JPS63314604A - Generating method for working program of industrial robot - Google Patents

Abstract

PURPOSE:To generate a highly accurate working program even with a rough teaching action by minimizing the sum total of square of the error of each of error vector components (x), (y) and (z) against each pair of variables of a conversion matrix and then calculating the variable value by the minimum square method. CONSTITUTION:The sum total of square of the error of each of error vector components (x), (y) and (z) against each pair of variables of a conversion matrix. Then the variable value is calculated by the minimum square method and used as the most approximate value of the conversion matrix. Thus the minimum number of teaching points is limited to three and the error of the conversion matrix is reduced in proportion to the number of teaching points. As a result, the coordinate converting accuracy is improved and a highly accurate working program is generated.

Description

[Detailed Description of the Invention] [Field of Industrial Application] The present invention relates to a method for creating a work program for an industrial robot, and in particular, a method for creating a work program for an industrial robot by coordinate transformation from a teaching program created in advance by teaching. Concerning a work program creation method.

[Conventional technology]

Conventionally, the following method has been used to create a work program by coordinate transformation from a teaching program created in advance by teaching. First, create a teaching program by teaching the 3 or 4 representative points and work points on the reference workpiece.Next, teach the 3 or 4 corresponding representative points on the target workpiece, and create a teaching program using these points. A transformation matrix is obtained from the three or four representative points. To obtain this transformation matrix, substitute the above three or one teaching point into the coordinate transformation formula including the transformation matrix, and create a 12-element simultaneous -
The following equation is set up and the coordinates of the work point of the teaching program are transformed using this transformation matrix to create a work program.

[Problem that the invention seeks to solve]

However, since this conversion matrix was originally calculated using three or four points obtained by human teaching, there is an inherent teaching error when teaching these representative points, and the conversion matrix is The accuracy was not good at ±2n+n. For this reason, conventional methods were suitable for rough work such as spot welding and painting, but were unsuitable for work that required precision such as arc welding and sealing, and in this case, the position was corrected again after conversion. I needed to.

As described above, in the conventional method, the teaching error directly causes the problem of poor accuracy of the converted program.

In order to improve accuracy using conventional methods, increasing the number of teaching points is meaningless in both 3-point teaching and 41-point teaching, and there is no other way than to spend time teaching each teaching point accurately. However, doing so would increase the cost of teaching, and it would be cheaper to teach all points and not use coordinate transformation, so it cannot be adopted in reality.

SUMMARY OF THE INVENTION Accordingly, an object of the present invention is to provide a method for creating a work program for an industrial robot I, which is capable of creating a highly accurate work program even with sloppy teaching.

[Means for solving problems]

The above purpose is to introduce an error vector into the equation of coordinate transformation including the transformation matrix, and to calculate the x, y, z of this error vector.
The sum of the squares of the errors of each component is minimized for each set of variables in the transformation matrix, the value of that variable is calculated by the method of least squares, and the transformed 7-trinox is calculated using that variable as the most probable value. This is achieved by a method for creating a work program for an industrial robot, characterized in that the coordinates of the work points of the teaching program are transformed using this transformation matrix.

[Effect]

The sum of the squared errors of the x, y, and z components of the error vector is minimized for each set of variables in the transformation matrix, and the value of that variable is calculated by the least squares method, and that variable is By using this value as a probable value, the minimum number of teaching points is set to 3, and when the number of teaching points is small, the error in the transformation matrix is reduced in proportion to that, and when the number of teaching points is large, the error in the transformation matrix is reduced proportionally, improving the accuracy of coordinate transformation, and increasing the accuracy. A high work program is created.

〔Example〕

Embodiments of the present invention will be described below with reference to the drawings, taking as an example a case where one robot performs coordinate transformation. The method of the present invention also applies when a program is created using a CAD system between two robots or robots of different models, or offline and converted into a program for an actual robot.
It can be applied to 1 type.

In FIG. 1, the symbol R is an industrial robot, W is a reference work, and W is a target work. The reference work W and the target work W are congruent. Point a on the reference work W
h is a point considered to be appropriate to be selected as a representative point when determining the transformation matrix, and points A to H on the target workpiece W are corresponding points. Further, a work point p is selected on the reference work W.

The robot R is first taught at least three of the points a to 11 on the reference workpiece W as representative points, and the work point p is taught, and a teaching program is created. , at least three points A to H on the target workpiece W corresponding to the representative point on the reference workpiece W are taught as representative points.Next, the representative point of the teaching program and the teaching on the target workpiece W are taught as representative points. A transformation matrix is determined according to the present invention using the representative points. Next, the coordinates of the work point p of the teaching program are transformed using this transformation matrix, and a work program for the work point P corresponding to the work point p on the target workpiece W is created. .

The conversion matrix is obtained from the representative points a to h of the teaching program and the teaching representative points A to H on the target workpiece W as follows.

