JPS6198404A - Coordinate conversion system for industrial robot - Google Patents

Abstract

PURPOSE:To simplify the conversion of coordinates without deteriorating the accuracy by using a conversion table related to a triangle formed by the continuous arms to convert the orthogonal data into the joint data. CONSTITUTION:When the wrist vectors PW are referred to as K1, K2 and K, the angles theta2 and theta3 can be shown by eta, xsi and phi (phi: arc sign ZW/K and eta: arc sign K2/K, etc.). This can solve a triangle. Therefore the lists of xsi and eta corresponding to the values of K are produced and both xsi and eta are obtained from the value of the list and the linear interpolation based on the given K. Then the angles theta2 and theta3 are obtained from the obtained xsi and eta. The list is previously produced so as to satisfy the desired accuracy in order to secure the accuracy of calculations.

Description

[Detailed Description of the Invention] [Field of Application of the Invention] The present invention relates to coordinate transformation processing for industrial robots, and in particular to reduction of CPU load (speeding up, stability of accuracy guarantee) related to coordinate transformation processing procedures in a control device. Coordinate transformation processing of navigational robots suitable for (improvement of) (related to washing).

[Background of the invention]

Conventional coordinate purchasing methods for industrial robots either directly obtain a nonlinear simultaneous equation or solve this equation using a convergence method, so (1) the time required for calculation processing is reduced; It's large. (2) In the method described above, it is difficult to guarantee the accuracy of the solution over the entire domain because it goes through complex processing, and in the method described later, the initial value is There is a drawback that it is difficult to establish the definiteness of the M degree guarantee because it is difficult to guarantee the determination method and the necessary number of loops.

Also, a technique has been proposed in which the orthogonal coordinate thread set for the robot is divided into cubic grids, joint data for each grid point is held as a table, and a convergence method is used with this as an initial value. In this case, the memory capacity required to store the table is too large to be practical, and A has the disadvantage that it inherits one of the weaknesses of the convergence method described above.

[Objective of the Invention] An object of the present invention is to provide a coordinate transformation procedure (algorithm) for an industrial robot that is fast (simple) and easy to guarantee the IF degree of the solution.

[Summary of the invention]

FIG. 1 shows a conceptual diagram of a general 5-axis vertical interlined robot mechanism.

The content of the present invention described below is applicable to either 5-axis or 6-axis systems, or even if the hand has a complicated mechanism (actually, the embodiment of the present invention is applicable to 6-axis systems). The wrist is] 1
The shaft is bent at 90°], and a simple shaft configuration is used in the explanation.

aI-θ shown in this figure (Figure 1) is called joint data and indicates the position of each axis (actuator) of one robot. It is usually given as an angle. In addition, in order to move the robot's control point to any point in space and perform a straight line or circular arc, position data of the control point on the orthogonal coordinate system is required. The established coordinate system is Σb, and the orthogonal coordinate values are called orthogonal data.

FIG. 2 shows the general format of orthogonal data and joint data. Here, N indicates the number of axes of the robot, and in FIG. 1, N=5.

Also, the orthogonal data is Σ of the control point. Xs expressed in coordinate system
04 to θn to describe the state of the hand in the y and Z components.
The ``with'' is added.

The above describes the general robot mechanism and its accompanying orthogonal,
Explained joint data. In order to actually operate the robot, joint data is used as commands to each actuator and teaching data, and orthogonal data is used to guide the robot's control point to a point on a straight line or arc. Which data to use depends on the purpose. Therefore, it is essential to convert joint data into orthogonal data, or conversely, convert orthogonal data into joint data. Correct transformation of the former,
The latter is called inverse transformation. Because these transformers are executed frequently and in real time during robot operation - the processing procedures that perform the transformations have strong demands on processing precision and are generally difficult to control. The positive transformation equation for the robot mechanism shown in FIG. 1, which is considered to be one of the problems, is given by the following equation (1). In general, positive transformation is a simple calculation, and there is some room for improvement in the processing of trigonometric functions, so it is not a problem.

Contents of equation (1) x = Cog (θ, ) ・(11sin
θ 2 + t, cos(s2+ θ ,)+
t4 co day θ 4)y = sin (θ, )
*(L, sin e 2+ L, 0os(#.

