JPH0774964B2 - Robot positioning error correction method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial field of application] The present invention relates to a method for correcting a positioning error of a robot in a system in which a robot is taught off-line using a CAD / CAM system to control the position and orientation of the robot,
Especially regarding the improvement of the entertainment positioning system.

[Prior Art] Industrial robots are used for welding, assembling, painting, etc. In order to fully automate this robot, improve the robot operation rate, and prevent collision between the robot and environmental members, robot off-line teaching that teaches a real robot by performing work simulation using a CAD / CAM system etc. Attention has been paid.

In this case, the positioning accuracy of the robot requires absolute positioning accuracy rather than position repeatability. Absolute positioning accuracy is the accuracy that represents the amount of deviation of the position and attitude reached by the actual robot with respect to the commanded position and attitude of the tip of the robot or the angle of each axis. The absolute positioning accuracy of this robot is not guaranteed, and when performing offline teaching using a CAD / CAM system, CAD / CA
In the M system, the position / orientation or angle command values for each axis are created assuming that there is no absolute positioning error of the robot.

The factor that causes errors in the robot's hand position and orientation in a CAD / CAM system is the geometrical difference between the teaching data on the CAD / CAM and the actual motion data of the robot. That is, as shown in FIG. 7, the robot 71 on the screen displayed on the CAD / CAM graphic display has the joint origin of θ = 0 according to the live value of the robot 72 shown in the design drawing, and each link length. L ₁ and L ₂ are defined with high precision, and accurate values for robot motion data are also generated on CAD / CAM.
However, when manufacturing the actual robot 73, a manufacturing error occurs and the origin error Δθ of each axis position detector and each link length error ΔL ₁ ,
ΔL ₂ occurs, and a base error Δ occurs during installation,
These errors cause geometrical differences between the CAD / CAM graphic model and the actual model, resulting in errors in the robot's hand position and orientation.

Several proposals have been made in the past to correct this error. For example, “NACHI CA” described on pages 64 to 69 of the Journal of the Robotics Society of Japan Vol. 3 No. 2 (published in April 1985).
"TS offline teaching system" or the robot minions as disclosed in the paper "Offline programming system for spot welding robots" published in the 48th Technical Information Processing (TIPS) Study Group held on July 3, 1986. A method of measuring the position / orientation and correcting the positioning accuracy of the hand (hereinafter referred to as Conventional Example 1). Or JP
The distance between a plurality of calibration positions and each joint angle at each calibration position are disclosed as disclosed in "Robot coordinate system calibration method" described in JP-A-62-28808 and JP-A-62-28809. As disclosed in the method of measuring and correcting the positioning accuracy of the hand (hereinafter referred to as Conventional Example 2), or the "origin correction method for an articulated robot" described in Japanese Patent Laid-Open No. 59-205282. There has been proposed a method (hereinafter, referred to as Conventional Example 3) in which two kinds of positioning are performed on the same point by left and right symmetrical arms, the deviation of the positioning is detected, and the origin is corrected to improve accuracy.

In the method disclosed in Conventional Example 1, the matrix [WF] indicating the position / orientation teaching data generated on the CAD / CAM is compared to the matrix [RF] indicating the position / orientation data actually operated by the real robot. And the matrix [W
Convert the conversion matrix between F] and [RF] into the position / posture conversion business example [RW]
Is calculated by the following formula [RW] = [RF] · [WF] ^-1 (1), and the teaching data on CAD / CAM for each teaching point is multiplied by this matrix [RW] to determine the robot positioning accuracy. Is being corrected. This matrix [RW] differs depending on the robot posture and teaching point, so interpolation is performed to improve accuracy.

Further, the method disclosed in Conventional Example 2 creates a simultaneous linear equation using the measured distance between calibration positions, the joint angle at each calibration position, and the link length at the time of design, and solves this equation to calculate the link length error. The positioning accuracy of the ballot is corrected by obtaining Δ and the mounting error Δ of each joint.

