CN115107024A - A kinematic parameter identification method of industrial robot based on laser tracker multi-station technology - Google Patents

Abstract

The invention discloses a kinematic parameter identification method of an industrial robot based on a laser tracker multi-station technology. The method firstly plans a theoretical path in the robot workspace, and obtains the planned path in a robot coordinate system based on the laser tracker multi-station technology measurement. Corresponding to the actual three-dimensional coordinates of the measurement points, the robot end positioning error is obtained based on the multi-station measurement model of the laser tracker; then, based on the kinematic model of the robot, a description of the relationship between the industrial robot end positioning error and 24 kinematic parameter errors is constructed. Finally, the LASSO algorithm is used to accurately identify the 24 kinematic parameters of the robot, so as to improve the positioning accuracy of the end of the robot industrial robot.

Description

A kinematic parameter identification of industrial robot based on laser tracker multi-station technology way of knowing

technical field

The invention relates to an error identification method for industrial robot kinematic parameters, in particular to a technical method based on multi-station laser tracker measurement, and belongs to the field of industrial robot kinematic parameter identification and error compensation.

Background technique

With the application of industrial robots to the fields of precision machining and precision assembly, the requirements for absolute positioning accuracy are getting higher and higher. The current level of absolute positioning accuracy of industrial robots is difficult to meet the requirements. How to further improve the absolute positioning accuracy of industrial robots? Positioning accuracy has become a top priority.

The absolute positioning error of the industrial robot is mainly caused by the kinematic parameter error, which accounts for more than 90% of the total error of the end of the industrial robot. The kinematic parameter error compensation of industrial robots can usually be divided into four aspects: establishing a kinematic model, building a measurement system to obtain positioning errors, parameter identification based on the robot kinematic error model, and positioning error analysis and compensation. Before identifying the kinematic parameters of the robot, the positioning error of the robot is obtained first. The commonly used measuring equipment are: ballbar, theodolite, three-coordinate measuring machine, multi-eye vision measuring system, laser tracking measuring system, etc. Taking into account the measurement accuracy, measurement efficiency, measurement range and portability, laser tracking measurement technology is undoubtedly the first choice for detecting the positioning error of the end of industrial robots. Because the measurement accuracy of the laser tracker is limited, and the measurement uncertainty will also increase with the increase of the measurement range. The laser tracker adopts a standard ball design method, and the deviation of its mechanical rotation axis will not significantly affect the measurement accuracy, which greatly improves the measurement accuracy of the laser tracker's spatial distance.

The invention uses the laser tracker multi-station measurement technology to measure the positioning error of the industrial robot. After the positioning error of the industrial robot is obtained, an error model is established to identify the kinematic parameters of the robot. When the least squares method is commonly used for parameter identification, the least squares calculation is small and the convergence speed is fast. However, when the complex coefficient matrix is a singular matrix, an error will be generated in the numerical calculation process that can affect the calculation result, which makes the parameter error identification. Accuracy is reduced. Therefore, the present invention proposes a LASSO algorithm to identify the kinematic parameters of industrial robots. The algorithm introduces a regularization term into the loss function, which effectively solves the problem of irreversible coefficient matrix in the process of solving the error matrix equation, and can identify more accurately kinematic parameter error.

SUMMARY OF THE INVENTION

Reference (application number/patent number: CN201610889315.5 "A four-axis machine tool calibration method based on laser tracker multi-station measurement") in the laser tracker multi-station measurement technology. The purpose of the present invention is to provide a kinematic parameter identification method of an industrial robot based on the multi-station technology of the laser tracker. First, the three-dimensional coordinates of the measurement points corresponding to the planned path under the robot coordinate system are obtained by using the multi-station technology of the laser tracker. And based on the multi-station measurement model of the laser tracker, the positioning error of the robot is obtained; then, based on the kinematic model of the robot, a positioning error model describing the relationship between the positioning error of the end of the industrial robot and the error of the 24 kinematic parameters is constructed; finally, using LASSO The algorithm can accurately identify the 24 kinematic parameters of the robot to improve the positioning accuracy of the end of the industrial robot.

In order to achieve the above object, the present invention adopts the following technical solutions to realize:

A method for identifying kinematic parameters of industrial robots based on laser tracker multi-station technology, the method includes the following steps:

Step 1: Plan the theoretical path of the absolute positioning error measurement of the industrial robot, and obtain the theoretical three-dimensional coordinates of the measurement point corresponding to the planned path in the robot coordinate system.

Step 2: Build the multi-station measurement model of the laser tracker in the coordinate system of the industrial robot.

