JPS61250705A - Coordinate conversion system for industrial robot - Google Patents

Abstract

PURPOSE:To obtain a proper control system in the relation with an actual work by using a normalized coordinate conversion matrix normalizing a refer ence coordinate conversion matrix so as to apply coordinate conversion. CONSTITUTION:After the operation of a conventional reference coordinate conversion matrix utilized for coordinate conversion by a block 1000 at first, the 2nd process correcting the result so as to cancel the change in the length attended with coordinate conversion is performed at the block 2000 and the effect of 3-dimensional distortion of a work being an object of job is excluded. After said reference coordinate conversion matrix is used to apply coordinate conversion for a position data (block 3000), the attitude data with respect to the controlled system is applied with coordinate conversion by using the normal ized coordinate conversion matrix.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Application of the Invention] The present invention relates to a coordinate transformation method for an industrial robot. In particular, the present invention relates to a coordinate transformation method that can be applied even when the workpiece to be worked on is distorted from the one at the time of teaching.

[Background of the invention]

Teaching industrial robots requires a lot of time and effort. Therefore, when the position and orientation of the workpiece to be worked on change, it is better to modify and use the data regarding the position and orientation included in the teaching program instead of re-teaching from the beginning.

This modification is a type of coordinate transformation. Industrial robots control the position of a welding torch, for example, by following a teaching program that has been converted.

Continuous control of posture. This control is based on the actual position of the workpiece, not on the workpiece at the time of teaching.

It will be suitable for your posture.

The work to be worked on may be distorted three-dimensionally compared to the one at the time of teaching. In coordinate transformation based on such a premise, the problem is the transformation of posture data. That is, it is difficult to reproduce the posture of a controlled object in relation to a three-dimensionally distorted workpiece.

[Purpose of the invention]

The present invention proposes a coordinate transformation method that can be effectively used even when a workpiece is distorted three-dimensionally.

[Summary of the invention]

The present invention includes a first step of calculating a reference coordinate transformation matrix. This matrix is a very common one used when performing coordinate transformations. It also has a second step of calculating a normalized coordinate transformation matrix. This matrix is a standard coordinate transformation matrix modified to eliminate changes in length due to coordinate transformation. One typical example of three-dimensional distortion of a workpiece is scaling at different ratios in each coordinate axis direction. This change is reflected in the contents of the reference coordinate transformation matrix.

However, in the normalized coordinate transformation matrix whose length is normalized, the influence of one or more scaling is excluded.

The present invention includes a third step of performing coordinate transformation of position data regarding the controlled object before transformation using a reference coordinate transformation matrix, and a fourth step of performing coordinate transformation of posture data regarding the controlled object using a normalized coordinate transformation matrix. The execution order of the third step and the forty-second step may be reversed. The position data and orientation data regarding the controlled object before conversion constitute a part of the teaching program.

It is corrected to the changed version by coordinate transformation. The industrial robot takes this corrected position and performs a play pack operation based on a teaching program including posture data.

[Embodiments of the invention]

Figures 2 and 3 show the appearance of an articulated industrial robot, with a fixed base 0 fixed at a predetermined position.
．． Swivel base 1. 1st arm 2, 2nd arm 1 bending axis 4. Furisode 5. It includes a twist shaft 6. This has six free variations in total, and controls the position and orientation of the controlled object 7 to which the twist shaft 6 is attached. The objects to be controlled 7 are welding torches, tools, etc.

Here, it is represented by a gauge rod. P is a point to be controlled, which is a kind of virtual point located at the tip of the gauge, and the gauge rod is illustrated to make the point P and its attitude to be controlled easier to understand. The reason for displaying mark 7 on the gauge rod is for the same reason.

The controlled point P is a fixed pace OK connected coordinate system XYZ
Use position pect A/ (!1, yl, 21
'It can hail as.' In addition, for posture control, two vectors '('1*'2*g3) and f
(fs, h, fa). The vector e coincides with the direction of the controlled object 7, and the controlled object point P
is a unit vector with the base point at . The vector f is a unit vector orthogonal to the vector e, and indicates the direction of the mark 7. Thus, the vector e.

f is a parameter indicating the orientation and rotation included in the attitude of the controlled object 7.