[Problems to be Solved by the Invention] In the method of Conventional Example 1 described above, the influence of the link length error Δ and the joint attachment error Δ on the robot hand position / orientation differs for each robot posture, that is, for each teaching point. For this reason, the robot hand positioning error cannot be effectively corrected unless the position / orientation conversion matrix is obtained for each teaching point, and the amount of required data becomes enormous if an accurate correction is attempted. was there.

Further, even if interpolation is performed to improve accuracy, only an approximate value can be calculated, and there is a problem that accurate correction cannot be performed.

In Conventional Example 2, since the angle of each joint at each calibration point of the robot is measured by the joint angle detector inside the robot body, each joint angle in a general-purpose robot in which the internal state of the robot is not disclosed However, there is a problem that this method cannot be applied.

Further, in the method of Conventional Example 2, the coordinate system on the base of the robot body, that is, the coordinate system of the coordinate system of the coordinate measuring machine for measuring the robot hand position and the robot hand position, that is, the coordinate system of the measuring machine, and the actual work The robot has three kinds of coordinate systems, that is, a working coordinate system which is a coordinate system of an object to be moved, and the hand position of the robot is corrected on the measuring machine coordinate system. The correction amount Δ, Δ of the hand position of the robot is different depending on how the reference coordinate is taken, so that the correction amount must be calculated every time when the measuring machine coordinate system and the work coordinate system do not match. There is also.

In the method of Conventional Example 3, the positional deviation is detected by the position data of each joint, that is, the encoder value. However, the encoder value of each joint of the industrial robot is not open to the public and Since the type is limited to the scalar type, there is a problem that it cannot be applied to a versatile robot.

Further, there is a method of measuring not only the robot hand but also a plurality of cameras, or a method in which the robot hand is provided with three light emitting diodes to obtain the tilt of the hand from a photographed image to measure the posture. A complicated system is required for measurement, and there is still a problem with versatility.

The present invention has been made to solve such a problem, and for example, without using the robot internal sensor,
We propose a robot positioning error correction method that can correct the absolute positioning error based only on the relative position information of several points of the robot operated by the position / orientation from the CAD / CAM system or the angle command value of each axis. That is the purpose.

[Means for Solving Problems] A robot positioning error correction method according to the present invention includes: (a) giving a plurality of positions / orientations or angle command values for each axis to a robot controller; and (b) each position described above.・ The hand position of the robot in the robot's base coordinate system corresponding to the command value of the posture or the angle of each axis is measured by a three-dimensional measuring device that is corrected in parallel to the robot's base coordinate system.・ The deviation between the command values of the posture or the angle of each axis and the deviation of the actual measurement value between the hand positions are calculated. (D) The deviation between the respective command values and the deviation between the actual measurement value between the hand positions and the robot The origin error of each axis of the robot is calculated using the Jacobian matrix indicating the minute rotation of each joint, and (e) the position / orientation or the command value of the angle of each axis is corrected by the origin error of each axis, and the robot Control the position and attitude of It is characterized in.

[Operation] In the present invention, the origin error of each axis of the robot, which has a large influence on the error, by the command values of a plurality of positions / orientations and the measurement value by the robot coordinate system of the relative position at which the hand position of the robot operates by these command values By determining, the absolute positioning accuracy of the robot is improved.

[Embodiment] FIG. 1 is a block diagram of an apparatus according to an embodiment of the present invention, in which 1 is a CAD / CAM system for performing offline teaching, 2 is a graphic display of a CAD / CAM system, and 3 is the present invention. A main part is a post-processor that implements the method, 31 is a storage unit, 32 is a minute relational expression calculation unit, 33 is a calculation unit, 4 is a robot, 41 is a robot controller, 42 is a robot mechanical unit. Reference numerals 5 denote input devices for inputting data to the post processor, which are used to input actually measured hand position data of the robot.

Before explaining the operation of this embodiment, the position of the hand of the robot 4 is measured using a three-dimensional measuring device to calculate the deviation amount of the rotation origin of the robot joint, that is, the origin error Δ of each axis position detector. The principle will be described with reference to FIG.