The theoretical three-dimensional coordinates P _i (x _i , y _i , z _i ) of the measurement points corresponding to the planned path in the robot coordinate system, i=1, 2, 3, ..., n, n represents the number of theoretical measurement points and is a positive integer ; The station coordinates of the laser tracker are B _j (X _j , Y _j , Z _j ), where j=1,2,3,...,m, where m represents the number of station coordinates and takes a positive integer; laser tracking The distance from the station B _j of the instrument to the initial measurement point P ₁ is d _j ; during the measurement process, the relative interference length of the cat's eye mirror measured by the laser tracker is l _ij . According to the formula of distance between two points in three-dimensional space, the following relationship is established:

The number of equations is m×n, and the number of unknowns is 4m+3n. In order to make the system of equations solvable, m×n≥4m+3n should be satisfied, then m and n satisfy m≥4 and n≥16.

Step 3: Based on the multi-station technology measurement of the laser tracker, the actual three-dimensional coordinates of the measurement points corresponding to the planned path in the robot coordinate system are obtained.

Step 4: Obtain the positioning error of the robot end.

P _ai (x _ai , y _ai , z _ai ) is the actual three-dimensional coordinates of the measurement point corresponding to the planned path in the robot coordinate system, ΔP _i =(Δx _i ,Δy _i , _Δzi ) ^T is the industrial robot at the measurement point i End positioning error.

Step 5: Use the improved D-H method to model the kinematics of the robot, and construct the homogeneous transformation matrix of the reference coordinate system of the adjacent joints.

Step 6: Establish the position error model of the industrial robot according to the homogeneous transformation matrix.

Step 7: Use the LASSO algorithm to solve the position error model of the industrial robot, and accurately identify the 24 kinematic parameter errors △X.

In order to solve the 24 kinematic parameter errors, the data need to be preprocessed.

The coefficient matrix J is normalized to have mean 0 and unit length. Normalize the matrix ΔP consisting of positioning errors to have a mean of 0, i.e.

where u is the number of equations, u=1,2,3,…,3n;

n—the number of measurement points;

p—the number of errors of the pth parameter, p=24.

使得

则LASSO的优化目标为A set of linear regression coefficients can be obtained

make

Then the optimization objective of LASSO is

where t is the harmonic parameter (greater than or equal to zero), and J is the coefficient matrix.

24 kinematic parameter errors were obtained by LASSO algorithm.

To sum up, compared with the prior art, the present invention has the following advantages and beneficial effects:

(1) To obtain the three-dimensional coordinates of the measurement point under the robot coordinate system, the laser tracker needs to establish a transformation matrix between the laser tracker coordinate system and the robot coordinate system. Usually, the matrix has poor precision and will introduce certain errors, and the present invention Using the laser tracker multi-station technology to measure the positioning error of industrial robots can effectively avoid the introduction of this error.

(2) The commonly used algorithm for identifying the parameter errors of industrial robots is the least squares method. The overdetermined equations are obtained by measuring the positioning errors of the measurement points under the planned path by the laser tracker, and the least squares solutions of the parameter errors are obtained. The least squares method has the advantages of fast convergence and small amount of calculation, but when the complex coefficient matrix is a singular matrix, resulting in irreversible or an ill-conditioned matrix, the kinematic parameter error solved by the ordinary least squares method is wrong, so this method Not stable. In the present invention, the LASSO algorithm is used to introduce a regularization term into the loss function, which effectively solves the problem that the coefficient matrix is irreversible in the process of solving the position error model of the industrial robot, can more accurately identify the kinematic parameter error, and effectively improves the industrial robot. absolute positioning error.

Description of drawings

Figure 1 is a schematic diagram of the laser tracker multi-station technology to measure the positioning error of an industrial robot;

Figure 2 is a schematic diagram of the kinematic modeling of the improved D-H method.

Detailed ways

The present invention will be further described in detail below with reference to the accompanying drawings, so that those skilled in the art can implement it with reference to the description. The specific implementation steps are as follows:

Step 1: Plan the theoretical path of the absolute positioning error measurement of the industrial robot.

The motion requirements of the robot during positioning error measurement in "Industrial Robot Performance Specification and Test Method GB/T12642-2013": When the robot moves between positions, all joints should move. According to this requirement, the sphere path is planned in the industrial robot workspace. In the robot coordinate system, the point (1600, 0, 900) is selected as the sphere center point of the sphere path, the radius is set to 500mm, and 60 spherical points are randomly generated. The teach pendant program controls the end of the robot to move from the ball center point to the spherical point and return to the ball center point, and walk through 60 spherical points in sequence.