What is shown in FIGS. 2 and 3 is the main body of the industrial robot, and illustrations of control units such as a control panel are omitted. This control unit has a central processing unit (CPU)
and storage devices. Processing programs or data are stored in the storage device. The program includes a teaching program, a program to execute (playback) it, a program to create a teaching program, etc., as well as a program to create a coordinate transformation matrix and a program to execute coordinate transformation. included.

Figure wJ1 illustrates the coordinate transformation method according to the present invention. In step 1000, input information 100.

101, a reference coordinate transformation matrix (matrix coefficient data) 102 is calculated.

Here, this is called the first step. This matrix is also used during general coordinate transformations. In that sense, it is quite ordinary, but we will use it as a standard in order to distinguish it from the later normalized coordinate transformation matrix. Step 2
000, a normalized coordinate transformation matrix (matrix coefficient data) 103 is calculated based on the reference coordinate transformation matrix 102. This is the second step.

This normalized coordinate transformation matrix excludes the influence of the above-mentioned directional scaling. Step 3000 corresponds to the third step [K].

The position data 104 before the change regarding the controlled object 7 is coordinate-transformed using the standard coordinate transformation machine IJ Lux 02.

Meanwhile, steps 4100, 4200, 4300.

Reference numeral 4400 indicates a fourth step of coordinate transformation of the posture data of the controlled object 7 before change.

First, in step 4100, a direction vector t (107) and a rotation vector f (108) are obtained from the posture data 106.
Calculate. This process can be omitted if the format of the posture data is one in which vectors e and j are used as parameters. In step 4200, coordinate transformation calculations are performed using the normalized coordinate transformation matrix 103.

This is the main operation of the conversion. The subsequent step 4300 is the vector '',1(109,
110) so that they are orthogonal to each other. This modification is performed on the rotation vector f' (110), but the pect/L'l after the change, f
If (109, 110) are originally orthogonal, the calculation in step 4300 has no practical meaning. The vector & , f (111
, 112).

Posture data (113) after conversion is output. Step 4400 performs arithmetic processing opposite to that of step 106, and the posture data 106°113 before and after conversion.
The format of matches. Original position and posture data (1
04, 106) are not classified into position and orientation. For example, when the data is joint data (data based on articulated robots, where the rotation angle at each joint is a parameter).

An unillustrated step for calculating the position data 104 from there is also required. On the other hand, if the industrial robot has, for example, five degrees of freedom and there is no twist axis 6, then the rotation vector f
(108') is also no longer needed, so step 43
There is no need to process 00.

A supplementary explanation will be given regarding the first step (step 1000). Position data and posture data are
It shows how to move the controlled object 7, and should be modified according to the target work. Therefore, some feature points (corners and corners) on the workpiece are determined in advance as reference points, and the four reference points on the workpiece at the time of teaching are respectively set as po PI P2 pa.

On the other hand, if similar reference points on the work that is currently being worked on are respectively defined as Qo QI Q2 Qa, then a linear vector can be found.

R1=PIPOR2:P2POR3=P3PO81=Q
I QO52=Q2QOS:5=QaQ.

Here, a matrix M that satisfies the linear equation is found.

S1=M-RI S2=M-R2 S3=M-R3 These can be summarized as follows.

[518283]=MCR1R2R3]M” (818
2S3] (RI R2R3)-1 The matrix M shown above is the reference coordinate transformation matrix described above. By the way, 5iRi (t=1.2.3) has the following form.

Therefore, the reference coordinate transformation matrix M has a form of 3 rows and 3 columns.

The second step (step 2000) will be explained again. The coefficients of the reference coordinate transformation matrix M (102) and the normalized coordinate transformation matrix M (103) are expressed as follows.

Each coefficient of the above normalized coordinate transformation matrix M is obtained from the following normalization equation.

