KR102671823B1 - Apparatus and method for calibration of articulated robot using constraint condition of end effector - Google Patents

Abstract

The present invention relates to an apparatus and method for calibrating an articulated robot using constraints of an end effector. The present invention fixes the absolute socket at a known position with respect to the reference coordinate system of the articulated robot. Contact the ball installed on the end effector of the articulated robot with the absolute socket. By constraining the contact state between the absolute socket and the ball, the multi-joint robot is created in various postures and a set of joint angles is calculated from the encoder installed at the joint. Using each joint angle, model parameters that minimize the position error between the ball position calculated through forward kinematics and the absolute socket position are calculated. Then, the existing model parameters are updated with the calculated model parameters. In addition, the robot calibration device according to the present invention additionally installs a relative socket at a random position within the work area of the articulated robot, and uses each joint angle to determine the relative position of the relative socket and the position of the ball calculated by forward kinematics. After calculating the relative position error and calculating model parameters that simultaneously minimize the position error and relative position error, the existing model parameters can be updated with the calculated model parameters.

Description

Apparatus and method for calibration of articulated robot using constraint condition of end effector}

The present invention relates to a calibration device and method for a robot, and more specifically, to a calibration device and method for an articulated robot using constraints of an end effector that performs calibration to improve the work precision of the articulated robot.

The model parameters of articulated robots installed at industrial sites may vary due to aging, replacement of parts, repetitive work, etc. Accordingly, periodic calibration must be performed to ensure the work accuracy of the articulated robot.

The measurement method for calibration is a method of measuring the position of the end effector using an external measurement sensor such as a laser tracker or camera, and a method of measuring the joint angle of an articulated robot using constraint conditions. There is a way.

In the calibration method using a laser tracker, the laser tracker tracks a reflector attached to the end effector and measures the position of the end effector with high resolution. Therefore, it is widely used in industry to ensure high work accuracy of articulated robots. However, laser trackers are expensive equipment costing over hundreds of millions of won, and the measurement system is bulky and the installation and measurement process is complicated, making it difficult to use in the field.

The calibration method using a camera is simple to construct, but the measurement error is generally relatively large compared to the required work accuracy, making accurate estimation of model parameters difficult.

The calibration method using constraints is a method of creating a straight path or specific geometric constraints for the end effector using an arbitrary calibration jig and measuring the robot joint angles from the encoder. However, since differences in calibration accuracy occur depending on the shape of the jig, high manufacturing costs may be required for the processing precision of the jig. Absolute position information of the jig with respect to the reference coordinate system is required. As a result, tasks such as a separate calibration process to find the jig's coordinate system or installing the jig in an absolute position relative to a previously known reference coordinate system are necessary. Therefore, because the existing constraint conditions are largely dependent on the field conditions where the articulated robot is installed, their application may be limited depending on the field conditions.

Registered Patent Publication No. 10-2314092 (registered on October 12, 2021)

Therefore, the purpose of the present invention is to provide a calibration device and method for an articulated robot using constraints of an end effector that can be applied flexibly and quickly without being significantly dependent on the field conditions where the articulated robot is installed.

Another object of the present invention is to provide a calibration device and method for an articulated robot using end effector constraints that can minimize installation costs.

Another object of the present invention is to provide a calibration device and method for an articulated robot using end-effector constraints with high calibration accuracy.

In order to achieve the above object, the present invention includes a ball installed on the end effector of an articulated robot; At least one absolute socket fixed at a known position with respect to the reference coordinate system of the articulated robot; And after contacting the ball with the absolute socket, creating various postures for the articulated robot while restraining the contact state between the absolute socket and the ball, calculating a set of joint angles from an encoder installed at the joint, and calculating a set of joint angles for each joint angle. A control unit that calculates model parameters that minimize the position error between the position of the ball calculated by forward kinematics and the position of the absolute socket using a control unit that updates the existing model parameters with the calculated model parameters. A calibration device for a joint robot is provided.

The present invention also includes a ball installed on the end effector of an articulated robot; At least one absolute socket fixed at a known position with respect to the reference coordinate system of the articulated robot; At least one relative socket fixed to an arbitrary position within the work area of the articulated robot; And after contacting the ball installed on the end effector of the articulated robot with the absolute and relative socket, an encoder installed on the joint creates various postures for the articulated robot while restraining the state in which the absolute and relative socket and the ball are in contact. Calculate a set of joint angles from this, calculate model parameters that simultaneously minimize the position error and relative position error calculated by forward kinematics using each joint angle, and calculate the existing model parameters with the calculated model parameters. A calibration device for an articulated robot including a control unit for updating is provided. At this time, the joint angle set includes an absolute joint angle set calculated when the ball is in contact with the absolute socket, and a relative joint angle set calculated when the ball is in contact with the relative socket. The position error is calculated as the difference between the absolute position of the ball and the absolute socket calculated by forward kinematics using the absolute joint angle set. And the relative position error is calculated as the difference between the positions of the ball calculated by forward kinematics using the relative joint angle set.

The absolute socket and the relative socket each have a curved groove having a curvature corresponding to the ball formed on the upper surface so that the ball can rotate while being inserted and contacted.

The ball may be inserted into the curved groove and attached to the absolute socket and the relative socket by magnetic force.

The control unit may contact the ball to the absolute socket or the relative socket through direct teaching or programming in torque control mode.

The known position of the reference coordinate system of the articulated robot is at least one of the robot body and the base jig on which the robot body is installed.

When using only absolute sockets, the model parameters can be estimated using the nonlinear least squares method using Equation 1 below as the cost function.

[Equation 1]

: 정기구학(forward kinematics) 함수

: forward kinematics function

: 모델 파라미터 벡터

: Model parameter vector

: 절대 소켓의 개수

: Absolute number of sockets

:

번째 절대 소켓에 대한 측정점 개수

:

Number of measuring points for the second absolute socket

:

번째 절대 소켓의

번째 측정 관절 위치 벡터(

)

:

of the absolute socket

The measured joint position vector (

)

:

번째 절대 소켓의 위치 벡터

:

Position vector of the second absolute socket

When using absolute sockets and relative sockets, the model parameters can be estimated using the nonlinear least squares method using Equation 2 below as the cost function.

