CN106737855B - A Robot Accuracy Compensation Method Combining Pose Error Model and Stiffness Compensation - Google Patents

Abstract

The invention discloses a method for compensating robot accuracy by synthesizing a pose error model and stiffness compensation, comprising the following steps: step 1, establishing a robot motion model according to structural parameters of the robot; In the workspace, the target pose point is randomly given, and when the end of the robot moves to the designated point, the joint angle at this time is recorded; Step 4, use the position measuring instrument to measure the actual coordinates Pa of the given target pose point; Step 5, Use the least squares method to identify the error parameters; step 6, apply a load to the end of the robot, measure its deformation, and then return to step 3 to compensate the re-identified structural error to the motion model again, so as to eliminate the end caused by the deformation caused by the load. At the same time, the deformation data caused by the load is stored in the database for later precision compensation. The invention can significantly improve the absolute positioning accuracy of the robot, and is simple and efficient.

Description

A Robot Accuracy Compensation Method Combining Pose Error Model and Stiffness Compensation

technical field

The invention belongs to the technical field of robot calibration, in particular to a robot precision compensation method integrating a pose error model and stiffness compensation.

Background technique

With the promulgation of the "Made in China 2025 Outline", industrial robots will set off another development boom in my country. Accuracy, as an important index to measure the performance of industrial robots, includes repeated positioning accuracy and absolute positioning accuracy. Today's industrial robots have high repetitive positioning accuracy and low absolute positioning accuracy, which is not conducive to off-line programming and high-precision machining. The robot kinematics calibration is an effective means to improve the positioning accuracy of the robot, which mainly includes four stages: modeling, measurement, identification and compensation.

The traditional method for robot calibration only compensates for the errors caused by the kinematic model parameters, but does not consider the deformation caused by the load, and does not perform comprehensive compensation. In traditional stiffness compensation, a lot of formula derivation is needed to solve the deflection of each joint and the deflection of the arm, and establish a stiffness model. The process is complicated and the efficiency is low.

SUMMARY OF THE INVENTION

The technical problem solved by the present invention is to provide a robot precision compensation method that integrates a pose error model and stiffness compensation.

The technical solution for realizing the purpose of the present invention is: a robot precision compensation method integrating a pose error model and stiffness compensation, comprising the following steps:

Step 1. Establish a robot motion model according to the structural parameters of the robot; specifically:

Step 1-1. According to the DH method, establish a homogeneous transformation matrix between adjacent joints of the robot. The matrix is:

In the above formula, a _i is the length of the connecting rod, α _i is the torsion angle of the joint, d _i is the offset distance of the connecting rod, θ _i is the rotation angle of the joint, x is the X-axis coordinate of the connecting rod coordinate system, and z is the Z-axis of the connecting rod coordinate system. coordinate;

Step 1-2. Introduce the rotation Rot(y, β) around the y-axis to the homogeneous transformation matrix established in step 1-1 to eliminate the singularity between the intermediate links because the axes are parallel or nearly parallel, and the adjacent joints The homogeneous transformation matrix between is modified as:

In the above formula, β _i represents the rotation angle of the i-th rod coordinate system of the robot around the y-axis, y is the Y-axis coordinate of the connecting rod coordinate system, c is cos, and s is sin;

Step 1-3, add an extra parameter z _n to describe the translation of the tool coordinate system along the z-axis of the end link coordinate system, and establish the transformation matrix of the tool coordinate system relative to the end link coordinate system as:

Steps 1-4. For an N-joint robot, the kinematic relationship between the robot tool coordinate system and the base coordinate system obtained according to the above steps is:

T = ⁰ A ₁ × ¹ A ₂ × ² A ₃ × ³ A ₄ × ⁴ A ₅ × ⁵ A ₆ ×... × ^n-1 A _n

The value of n is 1...N, and N≥1, the kinematic relationship is the robot motion model.