In FIG. 2, TP _n (n = 1,2,3) is the command point of the hand position / orientation commanded on the CAD / CAM system 1, and RP _n (n = 1,2,3) is CAD / The reaching points reached by the hands of the robot 4 actually taught by the respective command points TP _n on the CAM1 are shown. _{n, n + 1} is the position / orientation vector between the command point TP _n and the command point TP _{n + 1} on CAD / CAM1, and _{n, n + 1} is the arrival point R of the robot 4.
The arrival position / attitude vector between P _n and the arrival point RP _{n + 1} is shown.

Robot 4 with command value generated on CAD / CAM system 1
When the robot is actually operated, the hand of the robot 4 does not reach the command point TP _n in the real space due to the origin error Δ, and the reached position / orientation is position / orientation error d _n (where n = Reach the reaching point RP _n which is deviated by 1, 2, 3). At this time, the arrival position / orientation vector _{n, n + 1} in the real space
Is expressed by the following equation. _{n, n + 1 = -d n} + n, n + 1 + d n + 1 ...... (2) _{where, = (r x, r y} , r z, r φ, r θ, r ψ) T ...... (3) = ( R _x , R _y , R _z , R _φ , R _θ , R _ψ ) T (4) where (r _x , ry _y , r _z ) is a vector indicating the hand position,
(R _φ , r _θ , r _ψ ) is a vector indicating the orientation of the hand, or a composite vector thereof. Is the same.

Therefore ₁₂ = If _{-d 1 + 12 + d 2 ......} (5) 23 = -d 2 + 23 + d 3 ...... (6) the position and orientation error _{d n} assuming a minute change due to the origin error delta, position and orientation error d _n is the Jacobian matrix by minute rotation Is expressed by the following equation.

d _n = ΔJ ^θ _n ▼ Δ _n (7) where Δ _n = (Δθ ₁ , Δθ ₂ ... Δθ _i ) T, i is the degree of freedom of the robot 4.

Here, taking an example of a 6-degree-of-freedom articulated robot, the equations (5), (6) and (7) and the measured position information R _x , R _y , R _z of the reaching position / orientation vector _{n, n + 1} are used. A method of obtaining the origin error Δ by setting the origin error d equal to Δ will be described.

(5), (6), (7) from equation _{^{(▲ J θ 2 ▼ - ▲}} J θ 1 ▼) Δ = 12 - 12 ......
_{^{(8) (▲ J θ 3}} ▼ - ▲ J θ 2 ▼) Δ = 23 - 23 ......
(9) The above equations (8) and (9) can be expressed by the following equations.

When the hand position of the robot 4 is measured by the three-dimensional measuring device, only the x-axis, y-axis, and z-axis positions are used, and therefore the right side of the equations (10) and (11) is shown in the fourth to sixth rows. Since the posture value cannot be obtained, take up to the third line of equations (10) and (11),
The following equation is obtained.

However, (▲ J ^θ _{n + 1} ▼-▲ J ^θ _n ▼) _{i = 1} to 3 indicate the first to third rows of the Jacobian matrix. Therefore, formula (12) to formula (13) And the origin error Δ can be obtained by calculating the Jacobian matrix ▲ J ^θ _n ▼.

Jacobi example J ^θ is as described in “Robot control” (published by the Society of Instrument and Control Engineers), pages 22 to 28.
When the unit rotation axis vector of the joint is based on the robot coordinate system x, y, z in the figure, the position vector from the center of the joint to the hand of the robot 4, the minute change of the hand is d, and the minute rotation angle of the joint is Δ. , The following equation is obtained from the rotational motion of the rigid body.

However, ( _n × _n ) represents an outer product, and dφ represents a minute displacement of the rotary joint. From the equations (14) and (7), the Jacobian matrix J ^θ can be calculated by the rotation axis vector of the joint of the robot 4 and the position vector from the joint center to the hand of the robot 4.

The operation of this embodiment constructed according to the above operation principle will be described below with reference to the flow chart shown in FIG.

