JP2024035977A - Offline teaching method for articulated robot, program, articulated robot, and information processing device - Google Patents

Abstract

The present invention provides an offline teaching method that can efficiently suppress unintended behavior of an articulated robot. [Solution] An offline teaching method for an articulated robot includes a step in which a simulator determines a range including a singular point and a vicinity of the singular point of the virtualized model among postures that a virtualized model of the articulated robot can take; The simulator controls the angle of each joint in the virtualized model to transition the posture of the virtualized model from the first posture to the second posture. In the step of transitioning the posture of the virtualized model from the first posture to the second posture, if the posture of the virtualized model is outside the range, the simulator calculates the angle of each joint using the Jacobian matrix, and transitions the virtualized model from the first posture to the second posture. When the posture of the model is within the range, the simulator calculates the angle of each joint using a learned model generated in advance. [Selection diagram] Figure 22

Description

The present disclosure relates to an offline teaching method and program for an articulated robot, an articulated robot, and an information processing device.

Conventionally, articulated robots have been known as industrial robots. When such an articulated robot is used on a production line or the like, it is necessary to teach the articulated robot in advance in order to make the articulated robot perform a desired operation.

Online teaching and offline teaching are known as such teaching methods. Online teaching is a method of directly teaching a robot on site using a teaching pendant. Offline teaching is a method of teaching a robot by generating teaching data on a computer and transmitting the teaching data to the robot. The former type of online teaching needs to be performed by workers who have received specialized training while the production line is stopped. For this reason, the latter type of offline teaching has been actively utilized in recent years.

When performing offline teaching, it is necessary to find the displacement of each joint from the multi-joint robot posture (position and posture of the manipulator hand). Such kinematics is called "inverse kinematics." As a solution method for inverse kinematics, the Jacobi method is known, which calculates the displacement of each joint by creating a locally linear relationship. The Jacobi method repeatedly solves an inverse problem in a local linear space, then solves the inverse problem in the next local linear space. In this case, no matter how small the differential of the variable to be controlled (the differential of the position and posture of the manipulator hand) is made, the variable to be controlled (the displacement of the joint that moves the link) may diverge. This posture of the robot is called a "singularity." A singularity is a posture that cannot be controlled due to the robot's structure. Note that the manipulator hand refers to the end effector part.

Japanese Unexamined Patent Publication No. 2006-227724 (Patent Document 1) discloses an entry determination unit that determines whether a robot has entered a singularity region based on a position command, joint data, and singularity region information; a singularity passing position command generation section that is activated based on the determination result of the section and generates and outputs a position command for the robot that has entered the singularity region to pass through the singularity region; A robot control device equipped with the following is disclosed ([Abstract]).

In addition, Japanese Industrial Standards (JIS) B8439-1992 (Patent Document 2) describes the forms of the robot's wrist as FLIP and NONFLIP (from the form of FLIP, the arm can be extended without changing the posture of the wrist). A flag such as 180° rotation around the axis is defined.

The control device of Patent Document 1 mentioned above specifies either FLIP or NONFLIP when instructing the robot to operate the wrist portion. Specifically, the control device always calculates the FLIP attitude and the NONFLIP attitude, and adopts the one with the smaller difference from the reference position. The reference position is the angle obtained by joint interpolation from the starting point to the ending point. Specifically, the reference position is calculated based on the joint data on the entrance side of the singularity region, the joint data on the exit side, and the interpolation period.

Furthermore, in recent years, arithmetic processing using trained models having neural networks has been performed in various fields. For example, Japanese Patent Laid-Open No. 6-339884 (Patent Document 3) discloses a method for learning an inverse kinematics model of a manipulator using a neural network.

Specifically, Patent Document 3 describes a function that is a composite function of a function f and trigonometric functions (sine, cosine) from the position and posture p of the hand of the manipulator to each joint angle θ of the manipulator, and that does not have a discontinuous region. Considering g1=sin(f(p))=sinθ and g2=cos(f(p))=cosθ, we create a neural system that inputs the position and posture p of the manipulator's hand and outputs sinθ and cosθ. The network trains an inverse kinematics model ([Summary]). With this configuration, even if there is a discontinuous region in the function f between the input p and the output θ of the inverse kinematics model to be learned, the function f of the entire work area can be calculated without dividing the work area of the manipulator. can be learned by a single neural network ([Summary]).

Japanese Patent Application Publication No. 2006-227724 Japanese Industrial Standard (JIS) B8439-1992 (Industrial robots - Programming language SLIM) Japanese Patent Application Publication No. 6-339884

In order to pass through a singular posture, it is necessary to uniquely determine the robot's posture. Therefore, in Patent Document 1, when passing through the wrist singular posture, the reference position (standard joint angle ), and it is necessary to select either the FLIP attitude or the NONFLIP attitude based on the calculation result. Furthermore, Patent Document 1 cannot support singular postures other than wrist peculiar postures (shoulder peculiar posture, elbow peculiar posture).

Patent Document 3 states, ``Since there is no discontinuous area (excluding singular points) in the function from (x, y) to (sin θ1, cos θ1, sin θ2, cos θ2), which is the sine and cosine of each joint angle, the neural As the disclosure states, ``it is possible to train a network,'' singular points and their vicinity are not targeted for learning.

The present disclosure provides an offline teaching method, a program, an articulated robot, and an information processing device that can efficiently suppress unintended behavior (runaway, stop, etc.) of an articulated robot at a singular point and its vicinity. It's about doing.

According to an aspect of the present disclosure, an offline teaching method for an articulated robot using a simulator includes a range of postures that include a singular point of the virtualized model and a vicinity of the singularity among postures that a virtualized model of the articulated robot can take. , a step in which the simulator determines, and a step in which the simulator transitions the posture of the virtualized model from a first posture to a second posture by controlling the angle of each joint in the virtualized model. In the step of transitioning the posture of the virtualized model from the first posture to the second posture, if the posture of the virtualized model is outside the range, the simulator calculates the angle of each joint using the Jacobian matrix, and transitions the virtualized model from the first posture to the second posture. When the posture of the model is within the range, the simulator calculates the angle of each joint using a learned model generated in advance.

