JPH0433006A - Control method for robot system - Google Patents

Abstract

PURPOSE:To improve accuracy for absolutely positioning of the hand of a robot by separately handling the warp error and geometrical error of the robot. CONSTITUTION:The warp error of the hand is calculated on the conditions of respective operational postures and hand operating loads by using a static rigidity diffraction model which can exactly express a relative warp characteristic when changing the hand operating load in each operational posture of a robot 1, and the error is converted to joint positional error. Next, the operational posture/operating load condition is made relative to the joint positional error by approximating a minimum binary polynomial or the like. Then, the warp error is corrected by applying the joint positional error after subtracting it from a joint positional command based on the ideal robot model of infinite static rigidity. Namely, the warp error is handled separately from the geometrical error, and accuracy is improved for identifying the geometrical error. Thus, the accuracy can be improved for absolutely positioning of the hand of the robot.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a robot system including an error calibration process and an error correction process for improving the absolute positioning accuracy of a robot hand.

[Conventional technology]

Conventionally, as a calibration method for a robot, two geometric errors, an error in the arm length of the robot and an error in the number of joints, are calculated from the robot hand position error at multiple points, as described in Japanese Patent Application Laid-Open No. 62-28808. There is a method of identifying each joint position by solving simultaneous equations using the least squares method, and determining the amount of correction for each joint position.

In addition, as described in Kawasaki Heavy Industries Branch Axis No. 98 (1987), pages 93 to 102, there is an example in which deflection errors and geometric errors of the robot are corrected to improve absolute accuracy during offline teaching. There is.

[Problem to be solved by the invention]

The conventional technology described in Japanese Patent Application Laid-Open No. 62-28808 does not consider the robot's deflection error separately from the geometric error, so joint position correction is performed based on pseudo-geometric errors that also include the deflection error. Therefore, there was a problem that there was a limit to improving the absolute positioning accuracy of the robot hand because the physical phenomenon was not represented correctly. In addition, since joint position correction of the robot is performed only on the joint positions when identifying geometric errors, there is a problem in that it cannot be applied directly when the load acting on the hand changes.

In addition, the conventional technology described in Kawasaki Heavy Industries Branch No. 98 handles both deflection errors and geometric errors, but only the joint deflection is considered as the deflection error, so the structure is similar to that of a direct drive robot. There is a problem that it cannot be applied to robots where the deflection of members is dominant, and the geometric error is not identified from the robot hand position error after removing the deflection error, so the identification accuracy of the geometric error is not sufficient. However, there is a problem that there is a limit to the absolute accuracy improvement of robot hands.

An object of the present invention is to improve the absolute positioning accuracy of a robot's hand by treating the robot's deflection error and geometric error separately.

[Means to solve the problem]

In order to achieve the above object, the robot system of the present invention uses a static stiffness analysis model that can almost accurately represent the relative deflection characteristics when the load acting on the hand changes in each operating posture of the robot.

By determining the hand deflection error under the hand acting load conditions, converting it to a joint position error, and then relating the motion posture/acting load condition and the joint position error using least squares polynomial approximation or neural network learning method,
During robot operation, the joint position error is subtracted from the joint position command based on an ideal robot model with infinite static stiffness, and given.
By correcting deflection errors and treating deflection errors and geometric errors separately, we aim to improve the accuracy of geometric error identification and correct it, thereby improving the absolute positioning accuracy of robot hands. It is.

[Effect]

When the robot gives each joint position command to the robot control device, it calculates and outputs the drive energy to be applied to each joint drive device, and by applying it to each joint drive device of the robot, the joints of the robot are driven, and the robot hand section is positioned at a predetermined position within the operating range.

The means of the present invention will be explained using FIGS. 11 to 16, taking a horizontal articulated robot as an example. Figure 11 shows an external view of the horizontal articulated robot, Figure 12 shows the deflection characteristics of the horizontal articulated robot, Figure 13 shows the static stiffness analysis model of the horizontal articulated robot, and Figure 14 shows the robot. FIG. 15 shows a robot model to be corrected for geometric errors, and FIG. 16 shows a flow chart for a method for correcting both geometric errors and deflection errors. FIG. 11 shows a first arm 23 that is rotationally driven by a single-axis drive motor 22, and a second arm 25 that is rotationally driven by a two-axis drive motor 24 provided at the tip of the first arm 23. Tool 2 on the hand installed in
6 and a wrist shaft 7 that is driven in the vertical direction, and the tool 26 is positioned by the 1° biaxial rotational movement and the vertical movement of the wrist shaft. Since the robot's deflection error is not easily affected by geometric errors such as arm length error, we will discuss a method for correcting it alone.