The center values of the representative points a to h of the standard work W soil in the x, y, z orthogonal coordinate system are (xi, yi, zi) (i
-1~nun is the number of teaching points), and the coordinate values of the corresponding representative points A-H on the target workpiece W in the X, Y, Z orthogonal coordinate system are (Xi, Yi, Zi) (i-1~n
When un is the number of teaching points) and T is the transformation 7-trix of both coordinate systems, the coordinate transformation formula is expressed as follows. In this case, is a matrix representing rotation, and is a vector representing translation.

Conventionally, in order to obtain this conversion 7-trix T, three points (
n = 3) or 1 point (n = 4) and substitute the teaching data into equation (1), tll to t33. xO, yQ
, zo, and solve the 12-dimensional simultaneous equations to obtain the transformation matrix 1. In particular, when teaching four points, it is as follows.

That is, the four representative points a to h (xi
, yi , zi ) (i = 1 to 4) and the corresponding four representative points A to H of the target work W soil (Xi, Yi, Z
i) For (i=1 to 4), use equations (4), (5), (6), and (7)
) becomes a 12-dimensional simultaneous -order equation, and as long as the four points are not on the same plane, equation (40506H7) can be solved, and t1
1-t33. xo, yO, and zo can be found.

However, as described above, these four teaching points include human teaching errors, and these errors are also included in the conversion matrix T obtained. Therefore, when converting the working point p using this matrix, ±21
This results in an error of about 11.

In the present invention, when an error vector is assumed, the error vector is introduced into equation (1) of coordinate transformation, and the sum of the squared errors of each of the x, y, and z components, that is, ΣδXI, Σδy1, Σδz+
Set (10) to each variable of ′■゛11 to t33. xo,
The variables 11 to t33°XO, yo, zo that are minimized for the set of yO, zo are determined by the method of least squares, and this variable is used as the most probable value.

This is an application of the least squares method to the calculation method of coordinate transformation matrices. Conventionally, by using the least squares method, which is a method for processing experimental data, to calculate the robot's coordinate transformation matrix, teaching errors can be reduced by teaching three or more points, even if the teaching is rough, and arc It is possible to provide practical functions that can also be used for welding and sealing.

Specifically, the most convenient of the x, y, and components of formula (10), or the appropriate combination of each component,
Each variable t11 to t33. If the simultaneous equations are solved by partial differentiation with respect to xo, yO, and zo and set to 0 (zero), the error will be minimized. That is, for example, the X component of equation (10), ΣδX1
2 with respect to each variable, partial differentiation is performed with respect to tll, and from 8Σδxi21 t 11 = 0, t11Σxi2+t12Σxiyi+t13Σzixi
+xOΣX1−ΣXi xi =O(11) is found,
Similarly, the first 12 to t33. xo, yO, z.

Partially differentiate with . As a result, t11 to L33. X(1,
A 12-dimensional simultaneous equation for yOlzO is obtained. In this simultaneous-order equation, ΣX12. Σxi y
Let A be a coefficient matrix consisting of coefficients such as i, ..., etc., and Σ
Let b be a constant vector consisting of terms Xi xi, and tll, t12. Let the variable vector consisting of variables such as π be π= (tll, t12. t13. t2
1. t22. t23°t31. t32. t
33. xO, yO, zo) t[where (...)
If we put t of t as a sign representing the transition value, then A・π=b (12> is the 1
It is a two-dimensional simultaneous equation. In this case b=<ΣXi
xi, ΣXi yi, ΣXi z
i.

ΣXi, ΣYi xi, ΣYiyi.

ΣYizi, ΣYi, ΣZi xi.

ΣZi yi , ΣZizi, ΣZi)t. Here, D is D=lAI.

Let be the determinant of A, and let Dk be the determinant of D with the first column replaced by vector b, then t11=D1/D, t12=D2/D.

t13=D3/D t21=D4/D, 722=D5/D, 't
23=D6/D t31=D7/D, t32=D8/D.

t33=D9/D xo = D10/D, yO = D'11/D.

z　O=　D　12/　D You can find the value of each variable like this.

When the data numbers are applied by performing the above steps, 12 equations are written, but in this case, the equations become indefinite, and the same is true even when teaching 2 or 3 points. To avoid this, at least four points of teaching data are required. Therefore, in order to solve the simultaneous equations (12), it is necessary to teach at least four points.

Note that, as in this embodiment, the reference work W and the target work W
In the case of a congruent combination, the vector π can also be found by teaching the three points of equation (3) representing rotation.

That is, t1=(tll, 112.t13) t2=(t21.t22.t23)t3=(t
31. 732. t33), then the vector t
1. t2. During t3 (ti, tj)=
O(i ≠ J) (ti, tj) = 1
(i = j) tl xt2 = t3
, t2 xt3 = t1.

t3 However, it is possible to solve it as a system of simultaneous-order equations. The specific formula calculation will be omitted since it is a modification of a simple mathematical formula.

The work program for the work point P on the target workpiece W is determined from the transformation matrix T thus determined. This calculation is done using the usual method. That is, the transformation matrix is substituted into equation (1), the coordinates of the work point p of the teaching program are transformed, and the coordinate values of the work point P corresponding to the work point P on the target workpiece W are determined.