According to another aspect of the present disclosure, a program causes a computer to execute the offline teaching method for an articulated robot.

According to yet another aspect of the present disclosure, the articulated robot operates based on offline teaching data generated by the offline teaching method for an articulated robot.

According to yet another aspect of the present disclosure, an information processing device includes a processor and a memory in which a simulation program for an articulated robot is stored. By executing the simulation program, the processor determines the range including the singular point of the virtual model and the vicinity of the singular point among the postures that the virtual model of the articulated robot can take, and determines the range of postures that the virtual model of the articulated robot can take, and By controlling the angle, the posture of the virtualized model is transitioned from the first posture to the second posture. When transitioning the posture of the virtualized model from the first posture to the second posture, if the posture of the virtualized model is outside the range, the processor calculates the angle of each joint using the Jacobian matrix, and transitions the virtualized model from the first posture to the second posture. When the posture of the model is within the range, the angle of each joint is calculated using a learned model generated in advance.

According to the present disclosure, it is possible to efficiently suppress unintended behavior of an articulated robot at a singular point and in the vicinity thereof.

FIG. 1 is a diagram showing a schematic configuration of an offline teaching system. FIG. 2 is a diagram showing a simplified structure of a robot. FIG. 3 is a diagram for explaining the coordinate system of each link of the robot. FIG. 3 is a diagram showing a wrist peculiar posture. FIG. 3 is a diagram showing a shoulder-specific posture. FIG. 2 is a diagram showing a unique elbow posture. Simulation results when the speed of the virtual model's hand in the Y-axis direction is 100 m/s and the speed in the X-axis direction and the speed in the Z-axis direction are zero, and the measured value of the rotational speed of the servo motor in the actual machine. FIG. It is a figure showing the simulation result when the speed of the hand in the Y-axis direction is 300 mm/s, and the measured value of the rotational speed of the servo motor. It is a figure showing the simulation result when the speed of the hand in the Y-axis direction is 500 mm/s, and the measured value of the rotational speed of the servo motor. It is a figure showing the simulation result when the speed of the hand in the Y-axis direction is 1200 mm/s, and the measured value of the rotational speed of the servo motor. FIG. 7 is a diagram showing a range near a singular point in a case where the hand speed is only in the Y-axis direction. It is a figure which showed the solution of the angle of the 4th joint. FIG. 2 is a schematic diagram for explaining a method of calculating joint angles at a singular point, near the singular point, and in a range other than the singular point (posture range). A case is shown in which the angular range of the fourth joint is limited to 0° or more and 180° or less. FIG. 7 is a diagram showing the root mean square error of verification data when there is only one intermediate layer and the number of neurons is varied from 1 to 50. FIG. 7 is a diagram showing the root mean square error of verification data when the number of intermediate layers having 15 neurons is changed from 1 layer to 10 layers. FIG. 7 is a diagram showing a regression plot of the fourth joint regarding test data as a performance analysis of the trained model. It is a figure which showed the regression plot of the 5th joint regarding test data. It is a figure which showed the regression plot of the 6th joint regarding test data. It is a figure which showed the simulation result of the angle of the 4th joint. It is a figure showing the simulation result of the angle of the 6th joint. FIG. 2 is a flow diagram showing the flow of processing executed by the information processing device during offline teaching.

DESCRIPTION OF THE PREFERRED EMBODIMENTS An offline teaching system according to an embodiment of the present invention will be described below with reference to the drawings. In the following description, the same parts are given the same reference numerals. Their names and functions are also the same. Therefore, detailed descriptions thereof will not be repeated.

<A. System configuration>
FIG. 1 is a diagram showing a schematic configuration of an offline teaching system. As shown in FIG. 1, the offline teaching system 1 includes an information processing device 10 and a robot system 20.

The information processing device 10 functions as a simulator. Information processing device 10 is typically a general-purpose computer. Information processing device 10 includes a processor 11 , a memory 12 , an input device 13 , a display device 14 , a communication interface 15 , and a bus 16 . The memory 12 stores in advance various programs such as a virtualization model 200, a simulation program 300, an operating system (not shown), and various data. The processor 11, the memory 12, the input device 13, the display device 14, and the communication interface 15 are communicably connected by a bus 16.

Robot system 20 includes a robot controller 21 and a robot 22. The robot controller 21 is communicably connected to the robot 22. The robot controller 21 controls the operation (posture) of the robot 22.

The virtual model 200 is a model in which the robot 22 is virtualized for simulation. The simulation program 300 is a program for offline teaching. The simulation program 300 is executed by the processor 11. Although details will be described later, the simulation program 300 includes a numerical solution program 310 that executes a numerical solution using a Jacobian matrix, and a trained model 320.

Specifically, when the trajectory (route information including motion speed) of the virtualized model 200 from the starting attitude to the ending attitude is input to the information processing device 10 via the input device 13, the processor 11 combines the trajectory information and the virtual The simulation model 200 is input into the simulation program 300, and the simulation program 300 is executed. This generates teaching data. The generated teaching data is sent to the robot controller 21 via the communication interface 15. As a result, the offline teaching of the robot 22 ends.

<B. Robot overview＞
FIG. 2 is a diagram showing a simplified structure of the robot 22. As shown in FIG. As shown in FIG. 2, the robot 22 is a six-axis articulated robot in this example. Specifically, the robot 22 is a vertically articulated robot (manipulator) with six degrees of freedom. In the following, an articulated robot having such a configuration will be described as an example.

The robot 22 has a first joint (first axis) 201, a second joint (second axis) 202, a third joint (third axis) 203, a fourth joint (fourth axis) 204, and a fifth joint (fourth axis) 204. It includes a joint (fifth axis) 205, a sixth joint (sixth axis) 206, and seven links 250 to 256. Each link is a part of an arm.

The correspondence between the first joint 201 and the sixth joint 206 with human movements is as follows. The first joint 201 is an axis around which the waist is rotated. The second joint 202 is an axis that moves the shoulder joint. The third joint 203 is an axis that moves the elbow joint. The fourth joint 204 is an axis around which the wrist is rotated. The fifth joint 205 is an axis for bending the wrist. The sixth joint 206 is an axis around which the fingertip is rotated.