[Equation 2]

: 정기구학 함수

: Regular kinematics function

: 모델 파라미터 벡터

: Model parameter vector

: 절대 소켓의 개수

: Absolute number of sockets

: 상대 소켓의 개수

: Number of relative sockets

:

번째 절대 소켓에 대한 측정점 개수

:

Number of measuring points for the second absolute socket

:

번째 상대 소켓에 대한 측정점 개수

:

Number of measurement points for the second partner socket

:

번째 상대 소켓에 대한 기준 측정 관절 위치 벡터

:

Reference measurement joint position vector for the first relative socket

:

번째 절대 소켓의

번째 측정 관절 위치 벡터(

)

:

of the absolute socket

The measured joint position vector (

)

:

번째 상대 소켓의

번째 측정 관절 위치 벡터(

)

:

of the second relative socket

The measured joint position vector (

)

:

번째 절대 소켓의 위치 벡터

:

Position vector of the second absolute socket

When repeatedly estimating model parameters using a nonlinear least squares method, the control unit can calculate optimal model parameters using Equation 3 below.

[Equation 3]

: 모델 파라미터 업데이트 벡터(

;

는 반복 횟수)

: Model parameter update vector (

;

is the number of repetitions)

: 절대 소켓 측정점에 대한 자코비안(Jacobian) 행렬

: Jacobian matrix for absolute socket measurement points

: 상대 소켓 측정점에 대한 자코비안 행렬

: Jacobian matrix for relative socket measurement points

: 상대 소켓에 대한 잔차 오차 벡터,

,

: Residual error vector for the counterpart socket,

,

: 절대 소켓에 대한 잔차 오차 벡터,

,

: Residual error vector for absolute sockets,

,

The present invention also includes the steps of fixing the absolute socket at a known position with respect to the reference coordinate system of the articulated robot; contacting the absolute socket with a ball installed on an end effector of the articulated robot; Calculating a set of joint angles from an encoder installed at a joint by creating various postures of the articulated robot while restraining the contact state between the absolute socket and the ball; Calculating model parameters that minimize the position error between the position of the ball calculated by forward kinematics and the absolute position of the absolute socket using each joint angle; and updating existing model parameters with the calculated model parameters. A calibration method for an articulated robot including a step is provided.

And the present invention includes the steps of fixing the absolute socket at a known position with respect to the reference coordinate system of the articulated robot, and fixing the relative socket at an arbitrary position within the work area of the articulated robot; contacting the absolute and relative sockets with a ball installed on an end effector of the articulated robot; Calculating a set of joint angles from an encoder installed at a joint by creating various postures of the articulated robot while restraining the contact state between the absolute and relative sockets and the ball; Calculating model parameters that simultaneously minimize the position error and relative position error calculated by forward kinematics using each joint angle; and performing calibration of the articulated robot using the calculated model parameters. Here, the relative position error is the first term part (in the absolute value) of Equation 2, and the position error is the second term part (in the absolute value) of Equation 2.

According to the present invention, by installing an absolute socket that provides absolute position information on the robot body or the base jig on which the robot body is installed in the design stage of the articulated robot, the coordinate system of the jig is separately established to create constraint conditions for the existing end effector. Tasks such as a separate calibration process for finding or installing a jig in an absolute position with respect to a previously known reference coordinate system can be omitted. For this reason, the robot calibration device according to the present invention is not significantly dependent on the field conditions where the articulated robot is installed and can be applied flexibly and quickly.

Since the robot calibration device according to the present invention makes contact with a ball joint mechanism between the ball installed in the end effector and the absolute socket, the joint angle can be obtained from the encoder by creating various postures while the ball is in contact with the absolute socket. Therefore, the absolute number of installed sockets can be minimized.

The robot calibration device according to the present invention restrains the state in which the ball and the absolute socket are in contact, creates several postures of the articulated robot, calculates a set of joint angles from the encoder, and uses each joint angle to calculate the forward kinematics ( It is possible to calculate model parameters that minimize the position error between the position of the ball calculated using forward kinematics and the absolute position of the absolute socket, and update the existing model parameters with the calculated model parameters.

When only the model parameters calculated based on the position error are used for the calibration of an articulated robot, the absolute socket position exists only in the area near the base jig of the articulated robot, so the arm length, tool length, and joint It may not be possible to obtain a wide configuration in the joint space due to angle limitations, interference, etc. This may reduce the observability of model parameters.

In order to compensate for this weakness, the robot calibration device according to the present invention additionally installs a relative socket at a random location within the work area of the articulated robot, and restrains the state in which the ball and the relative socket are in contact with a ball joint mechanism. , create several poses of the articulated robot, calculate a set of joint angles from the encoder, and use each joint angle to calculate the relative position error between the position of the ball calculated by forward kinematics and the relative position of the relative socket. And the robot calibration device according to the present invention can calculate model parameters that simultaneously minimize the position error and relative position error, and update existing model parameters with the calculated model parameters.

In this way, when model parameters calculated based on position error and relative position error are used for calibration of an articulated robot, a wide configuration can be obtained, thereby improving the observability of model parameters. In other words, the accuracy of calibration can be improved.

The robot calibration device according to the present invention can calibrate an articulated robot through the installation of a ball, an absolute socket, and a relative socket. Furthermore, the relative socket can be placed anywhere within the robot work area, so it can be installed in a separate location. Since no decision work is required, there is an advantage in minimizing installation costs.