The deflection error of the robot will be explained using the robot skeleton model shown in FIG. An ideal model when the static stiffness of the robot is infinite is shown by a solid line in the figure, and an actual model with deflection due to the finite static stiffness of the robot is shown by a broken line in the figure. From this, in the ideal model, the hand position is point A, whereas in the actual model it is point B, which causes deflection errors of ΔX, Δy, and Δ2 in the X+V+Z directions in the figure, and the position of each joint based on the ideal model. Commands cause hand positioning errors due to deflection.

This is due to the finite static rigidity of each robot member and connecting member, and has characteristics that vary significantly depending on the robot posture angle θ2, the weight of the tool gripped object, etc. The usual method for calculating this deflection error is to create a finite element model and calculate it, but from the perspective of correcting the robot's deflection error in the robot teaching system, it is important to It is necessary to reduce the time required, and it is necessary to simplify the calculation model. Here, as shown in Fig. 13, the robot is divided into five partial structures ■ to ■, and by applying a load to each partial structure end point [1 to 05] Using the gender matrix [K1], we calculate (3
) can determine the deflection error of each partial structure i.

cdxaydzδ8δTSδ2koT=[Ktl-'[Fx
, Fyt Fz, Mxt Myt Mz
lT (3) The homogeneous transformation matrix -IAt of each substructure i is expressed by equation (4).

(4) The robot hand position OT6 at this time is expressed by equation (5).

'Ts='At "Az"As 'Aa 'As
−(5) From this, each joint position/posture error d in the matrix
xttd ffi? d Zl t δ84. δ,
1. Homogeneous transformation matrix i of the ideal model when δzi=o
〇Tl5(
From the fourth column component of equation (7)), the hand position error ΔX in each direction,
Δy and Δ2 are determined.

'T S='Afu72A"33A"4 'A"6
...(6)Δ0Ts=0TIl-OTS
...(7) ΔX found from this result,
Δy, Δ2 are each joint position error Δθ, Δθ2. By giving each joint position command θi, θ2 θ3 as shown in equation (8), the hand positioning error is compensated and the absolute positioning accuracy is significantly improved.

81'=01-Δθi, 02'=θ2-Δθ2. θs'
=ds−Δd3 (8) FIG. 14 shows a flowchart of deflection error correction.

Stepping and hand teaching position 9 When the applied load conditions are given, the deflection error of the hand is calculated using the method described above in step 2. The deflection error of the 0 hand is converted to a joint position error in step 3, and in step 4 the equation is By correcting the joint position command based on (8) and inputting it to the robot control device, the drive energy of each joint drive device of the robot is calculated and output, and the robot is driven.

In addition, in steps 2 and 3, each joint position error is calculated by performing least squares polynomial approximation based on the results of pre-calculation for each joint position and hand action load in the robot hand teaching device, or by applying a neural network learning method. This can be done in one step.

Next, a method for correcting both geometric errors such as robot arm length error, encoder origin offset error, and robot installation error as well as deflection error will be described using FIGS. 15 and 16. The calibration position and applied load conditions within the robot's motion range are determined (step 1), and the hand positioning errors ΔX(q), ΔY(q), and Az(1) at a certain point q within the robot's motion range are determined. measured (
Step 2) in FIG. 16, the deflection errors ΔXdez(q) and ΔYiet(q) of the hand are calculated from the above-mentioned static stiffness analysis model based on the robot's operating posture and the load acting on the hand at that time.

When ΔZ-exCq) is calculated (step 3), the positioning error of the hand due to the geometrical error of the robot is
geo(q), ΔYieo(q), and ΔZgeo(q) are obtained using equation (9) (step 4).

ΔXgeo(q)=Δx(q)−ΔX1ez(q)ΔY
geo(q)=ΔY(1)−ΔYiei(q)ΔZ0゜(1)=Δz(q)−ΔZae1(q) ・=(9
) This value is used to identify geometric errors. here,
The lengths al, a2. in the skeleton model of the robot shown in FIG. Ql, 122. Q8 error and joint position θi. θ2. da's joint position detector origin offset errors Δal, ΔFIZvΔQl, ΔQz.

Δ28. Δθi. Δθ2. Δda and the installation errors ΔX, Δy, and Δ2 in each direction at the nodal point are handled. In this case, the homogeneous transformation matrix ' -IA due to the geometric error and the hand position error ΔOT5 are expressed by equations (10) and (11).

Δ'T5='A1 lAx "AS 3A4 'A11
-(OAt 'AX 2A3 "A4 'AriΔ=O・
(11) In equation (11), the second term on the right side indicates the case where all the geometric error terms in equation (10) are zero.