+#,) +14Coeθ4) z=t, cos θ, -t, Sin (e
2 + θ 3)-t4sin a 4 04° θ4 θF15 The problem is the inverse transformation. A flowchart of the inverse conversion procedure in the robot mechanism of this example is shown in FIG. The inverse transformation process will be described below with reference to FIG. In FIG. 3, the first process 61 is a parameter θ4 related to the state of the hand. Regarding θsK, mentioned above (
1) As shown in equation 1), in general, the joint data θ4. θ,
is used in that case, so it is sufficient to simply transfer it. Next, the second processing procedure 32 is to obtain θ1, which is described above (1
) By simply dividing X and 7 in the formula, y / x =
Since tan θ1 is obtained, the following formula (2) is simply calculated.

(2) Contents of formula θ, = arctan (y / x I Finally, the third
Process 35 of I@a, θ2. θ, which requires a somewhat complicated operation. First, according to the following formula (3), vector ipw=t
(Calculate Xw Yw Zwl. Equation (4) shows the meaning of the value obtained using equation (3).
) is shown in Figure 4 as the content of equation (3).
θ4Yw=−Xsinθ, +Ycosθ.

Z w = Z + 14 sin a.

(4) Contents of formula Xw=4. sinθ, +z, Co5(θ2+θ,)Y
w=O Zw=t2 COsσ, -4,5in(θ2+θ,). From FIG. 4, it can be seen that the vector Pw indicates the position of the base of the robot's wrist, and it can also be seen that equation (4) has the same meaning.

Next, using Pw found in equation (4), the following equation (5) is used to obtain, ! Calculate. In this case, the disadvantage of the value of 2 is that the robot wrist vector P in the coordinate system Σθ rotated by the angle θ2 to the clock (B) 9 as shown in section alU.
w, and the equation (6) is obtained by resolving this into an equation. (6)
In order to find the value of 02 from the equation, the content of simultaneous equation (5) includes
, )K2=pressure 7 7 In the contents of equation (6), =Xwsinθ2+ZwCosθ2=2=XwC
osθ, −Zw day inl + 2 (6) is solved and the following equation (7) is obtained.
You can find out what you need by asking.

(7) Contents of formula a, = arctan (” ' ” -” '
2) K, Xw+, and Zw.Finally, θ can be obtained by using the following relational expression (8) and solving it by calculating the equation (9).

(8) Contents of formula K” = 1.’ + L: + 21. sin θ.

Contents of Equation (9) According to the procedure explained above, the forward and reverse transformations of the robot mechanism shown in Fig. 1 can actually be performed. θ7. Regarding the inverse transformation procedure to obtain θ3, we will supplement its graphical meaning.

After dividing both sides of the equation (6) by K (=6W), the quantities ψ and η defined by the following equation (10) are summarized and rearranged to obtain equation (11).

Contents of equation (10) Cos ψ if 8i
n(C〇, -ψ) Equation (11) can be further simplified into the following relational expression.

Contents of equation (11') η+02+ψ=π/2 A diagram illustrating the sound emission of η and ψ is shown in FIG. From this, it can be seen that the dependence θ2 can also be obtained by applying the cosine theorem and arctan to the values of η and ψ. In other words, the robot's second. It turns out that it is difficult to solve the triangle made up of the third arm (to find η).

Similarly, for θ, it can be solved by solving the same triangle as −02, and in equation (8) above, using the angle δ shown in Figure 5, we can solve 1 of δ=π−θ. By substituting the yoke, we get the following equation (12), which simply shows the cosine theorem, and the content of the η equation is K' := 424 ts"+ 2 t 2 t 3
It's just C0EIδ.

As mentioned above, part of the inversion procedure for a robot mechanism is simply solving a triangle. This is the first premise of non-invention.

Next, the second premise of the present invention, which is the fact that the operation of solving this triangle can be obtained with high accuracy by drawing a table and by linear interpolation, will be explained using equation (12) as an example.