Figure 1 is a diagram showing a calibration device for an articulated robot using constraint conditions of an end effector according to a first embodiment of the present invention.
Figure 2 is a perspective view showing the ball tool of Figure 1.
Figure 3 is a perspective view showing the socket of Figure 1.
Figure 4 is a partial cross-sectional view showing a state in which the light of a ball tool is in contact with a socket.
Figure 5 is a diagram showing the state in which the robot is transformed into various postures while the ball is in contact with the absolute socket.
Figure 6 is a flowchart showing a calibration method of an articulated robot using constraint conditions of an end effector according to the first embodiment of the present invention.
Figures 7 and 8 are diagrams showing a simulation process to confirm the accuracy of calibration according to the method of Figure 5,
Figure 7 is a graph showing the position error results before and after calibration for calibration data,
Figure 8 is a graph showing the position error results before and after calibration for calibration verification data.
Figure 9 is a diagram showing a calibration device for an articulated robot using constraint conditions of an end effector according to a second embodiment of the present invention.
Figure 10 is a diagram showing a calibration device for an articulated robot using the constraint conditions of the end effector according to a third embodiment of the present invention.
Figure 11 is a flowchart showing a calibration method of an articulated robot using the constraint conditions of the end effector according to the third embodiment of the present invention.
Figures 12 to 16 are diagrams showing simulation results to confirm the accuracy of calibration according to the method of Figure 11,
Figure 12 is a photograph showing the articulated robot and calibration device used in the experiment,
Figure 13 is a graph showing the position error before and after calibration for calibration measurement data,
Figure 14 is a graph showing the relative position error before and after calibration for calibration measurement data,
Figure 15 is a graph showing the position error before and after calibration for calibration verification data;
Figure 16 is a graph showing the relative position error before and after calibration for calibration verification data.
Figures 17 to 20 are diagrams showing the results of calibration algorithm experiments to confirm the accuracy of calibration according to the method of Figure 11,
Figure 18 is a graph showing the position error before and after calibration,
Figure 18 is a graph showing the relative position error before and after calibration,
Figure 19 is a graph showing the position error before and after calibration for calibration verification data;
Figure 20 is a graph showing the relative position error before and after calibration for calibration verification data.

It should be noted that in the following description, only the parts necessary to understand the embodiments of the present invention will be described, and descriptions of other parts will be omitted without departing from the gist of the present invention.

The terms or words used in the specification and claims described below should not be construed as limited to their usual or dictionary meanings, and the inventor should use the concept of terminology appropriately to explain his/her invention in the best way. It must be interpreted as meaning and concept consistent with the technical idea of the present invention based on the principle that it can be defined clearly. Therefore, the embodiments described in this specification and the configurations shown in the drawings are only preferred embodiments of the present invention, and do not represent the entire technical idea of the present invention, and therefore, various equivalents can be substituted for them at the time of filing the present application. It should be understood that there may be variations.

Hereinafter, embodiments of the present invention will be described in more detail with reference to the attached drawings.

[First Example]

Figure 1 is a diagram showing a calibration device for an articulated robot using constraint conditions of an end effector according to a first embodiment of the present invention. Figure 2 is a perspective view showing the ball tool of Figure 1. Figure 3 is a perspective view showing the socket of Figure 1. Figure 4 is a partial cross-sectional view showing a state in which the light of a ball tool is in contact with a socket. And Figure 5 is a diagram showing the state in which the robot is transformed into various postures while the ball is in contact with the absolute socket.

Referring to FIGS. 1 to 5 , the calibration device 200 according to the first embodiment is a device that performs calibration of the articulated robot 100 using the constraint conditions of the end effector 30.

The calibration device 200 according to this first embodiment includes a ball 43, an absolute socket 50, and a control unit 90. The ball 43 is installed in the end effector 30 of the articulated robot 100. At least one of the absolute sockets 50 is fixed at a known position with respect to the reference coordinate system of the articulated robot 100. And the control unit 90 brings the ball 43 into contact with the absolute socket 50. The control unit 90 creates various postures for the articulated robot 100 while restraining the contact state between the absolute socket 50 and the ball 43 and calculates a set of joint angles from the encoder installed at the joint. The control unit 90 uses each joint angle to calculate model parameters that minimize the position error between the position of the ball 43 calculated through forward kinematics and the position of the absolute socket 50. Then, the control unit 90 updates the existing model parameters with the calculated model parameters.

The calibration device 200 according to the first embodiment may further include a storage unit 70.

The articulated robot 100 is installed on the base jig 80. The articulated robot 100 includes a robot body 10 fixedly installed on the base jig 80, a robot arm 20 having multiple joints connected to the robot body 10, and an end of the robot arm 20. It includes an end effector (30) installed in. Although not shown, encoders are installed at each of the plurality of joints included in the robot arm 20. The angle of the joint can be calculated from the encoder signal.

The ball 43 is installed in the end effector 30. The ball 43 is installed in the end effector 30 in the form of a ball tool 40. The ball tool 40 includes a tool body 41 and a ball 43. One side of the tool body 41 is installed on the end effector 30, and a ball 43 is installed on the other side.

The absolute socket 50 is installed at a known position with respect to the reference coordinate system of the articulated robot 100 and provides absolute position information of the reference coordinate system. Here, the known position with respect to the reference coordinate system of the articulated robot 100 includes the robot body 10. The installation position of the absolute socket 50 is determined at the design or installation stage of the articulated robot 100. The absolute socket 50 can be installed together when installing the articulated robot 100 on the base jig 80. For example, when the installation position of the absolute socket 50 is in the robot body 10, the installation position of the absolute socket 50 may be determined at the design stage of the articulated robot 100. When the installation position of the absolute socket 50 is in the base jig 80, the installation position of the absolute socket 50 may be determined in the installation step of the articulated robot 100.

In this way, by installing the absolute socket 50 that provides absolute position information to the robot body 10 or the base jig 80 in the design stage of the articulated robot 100, the existing constraints of the end effector 30 are eliminated. In order to do this, tasks such as a separate calibration process to find the coordinate system of the jig or installing the jig in an absolute position with respect to a previously known reference coordinate system can be omitted. For this reason, the calibration device 200 according to the first embodiment is not significantly dependent on field conditions where the articulated robot 100 is installed and can be applied flexibly and quickly.

After the ball 43 of the end effector 30 is in contact with the absolute socket 50, the absolute socket 50 is connected to the ball 43 so that the articulated robot 100 can create various postures while restraining the contact state. ) A curved groove 51 having a curvature corresponding to the ball 43 is formed on the upper surface so that it can rotate while being inserted and contacted. That is, contact is made between the ball 43 installed on the end effector 30 and the absolute socket 50 using a ball joint mechanism.

In the calibration of a general articulated robot 100, the number of absolute position measurement points must be sufficiently large to provide more conditional expressions than the number of robot parameters. However, since the absolute socket 50 according to the first embodiment can create various postures while the articulated robot 100 is in contact with the ball 43 and calculate a set of joint angles from this, The number of absolute sockets (50) installed can be reduced compared to before.