Link 250 connects the base and first joint 201. Link 251 connects first joint 201 and second joint 202. Link 252 connects second joint 202 and third joint 203. Link 253 connects third joint 203 and fourth joint 204. Link 254 connects fourth joint 204 and fifth joint 205. Link 255 connects fifth joint 205 and sixth joint 206. An end effector 290 is attached to the tip of the link 256.

The robot 22 includes a servo motor for driving each joint. When a command is sent from the robot controller 21 to the servo motor, the servo motor rotates in accordance with the command. As a result, the joint corresponding to the servo motor that received the command is driven.

FIG. 3 is a diagram for explaining the coordinate system of each link of the robot 22. As shown in FIG. 3, the robot 22 has seven link coordinate systems Σ _i (0≦i≦6). Each link coordinate system Σ _i is a three-dimensional orthogonal coordinate system consisting of an X _i axis, a Y _i axis, and a Z _i axis. Further, in the following, the angle of each joint is assumed to be θ _i . In this example, the distances d1, d2, d3, d4, d5, and d6 between the coordinate systems are 640 mm, 1190 mm, 200 mm, 305 mm, 1160 mm, and 225 mm, respectively.

<C. Singularity and vicinity of singularity>
The singular point and the vicinity of the singular point will be explained below. Specifically, first, singularity will be briefly explained. Next, the vicinity of the singular point will be explained. After that, a method for setting the singular point and the vicinity of the singular point when performing this simulation will be explained.

(c1. Singularity)
In the following, x represents a vector in the orthogonal coordinate system and indicates the position and orientation of the tip of the robot 22. In the three-dimensional orthogonal coordinate system, x represents the position and rotation angle. q is a variable (vector) indicating the posture in the joint coordinate system. In this case, the virtual model 200 of the robot 22 is described as shown in equation (1) below.

In equation (1), f(q) is a nonlinear function of variable q. It is necessary to calculate a variable q for a series of predetermined tip positions x. Therefore, it is necessary to find the inverse function of equation (1) as shown in equation (2) below.

Note that in equation (2), the right side represents the inverse mapping from q to x. Analytically determining equation (2) requires a large burden. Therefore, in the numerical method of solving equation (2), both sides of equation (1) are differentiated with respect to time. As a result, the kinematic relationship expressed by the following equation (3) is obtained.

By transforming equation (3), equation (4) is obtained.

However, J(q) is a Jacobian matrix (Jacobian) that depends on variables. J(q) is obtained by differentiating f(q) with respect to q, as shown in equation (5).

The Jacobian matrix is a function that changes over time because it depends on the variable q. Therefore, in a specific state called a singular state, the rank of J(q) (the rank of the matrix) decreases. Therefore, for a given trajectory dx, the inverse transformation of equation (2) will lead to an arbitrarily large value dq. If an arbitrarily large value dq is derived, the axis will rotate at high speed and the robot 22 will run out of control.

In this way, no matter how small the differential of the variable to be controlled (the time differential of x) is made, the variable to be controlled (the time differential of q) may diverge. Such a posture of the robot 22 is a "singularity". The robot 22, which is a six-axis articulated robot, has the following three singular points (also referred to as "singular postures").

FIG. 4 is a diagram showing a unique posture of the wrist. As shown in FIG. 4, the fourth joint 204 and the sixth joint 206 are in a straight line, and the hand (that is, the end effector 290) is moved in the Y direction from this posture, or the hand is moved in the Y direction and the posture is When the robot 22 attempts to pass through, extremely large shaft angular velocities are commanded in the opposite direction to the fourth joint 204 and the sixth joint 206, and as a result, the robot 22 runs out of control. At this time, even if the hand is moved in the Z direction, runaway will not occur.

FIG. 5 is a diagram showing a shoulder-specific posture. As shown in FIG. 5, if the fifth joint 205 is located on the rotation axis of the first joint 201, as indicated by the broken line, the robot 22 will run out of control when the hand is moved in a specific direction.

FIG. 6 is a diagram showing a unique elbow posture. As shown in FIG. 6, when the second joint 202, the third joint 203, and the fifth joint 205 are in a straight line, the robot 22 runs out of control when the hand is moved in a specific direction.

For convenience of explanation, the following description will focus on the unique wrist posture shown in FIG. 4.

(c2. Near singularity)
When the degree of operability w is defined by the following equation (6), the degree of operability w increases as the distance from the singular point increases. Note that "manipulability" is one of the kinematic indicators for quantitatively evaluating how freely the position and posture of the end effector 290 attached to the tip of the robot arm can be manipulated.

The following equation (7) is a modification of the above-mentioned equation (4).

In Equation (6), only the determinant of the Jacobian matrix is considered for the degree of manipulability. In equation (6), the hand speed vector of the robot 22 is not considered. However, as shown in equation (7), the angular velocity of the joint (time differential of q) is determined by the inverse of the determinant of the Jacobian matrix, the cofactor matrix (adj(J)) of the Jacobian matrix, and the vector of hand velocity. (time differential of x). Since the runaway of a joint near a singular point is determined from the angular velocity of the joint, the vicinity of the singular point should be defined by the angular velocity of the joint. In this example, the unit of angular velocity is "rpm".

Therefore, in this embodiment, as shown in the following equation (8), the angular velocity of the joint commanded in the simulation is determined by the servo motor (not shown) of the robot 22 (specifically, the servo motor that drives the joint). The range exceeding the maximum rotational speed is defined as "near the singularity". Note that the right side of equation (8) is the maximum rotational speed of the servo motor.

Specifically, the range in which the angular velocity (rpm) of a predetermined joint among the plurality of joints in the virtual model 200 exceeds the maximum rotational speed (rpm) of a motor (virtual motor) that moves the predetermined joint is defined as Defined as "near the singularity". As the maximum rotational speed of the motor, for example, a catalog value of the motor (actual machine) can be used.