When formula (11) is calculated, formula (12) is calculated for the hand position error.
) is established.

ΔXgeO=CO8θiΔat+cos(θl+02)
Δaz-a1sirlθiΔθi-aZs button (θ engineering + θ
z) (Δθ engineering + Δθ2) + ΔXΔYgeo=sinθi
Δax+5in(θi+02)Δa2+a tcosθ
iΔθi+ a2JOA8 (θi+02) (Δθi+
Δθ2)+ΔyΔZgeo=Δ2+ΔQ1+ΔQ2+Δ
d3−Δ12s−(12) From this, it is not possible to separate each error in the two directions, but in the X direction,
In the X direction, by obtaining measured data for three or more points, six or more simultaneous equations can be obtained, and geometric errors Δal, Δa2. Δθi. Δθ2. ΔX and Δy can be determined (step 5). Based on the above data, the robot hand teaching device (x, y, z) is calculated using the formula (13)
Installation errors and two-direction dimensional errors are corrected by correcting as follows: x' = x - Δ X Y' = Y - Δy z' = z - Δz sea
-(13) Arm length error Δa1. Δa2 and joint position detector origin offset error Δθi. Teaching position (X', Y', Z') based on inverse kinematics considering Δθ2
By converting to the joint position il (θi.θz, d8), a joint position command with geometrical errors corrected is generated (step 6). Based on this result, the above-mentioned deflection error correction (see equation (8)) is performed (step 7) to remove errors caused by geometric errors and deflection errors of the robot hand, and to correspond to the minimum joint positioning resolution. This makes it possible to obtain absolute positioning accuracy for the robot hand.

〔Example〕

The first embodiment of the present invention will be described below with reference to FIGS. 1 to 7 and 1.
This will be explained using FIG. 3, FIG. 14, and FIG. 17. 1st
The figures show the external appearance of the robot system of the present invention, Fig. 2 shows details of the calibration device shown in Fig. 1, Fig. 3 shows a skeleton model of the robot shown in Fig. 1, and Figs. , FIG. 6 shows the X of the robot's hand in FIG. 3, respectively.
direction.

Figure 7 shows the finite element model of the robot in Figure 1, and Figure 17 details the deflection error correction step 3. 2 shows a flowchart of the deflection error correction shown in FIG. The robot system of the present invention is suitable for off-line teaching, and is characterized in that deflection errors are corrected based on a static stiffness analysis model of the entire robot. In this embodiment, a robot system having the above-mentioned deflection error correction method will be described.

Figure 1 shows the overall configuration of this robot system.
The worker 3 inputs a position command based on an ideal model of the robot (infinite static rigidity model) into the computer 4 and transmits it to the robot control device 2 .

The robot control device 2 detects the current position of each joint of the robot from each joint position detector, and converts the position command into a joint position command and generates a driving force command (for example, a motor torque command) for each joint drive device based on the position deviation. ) and supplies each joint drive energy to the robot via the amplifier. By rotationally driving each joint of the robot, the tip of the wrist axis is positioned near the target position within a position error range corresponding to the resolution of each joint position detector. FIG. 14 shows a flowchart of deflection error correction. Teach position of robot hand.

When the applied load conditions are given (step 1), the hand deflection error is calculated based on the static model (step 2).
, is converted into a joint deflection error (step 3), and a corrected joint position command is generated. Here, the step (step 2) of determining the hand deflection error using the static stiffness analysis model will be described.

There is no way to accurately measure the absolute deflection error of a robot's hand other than comparing it with hand deflection data in a zero-gravity field. Here, by measuring the difference in hand deflection error (referred to as hand relative deflection error) when the hand is attached with a hand load and when the hand is unloaded (when the hand is under a small load), a finite element created in advance based on the robot drawing is used. Check the validity of model calculations and perform all motion postures based on the finite element model.

A method was used to calculate the absolute hand deflection error under hand load conditions. A calibration device 5 for measuring the relative deflection of the hand is provided on the robot hand and the workbench 6, and the displacement detection data of the calibration device [5 is A/D converted and taken into the computer, and data processing is performed. It will be done.

The details of the calibration device 5 will be explained using FIG. 2. A minute weight 8 is coupled to the wrist shaft 7 of the robot hand. Weight 9 that can be attached and detached to minute weight 8
It is possible to change the load acting on the hand by attaching and detaching. In order to measure the vertical direction (Z direction) deflection of the wrist shaft 7, a gap sensor 11 (for example, an eddy current sensor) is used.
and a sensor target 10 (made of aluminum foil, for example) mounted on the wrist shaft 7 are arranged to face each other in the vertical direction.