It is desirable to design the ball 43 and absolute socket 50 with precise tolerances to improve measurement accuracy. For example, the center of the ball 43 and the center of the curved groove 51 of the absolute socket 50 must exist within a precise position with respect to each reference coordinate system. There must be a precise position between the center of the ball 43 and the center of the sphere including the curved groove 51 of the absolute socket 50. And the ball 43 and the curved groove 51 must be processed to have precise sphericity. That is, the sphere formed by the ball 43 and the curved groove 51 is formed to have substantially the same size.

In order for the ball 43 to be stably inserted into the absolute socket 50, the curved groove 51 is formed smaller than the hemisphere.

In addition, in order for the ball 43 to be stably inserted into the absolute socket 50, a magnetic ball joint mechanism (Magnetic Ball) is installed in which the ball 43 is inserted and attached to the curved groove 51 by magnetic force in the absolute socket 50. Joint Mechanism).

The storage unit 70 stores a program necessary for controlling the operation of the calibration device 200 and information generated during execution of the program. The storage unit 70 stores an executable program that performs calibration. In other words, the execution program calculates the joint angle from the encoder signal and is a model that minimizes the position error between the position of the ball 43 calculated through forward kinematics using the calculated joint angle and the absolute position of the absolute socket 50. Parameters are calculated, and calibration of the articulated robot 100 is performed using the calculated model parameters.

And the control unit 90 is a microprocessor that performs overall control operations of the articulated robot 100. In particular, the control unit 90 performs overall control operations of the calibration device 200.

The control unit 90 can perform calibration of the articulated robot 100 using the ball 43 and the absolute socket 50 as follows. First, the control unit 90 drives the robot arm 20 to bring the ball 43 into contact with the curved groove 51 of the absolute socket 50. Next, the control unit 90 creates several postures for the articulated robot 100 while constraining the contact state between the absolute socket 50 and the ball 43 and calculates a set of joint angles from the encoder installed at the joint. Next, the control unit 90 calculates model parameters that minimize the position error between the position of the ball 43 calculated by forward kinematics and the position of the absolute socket 50 using each joint angle. Then, the control unit 90 updates the existing model parameters with the calculated model parameters.

As shown in FIG. 4, the control unit 90 can teach the articulated robot 100 to bring the ball 43 into contact with the absolute socket 50. Teaching can be performed through direct teaching or programming in torque control mode.

When the ball 43 and the absolute socket 50 contact each other, only the center of the ball 43 and the center of the absolute socket 50 are constrained, so the orientation of the end effector 30 or the ball 43 is constrained. It doesn't work. By utilizing the constraint condition between the ball 43 and the absolute socket 50, as shown in FIG. 5, the contacted ball 43 and the absolute socket 50 maintain the same position while the robot arm 20 Several postures can be created. The control unit 90 may read encoder signals for various postures of the robot arm 20, calculate a set of joint angles for the read encoder signals, and store them in the storage unit 70.

) 간의 위치 오차를 최소화하는 모델 파라미터를 산출한다. 여기서 수학식 1은 모델 파라미터를 추정하기 위해 사용되는 비용함수이다. 모델 파라미터는, 절대 소켓(50)만을 이용하는 경우, 수학식 1에 따른 비용함수로 산출한 값을 이용한 비선형 최소제곱법(nonlinear least squares method)을 사용하여 추정할 수 있다.Since the positions of TCP (Tool center point) calculated by each joint angle, that is, the center of the ball 43, are all the same, the control unit 90 can calculate model parameters by solving an optimization problem such as Equation 1 below. there is. That is, the control unit 90 calculates the position of the ball 43 using regular kinematics using each joint angle ( ) and the position of the absolute socket 50 (

) Calculate model parameters that minimize the position error between Here, Equation 1 is the cost function used to estimate model parameters. When using only the absolute socket 50, model parameters can be estimated using the nonlinear least squares method using the value calculated by the cost function according to Equation 1.

: 정기구학(forward kinematics) 함수

: forward kinematics function

: 모델 파라미터 벡터

: Model parameter vector

: 절대 소켓의 개수

: Absolute number of sockets

:

번째 절대 소켓에 대한 측정점 개수

:

Number of measuring points for the second absolute socket

:

번째 절대 소켓의

번째 측정 관절 위치 벡터(

)

:

of the absolute socket

The measured joint position vector (

)

:

번째 절대 소켓의 위치 벡터

:

Position vector of the second absolute socket

Additionally, the control unit 90 can improve the work precision of the articulated robot 100 by performing calibration of the articulated robot 100 using the calculated model parameters.

The calibration method of the articulated robot 100 using the calibration device 200 according to the first embodiment will be described with reference to FIGS. 1 to 6 as follows. Here, FIG. 6 is a flowchart showing a calibration method of the articulated robot 100 using the constraint conditions of the end effector 30 according to the first embodiment of the present invention.

First, in step S10, the absolute socket 50 is fixed at a known position with respect to the reference coordinate system of the articulated robot 100. At this time, the absolute socket 50 may be installed in advance at the stage of installing the articulated robot 100 in the field.

Next, in step S20, the control unit 90 contacts the ball 43 installed on the end effector 30 of the articulated robot 100 with the absolute socket 50.

Next, in step S30, the articulated robot 100 is created in various postures while restraining the contact state between the absolute socket 50 and the ball 43, and the control unit 90 calculates a set of joint angles from the encoder installed at the joint. .

Subsequently, in step S40, the control unit 90 calculates model parameters that minimize the position error between the position of the ball 43 calculated by forward kinematics and the absolute position of the absolute socket 50 using each joint angle. That is, the model parameters can be calculated using Equation 1.

And in step S50, the control unit 90 updates the existing model parameters with the calculated model parameters.

In order to confirm the accuracy of the calibration method according to the first embodiment, a simulation was performed as shown in FIGS. 7 and 8. Here, FIGS. 7 and 8 are diagrams showing a simulation process for confirming the accuracy of calibration according to the method of FIG. 5. FIG. 7 is a graph showing the position error results before and after calibration for calibration data, and FIG. 8 is a calibration verification diagram. This is a graph showing the position error results before and after calibration of the data.