More specifically, even at the singular point, the angular velocity of the joint commanded through simulation exceeds the maximum rotational speed of the servo motor. Therefore, the range in which the angular velocity of the joint exceeds the maximum rotational speed of the servo motor includes the singular point and the vicinity of the singular point.

7 to 10 are diagrams illustrating the vicinity of the singular point of the fourth joint 204. FIG. 7 shows the simulation results when the hand speed of the virtual model 200 in the Y-axis direction is 100 m/s, and the speed in the X-axis direction and the speed in the Z-axis direction are zero (the fourth FIG. 3 is a diagram showing a measured value of the maximum rotational speed of a servo motor in an actual machine (robot 22); Note that the “hand” refers to the model portion of the end effector 290 in the virtualized model 200.

In the simulation, first, the hand of the virtual model 200 was moved within a certain range in the Y-axis direction. Thereafter, the height of the hand of the virtualized model 200 in the Z-axis direction is changed by a predetermined height, and the virtualized model 200 is again moved within a certain range in the Y-axis direction. This process was repeated.

In this case, when the height of the hand of the virtualized model 200 exceeded Z11 (<2030 mm), the fourth joint of the virtualized model 200 began to move out of control. When the height of the hand of the virtualized model 200 exceeded Z12 (>2030 mm), the runaway of the fourth joint of the virtualized model 200 stopped. Therefore, when the speed of the hand of the virtual model 200 in the Y-axis direction is 100 m/s, the range near the singularity in the Z-axis direction of the fourth axis is from Z11 to Z12. Note that in this example, Z=2030 mm is the singular point.

It can be seen that the command rotation speed diverges at the singular point (Z=2300 mm). When Z is greater than or equal to _Z11 and less than or equal to _Z12 , the actual servo motor cannot achieve the commanded rotational speed. Such simulations show that the joints rotate rapidly near the singularity.

Furthermore, the speed in the Y-axis direction of the hand of the virtual model 200 was changed to 300 mm/s, 500 mm/s, and 1200 mm/s, and the same simulation as above and the servo motor in the actual machine (robot 22) were performed. The rotation speed was measured.

FIG. 8 is a diagram showing the simulation results when the speed of the hand in the Y-axis direction is 300 mm/s and the measured value of the rotational speed of the servo motor. As shown in FIG. 8, when Z is greater than or equal to Z ₁₃ (<Z ₁₁ ) and less than Z ₁₄ (>Z ₁₂ ), the actual servo motor cannot achieve the commanded rotational speed. Note that in this example, Z ₁₃ is 1950 mm, and Z ₁₄ is 2100 mm.

FIG. 9 is a diagram showing the simulation results when the speed of the hand in the Y-axis direction is 500 mm/s and the measured value of the rotational speed of the servo motor. As shown in FIG. 9, when Z is greater than or equal to Z ₁₅ (<Z ₁₃ ) and less than Z ₁₆ (>Z ₁₄ ), the actual servo motor cannot achieve the command rotation speed.

FIG. 10 is a diagram showing simulation results when the speed of the hand in the Y-axis direction is 1200 mm/s and the measured value of the rotational speed of the servo motor. As shown in FIG. 10, when Z is greater than or equal to Z ₁₇ (<Z ₁₅ ) and less than Z ₁₈ (>Z ₁₆ ), the actual servo motor cannot achieve the commanded rotational speed.

Based on FIGS. 7 to 10, it can be seen that as the hand speed increases, the range near the singularity increases. This is because, as explained based on equation (7), the angular velocity of a joint is the product of the inverse matrix of the Jacobian matrix and the hand speed, so even if the position and posture are the same, the hand speed and This is because the angular velocity of the joint changes depending on the direction.

FIG. 11 is a diagram showing the range near the singularity when the hand speed is only in the Y-axis direction. Specifically, FIG. 11 is a diagram showing the range near the singular point when the differential value of x is expressed by the following equation (9).

More specifically, FIG. 11 is a diagram showing the range near the singular point on the YZ plane by hand speed when the X coordinate is fixed at a certain value. In FIG. 11, the differentiation of Y (magnitude of hand speed in the Y-axis direction) in Equation (9) is expressed as Equation (10) below, and a boundary line expressed by Equation (11) below is illustrated. The inside of each boundary line is near the singularity. Further, a singular point exists inside the boundary line where the hand speed is 100 mm/s.

As shown in FIG. 11, as the hand speed in the Y-axis direction increases, the range near the singularity becomes wider. In addition, when considering the case where the hand speed is only in the Z-axis direction and examining the range near the singularity by hand speed in the same way as above, it was found that the shape near the singularity changes depending on the direction of the hand speed. .

As described above, it was found that the range near the singularity changes depending on the magnitude and direction of the hand velocity vector. Therefore, in the present embodiment, offline teaching data is generated in consideration of the vicinity of a singular point defined according to the hand speed vector.

<D. Behavior at singular points and near singular points when using Jacobian matrix>
As described above, at a singular point and in the vicinity of the singular point, the value of the determinant of the Jacobian matrix becomes small, and the inverse of the determinant diverges. Therefore, according to equation (7), the variable to be controlled (time differential of q) diverges. The divergence mode will be specifically explained below. In detail, we will explain the general solution of inverse kinematics.

Referring again to FIG. 3, once the angle θ ₁ of the first joint 201, the angle θ ₂ of the second joint 202, and the angle θ ₃ of the third joint 203 are found, from the base coordinate system Σ ₀ A homogeneous transformation matrix ⁰ T ₃ to the coordinate system Σ ₃ can be calculated. A homogeneous transformation matrix ³ T ₆ from the coordinate system Σ ₃ to the hand coordinate system Σ ₆ can be expressed by the following equation (12).

⁰ T ₆ is a homogeneous transformation matrix from the coordinate system Σ ₀ to the coordinate system Σ ₆ , and can be calculated from the command value. Therefore, the right side of equation (12) can be calculated.