The gap sensor 11 is fixed to the mounting base 6 by a magnetic stand 12, and by detecting its output, it is possible to measure the relative deflection in the vertical direction when the weight of the weight is varied. The gap sensor 11 is connected to a sensor amplifier 13. The computer 4 via the A/D converter 14
By connecting to the computer, the computer can receive and process data. Here, the data processing refers to, for example, a process of plotting the relationship between the relative deflection error and the load acting on the two hands at the robot's motion posture angle on a CRT. FIG. 3 shows the operating posture angle θ2, the load acting on the hand F2, and the coordinate system of the robot shown in FIG. In the figure, ΔX, Δy.

Δ2 each represents a deflection in the positive direction at the tip of the hand (actually, there is also a negative amount). Figure 4 shows an example of the relative deflection measurement results in each direction when the calibration device in Figure 2 is applied to a horizontally long jointed direct drive robot with a first arm length of 400 (■) and a second arm length of 300 (nu). ,
It is shown in FIGS. 5 and 6. In the figure, the load acting on the hand is 69N.
corresponds to the large payload capacity of one robot. From this, it can be seen that the amount of relative deflection of the robot in each direction changes greatly depending on the robot's operating posture angle θ29 and the load acting on the hand F2. The finite element model of this robot is shown in Figure 7. In this model, the structural members of the robot are modeled as shell elements, the power transmission members such as bearings and belts are modeled as spring elements, and the shaft members are modeled as beam elements.The lid, wrist shaft drive motor, etc. are modeled by applying them as concentrated loads. There is. The relative deflection characteristics determined by this model almost matched the actual measurement results shown in Figures 4 to 6@. However, since calculation of one model requires a huge amount of computer memory capacity and calculation time, it is not practical to install it in the offline teaching computer 4 shown in FIG. Therefore, this robot model was replaced with a simplified model consisting of a partial structure of five blocks as shown in FIG. In this replacement, the staticity matrix (6x6) of each substructure corresponding part is determined from the finite element model in Figure 7, and the direction of each substructure is calculated based on the acting load and moment at the end of each substructure. A method of determining the hand deflection error using equations (4) to (7) was used by determining the amount of deflection and entering it as a displacement component in the homogeneous transformation matrix of each partial structure.

The relative deflection characteristics obtained using this simplified model almost matched the actual measurement results shown in FIGS. 4 to 6.

Next, a method (step 3 in FIG. 14) for determining each joint position error for correcting the hand deflection error by correcting each joint position command will be described. Robot hand position error (ΔX, Δy.

A known method for converting Δ2) into a joint position error (Δθi.Δθ2.Δda) is to use an inverse Jacobian matrix J-1 as shown in equation (14).

(ΔX, Δy, ΔZ)” = J-1 (Δθ engineering, Δθ2.Δ
d 3) T-(14) In this case, based on the ideal model, (xt y +2) and (θi.θz, da) are expressed as equation (1
The Jacobian determinant IJI, which is related by 5) and is the denominator of the inverse Jacobian matrix, is shown by equation (16). Here, P indicates the pole screw pitch when converting the rotational displacement θ3 of the wrist vertical axis drive motor into a two-direction linear displacement d8 via the ball screw, and since the position command for the vertical axis is given as θ8, here Expressed using θ8.

x = a xcosθi+ azcos(θi+θ
2) y = a 1sinθl+a zsin(θi
+02)2■ It can be seen from this that at 02=O, the robot is in a singular posture and the inverse Jacobian matrix cannot be determined. This also indicates that it is not possible to correct the hand position error by joint position command correction near the singular posture.In order to correct the position near the singular posture, a micromanipulator is installed at the hand, and a redundant degree of freedom is required. It is necessary to apply this and avoid singular postures. Here, we only perform joint position correction in the very vicinity of the singular posture, and do not consider operations performed at positions where position correction is not possible. However, in order to improve the accuracy of position correction at positions slightly distant from the singular posture, we used a position correction method using inverse kinematics. This method has a deflection error (Δ1det+Δ'/aex).

Based on the inverse kinematics equation shown in equation (18), the joint position (θi θ2 08'
), and the joint position error (Δθi.Δθ2.Δθ3) is determined using equation (19).

x' = x + 8 to
+a2cosθ2)X'(a z+ a 2CO8θ2
)Y'-a2.51nθ2X')H θa =Z J (18) Δ θi=01' -01 Δ θ2=02' -02 By calculating in this way, stable joint position errors can be obtained even near singular postures. becomes possible to calculate.

FIG. 17 shows a flowchart of the deflection error correction in the case where step 3 of the deflection error correction takes different work procedures depending on the value of the robot's operating attitude angle θ2.