The simulation progress is as follows. In this simulation, Robostar RA004, as shown in Figure 9, was used as an articulated robot. A virtual articulated robot 100 is created based on the model parameters. Afterwards, a pose vector set is created with several orientations added for a given point. Among the generated pose vector sets, approximately 80% are used for calibration and approximately 20% are used for verification. The joint angles for the pose vector set are calculated using inverse kinematics. This corresponds to the joint angle read from the encoder in real life situations.

Model parameters were estimated by solving the nonlinear least squares method in the direction of minimizing the error (position error) between the given absolute position data and the TCP position of the nominal model corresponding to the joint angle.

To verify the estimated model parameters, the position error for one absolute socket point was calculated.

Table 1 shows the errors before calibration, and Table 2 shows the errors after calibration. In Tables 1 and 2, mean represents the average, min represents the minimum value, and max represents the maximum value.

As shown in FIG. 7 and Table 1 and Table 2, it can be seen that the position error for the absolute socket is significantly reduced according to the calibration method according to the first embodiment. That is, it can be confirmed that the calibration method according to the first embodiment can achieve high work accuracy.

Table 3 shows the verification results before calibration, and Table 4 shows the verification results after calibration.

According to FIG. 8 and Tables 3 and 4, it can be seen that the calibration method according to the first embodiment significantly reduces the position error even when verifying an absolute socket. That is, it can be confirmed that the calibration method according to the first embodiment can achieve high work accuracy.

In this way, since the robot calibration device 200 according to the first embodiment contacts the ball 43 installed on the end effector 30 and the absolute socket 50 with a ball joint mechanism, the ball 43 ) Since the joint angle can be obtained from the encoder by creating various postures while in contact with the absolute socket 50, the number of installed absolute sockets 50 can be minimized.

The calibration device 200 according to the first embodiment restrains the state in which the ball 43 and the absolute socket 50 are in contact, creates several postures of the robot, calculates a set of joint angles from the encoder, and calculates a set of joint angles from the encoder. Using the angle, model parameters that minimize the position error between the position of the ball 43 calculated by forward kinematics and the absolute position of the absolute socket 50 are calculated, and the articulated robot 100 is calibrated using the calculated model parameters. It can be done.

The calibration device 200 according to the first embodiment can perform calibration without disassembling the articulated robot 100.

The calibration device 200 according to the first embodiment performs calibration using the constraint conditions of the ball 43 and the absolute socket 50, and the installation space is not large, so it can be applied even in a narrow work space and is a multi-joint It can be applied flexibly and quickly without being greatly dependent on the field conditions where the robot 100 is installed, and can be implemented at low cost compared to existing calibration devices.

The calibration device 200 according to the first embodiment can easily perform calibration regardless of the operator's skill level.

Since the calibration device 200 according to the first embodiment does not use a separate sensor, sensor error can be blocked.

And the calibration device 200 according to the first embodiment is capable of automating periodic calibration.

[Second Embodiment]

Meanwhile, in the first embodiment, an example in which the absolute socket 50 is installed on the base jig 80 is disclosed, but it is not limited to this. For example, as shown in FIG. 9, the absolute socket 50 may be installed on the robot body 10.

Figure 9 is a diagram showing the calibration device 300 of the articulated robot 100 using the constraint conditions of the end effector 30 according to the second embodiment of the present invention.

Referring to FIG. 9, the calibration device 300 according to the second embodiment includes a ball 43, an absolute socket 50, and a control unit 90. The ball 43 is installed on the end effector 30 of the articulated robot 100. At least one of the absolute sockets 50 is fixed at a known position with respect to the reference coordinate system of the articulated robot 100. And the control unit 90 brings the ball 43 into contact with the absolute socket 50. The control unit 90 creates various postures for the articulated robot 100 while restraining the contact state between the absolute socket 50 and the ball 43 and calculates a set of joint angles from the encoder installed at the joint. The control unit 90 uses each joint angle to calculate model parameters that minimize the position error between the position of the ball 43 calculated by forward kinematics and the position of the absolute socket 50. Then, the control unit 90 updates the existing model parameters with the calculated model parameters.

The calibration device 300 according to the second embodiment may further include a storage unit 70.

Here, the absolute socket 50 is installed at a known position with respect to the reference coordinate system of the articulated robot 100 and provides absolute position information of the reference coordinate system. Here, the known position in the reference coordinate system of the articulated robot 100 is the robot body 10. An example in which a plurality of absolute sockets 50 are installed in the robot body 10 is disclosed.

As such, the calibration device 300 according to the second embodiment has the same structure as the calibration device 200 according to the first embodiment, except that the absolute socket 50 is installed on the robot body 10.

Since the calibration device 300 according to the second embodiment has substantially the same structure as the calibration device 100 according to the first embodiment, the same effect as the calibration device 100 according to the first embodiment can be expected. there is.

[Third Embodiment]

Meanwhile, the calibration devices 200 and 300 according to the first and second embodiments disclose an example of performing calibration using the ball 43 and the absolute socket 50, but are not limited to this. For example, as shown in FIG. 10, at least one relative socket 60 is additionally fixed to an arbitrary position within the work area of the articulated robot 100, so that the ball 43, the absolute socket 50, and the relative socket ( Calibration of the articulated robot 100 can be performed using 60).

Figure 10 is a diagram showing the calibration device 400 of the articulated robot 100 using the constraint conditions of the end effector 30 according to the third embodiment of the present invention.

Referring to FIG. 10, the calibration device 400 according to the third embodiment includes a ball 43, an absolute socket 50, a relative socket 60, and a control unit 90. The ball 43 is installed in the end effector 30 of the articulated robot 100. At least one of the absolute sockets 50 is fixed at a known position with respect to the reference coordinate system of the articulated robot 100. At least one of the relative sockets 60 is fixed to an arbitrary position within the work area of the articulated robot 100. The control unit 90 contacts the ball 43 installed on the end effector 30 of the articulated robot 100 with the absolute and relative sockets 60. The control unit 90 creates several postures for the articulated robot 100 while restraining the contact state between the absolute and relative sockets 60 and the ball 43 and calculates a set of joint angles from encoders installed at the joints. The control unit 90 calculates model parameters that simultaneously minimize the position error and relative position error calculated by forward kinematics using each joint angle. Then, the control unit 90 performs calibration of the articulated robot 100 using the calculated model parameters.

