JPS63133002A - 3-d coordinate measuring apparatus - Google Patents

Abstract

PURPOSE:To measure the position and attitude of an object simply at a high accuracy in a 3-D space, by determining parameters with a first calculator to obtain an origin vector, an attitude vector and the like with a second calculator from the parameters. CONSTITUTION:Feature points 1-n are taken with a TV camera 21 at (n) points on an object 22. Image output signals from the TV camera 21 are processed with an image processor 23 to determine the position (pi, qi) of the feature points 1-n in an image coordinate system. Parameters k1-k11 are determined with a calculator 24 according to the formula I from the image position (pi, qi) of the feature points 1-n and a 3-D position (aj, bj, cj) (wherein j=1-n) of feature points 1-n in an object coordinate system. Then, an origin position vector R=(rx, ry, rz) and an attitude vector L=(lx, ly, lz) in an object coordinate system (a, b, c) are determined with a calculator 25 according to the formula II from the parameters k1-k11.

Description

DETAILED DESCRIPTION OF THE INVENTION (Field of Industrial Application) The present invention relates to an apparatus for measuring the position of an object in a three-dimensional space using a camera.

(Conventional technology) In factory automation, televisions, cameras (visual sensors)
The need often arises to determine the position of an object using .

For example, when inserting a bottle into a hole drilled on a flat surface, the flat surface must be set in the correct position and orientation.

In order to set the plane in the correct position and orientation, it is necessary to measure the position and orientation of the plane. Kneebing hang (
Yubin Hung) and others in 1985.
IEEE International Conference on Robotics and Automation (IEEE I)
international conference
Robotics and Automation
) on pages 80 to 85 of the proceedings of ``Pudge Plunging Touno Planar Point Set (Pa5s
ive ranging to known plana
There is a method described as r point 5ets), 4. This paper describes a method for measuring the position of four marks in a three-dimensional space by capturing images of four marks marked on a plane with a known geometrical relationship using a television camera. That is, assuming that the two-dimensional positions (a, b) of the four marks on the plane are known,
The position of each mark in three-dimensional space is calculated from the position (p, q) of each mark in a two-dimensional image coordinate system measured by a television camera and the two-dimensional position (a, b) on the plane. . Therefore, by this method, the position and orientation of the plane can be measured.

(Problem to be Solved by the Invention) However, when applying the above-mentioned conventional method to a three-dimensional object, the surface of the object is divided into planes, and the measurement method regarding the two-dimensional plane is sequentially applied to each plane. The disadvantage is that the procedure is complicated and the amount of calculation is large. Furthermore, there may be cases where the surface of the object cannot be sufficiently divided into planes.

SUMMARY OF THE INVENTION An object of the present invention is to provide a position/orientation measuring means applicable to three-dimensional objects in order to overcome the drawbacks of conventional methods. More specifically, an object of the present invention is to provide a means for measuring at least one of the position and orientation of a three-dimensional object without dividing the surface of the three-dimensional object into planes.

(Means for Solving the Problems) Means provided by the present invention in order to solve the above-mentioned problems and achieve the above objects is to use a camera to create a three-dimensional coordinate system whose origin is the center of the lens of the camera. In a device that measures at least one of the position or orientation of a three-dimensional object in a camera coordinate system, n points (
a camera that images an object having feature points (n≧6); and a camera that processes an image output signal of the camera to determine the position (p, q) of each feature point in a two-dimensional image coordinate system with the focal point of the lens as the origin. ), and an object coordinate system (a*) that describes the shape of the object in three-dimensional coordinates.
The coordinate values (
al,b+pc+)(:i-1,2°...,n) and the image coordinate value of the feature point (p,.

q+) (i-1, 2, . . . , n) as a parameter in a perspective projection relationship, a first calculation device that determines ~kll, and -wk, as the determined parameter.

from the position vector R of the origin of the object coordinate system (a, b, c) in the camera coordinate system (x, y * z)
−(rt #ry, r*), a-axis direction cosine vector L−(i,,,j2.,!,), b-axis direction cosine vector M=(m,,m,,m,) and the direction cosine vector of the a-axis (nA1nFynt), (where,
r,,=g f'/k% + k,! +f'
”k%.

r,! -f'/-zks"+ky"+f"
k+e”.

T ts 糟f'/ ka” + k, 1+ f ”k
1% and f is the focal length of the camera/lens system) rg-,
r, /f' ry ” k s r t/ f' Rt -k * r g/ f' r f! y -k
* T t/ f' * fl t-k e T *
m z =k s T t/ f' + ! 11y
"k t r 7 f' + mt" k r *
T wn x −k a T w/ f * ny
−k s T */ f * n m ” k t
and a second calculation device that calculates r T *.

(Function) The measurement system consisting of the television camera 21 shown in FIG. 2 and the three-dimensional object 22 is as shown in FIG.
A three-dimensional coordinate system (camera coordinate system) (x, y,
x), image coordinate system (image coordinate system) (p, q)
, an object coordinate system (a
, b, c) In the present invention, all of these coordinate systems are orthogonal coordinate systems.

Furthermore, the object coordinate system (a
* b * C) coordinate values at (a (g b
l*c, ), 15m1, 2. ..., n, and these coordinate values (a I * t) I * CI) are all known.

The three-dimensional coordinate system (x + y, z) is an orthogonal coordinate system for describing three-dimensional space, and its origin O coincides with the center of the lens as shown in Figure 3, and the z-axis coincides with the optical axis of the lens. It shall coincide with the axis. Also, a two-dimensional image coordinate system (
p, q), and p.

The q axes are parallel to the X e F axes, and the origin is the intersection of the lens optical axis (two axes) and the plane.