The reference coordinate transformation matrix M is used in the coordinate transformation in the third process (step 3000), and the normalized coordinate transformation matrix M is used in step 4200 in the fourth process. Therefore, in step 4200, the following calculation is performed. Here'('1 r '2 t'
3) and f (h, fz, f3) are vectors for changing the posture, those without a dash indicate before conversion, and those with a dash indicate after conversion.

In step 4300, the following calculation is performed. Here, /, f/ are the direction vector (109) and rotation vector (1) after being converted in step 4200.
10). Further, the direction vector (109) and 111 are the same. On the other hand, f indicates the rotation vector corrected in step 4300, and is expressed by a linear equation.

f=, f (e, f )*e where 0 indicates the inner product of two vectors / , , /, and the tree is the inner product of two vectors 0. Let the cross product of e be hail. The above vector f (112) is the vector -(1
09 or 111).

Here, regarding coordinate transformation of posture data, Figures 4 to 9
This will be explained using figures. Figure 4 shows the workpiece 5000 during teaching.
The seventh factor is related to the actual work 5000 to be worked on. In FIG. 4, the controlled object 7 is also shown to show attitude data at a certain teaching point taught in advance. This point is the same for Figure @7, but in the case of Figure 7, it is assumed that the posture data has been changed after coordinate transformation. Figure 5,
FIG. 6 shows the orientation of the controlled object 7 with respect to FIG. 4, and FIGS. 8 and 9 show similar orientations with respect to FIG. 7. As mentioned above, the posture data includes the workpiece 5000,
The angle α in FIGS. 5 and 6 indicates the direction of the controlled object 7 to be grasped in relation to the
, β, γ, δ and the angles α′, β′ in FIGS. 8 and 9
, γ′, and δ′ have the following relationship.

This equation also defines the coordinate transformation of posture data according to the present invention.

Vector RI R2R3 in Figures 4 and 7: td
and s, s2 and s3 are the input information lOO and 101 used in step 1000, but in the cases of FIGS. 4 and 7, the works 5000, 5000
with its own angular change. For this reason, FIG.

A problem as explained in FIG. 11 occurs.

Figure 10 is before the change, and Figure 11 is after the change.
Specifications regarding posture data in FIG. 10)
f (107, 108) are orthogonal to each other. However, the vectors / , , / in FIG. 11 after performing step 4200 are not orthogonal to each other. This is due to the change in angle.

The rotation is outside the definition of vector /.

As mentioned above, in step 4300, the vector f'(1
This is why we modify 10) to vector f (112).

next, ! This will be explained using FIGS. 12 to 17. Each of these figures is I! This corresponds to FIGS. 4 to 9. However, in Figures 4 to 9, the workpieces 5000 and 5000
'Each pect along each side of ' (R1-Ra eS1~
S3) is assumed to exactly match that of the input information 100° 101 corresponding to each reference point, but this is not common. Therefore, in FIGS. 12 to 17, vectors G1□, G1□, G13. G21. G2□.

G23 was used. These vectors may or may not be sita vectors (R1-R3, S1-S3) corresponding to the reference points. In the cases shown in FIGS. 12 to 17, the works 5000 and 5000 are enlarged or reduced in different directions. Furthermore, this is a case where the image is not uniformly enlarged or reduced.

However, in the above-mentioned normalized coordinate transformation matrix IJTx M', changes in length of 1 or more are eliminated. Therefore, the coordinate transformation in step 4200 is performed at the angle 1 before the change in FIGS. 13 and 14. 1 = l between m and the angle 1, rx' after the changes in Figures 16 and 17
This establishes the relationship m = m. By the way, if you apply the standard coordinate transformation matrix M as it is to the IJ Lux (non-normalized transformation matrix).

The one shown in FIG. 18 is changed as shown in FIG. 19. 18th
In the figure, the orientation of the controlled object 7 before the change is the workpiece 5000.
The corner is oriented from the vicinity of the intersection point POO of the topmost end and the rightmost end. The orientation of the controlled object 7 after the change in FIG. 19 is oriented toward the corner from the vicinity of the intersection point POO between the top end and the right end of the workpiece 5000, and the orientation of the controlled object 7 is correct in relation to the entire workpiece 5000. The coordinates have been transformed. but.