At this time, the joint angle set includes an absolute joint angle set calculated when the ball 43 is in contact with the absolute socket 50 and a relative joint angle set calculated when the ball 43 is in contact with the relative socket 60. Includes.

The position error is calculated as the difference between the position of the ball 43 and the absolute socket 50 using regular kinematics using a set of absolute joint angles.

And the relative position error is calculated as the difference between each position calculated using the joint angle set. For example, it can be calculated as an error between the position of the ball 43 calculated using the first measured joint angle and the position of the ball 43 calculated using the remaining joint angles.

The calibration device 400 according to the third embodiment may further include a storage unit 70.

Here, the relative socket 60 has a similar structure to the absolute socket 50, except that the installation location is different. That is, a curved groove 61 having a curvature corresponding to the ball 43 is formed on the upper surface of the mating socket 60 so that the ball 43 can be inserted and contacted.

The relative socket 60 improves the observability index for identifying model parameters when performing calibration and provides information to improve location accuracy in a designated work area. Since the relative socket 60 does not require absolute position information about the reference coordinate system, it can be placed at any position within the work area of the articulated robot 100.

The relative socket 60 can be directly fixed to any position within the work area of the articulated robot 100, but is fixed using a fixing jig 63 and an installation stand 65. That is, the fixing jig 63 is fixed to the work area of the articulated robot 100. An installation stand 65 having a certain height is installed on the fixing jig 63. And the counterpart socket 60 is installed at the top of the installation stand 65. Of course, the curved groove 61 of the counterpart socket 60 is installed so that it faces upward.

The counterpart socket 60 can be installed at various heights by adjusting the length of the installation stand 65. Since the relative socket 60 is fixed to an arbitrary position within the work area of the articulated robot 100, it is installed in a position farther from the robot body 10 than the absolute socket 50.

In order for the ball 43 to be stably inserted into the mating socket 60, the ball 43 can be implemented as a magnetic ball joint mechanism in which the ball 43 is inserted and attached to the curved groove 61 by magnetic force to the mating socket 60. there is.

The control unit 90 can estimate model parameters using a nonlinear least squares method using Equation 2 below as a cost function.

: 정기구학 함수

: Regular kinematics function

: 모델 파라미터 벡터

: Model parameter vector

: 절대 소켓의 개수

: Absolute number of sockets

: 상대 소켓의 개수

: Number of relative sockets

:

번째 절대 소켓에 대한 측정점 개수

:

Number of measuring points for the second absolute socket

:

번째 상대 소켓에 대한 측정점 개수

:

Number of measurement points for the second partner socket

:

번째 상대 소켓에 대한 기준 측정 관절 위치 벡터

:

Reference measurement joint position vector for the first relative socket

:

번째 절대 소켓의

번째 측정 관절 위치 벡터(

)

:

of the absolute socket

The measured joint position vector (

)

:

번째 상대 소켓의

번째 측정 관절 위치 벡터(

)

:

of the second relative socket

The measured joint position vector (

)

:

번째 절대 소켓의 위치 벡터

:

Position vector of the second absolute socket

As described above, the control unit 90 calculates model parameters that simultaneously minimize the position error and the relative position error. In Equation 2, the right item corresponds to the position error, and the left item corresponds to the relative position error.

) 간의 차이로 산출한다.The position error is, in Equation 2, the position of the ball 43 in forward kinematics using an absolute joint angle set ( ) and the absolute position of the absolute socket 50 (

) is calculated as the difference between

And the relative position error is calculated as the difference between each position calculated using the joint angle set. For example, the relative position error is the reference position ( ) and the position of each remaining joint angle.

The reason why the calibration device 400 according to the third embodiment performs calibration using the absolute socket 50 and the relative socket 60 is as follows.

As in the first and second embodiments, when only the model parameters calculated based on the position error are used for robot calibration, the position of the absolute socket 50 exists only in the area near the base jig 80 of the robot, It can be effectively used when the work area of the articulated robot 100 is not large.

However, in the case of the first and second embodiments, since the position of the absolute socket 50 exists only in the area near the base jig 80 of the robot, there are limitations on the arm length, tool length, and joint angle, Due to interference, etc., it may not be possible to obtain a wide configuration in the joint space. This is because it can reduce the observability of model parameters.

Therefore, the calibration device 400 according to the third embodiment additionally installs a relative socket 60 at an arbitrary position within the work area of the articulated robot 100, and the ball 43 and the relative socket 60 are ball joints. After restraining the contact state with a mechanism, several postures of the articulated robot 100 are created, a set of joint angles is calculated from the encoder, and the position of the ball 43 calculated by forward kinematics using each joint angle is calculated. The relative position error between the relative positions of the relative sockets 60 is calculated. And the calibration device 400 according to the third embodiment calculates model parameters that simultaneously minimize the position error and relative position error, and performs calibration of the robot with the calculated model parameters.

On the other hand, it is possible to consider a method of calibrating the robot by calculating model parameters that minimize the relative position error using only the relative socket 60.

However, the reason why only the counterpart socket 60 should not be used is as follows. This is because when calculating model parameters using information measured at the counterpart socket 60, there are multiple solutions to the model parameters.

Therefore, an absolute socket 50 is required for uniqueness of model parameters. In other words, the absolute socket 50 provides absolute position information for uniqueness of model parameters, and the relative socket 60 obtains optimal model parameters in the entire work area or in the area of interest among them and improves the observability index.

And the control unit 90 can increase the accuracy of calibration by repeatedly performing the process of calculating model parameters. At this time, when the control unit 90 repeatedly estimates model parameters using the nonlinear least squares method, it can calculate optimal model parameters using Equation 3 below.