Step 2. Establish a robot error model according to the robot motion model established in Step 1; specifically:

Step 2-1. The error dA _i between the actual conversion matrix of the intermediate link and the nominal conversion matrix is obtained by the differential transformation principle:

and

A _i is the intermediate link conversion matrix;

Step 2-2. Obtain the transformation matrix error of the tool coordinate system relative to the end link coordinate system by the differential transformation principle:

An _is the transformation matrix between the tool coordinate system and the end link coordinate system;

Step 2-3. For the N-joint robot, the final error model is the error of the intermediate link plus the error of the tool coordinate system relative to the transformation of the end link. After the total differential, the following formula is obtained:

where p is the end position coordinate;

Write it as:

Δp=J _δ ΔX

where ΔX=(Δθ ₁ ... Δθ _n , Δα ₁ ... Δα _n , Δa ₁ ... Δa _n , Δd ₁ ... Δd _n , Δβ ₁ ... Δβ _n , Δz _n ) ^T represents the robot The structural error J _δ of each connecting rod is the identification Jacobian matrix.

Step 3. In the working space of the robot, the target pose point is freely given, and its nominal coordinate is Pn. When the end of the robot moves to the specified point, the joint angle at this time is recorded;

Step 4. Use a position measuring instrument to measure the actual coordinates Pa of the given target pose point;

Step 5. Use the least squares method to identify the error parameters, and compensate the identified structural errors to the nominal parameters of the robot motion model to verify whether the requirements are met. If the requirements are met, perform the next step, otherwise return to step 3;

Compensating the identified structural errors to the nominal parameters of the motion model is to add the structural parameters to the identified error parameters;

Verifying whether the requirements are met specifically refers to: measuring the actual coordinates, comparing with the data before compensation, whether the tolerance range is ±0.2mm, if it is within the tolerance range, it meets the requirements, otherwise it does not meet the requirements.

Step 6. Apply a load at the end of the robot, measure its deformation, and then go back to step 3 to compensate the re-identified structural error to the robot motion model again, so as to eliminate the end pose error caused by the deformation caused by the load, and at the same time, reduce the deformation caused by the load. The deformation data is stored in the database for later precision compensation. Apply a load at the end of the robot, and measure its deformation as follows:

Step 6-1. Within the rated load range, apply different mass loads to the end of the robot, use the stress-strain gauge to measure the deformation of each part of the robot, and use the instrument to measure the actual coordinates of the robot reaching the designated point at this time;

Step 6-2: Process the measurement results, obtain the curve of the deformation amount of each part of the robot changing with the load, and obtain the curve of the robot end position error changing with the load.

Compared with the prior art, the present invention has the following significant advantages: (1) The kinematics model used in the present invention adds a tool coordinate system on the basis of the MDH method to form a 6-parameter model, so that the motion model is more complete and can be better describe the robot model. (2) The method of the present invention adopts the least square method for the identification of the structural error of the robot, and can quickly obtain the identification result of the structural error by using software such as matlab. (3) After the method of the present invention performs compensation according to the pose error model, the deformation amount caused by the end load of the robot is compensated twice, and at the same time, there is no need to establish a stiffness model for the robot, and the complex calculation and derivation process is omitted. (4) The method of the present invention obtains the change curve of the deformation amount of the robot body against the load, so that the robot can retrieve offline results when encountering similar working conditions, and improve the online work efficiency of the robot.

The present invention will be described in further detail below with reference to the accompanying drawings.

Description of drawings

FIG. 1 is a flow chart of a method for compensating robot accuracy by combining a pose error model and stiffness compensation according to the present invention.

Figure 2 shows the deformation of the end of each arm caused by the load applied to the end of the robot. Figure (a) is the bending deformation diagram of the arm, Figure (b) is the stretching deformation of the arm, and Figure (c) is the arm. Torsional deformation diagram of the rod.

Detailed ways

With reference to Fig. 1 and Fig. 2, a robot precision compensation method for comprehensive pose error model and stiffness compensation of the present invention includes the following steps:

Step 1. Establish a robot motion model according to the structural parameters of the robot; specifically:

Step 1-1. According to the DH method, establish a homogeneous transformation matrix between adjacent joints of the robot. The matrix is:

In the above formula, a _i is the length of the connecting rod, α _i is the joint torsion angle, d _i is the connecting rod offset distance, θ _i is the joint rotation angle, X is the X axis of the connecting rod coordinate system, and Z is the Z axis of the connecting rod coordinate system.