The rotation matrix component ³ R ₆ of ³ T ₆ on the left side of equation (12) (that is, the upper left 3 rows and 3 columns small matrix (9 components) included in ³ T ₆ ) is expressed by the following equation (13). The rotation matrix component ³ R ₄ of the homogeneous transformation matrix ³ T ₄ , the rotation matrix component ⁴ R ₅ of the homogeneous transformation matrix ⁴ T ₅ , and the rotation matrix of the homogeneous transformation matrix ⁵ T ₆ as shown in equation (15) from Using the components ⁵ and _R6 , the following formula (16) is obtained. Note that C _i represents cos θ _i and S _i represents sin θ _i . R ₁₁ , R ₂₁ , R ₃₁ , R ₁₂ , R ₂₂ , R ₃₂ , R ₁₃ , R ₂₃ , and R ₃₃ are components (elements) of the rotation matrix component ³ R ₆ , respectively. Furthermore, hereinafter, the rotation matrix component is also simply referred to as a "rotation matrix."

From equation (16), the angle θ ₄ of the fourth joint 204 is as shown in equation (17) below. The angle θ ₅ of the fifth joint 205 is expressed by the following equation (18). The angle θ ₆ of the sixth joint 206 is expressed by the following equation (19). However, in equations (17) and (19), k is an arbitrary integer.

Since equation (17) and equation (19) include an arbitrary integer k, there are a plurality of solutions for angle θ ₄ and a plurality of solutions for angle θ ₆ , respectively.

FIG. 12 is a diagram showing the solution for the angle θ ₄ . As shown in FIG. 12, even if the domain is limited to 0°≦θ ₄ ≦360°, two solutions exist.

The angle θ ₄ of the fourth joint 204 is displaced by about 180° in the vicinity where the value (R ₁₃ /R ₃₃ ) of the horizontal axis becomes 0. Specifically, when the angle θ ₄ of the fourth joint 204 _is solved by a numerical solution using a Jacobian matrix, the determinant of the Jacobian _matrix is Since the inverse matrix of becomes large, the angle θ ₄ suddenly changes from 90° to 270° when R ₁₃ /R ₃₃ changes from negative to positive (or from positive to negative).

In this way, if a numerical solution method using a Jacobian matrix is used at a singular point and in the vicinity of the singular point, the robot 22 will run out of control. Therefore, at the singular point and in the vicinity of the singular point, the method described below is used instead of using the numerical solution method using the Jacobian matrix (more specifically, the numerical solution program 310).

<E. Applying the trained model>
(e1. Range to which trained model is applied)
FIG. 13 is a schematic diagram for explaining a method of calculating joint angles at a singular point, the vicinity of the singular point, and other ranges (posture ranges). That is, it is a diagram for explaining a simulation method.

As shown in FIG. 13, when the posture of the virtual model 200 is outside the range 30 including the singular point and the vicinity of the singular point of the virtual model 200, as indicated by an arrow 31, the processor 11 calculates the Jacobian matrix. to calculate the angle of each joint. Specifically, the processor 11 uses the numerical solution program 310 to calculate the angle of each joint.

Thereafter, as shown by an arrow 32, the processor 11 uses the trained model 320 generated in advance until the posture of the virtualized model 200 is within the range 30 at point P1 and then outside the range 30 from point P2. Use the angle of each joint to calculate the angle of each joint. That is, when the posture of the virtual model 200 is within the range 30, the processor 11 uses the learned model 320 to calculate the angle of each joint. Note that the outer surface of the range 30 is a boundary surface that defines the vicinity of the singular point.

When the posture of the virtual model 200 goes outside the range 30 that includes the singular point of the virtual model and the vicinity of the singular point, as shown by an arrow 33, the processor 11 again calculates the angle of each joint using the Jacobian matrix. calculate.

For example, if the attitude of the virtualized model 200 at the starting point of the arrow 31 in FIG. I can say that I will do it.

The processor 11 controls the angle of each joint in the virtualized model 200 to transition the posture of the virtualized model 200 from the first posture to the second posture. At this time, when the posture of the virtualized model 200 is outside the range 30, the processor 11 calculates the angle of each joint using the Jacobian matrix, and when the posture of the virtualized model 200 is within the range 30, the processor 11 calculates the angle of each joint using the learned model 320. Calculate the angle of each joint using

Further, the range 30 (that is, the singular point and the vicinity of the singular point) can be summarized as follows.

Among the postures that the virtualized model 200 can take, the range 30 including the singular point and the vicinity of the singularity of the virtualized model 200 is determined by the speed at which the posture of the virtualized model 200 is changed, as explained based on FIG. 11. This will be determined individually.

The range 30 when the speed at which the posture of the virtualized model 200 is changed is the first speed (for example, 300 mm/s in the example of FIG. 11) is the second speed (in the example shown in FIG. In the example of No. 11, the range is wider than the range 30 in the case of, for example, 100 mm/s).

Specifically, as explained based on equation (8), the range 30 is defined as the angular velocity (rpm) of a predetermined joint among the plurality of joints in the virtualized model 200 among the postures that the virtualized model 200 can take. , is a range exceeding the maximum rotational speed (rpm) of the servo motor that moves the predetermined joint.

(e2. Generation of trained model)
Next, a method for generating the trained model 320 used in the range 30 (that is, the singular point and the vicinity of the singular point) will be described.

Referring again to FIG. 12, for the fourth joint 204, as described above, there are two solutions even if the range is limited to 0°≦θ ₄ ≦360°. Therefore, even if a learning model (neural network) is generated with the inputs being R ₃₃ and R ₁₃ and the output being θ ₄ , the learning accuracy will be significantly reduced because it will have one input and two outputs.

If the range is limited to 90°≦θ ₄ ≦270°, one input and one output will be required. However, when the range is limited to 90°≦θ ₄ ≦270°, when R ₁₃ /R ₃₃ changes from negative to positive (or from positive to negative), the angle θ ₄ changes by 180°. Resulting in.

FIG. 14 shows a case where the range is limited to 0°≦θ ₄ ≦180°. As shown in FIG. 14, by limiting the variable range to 0°≦θ ₄ ≦180°, the above-mentioned change of 180° can be suppressed. However, the function is not continuous near where the value of R ₁₃ /R ₃₃ is 0 (ie, at a singular point). Therefore, it is difficult to specify the solution using numerical methods.