: 모델 파라미터 업데이트 벡터(

;

는 반복 횟수)

: Model parameter update vector (

;

is the number of repetitions)

: 절대 소켓 측정점에 대한 자코비안(Jacobian) 행렬

: Jacobian matrix for absolute socket measurement points

: 상대 소켓 측정점에 대한 자코비안 행렬

: Jacobian matrix for relative socket measurement points

: 상대 소켓에 대한 잔차 오차 벡터,

,

: Residual error vector for the counterpart socket,

,

: 절대 소켓에 대한 잔차 오차 벡터,

,

: Residual error vector for absolute sockets,

,

The calibration method of the articulated robot 100 using the calibration device 400 according to the third embodiment will be described with reference to FIGS. 10 and 11 as follows. Here, FIG. 11 is a flowchart showing a calibration method of the articulated robot 100 using the constraint conditions of the end effector 30 according to the third embodiment of the present invention.

First, in step S110, the absolute socket 50 is fixed at a known position with respect to the reference coordinate system of the articulated robot 100, and the relative socket 60 is fixed at a random position within the work area of the articulated robot 100. . At this time, the absolute socket 50 may be installed in advance at the stage of installing the articulated robot 100 in the field. The relative socket 60 can be fixed within the work area of the articulated robot 100 when performing calibration.

Next, in step S120, the control unit 90 contacts the ball 43 installed on the end effector 30 of the articulated robot 100 with the absolute and relative sockets 60.

Next, in step S130, the control unit 90 creates several postures for the articulated robot 100 while restraining the contact state between the absolute and relative sockets 60 and the ball 43 and calculates a set of joint angles from the encoder installed at the joint. do.

At this time, the joint angle set is calculated while the ball 43 is in contact with one of the absolute socket 50 and the relative socket 60.

Therefore, when performing steps S120 and S130, the absolute joint angle set can be calculated first and then the relative joint angle set can be calculated.

Conversely, the relative joint angle set can be calculated first and then the absolute joint angle set can be calculated.

Next, in step S140, the control unit 90 calculates model parameters that simultaneously minimize the position error and relative position error calculated by forward kinematics using each joint angle using Equation 2.

And in step S150, the control unit 90 updates the existing model parameters with the calculated model parameters.

Meanwhile, the control unit 90 may repeatedly perform steps S120 to S140 for calculating model parameters, and in this case, optimal model parameters can be calculated using Equation 3.

In order to confirm the accuracy of the calibration method according to the third embodiment, simulations were performed as shown in FIGS. 12 to 16. Here, Figure 12 is a photograph showing the articulated robot and calibration device used in the experiment. Figure 13 is a graph showing the position error before and after calibration for calibration measurement data. Figure 14 is a graph showing the relative position error before and after calibration for calibration measurement data. Figure 15 is a graph showing the position error before and after calibration for calibration verification data. And Figure 16 is a graph showing the relative position error before and after calibration for the calibration verification data.

In the calibration algorithm simulation according to the third embodiment, Robostar RA004 was used as an articulated robot. In the calibration algorithm experiment, Neuromeca Indy7 was used as an articulated robot. The ball 43 was brought into contact with the absolute socket 50 or the relative socket 60 through direct teaching. While restraining the ball 43 in contact with the socket, the multi-joint robot was created in various postures and the joint angle set was calculated from the encoder installed at the joint. The model parameters that simultaneously minimize the position error and relative position error calculated using the calculated joint angle set were calculated using Equation 2.

The simulation progress is as follows. A virtual articulated robot 100 is created based on the model parameters. Then, for the given absolute and relative socket points, a set of pose vectors is generated with some added orientations. Of the generated pose vector set, approximately 80% are used for calibration and approximately 20% are used for verification. The joint angles for the pose vector set are calculated using inverse kinematics. This corresponds to the joint angle read from the encoder in real life situations.

The difference between the given absolute socket position data and the TCP position of the nominal model corresponding to the joint angle is defined as the absolute socket error (position error), and the relative socket corresponds to the position calculated based on the first measurement point and the remaining joint angle. The error with the TCP position is defined as a relative socket error (relative position error).

Table 5 shows the errors before calibration, and Table 6 shows the errors after calibration.

As shown in Figures 13, 14, Table 5, and Table 6, it can be seen that errors for the absolute socket, relative socket, and both sockets are significantly reduced according to the calibration method according to the third embodiment. That is, it can be confirmed that the calibration method according to the third embodiment can achieve high work accuracy.

Table 7 shows the verification results before calibration, and Table 8 shows the verification results after calibration.

As shown in Figures 15, 16, Table 7, and Table 8, according to the calibration method according to the third embodiment, it can be seen that the error is significantly reduced in the verification of the absolute socket, relative socket, and both sockets. . In other words, it can be confirmed that the calibration method according to the third embodiment can achieve high work accuracy.

Figures 17 to 20 are diagrams showing the results of a calibration algorithm experiment to confirm the accuracy of calibration according to the method of Figure 11. Figure 18 is a graph showing the position error before and after calibration. Figure 18 is a graph showing the relative position error before and after calibration. Figure 19 is a graph showing the position error before and after calibration for calibration verification data. And Figure 20 is a graph showing the relative position error before and after calibration for the calibration verification data.

Table 5 shows the errors before calibration, and Table 6 shows the errors after calibration.

As shown in Figures 17, 18, Table 9, and Table 10, it can be seen that errors for the absolute socket, relative socket, and both sockets are significantly reduced according to the calibration method according to the third embodiment. That is, it can be confirmed that the calibration method according to the third embodiment can achieve high work accuracy.

Table 11 shows the verification results before calibration, and Table 12 shows the verification results after calibration.

As shown in Figures 19, 20, Table 11, and Table 12, according to the calibration method according to the third embodiment, it can be confirmed that the error is significantly reduced in the verification of the absolute socket, relative socket, and both sockets. . That is, it can be confirmed that the calibration method according to the third embodiment can achieve high work accuracy.

Meanwhile, the embodiments disclosed in the specification and drawings are merely provided as specific examples to aid understanding, and are not intended to limit the scope of the present invention. It is obvious to those skilled in the art that in addition to the embodiments disclosed herein, other modifications based on the technical idea of the present invention can be implemented.