Step 1-2. Introduce the rotation Rot(y, β) around the y-axis to the homogeneous transformation matrix established in step 1-1 to eliminate the singularity between the intermediate links because the axes are parallel or nearly parallel, and the adjacent joints The homogeneous transformation matrix between is modified as:

In the above formula, β _i represents the rotation angle of the i-th rod coordinate system of the robot around the y-axis, y is the Y-axis of the connecting rod coordinate system, c is cos, and s is sin;

Step 1-3, add an extra parameter z _n to describe the translation of the tool coordinate system along the z-axis of the end link coordinate system, and establish the transformation matrix of the tool coordinate system relative to the end link coordinate system as:

Steps 1-4. For an N-joint robot, the kinematic relationship between the robot tool coordinate system and the base coordinate system obtained according to the above steps is:

T = ⁰ A ₁ × ¹ A ₂ × ² A ₃ × ³ A ₄ × ⁴ A ₅ × ⁵ A ₆ ×... × ^n-1 A _n

The value of n is 1...N, N≥1, and the kinematic relationship is the robot motion model.

Step 2. Establish a robot error model according to the robot motion model established in Step 1; specifically:

Step 2-1. The error dA _i between the actual conversion matrix of the intermediate link and the nominal conversion matrix is obtained by the differential transformation principle:

and

A _i is the intermediate link transformation matrix.

Step 2-2. Obtain the transformation matrix error of the tool coordinate system relative to the end link coordinate system by the differential transformation principle:

An _is the transformation matrix between the tool coordinate system and the end link coordinate system.

Step 2-3. For the N-joint robot, the final error model is the error of the intermediate link plus the error of the tool coordinate system relative to the transformation of the end link. After the total differential, the following formula is obtained:

where p is the end position coordinate.

Write it as:

Δp=J _δ ΔX

where ΔX=(Δθ ₁ ... Δθ _n , Δα ₁ ... Δα _n , Δa ₁ ... Δa _n , Δd ₁ ... Δd _n , Δβ ₁ ... Δβ _n , Δz _n ) ^T represents the robot The structural error J _δ of each connecting rod is the identification Jacobian matrix.

Step 3. In the working space of the robot, the target pose point is freely given, and its nominal coordinate is Pn. When the end of the robot moves to the specified point, the joint angle at this time is recorded;

Step 4. Use a position measuring instrument to measure the actual coordinates Pa of the given target pose point;

Step 5. Use the least squares method to identify the error parameters, and compensate the identified structural errors to the nominal parameters of the robot motion model to verify whether the requirements are met. If the requirements are met, perform the next step, otherwise return to step 3;

Compensating the identified structural errors to the nominal parameters of the motion model is to add the structural parameters to the identified error parameters;

Verifying whether the requirements are met specifically refers to: measuring the actual coordinates, comparing with the data before compensation, whether the tolerance range is ±0.2mm, if it is within the tolerance range, it meets the requirements, otherwise it does not meet the requirements.

Step 6. Referring to Figure 2, applying a load to the end of the robot will cause deformation of the arm, resulting in a positioning error of the end of the robot. Apply a load at the end of the robot, measure its deformation, and then return to step 3 to compensate the re-identified structural error to the robot motion model again, so as to eliminate the end pose error caused by the deformation caused by the load, and at the same time, the deformation data caused by the load will be Stored in the database for later precision compensation. Specifically:

Step 6-1. Within the rated load range, apply different mass loads to the end of the robot, use the stress-strain gauge to measure the deformation of each part of the robot, and use the instrument to measure the actual coordinates of the robot reaching the designated point at this time;

Step 6-2: Process the measurement results, obtain the curve of the deformation amount of each part of the robot changing with the load, and obtain the curve of the robot end position error changing with the load.

To sum up, the present invention discloses a method for compensating robot accuracy by integrating a pose error model and stiffness compensation. A target pose is randomly given in the robot workspace to record nominal coordinates and joint angles, and the actual pose of a given point is measured. The robot error model is established, the error is identified by the least square method, and the identified error is compensated to the nominal parameters of the motion model, and then a load is applied to the end of the robot, the deformation is measured, and the secondary compensation is performed. Realize the compensation of the absolute positioning accuracy of the robot. The invention can significantly improve the absolute positioning accuracy of the robot, and is simple and efficient.