Therefore, by using machine learning, we limit the range to 0°≦θ ₄ ≦180° and attempt to specify a solution. Specifically, in order to construct an inverse kinematics model by machine learning, a training dataset is generated. A learning data set is generated such that at least the value of R13/R33 and the angle of the fourth joint 204 satisfy the relationship shown by the solid line graph in FIG.

A detailed explanation is as follows. The rotation matrix component ³ R ₆ when there is a geometric error in the link parameters of the fourth joint 204, the fifth joint 205, and the sixth joint 206 becomes very complicated compared to equation (16), and the analysis It is difficult to solve the problem. Therefore, a trained model 320 is generated using the training data set, and the above solution is calculated using the generated trained model 320. In this manner, in this embodiment, a discontinuous function is constructed using a neural network. A more detailed explanation is as follows.

Derivation of the angles θ ₄ , θ ₅ , θ ₆ which are the three solutions by the numerical solution method results in the problem of solving nine nonlinear simultaneous equations included in the following equation (20).

However, the rotation matrix component ³ R ₆ on the right side is a 3-by-3 matrix that can be calculated using the solution of angle θ ₁ , angle θ _{2 ,} and angle θ ₃ . A learning model to be described later is created in advance, and the processor 11 is caused to perform machine learning using the input as ³ R ₆ and the outputs as θ ₄ , θ ₅ , and θ ₆ based on the above equation (20). In order to avoid a displacement close to 180° in the joint angle, the learning data is intentionally biased, as shown in FIG. 14, for example. Specifically, a three-dimensional grid point group with a width of 0.1° is created with 0°≦θ ₄ ≦180°, -100°≦θ ₅ ≦100°, and 0°≦θ ₆ ≦180°, and randomly 5000 points are extracted and used as 5000 sets of learning data (teacher data).

The three-dimensional lattice point group will be explained as follows. The angles θ ₄ , θ ₅ , and θ ₆ are vectors with 1800, 2000, and 1800 elements, respectively, so the combination of these angles is 6,480,000,000 (=1800×2000 ×1800). The three-dimensional lattice point group represents each of the above-mentioned 6,480,000,000 points in a three-dimensional orthogonal coordinate system having angles θ ₄ , θ ₅ , and θ ₆ as axes.

Specifically, the angles θ ₄ , θ ₅ , θ ₆ extracted as above are substituted into the left side of equation (20), and the input data is converted to [R ₁₁ , R ₂₁ , R ₃₁ , R ₁₂ , R ₂₂ , R ₃₂ , R ₁₃ , R ₂₃ , R ₃₃ ] ^T , a data set (a data set including 5000 sets of teacher data) is created in which the output data is set to lower collection angles θ ₄ , θ ₅ , θ ₆ . The created dataset was divided into training data and test data, and a neural network was used for learning and verification. In this example, 3500 sets of training data, 750 sets of test data, and 750 sets of verification data were used.

Next, the data structure of the learning model will be explained. Representative hyperparameters of neural networks include the number of intermediate layers and the number of neurons. The larger the number of layers and neurons in the intermediate layer, the more complex learning can be accommodated. However, if the number of layers and the number of neurons in the intermediate layer are too large, overfitting will occur and the generalization performance will deteriorate.

Therefore, we focused on the root mean squared error (RMSE) of the verification data and investigated the relationship between the number of neurons and the number of layers and the residual error. First, the number of neurons in the middle layer is determined using a single-layer neural network, and then the number of layers in the middle layer is determined by increasing the number of middle layers with the same number of neurons.

FIG. 15 is a diagram showing the root mean square error of verification data when there is only one intermediate layer and the number of neurons is varied from 1 to 50. Based on the results shown in FIG. 15, the number of neurons in the middle layer of the learning model was set to 15.

FIG. 16 is a diagram showing the root mean square error of the verification data when the number of layers in the intermediate layer having 15 neurons is changed from 1 layer to 10 layers. Based on the results shown in FIG. 16, the number of intermediate layers of the learning model was set to three.

As for the other specifications of the neural network, the learning algorithm of the learning program was the Levenberg-Marquardt method, and the error function was the mean square error.

17 to 19 are diagrams showing performance analysis results of the learned model 320. FIG. 17 is a diagram showing a regression plot of the fourth joint 204 regarding the test data. Similarly, FIG. 18 is a diagram showing a regression plot of the fifth joint 205 with respect to the test data. FIG. 19 is a diagram showing a regression plot of the sixth joint 206 with respect to the test data.

It can be seen from FIGS. 17 to 19 that the inverse kinematics model can be learned accurately by the neural network. However, several points deviated from the y=x line, resulting in prediction errors.

(e3. Simulation results)
FIG. 20 is a diagram showing a simulation result of the angle θ ₄ of the fourth joint 204. FIG. 21 is a diagram showing a simulation result of the angle θ ₆ of the sixth joint 206.

As shown in FIGS. 20 and 21, when the trained model 320 is used, when the Y coordinate value changes from negative to positive (when passing through a singular point or near a singular point), the fourth joint 204 It can be seen that no sudden displacement of 180° occurs at the sixth joint 206.

<F. Control structure of offline teaching>
FIG. 22 is a flow diagram showing the flow of processing executed by the information processing device 10 during offline teaching.

As shown in FIG. 22, in step S1, the information processing device 10 (more specifically, the processor 11) determines the range of the singularity and the vicinity of the singularity of the virtualized model 200 of the robot 22, as shown in FIG. is determined by operating speed. In step S2, the processor 11 receives a designation of a trajectory from the start attitude to the end attitude (target attitude) of the movement of the virtual model 200 based on the user's input. The trajectory is route information including operating speed. In step S3, a range (for example, range 30 shown in FIG. 13) according to the specified operating speed is set from among the plurality of ranges determined in step S1.

In step S4, the processor 11 starts moving the virtual model 200 along the specified trajectory. That is, processor 11 starts simulation. In step S5, the processor 11 determines whether the posture of the virtualized model 200 is outside the set range.