First, the procedure for obtaining the origin error Δ will be described. When the detection start signal of origin error Δ is input (step
20), First, each designated point T commanded on the CAD / CAM system 1.
A set value ▲ ^k _n ▼ (however, the number of measurement points n = 1 to 3 corrected repeated rotation k = 0) of the rotation angle of the joint following P _n is obtained (step 21). The origin error Δθ ° in this initial stage is set to zero (step 23), and the initial setting value _n ¹ of the rotation of the joint is sent from the post processor 3 to the robot control means 41 to indicate the hand of the robot 4 to each instruction on the CAD / CAM system 1. It sequentially moves to each reaching point RP _n corresponding to the point TP _n (step 29). Each reaching point PR according to the movement of the hand position of the robot 4
The position of _n is sequentially measured by the coordinate measuring machine and sent from the input device 5 to the post processor (step 25).

When measuring the hand position of the robot 4 with this three-dimensional measuring device, as shown in FIG. 5, the coordinate system of the surface plate 9 on which the three-dimensional measuring device is installed, that is, the measuring device coordinate system (x _c , y _c , z _c ) and the robot base coordinate system (x _R , y _R , z _R ) of the actual robot 4 mounted on the robot pedestal 10 must be parallel.
Therefore, actually, before measuring the hand position of the robot 4 with the three-dimensional measuring device, the installation error of the three-dimensional measuring device is corrected.

This correction starts with the first link on the Z _R axis of the robot 4.
11 only is rotated to measure the coordinates of P _0, P _1, 3 point P ₂ points, to identify a plane passing through the P _0, P _1, P ₂ points. Next 3 points P ₀ , P ₁ ,
The intersection (0,0, a) between the plane passing through P ₂ and the z _c axis of the measuring instrument coordinate system (x _c , y _c , z _c ) and the rotation α around the x _c axis and the rotation control y _c Then, the rotation β of is obtained and the inclination correction matrix shown in the following equation (15) is obtained.

= Trans (0,0, a) Rot ＋ (x, α) Rot ＋ (y, β) ……
(15) The inverse matrix ^-1 of this tilt correction matrix is set to the measuring instrument coordinate system (x _c , y
_c, by multiplying the three-dimensional measurement instrument 5 measured at z _c) can be obtained measurements based on the robot-base coordinate system _{(x R, y R, z} R).

Each reaching point RP _n of the hand of the robot 4 obtained as described above
Position information is sent to the minute relational expression calculating means 32,
Position information of the CAD / CAM system 1 on the designated point TP _n from the storage means 31 for each instruction point TP _n position information is stored in is sent to the micro-relationship calculating means 32, these in small relationship calculating means 32 From the position information and the Jacobian matrix ▲ J ^θ _N ▼, the minute relational expression shown in Expression (13) is calculated,
The calculation means 33 solves the minute relational expression to obtain the origin error Δ ¹ (step 26).

Since the origin error Δ is assumed to be a minute amount, the above operation may be repeated to accurately obtain the origin error Δ (step 29). That is, the origin error Δ ¹ calculated as shown in FIG. 4 is sent to the robot controller 41 to correct each initial setting value _n ^1, and the corrected value
_The robot 42 is operated by _n ² = _n ¹ + Δ ¹ (step 24), and each reaching point is reached.
Position information of RP _n is measured (step 25) and the origin error Δ
By repeating the above operation for obtaining ² , the obtained origin error Δ ^k reaches the convergent boundary value ε, for example, the value at which the hand positioning accuracy of the robot 4 reaches the position reproduction accuracy of the robot 4 (step 27). Sum of origin errors Δ ^k obtained repeatedly Is obtained to obtain the origin error Δ (step 28).

Next, when actually operating the robot (Step 2
2) The origin error Δ is added to the command value _in to obtain _n, and the robot is operated based on this value (step 30).

Table 1 shows the result of calculating the origin error Δ of each axis by concretely applying this embodiment to a 5-DOF articulated robot. In order to calculate the accurate origin error Δ, the theoretical second
As shown in the figure, it is sufficient to measure the reaching points RPn of three robot hands, but Table 1 is based on the data of the reaching points RPn (n = 1 to 5) of 5 points in consideration of the measurement error. The following shows the case of calculation.