Here, when the robot is in an operating posture far from the singular posture, we decided to use the inverse Jacobian matrix for ease of calculation. Step 4 uses the joint position error obtained in step 3 to create a corrected joint position command (
θi θ2 θ8') is generated and given as a command to correct the position. By executing this step, it becomes possible to obtain high absolute positioning accuracy at the robot hand.

01'=01-Δθi 02'=02-Δθ2 08'=03-Δθ8...(20
) This method can be applied to cases where the load acting on the hand is a translational load in the other direction, a moment load, or when both a translational load and a moment load are applied, as it is possible to calculate the deflection error using a static stiffness analysis model.

Next, a second embodiment of the present invention will be described using FIGS. 8 to 10 and FIG. 18. This embodiment describes a method for shortening the calculation time for deflection error correction by converting steps 2 and 3 in the flowchart of deflection error correction shown in FIG. 14 into one step. Figure 8 shows
The operating area of the robot is shown, and FIG. 9 shows the relationship between the standard interpolation of the position approximation error at the interpolation point and the number of polynomial terms when the joint position error of the robot and the joint position/hand action load are related by polynomial approximation. FIG. 10 shows a block diagram when the joint position error of the robot and the joint position/hand action load are related by the neural network learning method, and FIG. 18 shows a flowchart of deflection error correction in this embodiment.

The deflection error correction method of this embodiment will be explained using FIG. 18. Compared to the flowchart in FIG. 14 described in the first embodiment, steps 2 and 3 are combined into one step, so
The time required for all steps of deflection error correction can be reduced. However, this method uses a static stiffness analysis model that can perform characteristic analysis that matches the actual measurement results described in the first embodiment to perform various motion postures.

1 based on the results calculated in advance for the hand action load.
Since it is divided into steps, when applying it to an unknown robot, it is not possible to convert it into one step without first performing step 2.3 described in the first embodiment.

An example in which the joint position error and the joint position 2 hand action load are related by polynomial approximation will be explained using FIGS. 8 and 9.

i-axis joint position error Δθi and joint position θi. ..., θ.

, the translational loads acting on the hand Fl, . . . Fl, and the moment loads acting on the hand M 1 , .

Δθr=L(θi...., θ., F,...l F
Mt Mlt...2M5) Yaso=Σ(f, (θt(q
)t ”'tθn(q), Ft(J,-,Fll(q
)t Mt(q).

q:1 -. Ms(q))−Δθt(q)F
-(22) In formula (22), the subscript q is the teaching point q
This indicates that the data is from . When determining the number of terms in the polynomial, the equation ( The number of terms that minimized the standard deviation σ of the polynomial approximation error E based on 23) was used. Here, the representative point υ is used, and i indicates the axis.

i t(u)=l f l(θt(t+), '-, θ
n(u), Fz(υ), −, F, (a).

ML (υ), ..., MS (υ)) - Δθi (υ) In determining the coefficients of this polynomial, Δθi. θt,
One possible method is to minimize Δpre in equation (22) based on the least squares method from the data of Flg Mt (referred to as teaching data).

Here, in the movable range of the robot shown in Figure 8, the polynomial approximation calculation area that includes the standard work area used for various performance evaluations is calculated in the case of 311 joints and 1 hand load (Z-direction translational load). The calculation was performed assuming that the number of teaching data was 367 and the number of test data was 100. The reason for setting the approximate calculation area in this way is to increase the accuracy of polynomial approximation in the standard work area, since the accuracy of polynomial approximation decreases at the edges of the calculation area. As a result, the relationship between the standard deviation and the number of polynomial terms was as shown in FIG. 9, and since the standard deviation was the minimum when the number of polynomial terms was 25, this is considered to be the best number of polynomial terms. For this number of polynomial terms, we calculated the deflection error correction accuracy of the test data when all steps of deflection error correction shown in Fig. 18 are performed and when there is no correction, and when the resolution of each axis position detector is infinitesimal. 19 The results are shown in Table 2, and this correction resulted in a deflection error correction accuracy that is approximately below the resolution of each axis position detector (see Table 3), so it is possible to obtain a deflection error correction accuracy that is equivalent to the resolution of each axis position detector. It became clear that

In addition, in this example, the polynomial approximation calculation region is single, but in order to obtain a polynomial that covers the entire operating range, it is possible to improve the approximation accuracy by dividing it into multiple regions and finding a polynomial approximation formula for each region. can. Especially singular posture (
The area near the outer periphery of the robot movable range (θ2=0°) needs to be a separate area.