If it is determined that it is outside the range (YES in step S6), the processor 11 calculates the joint angle θ _i of the virtualized model 200 using the Jacobian matrix in step S6, and applies the calculation result to the calculation period. is stored in the memory 12 in association with time information based on the time information. That is, the processor 11 uses the numerical solution program 310 to calculate the joint angle θ _i by numerical solution.

If it is determined that it is within the range (NO in step S6), the processor 11 calculates the joint angle θ _i of the virtualized model 200 using the above-mentioned learned model 320 in step S8, and The result is stored in the memory 12 in association with time information based on the calculation cycle.

In step S7, the processor 11 determines whether the posture of the virtualized model 200 has reached the final posture. If it is determined that the end posture has been reached (YES in step S7), the processor 11 ends the series of processes. If it is determined that the end posture has not been reached (NO in step S7), the processor 11 determines in step S9 whether or not the next calculation cycle has arrived.

If it is determined that the next calculation cycle has arrived (YES in step S9), the processor 11 advances the process to step S5. If the next calculation cycle has not arrived (NO in step S9), the processor 11 waits until the next calculation cycle arrives.

When the above-described processing is completed in the information processing device 10, the information stored in the memory 12 (ie, offline teaching data) is transmitted to the robot controller 21 of the robot system 20 (see FIG. 1).

<G. Summary＞
(g1. Offline teaching method)
The offline teaching method for the robot 22 using the simulator described above can be summarized as follows.

(1) The offline teaching method includes the steps of determining a range including the singular point of the virtual model 200 and the vicinity of the singular point among the postures that the virtual model 200 of the robot 22 can take, and and a step of transitioning the attitude of the virtualized model 200 from the first attitude to the second attitude by controlling the angle of the virtual model 200 .

In the step of transitioning the posture of the virtualized model 200 from the first posture to the second posture, when the posture of the virtualized model 200 is outside the above range, the processor 11 calculates the angle of each joint using the Jacobian matrix. , when the posture of the virtualized model 200 is within the above range, the processor 11 uses the learned model 320 to calculate the angle of each joint.

According to such a configuration, since the angle of each joint is calculated using the learned model 320 in the range including the singular point and the vicinity of the singular point, there is no need to perform a numerical solution using a Jacobian matrix. Moreover, according to such a configuration, when passing through a range including a singular point and a vicinity of the singular point regarding the wrist, for example, the difference between the reference joint angles in each of the FLIP posture and the NONFLIP posture is calculated. There is no need to perform the calculation process and the process of selecting either the FLIP attitude or the NONFLIP attitude based on the calculation result.

Therefore, according to the offline teaching method described above, it is possible to efficiently suppress unintended behavior (runaway, stop, etc.) of the robot 22 at the singular point and in the vicinity thereof.

(2) The above-mentioned ranges are individually determined according to the speed at which the posture of the virtualized model 200 is changed. According to such a configuration, the range in which the trained model 320 is used instead of the Jacobian matrix can be set depending on the speed at which the posture of the virtualized model 200 is changed.

(3) The range when the speed is the first speed is wider than the range when the speed is the second speed, which is slower than the first speed. The faster the speed at which the posture of the virtualized model 200 is changed, the wider the range near the singularity becomes. Therefore, the faster the speed, the wider the range in which the learned model 320 is used, making it possible to suppress unintended behavior of the robot 22.

(4) The above range is such that, among the postures that the virtual model 200 of the robot 22 can take, the angular velocity of a predetermined joint among the plurality of joints in the virtual model 200 is the maximum rotational speed of the motor that moves the predetermined joint. The range exceeds. Thereby, the singular point and the vicinity of the singular point can be defined.

(5) The robot 22 is a six-axis vertical articulated robot. If the rotation angle of the fourth joint 204 of the robot 22 is an angle θ ₄ , the rotation angle of the fifth joint 205 is an angle θ ₅ , and the rotation angle of the sixth joint 206 is an angle θ ₆ , the trained model 320 uses the input as described above. This is a rotation matrix ³ R ₆ with 3 rows and 3 columns as shown in Equation (20), and was generated using teacher data with outputs as angles θ ₄ , θ ₅ , and θ ₆ .

(6) In the training data, angle θ ₄ and angle θ ₆ are 0° or more and 180° or less, and angle θ ₅ is −100° or more and 100° or less. According to this, it is possible to suppress sudden changes in the fourth joint 204, the fifth joint 205, and the sixth joint 206.

(7) The trained model 320 receives the rotation matrix ³ R ₆ as input, and outputs angles θ ₄ , θ ₅ , and θ ₆ as the angles of each joint.

(g2. Information processing device 10)
The information processing device 10 is summarized as follows.

The information processing device 10 includes a processor 11 and a memory 12 in which a simulation program 300 for the robot 22 is stored. By executing the simulation program 300, the processor 11 (i) determines a range including the singularity of the virtualized model 200 and the vicinity of the singularity among the postures that the virtualized model 200 of the robot 22 can take; ii) By controlling the angle of each joint in the virtualized model 200, the posture of the virtualized model 200 is transitioned from the first posture to the second posture.

When transitioning the posture of the virtual model 200 from the first posture to the second posture, the processor 11 calculates the angle of each joint using the Jacobian matrix when the posture of the virtual model 200 is outside the above range. However, when the posture of the virtual model 200 is within the above range, the learned model 320 is used to calculate the angle of each joint. Moreover, according to such a configuration, when passing through a range including a singular point and a vicinity of the singular point regarding the wrist, the processor 11 calculates the reference joint angle in each of the FLIP posture and the NONFLIP posture. There is no need to perform the process of calculating the difference between the two positions and the process of selecting either the FLIP attitude or the NONFLIP attitude based on the calculation result.

Therefore, according to the information processing device 10, it is possible to efficiently suppress unintended behavior (runaway, stop, etc.) of the articulated robot at the singular point and in the vicinity thereof.

<H. Modified example>
(1) The robot 22 is not limited to six axes. The above-described processing method using a learned model at a singular point and near the singular point can also be applied to an N-axis articulated robot (N is an arbitrary natural number of 3 or more).