100: Articulated robot
10: Robot body
20: Robot arm
30: End effector
80: Base jig
200, 300, 400: Calibration device
40: Ball tool
41: tool body
43: ball
50: absolute socket
51, 61: curved groove
60: relative socket
63: Fixed jig
65: Installation stand
70: storage unit
90: control unit

Claims (13)

A ball installed in the end effector of an articulated robot;
At least one absolute socket fixed at a known position with respect to the reference coordinate system of the articulated robot; and
After contacting the ball with the absolute socket, the articulated robot is created in various postures while restraining the state in which the absolute socket and the ball are in contact, and a set of joint angles is calculated from an encoder installed at the joint, and each joint angle is calculated. A control unit that calculates model parameters that minimize the position error between the position of the ball calculated by forward kinematics and the position of the absolute socket, and updates the existing model parameters with the calculated model parameters,
The model parameters are estimated using a nonlinear least squares method using Equation 1 below as a cost function when only an absolute socket is used.
[Equation 1]

: forward kinematics function
: Model parameter vector
: Absolute number of sockets
: Number of measuring points for the second absolute socket
: of the absolute socket The measured joint position vector ( )
: Position vector of the second absolute socket A ball installed in the end effector of an articulated robot;
At least one absolute socket fixed at a known position with respect to the reference coordinate system of the articulated robot;
At least one relative socket fixed to an arbitrary position within the work area of the articulated robot; and
After contacting the ball installed on the end effector of the articulated robot with the absolute and relative socket, the articulated robot is created in various postures while restraining the state in which the absolute and relative socket and the ball are in contact, from the encoder installed on the joint. Calculate a set of joint angles, calculate model parameters that simultaneously minimize the position error and relative position error calculated by forward kinematics using each joint angle, and update existing model parameters with the calculated model parameters. It includes a control unit that does,
The joint angle set includes an absolute joint angle set calculated when the ball is in contact with the absolute socket, and a relative joint angle set calculated when the ball is in contact with the relative socket,
The position error is calculated as the difference between the absolute position of the ball and the absolute socket calculated by forward kinematics using the absolute joint angle set,
The relative position error is calculated as a difference between the positions of the balls calculated by forward kinematics using the relative joint angle set. According to paragraph 2,
The absolute socket and the relative socket are each,
A calibration device for an articulated robot, characterized in that a curved groove having a curvature corresponding to the ball is formed on the upper surface so that the ball can rotate while being inserted and contacted. According to paragraph 3,
A calibration device for an articulated robot, characterized in that the ball is inserted into the curved groove and attached to the absolute socket and the relative socket by magnetic force. According to clause 4,
The control unit is a calibration device for an articulated robot, characterized in that the control unit contacts the ball with the absolute socket or the relative socket through direct teaching or programming in torque control mode. According to claim 1 or 2,
A calibration device for an articulated robot, characterized in that the known position regarding the reference coordinate system of the articulated robot is at least one of the robot main body and the base jig on which the robot main body is installed. According to paragraph 1,
The absolute socket is,
A calibration device for an articulated robot, characterized in that a curved groove having a curvature corresponding to the ball is formed on the upper surface so that the ball can rotate while being inserted and contacted. According to paragraph 2,
The model parameters are estimated using a nonlinear least squares method using Equation 2 below as the cost function when using an absolute socket and a relative socket. Calibration device for an articulated robot.
[Equation 2]

: Regular kinematics function

: Model parameter vector

: Absolute number of sockets

: Number of relative sockets

:

Number of measuring points for the second absolute socket

:

Number of measurement points for the second partner socket

:

Reference measurement joint position vector for the first relative socket

:

of the absolute socket

The measured joint position vector (

)

:

of the second relative socket

The measured joint position vector (

)

:

Position vector of the second absolute socket According to clause 8,
The control unit is a calibration device for an articulated robot, wherein when model parameters are repeatedly estimated using a non-linear least squares method, the control unit calculates optimal model parameters using Equation 3 below.
[Equation 3]

: Model parameter update vector (

;

is the number of repetitions)

: Jacobian matrix for absolute socket measurement points

: Jacobian matrix for relative socket measurement points

: Residual error vector for the counterpart socket,

,

: Residual error vector for absolute sockets,

,

fixing the absolute socket at a known position with respect to the reference coordinate system of the articulated robot;
contacting the absolute socket with a ball installed on an end effector of the articulated robot;
Calculating a set of joint angles from an encoder installed at a joint by creating various postures of the articulated robot while restraining the contact state between the absolute socket and the ball;
Calculating model parameters that minimize the position error between the ball position calculated by forward kinematics and the absolute socket position using each joint angle; and
Comprising: updating existing model parameters with the calculated model parameters,
The model parameters are estimated using a nonlinear least squares method using Equation 1 below as the cost function when only an absolute socket is used.
[Equation 1]

: forward kinematics function

: Model parameter vector

: Absolute number of sockets

:

Number of measuring points for the second absolute socket

:

of the absolute socket

The measured joint position vector (

)

:

Position vector of the second absolute socket delete fixing the absolute socket at a known position with respect to the reference coordinate system of the articulated robot, and fixing the relative socket at a random position within the work area of the articulated robot;
contacting the absolute and relative sockets with a ball installed on an end effector of the articulated robot;
Calculating a set of joint angles from an encoder installed at a joint by creating various postures of the articulated robot while restraining the contact state between the absolute and relative sockets and the ball;
Calculating model parameters that simultaneously minimize the position error and relative position error calculated by forward kinematics using each joint angle; and
Comprising: updating existing model parameters with the calculated model parameters,
The joint angle set includes an absolute joint angle set calculated when the ball is in contact with the absolute socket, and a relative joint angle set calculated when the ball is in contact with the relative socket,
The position error is calculated as the difference between the absolute position of the ball and the absolute socket calculated by forward kinematics using the absolute joint angle set,
The relative position error is calculated as a difference between the positions of the balls calculated by forward kinematics using the relative joint angle set. According to clause 12,
The model parameters are estimated using a nonlinear least squares method using Equation 2 below as the cost function when using an absolute socket and a relative socket. A calibration method for an articulated robot.
[Equation 2]

: Regular kinematics function

: Model parameter vector

: Absolute number of sockets

: Number of relative sockets

:

Number of measuring points for the second absolute socket

:

Number of measurement points for the second partner socket

:

Reference measurement joint position vector for the first relative socket

:

of the absolute socket

The measured joint position vector (

)

:

of the second relative socket

The measured joint position vector (

)

:

Position vector of the second absolute socket

Images