Table 1 Deflection error correction results (polynomial approximation) Table 2 Deflection error (no correction) Table 3 Position detector resolution in each direction Next, the joint position error due to the deflection error and the joint position/hand action load are related based on the neural network learning method. The method of attaching the information will be explained using FIG. 10. 10th
The figure shows joint position θi. Time node position error Δθi. given θ2°da and hand action load F2. Δθ2. In order to estimate Δd3, (θi.θx, da, Fz) and (Δθl,
Δθ2. Δda) data to neural network 1
Give it to 8 students and let them learn. The neural network 18 has an input layer 19. Hidden reservoir 20. It has a three-layer structure with an output layer 21, and calculations from the input layer 19 to the hidden layer 20 and from the hidden layer 20 to the output layer 21 are performed using the weighting coefficient shown in equation (26) based on the deviation between the teacher data 17 and the output 16. It has an error backpropagation type configuration in which weighting calculation shown in equation (24) is performed based on a correction algorithm.

Input: [υmouth=(θwork, θ2. dmuF2) Hidden scrap entry crab u7=Σω1υ] Hidden layer ratio crab υ';=f(u':) Output scrap entry crab U? = ΣωIat)'j Output output output crab u'7 = Δθt = f (u?)
-(24) Here, the function f is a sigmoid function shown by equation (25).

Also, the weighting coefficient ω1. is corrected by adding the calculation result of the following formula each time the training data tJ and the output 0 are repeated.

ω l J (n”l) = ω 1□(,) +
Δ ω ,, (n) Δω1□=ηδ, 0□
...(26) Here, η: learning rate.

In this way, learning continues until the square error between the teacher data tJ and the output OJ no longer decreases, and when learning is performed for multiple points within the operating area, each weighting coefficient is determined,
The learning blocks below the dashed-dotted line in FIG. A joint position error 16 is calculated. neural network 1
8, the input layer has 4 elements, the hidden layer has 20 elements, and the output layer has 3 elements, and 30 points in the calculation area shown in FIG. As a result, the results shown in Table 4 were obtained. It has been found that by using a neural network, approximately the same approximation accuracy can be obtained on average even if fewer points are used than when polynomial approximation is used (367 points).

Table 4 Deflection correction results using neural network learning method)
From the above, the robot system having the deflection error correction method described in this example can perform joint position error correction corresponding to deflection errors in an extremely short calculation time during off-line teaching, and can compensate for joint position errors corresponding to the joint position detector resolution. It is possible to obtain high absolute positioning accuracy.

Next, a third embodiment of the present invention will be described using FIGS. 15, 16, and 19. This example is based on the first example. By combining the deflection error correction method described in the second embodiment and the geometric error correction method, higher absolute positioning accuracy of the robot can be obtained. FIG. 19 shows the appearance of a robot system including a robot overall positioning error measuring device. The hand positioning errors of the entire robot system are ■deflection error, ■geometric error (arm length drive difference, joint position detector origin offset error).

(robot installation error, etc.); (2) error due to joint position detector resolution; and (2) tool/workbench installation error. Here, we will deal with the case where (2) is not used.

(2) is usually significantly smaller than (2) and (2), and in a system in which position error is corrected by joint position command correction, it provides a position error correction limit. Additionally, since there is little interdependence between ■ and ■, they can be treated independently. In this embodiment, the three-dimensional position measuring device 27 shown in FIG. 19 detects the relative position of the robot hand position and the robot work coordinate system, and detects the relative position of the robot hand position and the robot work coordinate system, and detects the hand position due to geometric errors excluding the pre-calculated deflection error component. We will describe a method for extracting position error components, identifying geometric errors, and correcting them.

The flow of the position error correction method of this embodiment will be explained using FIG. First, multiple positions for calibrating the robot and loads acting on the hand are given (Step 1). For example, the device shown in Fig. 19 is used to measure the three-dimensional position of the robot hand and determine the joint positions at that time. Data is collected, and the positioning error Δt (=(ΔX, Δy, ΔZ)) in the work coordinate system of the hand is calculated (
Step 2). Next, the deflection error Δma, corresponding to each calibration position and hand acting load. is calculated based on the method described in the first or second embodiment (step 3). Next, by subtracting the positioning error in the work coordinate system of the hand measured in step 2 and the deflection error of the hand calculated in step 3, the error Δ'i'* due to the geometric error of the hand is calculated. Calculate eo ("Δmar Δmar et)" (step 4). Next, identify the geometric error (step 5), correct the robot teaching position according to the geometric error (step 6), and correct the robot joint. Correct the positional deflection error correspondence amount (step 7).In the above positioning error correction step, step 2.5
．． 6 will be explained in detail. In step 2, the three-dimensional position measuring device (see Figure 19) has a highly rigid structure and is equipped with a high-resolution position detector, and a contact provided at the end of the device determines the robot hand position. Then, a position at which a certain contact pressure is reached with a plurality of points in the work coordinate system (for example, three points A, B, and C in the figure) is detected as that position, and three-dimensional position detection is performed. Measurement points A, B, and C are set equidistantly from the origin of the work coordinate system in the horizontal plane, and the three-dimensional position of the work coordinate system origin is calculated by finding the intersection of the perpendicular bisectors of these two points. Then, find the relative position between that position and the robot hand position, and find the difference between the relative position of the hand as seen from the robot coordinate system origin, which is found based on the ideal model from the position detection value of each joint position detector. This makes it possible to clarify the positioning error of the hand. Next, regarding step 5, as mentioned in the (effect) section, step 15
By determining each geometrical error based on the hand positioning error (formula (12)) caused only by the geometrical error considered in the model in the figure, it becomes possible to identify the geometrical error.