In the above object coordinate system (a * b * c), a, b,
Let the unit direction cosine vectors in the three-dimensional space (1, 3F, Z) of the a-axis be L-C1,,1,,N,''), M
−(mt, m,, mI+), N=(nt+ n,, n,
) the origin is Rm (y, , y, , y, )
Then, the position of point (a, b, c) in three-dimensional space
(x.

y, z) is represented by X=R+aL+bM+cN. On the other hand, the perspective projection image (
Since p, q) is p=f, /, q-f'y8, the image (p, q) in the image coordinate system of the point (a, b, c) in the object coordinate system is expressed by the following equation ( la).

(1b).

here, It is.

Therefore, the perspective projection image of each feature point (al+ 1)I+ l:I) is ('p++ q+)i=1.2,...
, n, the following equation holds.

From this, if we rearrange the previous equation (3), we get the following parameter: ~ICt+
A linear equation for is obtained.

JQ-U ... (4) However, here, the solution that minimizes the root mean square error (l small square solution) Q
is Q-(J"J)-'J"U...(
5) is given by

Here, since the vectors L, M, and N are unit vectors, fl , '+ l , "+ l , "x mf"+ f
n,”+m%w n,”+n,”+n,s fi
l...(6) holds true. Substituting the previous equation (1b) into the previous equation (6), we get *”+ ks”+ r ”ks’-kx”+ ky”
+ f'"k+*"...(7) From the previous equation (7), if the focal length r is known, rl is...
(8a) It can be found by either of the following. However, if r8 is found, from the previous formula (1b), rzr rye L-(j! g, l y, j! ++
) *M! (fn!, my Hfn g)
+N-(nz, nyHng) is determined by the following formula.

(Embodiment) FIG. 1 is an overall configuration diagram showing an embodiment of the present invention. A television camera 21 images n feature points 1 to n on an object 22 in FIG. The apex of an object, the center of a hole, etc. may be selected as the feature point. Further, a specific mark may be added to the object.

The image processing device 23 is a device that processes the image output signal of the television camera 21 and determines the position (p+, q+) (it to n) of each feature point 1 to n in the image coordinate system. Many image processing devices currently on the market have such feature extraction functions and image processing functions, and the present invention is premised on the use of such image processing devices.

The calculation device 24 in FIG. 1 calculates the image position (p+, q+) (i=1 to n) of the feature point and the three-dimensional position (a l rb r , c ) of the feature point in the object coordinate system.
This is a device that calculates ~k11 as a parameter from r ) (i −1 to n ) according to the above equation (5).

The calculation device 25 calculates the origin position vector R−(r
Engineering.

rF+rri+posture vector L-(Q,,l,,fl
,).

M ” (m t + m y + m s ),
This is a device for calculating N'' (n x , ny , n , ). The above calculation devices 24 and 25 can be easily realized by a microcomputer.

(Effects of the Invention) As described above, according to the present invention, it is possible to obtain a device that measures the position and orientation of an object in a three-dimensional space with high precision.

[Brief explanation of the drawing]

FIG. 1 is a block diagram showing an embodiment of the present invention, FIG. 2 is a perspective view showing a measurement system consisting of a television camera 21 and a three-dimensional object 22, and FIG. 3 is a perspective view for explaining the invention in detail. FIG. 2 is a coordinate system correspondence diagram for explaining the correspondence between three-dimensional coordinate systems (a, b, c) and (x, y, z) and an image coordinate system (p, q). 1.2.3 to 18...Feature point, 21...TV camera, 22...Object, 23...Image processing device, 24
, 25, ... calculation device.

Claims (1)

[Scope of Claims] A device that uses a camera to measure at least one of the position or orientation of a three-dimensional object in a camera coordinate system, which is a three-dimensional coordinate system with the origin at the center of the lens of the camera. a camera that images an object having n feature points (n≧6) with a known value, and a two-dimensional image coordinate system that processes the image output signal of the camera and has the focal point of the lens of each feature point as the origin. position (p, q) in
and an image processing device that measures the n in an object coordinate system (a, b, c) that describes the shape of the object in three-dimensional coordinates.
Coordinate values of feature points (a_i, b_i, c_i) (i=
1, 2, ..., n) and the image coordinate value of the feature point (
p_i, q_i) (i=1, 2, ..., n), the perspective projection relation p_i=(k_1+a_ik_2+b_ik_3+c_
ik_4)/(1+a_ik_9+b_ik_1_0+
c_ik_1_1) q_i=(k_6+a_ik_8+
b_ik_7+c_ik_8)/(1+a_ik_9+
a first calculation device that calculates parameters k_1 to k_1_1 in the camera coordinate system (x, y, z) from the determined parameters k_1 to k_1_1;
, b, c) position vector R=(r_x, r_y
, r_z), a-axis direction cosine vector L=(l_x, l
_y, l_z), b-axis direction cosine vector M=(m_x
, m_y, m_z) and the direction cosine vector of the c-axis (n
_x, n_y, n_z), r_z=r_z_1, r_
z_2, r_z_3 or (r_z_1+r_z_2+r
_z_3)/3 (where r_z_1=f/√(k_2
^2+k_■^2+f^2k_9^2), r_z_2=
f/√(k_8^2+k_7^2+f^2k_1_0^
2), r_z_3=f/√(k_4^2+k_■^2+
f^2k_1_1^2) f is the focal length of the camera/lens system) r_x=k_1r_z/f r_y=k_5r_z/f l_x=k_2r_z/f, l_y=k_6r_z/f
, l_z=k_9r_zm_x=k_3r_z/f, m
_y=k_7r_z/f, m_z=k_1_0r_zn
_x=k_4r_z/f, n_y=k_8r_z/f,
and a second calculation device that calculates n_z=k_1_1r_z.