Step 2: Build the multi-station measurement model of the laser tracker of the industrial robot. The schematic diagram of the model is shown in Figure 1. The target lens of the laser tracker is fixedly linked to the end of the industrial robot. 60 spherical points are planned in the robot workspace. Considering the measurement accuracy and the time required for the experiment, the number of laser tracker stations is determined to be 4.

Step 3: Based on the multi-station technology measurement of the laser tracker, the actual three-dimensional coordinates of the measurement points corresponding to the planned path in the robot coordinate system are obtained.

Step 4: Obtain the positioning error of the robot end.

Step 5: Use the improved DH method to model the kinematics of the robot: r is the number of degrees of freedom of the industrial robot, r=1,2,3...,6. Determine the direction of the Z _r axis as the axial direction along the joint axis r; the origin Or is the intersection of the joint axis _r +1 and the r axis or the intersection of the common vertical line and the joint axis Z _r ; the X _r axis is along the common vertical line a _r The axial direction of the shaft points from the joint axis r to the joint axis r+1. If the joint axis r and the joint axis r+1 intersect, the X _r axis is specified to be perpendicular to the plane where the two joint axes are located; the Y _r axis is determined according to the right hand. Then determine; when the first joint variable is 0, it is specified that the coordinate system {0} and the coordinate system {1} coincide, and for the coordinate system {n}, the origin and the direction of the x _n axis can be arbitrarily selected, but when selecting Try to make the connecting rod parameter 0. The meaning of the parameters of the improved DH method is: ① the length of the connecting rod a _r : defined as the distance from Z _r to Z _r+1 , the direction along the X _r axis is positive, and its essence is the length of the common perpendicular; ② the connecting rod rotation angle α _r : Defined as the angle from Z _r to Z _r +1, positive rotation around the X _i axis is positive; ③ Link offset distance _{dr : Defined as the distance from X r -1 to X r , along} the Z axis The _r -axis points to be positive. Its essence is the distance between two common perpendiculars. ④Joint angle θ _r : It is defined as the angle of rotation from X _r -1 to X _r , and the positive rotation around the Z _r axis is positive. The improved DH method is to establish the origin of the connecting rod coordinate system at the head end of the corresponding joint connecting rod. Compared with the standard DH method, the establishment of the system is clearer and easier to understand and observe. The schematic diagram of the improved DH modeling is shown in Figure 2.

The homogeneous transformation matrix of the adjacent joint reference coordinate system is constructed as:

Step 6: Establish the position error model of the industrial robot according to the homogeneous transformation matrix.

The pose of the end of the industrial robot in the base coordinate system is:

This parameter identification method only needs the position information P(x, y, z) of the measurement point, so it can be obtained from the above formula:

In order to identify the kinematic parameters of the robot more clearly, the above formula is linearized as

P=F(a ₁ ,a ₂ ,…,a ₆ ,d ₁ ,d ₂ ,…,d ₆ ,α ₁ ,α ₂ ,…,α ₆ ,α ₁ ,α ₂ ,…,α ₆ , θ ₁ , θ ₂ ,...,θ ₆ ) (8)

In the above formula, F(·) is a function of the kinematic parameters of the robot.

Due to the slight error between the actual kinematic parameters and the internal kinematic parameters of the robot controller, the end positioning error is caused. Therefore, the actual position of the industrial robot end effector can be written as:

P _a =F(a ₁ +Δa ₁ ,...,a ₆ +Δa ₆ ,d ₁ +Δd ₁ ,...,d ₆ +Δd ₆ ,α ₁ +Δα ₁ ,...,α ₆ + Δα ₆ ,θ ₁ +Δθ ₁ ,...,θ ₆ +Δθ ₆ ) (9)

In the above formula, Δa _r represents the error of the link length parameter; Δd _r represents the error of the link offset parameter; Δα _r represents the error of the link angle parameter; Δθ _r represents the error of the initial joint angle parameter.

The error in the kinematic parameter ΔP is usually small, so it can be written in the form of a linear equation by linearization:

According to the above formula, the end positioning error (Δx _i ,Δy _i ,Δz _i ) of the robot can be expressed as:

The above formula is a coefficient matrix, so the position error model is

是定位误差向量，

是运动学参数误差向量，

是构建的系数矩阵，i＝60。in

is the positioning error vector,

is the kinematic parameter error vector,

is the constructed coefficient matrix, i=60.