In equation (12), the geometric error in two directions Δ2. ΔQ
x, ΔQz, ΔQ3. Δd8 cannot be treated separately, but in the 1+'/direction, Δa1. Δaz, Δθ
i? Δθ21 Δx.

Since simultaneous equations for the six unknowns of Δy can be derived, each geometrical error can be uniquely determined by performing the experiment in step 2 for three calibration positions. Further, each geometrical error can be determined more accurately by setting the number of calibration positions to three or more, increasing the number of equations than the number of unknowns, and solving the equations using the method of least squares. Next, for step 6, the horizontal plane installation error ΔX, Δy and the vertical direction geometric error ΔZ g
Regarding eo, each amount is reduced from the hand position command (formula (1)
3)), and the arm length error Δ
at, Δa2 and position detector origin offset error Δθi
．． Δθ2 is a1→a1+Δa1. a
m→a2+Δ82. θi→θi+Δθig1lo t
It can be corrected by correcting θ2 → θ2 + ΔθZMeO and performing the following calculation, and the joint position error amounts ΔθigeO and Δθ2geO+ due to the deflection error.
is corrected by correcting the above quantities based on equation (27).

01'=θi+Δθi1110−Δθi48182'=
θ2+Δθ2geO−Δθ2. deld 3= d 3
−ΔZ 5ea−Δd 5aei −(27)
By using the robot system having the joint position error correction method based on the present embodiment described above, geometric errors can be identified more accurately than conventional methods, and it is possible to identify geometric errors caused by both deflection errors and geometric errors. Since the positioning error can be corrected, it becomes possible to obtain absolute positioning accuracy corresponding to the resolution of each joint position detector.

〔Effect of the invention〕

Since the present invention is configured as described above, it produces the effects described below.

(1) Since the deflection error of the robot is corrected separately from the geometric error, the correction can be performed accurately regardless of the operating posture of the robot and the load acting on the two hands.

(2) Joint position of the robot 2 Joint position errors caused by the load acting on the hand and the deflection error are related in one step using polynomial approximation or neural network learning within the robot's motion area, so the position correction data during offline teaching of the robot Creation time can be shortened.

(3) Since the robot's geometric errors are identified based on the hand positioning error data that is caused only by the geometric errors obtained by subtracting the hand deflection error from the robot's hand positioning error measurement results, it is possible to accurately identify the geometric errors. Identification and highly accurate absolute positioning error correction based on the identification result becomes possible.

[Brief explanation of the drawing]

Fig. 1 is an overall configuration diagram of a robot system according to a first embodiment of the present invention, Fig. 2 is a detailed explanatory diagram of the calibration device shown in Fig. 1, and Fig. 3 is a skeleton model of the robot shown in Fig. 1. Figures 4, 5, and 6 respectively show the operating posture of the robot shown in Figure 1.
'/vZ direction relative deflection characteristic diagram, Figure 7 is a finite element model diagram of the robot in Figure 1, Figure 8 is a diagram of the robot's operating area, Figure 9 is polynomial approximation in the second embodiment of the present invention. Relationship diagram between approximation accuracy and number of polynomial terms when used. FIG. 10 is a deflection error correction block diagram when using the neural network learning method in the second embodiment of the present invention;
Fig. 11 is an external view of the horizontal articulated robot, Fig. 12 is a static deflection characteristic diagram of the robot shown in Fig. 11, Fig. 13 is a skeleton model of the robot shown in Fig. 11, and Fig. 14 is a diagram of the robot shown in Fig. 11. A flowchart of the deflection error correction method according to the first embodiment of the present invention, FIG. 15 is an explanatory diagram of the geometric error of the robot according to the third embodiment of the present invention, and FIG. 16 is a diagram showing the method for correcting the deflection error according to the third embodiment of the present invention. Flow chart of deflection error/geometric error correction method, No. 17
The figure is a detailed flowchart of the deflection error correction method according to the first embodiment of the present invention, FIG. 18 is a flowchart of the deflection error correction method according to the second embodiment of the present invention, and FIG. FIG. 2 is an external view of an example robot system. 1... Robot body, 2... Robot control device, 3
... worker, 4 ... computer, 5 ... calibration device, 6 ... workbench, 7 ... wrist axis,
8...Wrist shaft-coupled weight, 9...Removable weight,
DESCRIPTION OF SYMBOLS 10... Sensor target, 11... Gap sensor, 12... Magnet stand, 13... Sensor amplifier, 14... A/D converter, 15... Input, 1
6... Output, 17... Teacher data, 18... Neural network, 19... Input layer, 20... Hidden layer, 21... Output layer, 22... Single-axis drive motor,
23... First arm, 24... Two-axis drive motor, 2
5... Second arm, 26... Tool, 27... Three-dimensional position measuring device.