This is not good because 1=l does not hold. This is work 5000
This is because the direction of the controlled object 7 is determined in relation to the zero plane. This situation can be clearly understood by assuming that the controlled object 7 indicates, for example, the welding direction. This is the reason why a normalized coordinate transformation matrix material is used to transform posture data.

As is clear from the formula for normalization above.

The following equation holds true for each coefficient of the normalized coordinate transformation matrix M.

Therefore, it can be seen that it has been normalized.

The above relational expression holds true not only when the following is true, but also when it is not. Therefore, it is not necessary to determine whether the reference coordinate transformation matrix M is originally normalized. This point also applies to the modification of the vector f in step 4300K, and it is not necessary to determine in advance whether modification is necessary.

〔Effect of the invention〕

As described above, one aspect of the present invention is to calculate a normalized coordinate transformation matrix that is a normalized reference coordinate transformation matrix, and particularly perform coordinate transformation for posture data using this normalized coordinate transformation matrix. According to this, it becomes possible to realize an appropriate posture of the controlled object in relation to the actual workpiece.

[Brief explanation of drawings]

Each figure relates to an embodiment of the present invention or is for explaining the same. Figure 1 is a flowchart showing the basics of the conversion method, Figure 2 is a front view of an industrial robot (not available), @3
The figure is an enlarged view showing the main parts, Figure 4 is a perspective view showing the posture of the workpiece and the controlled object, Figures 5 and 6 are coordinate diagrams showing the orientation of the controlled object, and Figure 7 is the same as the figure 4. A perspective view showing the posture of the workpiece and the controlled object after coordinate transformation, Figures 8 and 9 are coordinate diagrams showing the orientation of the controlled object, and Figure 10 shows the direction vector and rotation vector of the controlled object. The perspective coordinate diagram shown in Figure @11 is a perspective coordinate diagram similar to the above, showing a situation where the direction vector and rotation vector are non-perpendicular. Figure 12 is a perspective view of another case showing the postures of the workpiece and the controlled object.
The figure and IE14 figure are coordinate diagrams showing the direction of the controlled object,
FIG. 1115 is a perspective view showing the posture of the workpiece and the controlled object after the coordinate transformation of FIG. 12, and FIGS. 16 and 817 are coordinate diagrams showing the orientation of the controlled object. Fig. 18 is a side view of yet another case showing the postures of the workpiece and the controlled object, and Fig. 19 is a side view showing the orientation of the workpiece and the controlled object after applying inappropriate white sum coordinates to those in Fig. 18. . In the figure, 1000 is the first process, and 2000 is the second process. 3000 is the third process a, 4100-4400 is the fourth process,
5000 and 5000 are workpieces, 7 is the controlled object, ε and e
is a direction vector, and f and f are rotation vectors. lθ0101 /1,3%! Le Mouth IJnth Incident Indication Patent Application No. 90838 of 1986 Name of the Invention Relationship with the 11 cases who correct the coordinate transformation method of a robot for the production season Patent Applicant Name ) 5101 Stock Accounting Hitachi Manufacturing Company Name Name Hitachi Keiyo Engineering Co., Ltd.
person

Claims (1)

[Claims] 1. In an apparatus that performs coordinate transformation on position data and orientation data regarding a controlled object to generate new position data and orientation data, a first step of calculating a reference coordinate transformation matrix; and a first step of calculating a reference coordinate transformation matrix; The second step is to calculate a normalized coordinate transformation matrix from the matrix assuming that there is no change in length due to coordinate transformation, and the third step is to perform coordinate transformation on the position data of the controlled object before transformation using the reference coordinate transformation matrix. 1. A coordinate transformation method for an industrial robot, comprising a step and a fourth step of performing coordinate transformation of posture data of a controlled object before transformation using a normalized coordinate transformation matrix.