Claims (3)

1. a robot precision compensation method of comprehensive pose error model and stiffness compensation, is characterized in that, comprises the following steps: Step 1. Establish a robot motion model according to the structural parameters of the robot; specifically: Step 1-1. According to the DH method, establish a homogeneous transformation matrix between adjacent joints of the robot. The matrix is: In the above formula, a _i is the length of the connecting rod, α _i is the torsion angle of the joint, d _i is the offset distance of the connecting rod, θ _i is the rotation angle of the joint, x is the X-axis coordinate of the connecting rod coordinate system, and z is the Z-axis of the connecting rod coordinate system. coordinate; Step 1-2. Introduce the rotation Rot(y, β) around the y-axis to the homogeneous transformation matrix established in step 1-1 to eliminate the singularity between the intermediate links because the axes are parallel or nearly parallel, and the adjacent joints The homogeneous transformation matrix between is modified as: In the above formula, β _i represents the rotation angle of the i-th rod coordinate system of the robot around the y-axis, y is the Y-axis coordinate of the connecting rod coordinate system, c is cos, and s is sin; Step 1-3, add an extra parameter z _n to describe the translation of the tool coordinate system along the z-axis of the end link coordinate system, and establish the transformation matrix of the tool coordinate system relative to the end link coordinate system as: Steps 1-4. For an N-joint robot, the kinematic relationship between the robot tool coordinate system and the base coordinate system obtained according to the above steps is: T = ⁰ A ₁ × ¹ A ₂ × ² A ₃ × ³ A ₄ × ⁴ A ₅ × ⁵ A ₆ ×... × ^n-1 A _n The value of n is 1...N, N≥1, the kinematic relationship is the robot motion model; Step 2, establish a robot error model according to the robot motion model established in step 1; the establishment of the robot error model is as follows: Step 2-1, the error dA _i of the actual transformation matrix and the nominal transformation matrix of the intermediate link is obtained by the differential transformation principle: and A _i is the intermediate link conversion matrix; Step 2-2. Obtain the transformation matrix error of the tool coordinate system relative to the end link coordinate system by the differential transformation principle: An _is the transformation matrix between the tool coordinate system and the end link coordinate system; Step 2-3. For the N-joint robot, the final error model is the error of the intermediate link plus the error of the tool coordinate system relative to the transformation of the end link. After the total differential, the following formula is obtained: where p is the end position coordinate; Write it as: Δp=J _δ ΔX where ΔX=(Δθ ₁ ... Δθ _n , Δα ₁ ... Δα _n , Δa ₁ ... Δa _n , Δd ₁ ... Δd _n , Δβ ₁ ... Δβ _n , Δz _n ) ^T represents the robot The structural error J _δ of each connecting rod is the identification Jacobian matrix; Step 3. In the working space of the robot, the target pose point is freely given, and its nominal coordinate is Pn. When the end of the robot moves to the specified point, the joint angle at this time is recorded; Step 4. Use a position measuring instrument to measure the actual coordinates Pa of the given target pose point; Step 5. Use the least squares method to identify the error parameters, and compensate the identified structural errors to the nominal parameters of the robot motion model to verify whether the requirements are met. If the requirements are met, perform the next step, otherwise return to step 3; Step 6. Apply a load at the end of the robot, measure its deformation, and then go back to step 3 to compensate the re-identified structural error to the robot motion model again, so as to eliminate the end pose error caused by the deformation caused by the load, and at the same time, reduce the deformation caused by the load. The deformation data is stored in the database for later precision compensation. 2. the robot precision compensation method of the comprehensive pose error model and stiffness compensation according to claim 1, it is characterized in that, in step 5, the structural error compensation that will identify is given to the robot motion model nominal parameter specifically by adding the structural parameter. The identified error parameters; Verifying whether the requirements are met specifically refers to: measuring the actual coordinates, comparing with the data before compensation, whether the tolerance range is ±0.2mm, if it is within the tolerance range, it meets the requirements, otherwise it does not meet the requirements. 3. the robot accuracy compensation method of the comprehensive pose error model and stiffness compensation according to claim 1, is characterized in that, in step 6, in step 6, apply load at the robot end, measure its deformation amount and be specifically: Step 6-1. Within the rated load range, apply different mass loads to the end of the robot, use the stress-strain gauge to measure the deformation of each part of the robot, and use the instrument to measure the actual coordinates of the robot reaching the designated point at this time; Step 6-2: Process the measurement results, obtain the curve of the deformation amount of each part of the robot changing with the load, and obtain the curve of the robot end position error changing with the load.