Specifically, the processing method using the trained model described above can be applied to a robot having a configuration in which any three consecutive axes (virtual axes of rotational axes) intersect at one point among N axes. . Specifically, the learned model can be applied to such continuous three-axis movements.

In other words, if j is a natural number greater than or equal to 1 and less than or equal to N-2, the processing method using the learned model described above is based on the line segment connecting the j-th joint and the j+2 joint next to the j-th joint. , can be applied to a robot having a configuration in which the j+1 joint is located between the j-th joint and the j+2 joint (a configuration in which three joints can be in a straight line). For example, as shown in FIG. 2 for an example of six axes, a configuration in which the fifth joint 205 is located on a line segment connecting the fourth joint 204 and the sixth joint 206 may be used. This is because with such a configuration, an analytical solution of inverse kinematics can be derived.

In this case, if the rotation angle of the j-th joint is an angle θ _j , the rotation angle of the j+1 joint is an angle θ _j+1 , and the rotation angle of the j+2 joint is an angle θ _j+2 , then the trained model inputs the following equation (21 ), and the rotation matrix ^j−1 _{R j+2 shown in} FIG. Note that equation (21) is obtained by expanding equation (20) using j.

Note that in such a configuration, the trained model receives the rotation matrix ^j−1 R _j+2 as input, and outputs the angles θ _j , θ _j+1 , and θ _j+2 as the angles of each joint.

Even with such a configuration, it is possible to efficiently suppress unintended behavior (runaway, stop, etc.) of the robot at the singular point and in the vicinity thereof.

(2) In the above example, the same unit system (rpm) was used as the unit system for the angular velocity of the joint and the maximum rotational speed of the motor that moves the joint. There is no need to use a system of units. At least one of the two unit systems may be "rad/s", "deg/s", or "rps". In this case, "the range in which the angular velocity of a predetermined joint exceeds the maximum rotational speed of the motor that moves the predetermined joint" means that when the units of both units are unified (for example, one system of units is used as the unit of the other) (When converting into a system), there is such a magnitude relationship.

The embodiment disclosed this time is an example, and is not limited to the above content only. The scope of the present invention is indicated by the claims, and it is intended that all changes within the meaning and range equivalent to the claims are included.

1 offline teaching system, 10 information processing device, 11 processor, 12 memory, 13 input device, 14 display device, 15 communication interface, 16 bus, 20 robot system, 21 robot controller, 22 robot, 30 range, 31, 32, 33 arrow, 200, 220 virtual model, 201 first joint, 202 second joint, 203 third joint, 204 fourth joint, 205 fifth joint, 206 sixth joint, 250, 251, 252, 253, 254, 255, 256 links, 290 end effectors, 300 simulation programs, 310 numerical solution programs, 320 trained models.

Claims (10)

An offline teaching method for an articulated robot using a simulator, the method comprising:
a step in which the simulator determines a range including a singular point and a vicinity of the singular point of the virtual model among postures that the virtual model of the articulated robot can take;
the simulator controlling the angle of each joint in the virtualized model to transition the posture of the virtualized model from a first posture to a second posture,
In the step of transitioning the posture of the virtualized model from the first posture to the second posture,
When the posture of the virtualized model is outside the range, the simulator calculates the angle of each joint using a Jacobian matrix,
An offline teaching method for an articulated robot, wherein when the posture of the virtualized model is within the range, the simulator calculates the angle of each joint using a learned model generated in advance. 2. The offline teaching method for an articulated robot according to claim 1, wherein the range is individually determined according to a speed at which the posture of the virtual model is changed. The offline teaching method for an articulated robot according to claim 2, wherein the range when the speed is a first speed is wider than the range when the speed is a second speed slower than the first speed. . The range is such that the angular velocity of a predetermined joint among the plurality of joints in the virtual model exceeds the maximum rotational speed of a motor that moves the predetermined joint, among the postures that the virtual model of the multi-joint robot can take. 2. The offline teaching method for an articulated robot according to claim 1, wherein the offline teaching method exceeds the above range. If N is a natural number greater than or equal to 3, and j is any natural number greater than or equal to 1 and less than or equal to N-2,
The multi-joint robot is an N-axis vertical multi-joint robot having a first joint to an N-th joint,
The j+1 joint between the j-th joint and the j+2 joint is located on the line segment connecting the j-th joint and the j+2 joint next to the j-th joint,
Assuming that the rotation angle of the j-th joint is an angle θ _j , the rotation angle of the j+1 joint is an angle θ _j+1 , and the rotation angle of the j+2 joint is an angle θ _j+2 ,
The trained model uses training data in which the input is a 3-by-3 rotation matrix ^j-1 R _j+2 shown in the following equation (1), and the outputs are angles θ _j , θ _j+1 , θ _j+2 The offline teaching method for an articulated robot according to any one of claims 1 to 4, wherein the method is a generated one.

The N is 6, the j is 4,
The offline method of the articulated robot according to claim 5, wherein angle θ ₄ and angle θ ₆ in the training data are 0° or more and 180° or less, and angle θ ₅ is −100° or more and 100° or less. teaching method. The multi-joint system according to claim 5, wherein the learned model outputs the angles θ _j , θ _j+1 , and θ j ₊₂ as the angles of each of the joints by receiving the rotation matrix ^j− 1 R _j+2 as an input. How to teach robots offline. A program that causes a computer to execute the offline teaching method for an articulated robot according to claim 1. An articulated robot that operates based on offline teaching data generated by the offline teaching method for an articulated robot according to claim 1. An information processing device,
a processor;
Equipped with a memory that stores a simulation program for an articulated robot,
By executing the simulation program, the processor
determining a range including a singular point of the virtualized model and a vicinity of the singularity among postures that the virtualized model of the articulated robot can take;
Transitioning the posture of the virtualized model from a first posture to a second posture by controlling the angle of each joint in the virtualized model,
When the posture of the virtualized model is transitioned from the first posture to the second posture, the processor uses a Jacobian matrix to change the posture of each joint when the posture of the virtualized model is outside the range. An information processing device that calculates an angle, and when the posture of the virtual model is within the range, calculates the angle of each joint using a learned model generated in advance.

Images