(12) If you create a table of the values of δ for (+g) of K given in equation (12), and interpolate between the tables with a straight line, the accuracy is approximated by the second derivative of δ with respect to K. Therefore, by differentiating equation (12) twice and finding the differential coefficient of δ with respect to KK, we get the following equation (13).Here, we want to see the overall trend.Equation (13) Considering that t2;'s is the content of , and substituting 1=1.=13, we get the following equation (14). Let's calculate the content value of equation (14) of this equation. For example, in the case of δ = 900, the value of the formula is 1/12, and for the envoy with δ = 90°, it is a very small value, partly because the 1 scale of t is originally quite large.As a result, , the value of δ can be found by drawing a table depending on K, and conversely, the number of data that is not included in the table (the interval of K) can be kept small (wide).

Based on the two assumptions mentioned above, by having a part of the inverse transformation of the robot mechanism as a table and interpolating between them, it can be performed with high precision, at high speed, and with as much memory as possible. things become possible. This is the invention.

[Embodiments of the invention]

Hereinafter, one embodiment of the present invention will be explained as shown in Figure 6~@8.
9th grade, I'll clarify.

・j Figure 6 is a system configuration diagram of this embodiment, which includes a robot mechanism 61 with 6 axes and a control device 62 for controlling it.
It is shown that it is made up of an auxiliary device 63 called a teaching box used when teaching the robot.

FIG. 7 shows a flowchart of the inverse transformation procedure in this embodiment, in which the inverse transformation procedure first transfers θ4 to θ, and then calculates θ1 by extending the method described above. 7
2. Find the coordinate Pw of the base of the wrist 73. The present invention uniquely uses the table method technique to calculate θ2. Find θ, 74
, indicates the end.

Figure 8 shows θ2. Procedure section 7 to find θ.
This is a flowchart detailing the processing contents of step 4 and showing the details of the implementation contents of the present invention. First, K (= JEτ ear Zw") is calculated for the input FW.810 Then, from this K, a table is created. Find the parameter T for subtraction82゜Here, T is an integer that satisfies the following relationship on the table.K
t and Kt-+-4 are equal
1□ Contents of Equation (15) Kt≦K(K1.-z <Since it is taken at a distance of τ, next calculate the parameter ξ for interpolation given by the following equation.83゜After that, η, A table regarding δ is drawn84, and the contents of equation (16) ξ= (K-Kt)/τ Kt, ηt, ηt+1, δt corresponding to Kt+1.

Find the value of δt+, and interpolate it according to the following equation to obtain ηk corresponding to K.

(17) Contents of formula η=(1-ξ) ηt+ξηt-t-.

Find δ = (1 - ξ) δt + ξδ1++ δk85, and finally calculate the following relational expression86 to find the content of equation (18) θ2=C δ-+7'k (ψ= arctan (
Y w/Xw) ) θ,; θ2 to π−δ. This shows that θ is being sought.

According to this embodiment, there are effects such as high speed processing of the inverse transformation procedure, easy guarantee of the consistency of the solution, and a slight reduction in memory capacity.

Let me explain a little bit.

As is well known, the control device 62 in FIG. 6 includes a CPU (central processing unit) and an R connected to it via a data node.
It has storage means of OM and RAM. A program for converting the nest 7 or inversely converting the image shown in FIG. 8 is stored in the ROM,
A conversion table executed by the CPU indicating the values of η and δ corresponding to each K in FIG. 5 is also stored in the ROM. This is calculated in advance and written in advance according to the predetermined length t2°1s of the robot arm. In the above example, K is from the absolute value of (12-1,) to t, +t, i,
A table with a constant interval J will be formed, such as , , Kt, Kt + 1, Kn. ○Therefore, writing the actual KtO value into the table is Unnecessary, parameter of Kt (attribution a)
It is sufficient to memorize T and the corresponding ηt and δt.

This is to arrange ηt and δt in II@K arrangement of T.

The relationship Kt=L+TJ holds between T and Kt, where L is the absolute value of (t2-LM). Therefore, it becomes as follows.

Kt-L T=- T corresponding to the value of K found in step 81 of FIG.
To find (82), substitute K for Kt in the above equation, and take the integer part of the old equation and set it as T. ηt is stored at the Tth position (Tth position in the table) indicated by this parameter (argument).