Claims (1)

[Claims] 1. In a control method for a robot system that enables off-line teaching of a robot, a hand positioning error between an actual robot placed in a work coordinate system and an ideal model in the robot coordinate system is defined as a geometric error. Step 1 of separating the errors caused by the deflection error; Step 2 of associating the joint position and hand load conditions of the robot with the joint position errors caused by the deflection error and identifying geometric errors; a step 3 of generating a joint position command corresponding to the motion trajectory as the difference between the joint position command corrected and generated based on the geometric error and the joint position error caused by the deflection error calculated based on the step 2; , step 4 of generating robot joint drive energy by receiving the joint position commands generated in step 3, and driving the robot with the robot joint drive energy. 2. In the robot system control method according to claim 1, step 1 is performed using a plurality of partial structures whose characteristics can be analyzed so that the deflection error of the hand almost matches the relative deflection characteristic determination result when the load acting on the hand is varied. When the hand deflection error is converted into each joint position error in step 2, when the robot is in the vicinity of the singular posture, the ideal hand position in the infinite static stiffness robot model and the hand deflection are calculated based on the static stiffness analysis model. The joint position error is determined by using the sum of the errors as the difference between the joint position determined based on inverse kinematics and the ideal joint position.
A robot system characterized in that the robot system is constructed by multiplying the deflection error of the hand by an inverse Jacobian matrix to obtain joint position errors when the robot is not in the vicinity of a singular posture. 3. In the robot system control method according to claim 1, the joint position error caused by the deflection error in step 2 is divided into one or more areas, and expanded to include each area. Joint position θ_i (i=1 to n) at multiple points in the area, translational load acting on the hand F_j (j=1 to m), moment load acting on the hand M_k
(k=1~s) and joint position error Δθ_i (i=1~n)
are related by polynomial approximation as shown in equation (1), and there are ▲mathematical formulas, chemical formulas, tables, etc.▼...(1) Polynomial coefficient a_i is expressed as a patent at r points in the area (representative point q). The joint position error Δθ_i(q) obtained by the method described in claim 2 and the least squares error Δ_■ shown in equation (2) of Δθ_i obtained from equation (1) are selected so as to be minimized, and ▲Math. , chemical formulas, tables, etc. ▼...(2) The number of polynomial terms is selected to maximize interpolation accuracy, and the polynomial is constructed by applying the polynomial of each enlarged area to each of the areas included therein. A method for controlling a robot system. 4. In the robot system control method according to claim 1, the joint position error caused by the deflection error in step 2 is divided into one or more areas, and within or in each area. The joint positions θ_i of the robot at multiple points within each enlarged area including
(i=1~n), hand action translational load F_j (j=1~m
), after learning using a neural network that inputs the hand action moment load M_k (k = 1 to s) and outputs the joint position error Δθ_i (i = 1 to n), and then uses the determined weighting coefficients etc. , a method for controlling a robot system, comprising: estimating a joint position error of the robot with respect to a joint position of an arbitrary robot in each area, a translational load acting on the hand, and a moment load acting on the hand. 5. In the method for controlling a robot system according to any one of claims 1 to 4, the determination of the hand position error caused by the geometric error in step 1 is performed using a geometric error within the operating range of the robot. This is done by subtracting the hand deflection error from the three-dimensional hand position error measurement result of the work coordinate system at a number of points that can form simultaneous equations greater than or equal to the error unknown. This is carried out by solving simultaneous equations obtained by equating the hand position error found as the product of the transformation matrices of each part including the geometric error with the hand position error caused by the geometric error, and in step 3, the geometric 1. A method for controlling a robot system, comprising: correcting joint position commands taking into consideration physical errors; and correcting joint position commands taking deflection errors into consideration.