In this way, according to this embodiment, the error vector x, y,
The sum of the squared errors of each z component is minimized for each set of variables in the transformation matrix, and the value of that variable is calculated by the method of least squares, and that variable is used as the most probable value of the transformation matrix. , the minimum number of teaching points is set to 3 points, and when the number of teaching points is small, the error in the transformation matrix decreases in proportion to the number of teaching points, and as the number of teaching points increases, the error in the transformation matrix decreases, improving the coordinate transformation accuracy and creating highly accurate work programs. Can be created.

Next, the method and results of a computer simulation conducted to confirm the effects of the present invention will be described.

First, a simulation method will be explained with reference to FIGS. 2 and 3.

From the locus pi system o-xyz not shown in Fig. 2(a) to Fig. 2(b)
This transformation converts a rectangular parallelepiped 12345678 whose points in the coordinate system o-xyz have coordinate values as shown in FIG.
This is a transformation obtained by rotating the rectangular parallelepiped by 10' around the axis and the Z axis, and then moving in parallel by 10 (I11) in the X-axis, X-axis, and 2-axis directions.At this time, the rectangular parallelepiped after the transformation is changed to 1゛2゜. If expressed as 3°4°5'6' 7°8°,
Solid 1″2″3″4″5″6″7″ shown in Figure 2(b)
8" is each point of the rectangular parallelepiped 1゛2°3'-1'5°6"
It is a solid that is created by adding an error of length ill which randomly differs in direction to 7'8' as an amount corresponding to the teaching error. Therefore, the solid body 1''2''3''4''5''6''7''8'' has a shape distorted from a rectangular parallelepiped, as shown by the two-dot chain line.

In Fig. 2(a), if the evaluation point is point P, then the rectangular parallelepiped 1
2345678 and solid 1″2″3″4″5″6″7″8
The coordinates of point P are transformed based on ``.At this time, in order to investigate the influence of the number of teaching points, a simulation is performed with the number of teaching points as 3, 4, 5, 6, and 8 points. are points 1.2.3 and points 1″, 2″,
3'' is taught, points 1, 2, 3, 4 and 1'', 2'', 3'', 4'' are taught in 4-point teaching, and points 1, 2, 3, 4... are taught in 5-point teaching. 5 and points 1″, 2″.

3″, 4″, 5″ are taught, and in the 6-point teaching, point 1.
2, 3.4.5.6 and points 1″, 2″, 3-.

4″, 5″, 6″ are taught and 1.8 points are taught, the point is 1.
．． 2, 3, 4, 5.6.7.8 and point 1″.

2'', 3'', 4'', 5'', 6'', 7'', 8'' were taught.

In this coordinate transformation, if there is no teaching error, from the rectangular parallelepiped 12345678 to the rectangular parallelepiped 1゛2"3'4' 5
'6'7'8' When transformed into a solid corresponding to
'(x',y',z'), and if there is a teaching error, that is, the rectangular parallelepiped 12345678 is a solid 1''2''3''4''
When converted to 5″6″7″8″, the point P (x, y, z) is
Assuming that the point at which is converted is P"(X",y",z"), the difference between point P" and point P" was evaluated as follows.

The simulation was created using random numbers for the teaching error, and the number of trials was 100.

In Fig. 9 showing the results of the simulation in Fig. 4, the bar line indicates the margin of error after 100 trials, and the black circle above the pa edge line indicates the average value.

From this figure, it can be seen that as the number of teaching points increases, the width of the error decreases, the average value approaches zero, and the influence of the teaching error decreases.

〔Effect of the invention〕

As is clear from the above, in the method for creating a work program for an industrial robot according to the present invention, even if the teaching error is large, as long as the number of teaching points is large, the apparent error can be reduced and a highly accurate work program can be created. Therefore, it can be applied to tasks such as arc welding and sealing, which require a relatively large amount of work, which were previously not practical.

[Brief explanation of the drawing]

FIG. 1 is a schematic diagram for explaining a method for creating a work program for an industrial robot according to an embodiment of the present invention, and FIG.
Figures (a) and (b) are diagrams for explaining the simulation method conducted to confirm the effects of the present invention, and Figure 3 shows the seat e of the rectangular parallelepiped shown in Figure 2 (a), gX
FIG. 4 is a graph showing the results of the simulation. In the figure, symbol R: robot, W: reference work,
W...Target work

Claims (1)

[Claims] At least three representative points on the target workpiece are taught, a transformation matrix is obtained from this and at least three corresponding representative points of a teaching program created in advance by the teaching, and the teaching is performed using this transformation matrix. In a method for creating a work program for an industrial robot that transforms the coordinates of the work points of the program and creates a work program, an error vector is introduced into the coordinate transformation equation including a transformation matrix, and the x, y, and z components of this error vector are Minimize the sum of the squares of the errors for each pair of variables in the transformation matrix, calculate the value of that variable by the least squares method, use that variable as the most probable value to find the transformation matrix, and calculate this transformation matrix. A method for creating a work program for an industrial robot, characterized in that a work point of a teaching program is transformed by coordinates.