In Table 1, i = 1 to 5 indicate each axis of the 5-DOF articulated robot.

Next, FIG. 6 shows the result of measuring the absolute positioning accuracy at any 18 points within the operating range of the robot 4 by correcting the positioning accuracy with the origin error Δθ _i shown in Table 1. Fig. 6 shows the number of correction repetitions on the horizontal axis and the absolute positioning accuracy (mm) on the vertical axis, and shows the change in absolute positioning accuracy due to the number of correction repetitions. The absolute positioning accuracy has been improved from 3.68 mm to 0.51 mm by error correction. Since the positioning repeatability guaranteed by the repeated positioning that is guaranteed by the specifications of the robot used for this measurement is ± 0.5 mm, the same positioning repeatability that is guaranteed by the robot specifications is obtained with two correction repeats. It was possible to obtain the absolute positioning accuracy with the accuracy of.

Further, in this embodiment, as described above, the geometrical relationship between the measuring instrument coordinate system and the robot base coordinate system is calculated when measuring the reaching point RPn of the hand of the robot 4, and the robot in the robot base coordinate system is calculated. Since the origin error Δ of 4 is obtained, it is not necessary to correct the robot itself after once correcting the origin error Δ, and it is sufficient to correct the base error Δ when the robot is installed. Positioning accuracy can be obtained.

In this embodiment, the case where each axis command value of the robot is given by the CAD / CAM system has been described, but a computer system or the like may give each axis command value of the robot.

[Effects of the Invention] As described above, according to the present invention, command values of a plurality of positions / orientations or angles of each axis and measured values of different positions at which the robot operates in the robot coordinate system based on these command values are used to measure each axis of the robot. The origin error is calculated and the absolute positioning accuracy of the robot is corrected using this calculated value.
The absolute positioning accuracy can be improved without using the detection value of the detector inside the robot.

Further, since the absolute positioning error can be corrected without using the robot internal detector, there is an effect that the absolute positioning accuracy of any general-purpose robot can be improved.

[Brief description of drawings]

FIG. 1 is a block diagram showing an embodiment of the present invention, FIG. 2 is an explanatory view showing the operating principle of the above embodiment, FIG. 3 is an explanatory view of the Jacobian matrix calculation in the above embodiment, and FIG. FIG. 5 is a flow chart showing the operation of the example, FIG. 5 is an explanatory view of the error correction of the measuring instrument coordinate system and the robot base coordinate system in the above embodiment, FIG. 6 is a change characteristic diagram of the absolute positioning accuracy according to the above embodiment, FIG. FIG. 7 is an explanatory diagram showing error classification of the hand position / orientation of the robot. 1 ... CAM / CAM system, 2 ... Graphic display, 3 ... Post processor, 4 ... Robot, 5 ...
… Input device, TP1 to TP3 …… Indicator on CAD / CAM system, RP1 to RP3 …… Robot hand reaching point.

Claims (2)

[Claims] 1. A method for correcting a positioning error of a robot in which a position / orientation or an angle of each axis is given as a command value to a robot controller to control the position / orientation of the robot. Or, the angle command value of each axis is given to the robot controller, and (b) the hand position of the robot in the robot base coordinate system corresponding to the command value of each position / orientation or each axis angle is set to the robot base coordinate system. (3) Obtain the deviation between the command value of each position / orientation or the angle of each axis and the deviation of the actual measurement value between the above hand positions. The origin error of each axis of the robot is obtained by using the deviation between the command values, the deviation of the actual measurement value between the hand positions, and the Jacobian matrix indicating the minute rotation of each joint of the robot. A command value of the angle of each axis is corrected at the origin error of said each axis, positioning error correction method of the robot, characterized in that to perform the position and posture control of the robot. 2. The method for correcting a positioning error of a robot according to claim 1, wherein the positioning error in the real space due to the origin error of each axis is repeatedly corrected.