Step 7: Use the LASSO algorithm to solve the position error model of the industrial robot, and accurately identify the 24 kinematic parameter errors, as shown in Table 1.

Table 1. Results of kinematic parameter error identification

Claims (10)

1. an industrial robot kinematics parameter identification method based on laser tracker multi-station technology, it is characterized in that: planning a theoretical path in the robot workspace; constructing a laser tracker multi-station measurement model of an industrial robot; based on a laser tracker The three-dimensional coordinates of the measurement points corresponding to the planned path in the robot coordinate system are obtained by the multi-station technology measurement; the positioning error of the robot end is obtained based on the multi-station measurement model of the laser tracker; the kinematic modeling of the robot is carried out by the improved D-H method, and the adjacent The homogeneous transformation matrix of the joint reference coordinate system; the position error model of the industrial robot is established according to the homogeneous transformation matrix, which expresses the relationship between the positioning error of the end of the industrial robot and the error of the 24 kinematic parameters; the LASSO algorithm is used to solve the equation system to accurately identify the 24 movements The scientific parameter error ΔX. 2 . The method for identifying the kinematic parameters of an industrial robot based on the multi-station technology of the laser tracker according to claim 1 , wherein the spherical motion path is planned in the industrial robot workspace, and 60 spherical points are randomly generated. 3 . 3. a kind of industrial robot kinematics parameter identification method based on laser tracker multi-station technology as claimed in claim 1, it is characterized in that, constructing the laser tracker multi-station measurement model of industrial robot to measure the positioning error of industrial robot . 4. a kind of industrial robot kinematics parameter identification method based on laser tracker multi-station technology as claimed in claim 1 is characterized in that, considering measurement accuracy and the time required for the experiment, it is determined that the laser tracker measurement model is four stations bit. 5. a kind of industrial robot kinematic parameter identification method based on laser tracker multi-station technology as claimed in claim 1, it is characterized in that, based on laser tracker multi-station technology measurement to obtain the corresponding measurement of the planned path under the robot coordinate system The actual 3D coordinates of the point. 6 . The method for identifying the kinematic parameters of an industrial robot based on the laser tracker multi-station technology according to claim 1 , wherein the end positioning error of the industrial robot is obtained based on the laser tracker multi-station technology measurement model. 7 . 7. a kind of industrial robot kinematics parameter identification method based on laser tracker multi-station technology as claimed in claim 1, it is characterized in that, carry out kinematic modeling to robot with improved DH method: r is the freedom of industrial robot The number of degrees, r=1,2,3...,6; the direction of the Z _r axis is determined as the axial direction along the joint axis r; the origin Or is the intersection of the joint axis _r +1 and the r axis or its public perpendicular line and the joint The intersection of the axes Z _r ; the X _r axis is along the axis of the common vertical line a _r axis, from the joint axis r to the joint axis r+1, if the joint axis r and the joint axis r+1 intersect, the X _r axis is specified to be perpendicular to the The plane where these two joint axes are located; the Y and _r axes are determined according to the right-hand rule; when the first joint variable is 0, it is specified that the coordinate system {0} and the coordinate system {1} coincide, and for the coordinate system {n}, its The origin and the direction of the x _n axis are arbitrarily selected, and the connecting rod parameter is set to 0 when selecting; the parameter meaning of the improved DH method is ① the connecting rod length a _r : defined as the distance from Z _r to Z _r+1 , along X The _r -axis points to be positive, and its essence is the length of the common vertical line; ② the connecting rod rotation angle α _r : defined as the angle from Z _r to Z _r +1, the positive rotation around the X _i axis is positive; ③ the connecting rod is offset Distance d _r : Defined as the distance from X _r -1 to X _r , which is positive along the Z _r axis; its essence is the distance between two common perpendiculars; ④ Joint angle θ _r : defined as the distance from X _r -1 Rotate to the angle of X _r , positive rotation around the Z _r axis is positive. 8. a kind of industrial robot kinematics parameter identification method based on laser tracker multi-station technology as claimed in claim 1, is characterized in that, based on the kinematics model established to robot with improved D-H method, construct adjacent joint reference Coordinate system homogeneous transformation matrix. 9 . The method for identifying the kinematic parameters of an industrial robot based on the laser tracker multi-station technology according to claim 1 , wherein a position error model of the industrial robot is established according to a homogeneous transformation matrix. 10 . 10 . The method for identifying kinematic parameters of an industrial robot based on laser tracker multi-station technology as claimed in claim 1 , wherein the 24-item kinematic parameter error ΔX is accurately identified by using LASSO algorithm to solve the equation system. 11 .

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