δt. Therefore, step 84 of FIG. 8 is easy to perform.

The deletion L is, so to speak, an initial value. When L = ni, the fifth
δ in the figure is 0. Normally, the minimum value of δ is larger than 0 for joint mechanism reasons, so it is preferable to set the initial value to a value larger than the absolute value of <tt-1s) to save the capacity of the conversion table.

The part that rotates like θ in FIG. 1 is generally called a swing base. t, is the first arm or upper j
The arm, t, is called the second arm or forearm. Front 5″ In the name explanation, 1t, 1
．． was also used as the length of the first arm and the second arm.

The pivot base (δ,) is vertical. Therefore, θ2 in FIGS. 4 and 5 is the angle of the first arm t with respect to the swing base. Similarly, θ3 is the angle of the second arm t with respect to the first arm t2. This angle may be defined as an angle of inclination with respect to a horizontal line as shown in FIG. Either one is fine, but 0. The above formulas related to are slightly modified for the first method.

As mentioned above, with respect to the conversion table iK, the constant interval +
J). It is also effective to change this point and change J. That is, the value of J can be added in inverse proportion to the value of equation (13) above. The above formula (13) is K
shows the M rate of the curve of δ for o Therefore,
This is because where the curvature is large, it is desirable to prepare a table with small increments of J to improve the interpolation product in step 85 in FIG.

"8[W,x?7786(DMiT"e+18)E°゛"0K" 1, and the value of ψ is also subject to calculation. One method would be to prepare another table corresponding to Yw/Xw, but since this arctan calculation itself can be processed at a fairly high speed, the merit of preparing another table is small.

Point Pw in Figure 4 is the boundary, the base part is the arm or arm mechanism, and the part beyond it is the hand mechanism (t4
). This hand mechanism provides a degree of freedom regarding the three-dimensional position as well as the posture of a workpiece (not shown) attached to the hand mechanism. Therefore, although the hand mechanism should preferably have three degrees of freedom, the present invention is applicable to hand mechanisms with any one to three degrees of freedom. That's move 4! This is because the contents of each right-hand side of equation (3) are simply modified as the configuration of tl changes.

〔Effect of the invention〕

According to the present invention, since coordinate transformation can be easily performed, processing speed and precision can be improved. This is specifically shown in FIG. 9, which shows that the processing speed is 20% and the accuracy is 70%. In other words,
According to this invention, it is possible to expect an economical effect in that it becomes possible to control a 6-axis robot with a CPU load for 5 axes using an all-in-one control device.

[Brief explanation of the drawing]

Figure 1 is a conceptual diagram of an articulated robot, Figure 2 is a data format diagram, Figure 3 is a flowchart of inverse transformation, and Figure 4 is a conceptual diagram of an articulated robot.
Figure 5 is an explanatory diagram explaining the present invention in detail, Figure 5 is an explanatory diagram 1 of the next step similar to Figure 4, Figure 6 is a system configuration diagram according to the present invention, and Figure 7 is a reverse diagram according to the present invention. Conversion flowchart - Figure 8 is a detailed flowchart, and Figure 9 is a performance ratio diagram. 12.1 in the figure. 62 is an arm, 62 is a control device, and 84 is a process for deriving parameters from a table. + 'r'2' of the drawing (No change in content) Figure 1 $3Z 2nd Seki boiled beans 7th Figure $ 5 Amendment form for recess procedure (method) Display of 11 cases Showa 1959 1'i Application No. 218445 Name of bow invention Industrial Rohot coordinate f conversion method t117 Person who corrects (・Kuji Prefecture Patent applicant 〆3I・151'll iL Ceremony 1F Hitachi
Manufacturer Name Hitachi Keiyo Engineering Co., Ltd. Agent

Claims (1)

[Claims] 1. A robot mechanism consisting of a plurality of consecutive arms;
An industry characterized in that, in a robot system comprising a control device for controlling the robot system, a conversion table regarding triangles formed by successive arms is provided during a conversion processing procedure between the position of the robot and the position of each actuator. Coordinate transformation method for robots. 2. A coordinate conversion method for an industrial robot, characterized in that the above conversion procedure includes a process of interpolating between data given in a table.