude angle relative to a pattern in which marks such as circles are placed at quarter positions on one circumference. [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 necessary to detect the position of the bolt in the bolt hole of the wheel and the wheel mounting portion of the vehicle body, and to align both positions to mount the wheel. 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. , the position of those holes,
That is, it is necessary to automatically detect the orientation of the parts. Furthermore, when a mobile object such as a mobile robot that moves within a space appropriately measures its own posture, a circular shape, such as a circular By displaying a simple and characteristic pattern with marks and detecting that pattern on the moving object, the attitude of the moving object itself can be measured. Conventionally, although attitude angle detection using such a mark pattern can be performed using relatively advanced pattern recognition technology, no method has been proposed that uses a simple and inexpensive device. [Problems to be Solved by the Invention] An object of the present invention is to provide a method for automatically detecting a three-dimensional posture relative to the mark pattern with high precision using a very simple and inexpensive device. There is a particular thing. [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 located at four equal positions on one circumference is formed on the x-axis, y-axis, and 2 which is in a position opposite to the center of the above circle in a state where it takes an appropriately rotated posture around the z-axis.
A technical technique that measures the positional deviation of a set of marks in two axial directions perpendicular to the line of sight and perpendicular to each other, and detects the three-dimensional posture angle relative to the mark pattern based on the ratio. means are 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 FIG. 2A, the mark pattern for detecting the relative three-dimensional posture in the present invention is a circle of approximately _{the same} diameter, a circle of approximately the same diameter,
In addition, there are marks 1 to 4 of arbitrary shapes, and this mark pattern is an x′y′z′ rotational coordinate that allows an arbitrary posture to be taken by giving rotation around each coordinate axis with respect to the xyz fixed coordinate system. On the x′y′ plane of the 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. In order to observe the mark pattern in the above rotating coordinate system from the xyz fixed coordinate system as shown in FIG. 2B, marks 1 and 2 in the xyz rotating coordinate system are
Let the coordinates of these marks be P ₁ ′ (r ₀ , 0, 0) P ′ ₂ (0, r ₀ , 0) respectively, and convert the coordinates of those marks to coordinates P ₁ and P ₂ in the xyz fixed coordinate system. , coordinates P ₁ and P ₂ can be expressed as follows by referring to Table 1. 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 marks 1 and 3 and for each of marks 2 and 4,
The positional deviation in the x-axis direction perpendicular to the viewing direction (z-axis direction) is defined as P31→(x) and P24→(x), and the positional deviation in the y-axis direction orthogonal to the z-axis and x-axis is defined as P31→ (y) and P42→(y), measure their positional deviations, and calculate γ ₁ , γ ₂ , and γ ₃ as follows, using a relatively simplified formula:
Relative attitude angles φ, ψ, and θ around the x-axis, y-axis, and z-axis 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・cos
φ・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・sinφ）r ₀ = tanθ・sinφ・tanψ/1+tanθ・sinφ・t
anψ……(2) γ ₃ =P31(x)/P42(y)=2(cosθ・tanψ
+sinφ・sinψ）r ₀ ／2cosθ・cosφ・r ₀ =cosψ／cosφ＋tanθ・tanφ・sinψ……(
3) As can be seen from equation (1) above, 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 can be calculated.
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. Next, considering the measurement errors when detecting the attitude angles of such a pattern, the measurement errors Δθ, Δφ, and Δψ for the attitude angles θ, φ, and ψ are determined by the above ratios γ ₁ , γ ₂ , and γ ₃ When the measurement accuracy for Δγ ₁ , Δγ ₂ and Δγ ₃ is expressed as follows. First, the measurement error Δθ for the attitude angle θ is (1)
From the formula, it is given by Δγ ₁ = 1/cos ² θ・Δθ ∴Δθ=cos ² θ・Δγ ₁ (5). Also, if we differentiate equation (3) and consider equation (5), A ₁ Δφ+B ₁ Δψ+C ₁ =0 ......(6) However, A ₁ = tanθ・sinψ+sinφ・cosψ B ₁ = sinφ(tanθ・sinφ・cosψ-sinψ) C ₁ = cos ² φ(tanφ・sinψ・Δγ ₁ -Δγ ₃ ). Similarly, by differentiating equation (2) and considering equation (5), A ₂ Δφ+B ₂ Δψ+C ₂ =0 ......(7) However, A ₂ = cosφ・sinψ・cosψ(1+tan ² θ) B ₂ = sinφ(1+tan ² θ) C ₂ = {(1+tanθ・sinφ・tanψ) ²・Δγ ₂ −(1+sin ² φ・tan ² ψ)・Δγ ₁ }cos ² ψ. Therefore, from equations (6) and (7) above, Δφ,
Δψ can be found. Δφ=C ₂ B ₁ −C ₁ B ₂ /A ₁ B ₂ −A ₂ B ₁ Δψ=C ₂ A ₁ −C ₁ A ₂ /B ₁ A ₂ −B _{2 A} 1Figures 3 to 7 are , which shows the measurement error when measuring the attitude angles θ, φ, and ψ. Figure 3 shows the change in the measurement error Δθ with respect to the attitude angle θ (in this case, Δθ is unrelated to the fluctuations in φ and ψ). be.)
FIGS. 4 and 5 show changes in Δφ and Δφ with respect to ψ when θ=0°, with the value of φ changed in several steps. In addition, Figs. 6 and 7 show φ
The change in Δφ and Δψ with respect to ψ when = 15° is expressed as θ
The value of is shown in several stages. In these drawings, it is assumed that the measurement error for 20 meshes is the ratio of KS meshes during input processing by the image input device for the above pattern, and the case where Δθ, Δφ, and Δψ are calculated by changing the value of KS is shown. It shows. Generally, when an image of the above pattern is captured with a 20 x 20 mesh using an image input device with a 64 x 48 mesh, the KS is 0.5~
0.25, and performing image processing at four times that amount (256) is common practice in television cameras, so by performing such image processing, the measurement accuracy simply increases. 1/4, making it easy to obtain excellent measurement accuracy. Note that the apparatus for implementing the attitude angle detection method described above converts the above 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 image two of the opposing positions in the above pattern. The configuration may be such that the positional deviations of the sets of marks can be measured and the above-mentioned calculations can be performed, thereby making it possible to detect the attitude angles θ, φ, and ψ. [Example] Display a figure as shown in FIG. 2A on a flat plate,
The plate is moved around the horizontal axis by the supporting arm at an angle φ
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°, The error was measured. 8 to 10 show the measurement results, the curves in the figures show the theoretical values explained above, and each point shows the measured values. Note that the value of KS above is 0.25
It is. Since this experimental result agrees well with the calculated value, the reliability of the calculated value has been confirmed. [Effects of the Invention] As described in detail above, according to the attitude angle detection method of the present invention, the three-dimensional attitude of the pattern can be automatically detected with high precision using a very simple and inexpensive device.

[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
7 to 7 are explanatory diagrams of errors in detecting attitude angles according to the present invention, and FIGS. 8 to 10 are graphs showing experimental results regarding the present invention. 1 to 4...mark.

Claims (1)

[Claims] 1. In a state where the patterns each having marks at four equal positions on the circumference of a circle are appropriately rotated around the x-axis, y-axis, and z-axis that are perpendicular to each other, the pattern is placed facing the center of the circle. Measures the positional deviation of two sets of marks at the same position in two axial directions perpendicular to the viewing direction and perpendicular to each other, and detects the three-dimensional attitude angle relative to the mark pattern based on the ratio. A method for detecting a three-dimensional attitude angle using a mark pattern.