A method for collecting and processing hand-eye calibration data to avoid singularity

Abstract

The present invention proposes a method for collecting and processing hand-eye calibration data of an industrial robot and a line profile sensor to avoid singularity. When calibrating the posture matrix of the hand-eye relationship matrix, in order to avoid matrix singularity in the calculation process, the industrial robot needs to drive the sensor to move linearly to at least 4 positions in different directions while keeping the terminal posture unchanged, wherein at least 4 positions cannot be coplanar and at least 3 positions cannot be colinear, and collect information from each position point to participate in the calculation. When calibrating the position matrix of the hand-eye relationship matrix, in order to avoid matrix singularity in the calculation process, the robot needs to drive the sensor to perform at least three posture changes, and collect information from each posture point to participate in the calculation. This method can not only effectively avoid the occurrence of singular matrices in the hand-eye calibration process, but also improve the calibration accuracy.

Description

Technical Field

[0001] The present invention belongs to the field of measurement and control automation technology, and in particular relates to a data acquisition and processing method for "hand-eye calibration" before using a line laser sensor on an industrial robot to perform an operation (here "hand" refers to the industrial robot and "eye" refers to the line laser sensor), that is, through appropriate data acquisition and processing, the relationship between the sensor's measurement coordinate system and the robot's flange coordinate system is accurately determined. Background Art

[0002] The industrial robot clamps the line laser sensor to scan the workpiece, and can obtain information such as the position, shape and geometric parameters of the workpiece. It is widely used in welding, assembly, inspection and other occasions. Since the motion coordinate system of the industrial robot and the measurement coordinate system of the line laser sensor are relatively independent, in order to use the measured coordinates to control the movement of the robot, it is necessary to calibrate the relationship between the robot end coordinate system and the sensor's measurement coordinate system in advance. The obtained posture matrix is ​​called the hand-eye calibration matrix, which includes the posture matrix and the position matrix.

[0003] The robot hand-eye calibration method introduced in the document "Research on Robot Hand-Eye Calibration and Precision Analysis" (Combined Machine Tools and Automated Processing Technology, Jan. 2018, No. 1) uses a standard sphere with a known radius as an auxiliary tool. The standard sphere is fixed in the workspace of the industrial robot. The robot drives the sensor to move to different positions. At each position, the sensor emits a line laser to illuminate the standard sphere. By collecting the robot posture information and the outer contour information of the standard sphere, the hand-eye relationship matrix is ​​calculated. The "246" method used is that the calibration process is divided into two steps: posture matrix calibration and position matrix calibration. When calibrating the posture matrix, the robot keeps the posture angle unchanged, moves linearly to 4 positions, and uses the collected 4 sets of data to solve; when calibrating the position matrix, the robot moves to 6 positions with different postures, and uses the collected 6 sets of data to solve. This method is more convenient, but in the process of calculating the posture matrix, the relationship between the 4 positions of the robot's linear movement is not given. If the 4 positions are coplanar or any 3 positions are colinear, the matrix singularity problem will be encountered during the solution process, resulting in an inability to solve. At the same time, the constraints and calculation methods when the robot moves more than 4 linear positions are not given. In the process of calculating the position matrix, it is not explained why 6 sets of data are selected, and the calculation results are incorrect. The above problems affect the correctness of the calibration results and further limit the application of robots and sensors.

[0004] The present application is aimed at the problems existing in the above-mentioned calibration method. By properly setting the layout of each position point of the robot's linear movement during data acquisition and the number of times the robot changes its posture and moves, the calibration problem of the posture matrix and the position matrix in hand-eye calibration is effectively solved based on the matrix solving method. Summary of the invention

[0005] The present invention provides a data collection and processing method for avoiding singularities in the process of solving a hand-eye calibration matrix.

[0006] Assume that the base of the industrial robot is fixed on the ground or on the mounting platform, its base coordinate system is represented by {B}, the end coordinate system is represented by {E}, the measurement coordinate system of the line laser sensor is represented by {C}, and the line laser sensor is fixed on the end of the robot. The standard sphere is fixed on the ground or on the mounting platform in the robot's workspace, the center position of the sphere is recorded as A, and the position matrix of A in {B} is recorded as (x, y, z represent the three spatial coordinate components, and the T in the upper right corner represents transposition). Similarly, the position matrix of A in {C} is recorded as The pose transformation relationship from {E} to {B} is given by the pose matrix and the position matrix The joint representation is that the pose transformation relationship from {C} to {E} is represented by the pose matrix and the position matrix Joint representation. can be read by the robot controller, This constitutes the required hand-eye calibration matrix.

[0007] According to the coordinate transformation relationship, the position matrix of the same point A in different coordinate systems {B} and {C} and Has the following relationship:

[0008]

[0009] Calibration attitude matrix When the robot moves linearly in a fixed posture, the line laser is ensured to illuminate the surface of the standard ball. Record the position of the coordinate system {E} corresponding to each position in {B} and posture Calculate the coordinates of the sphere center A corresponding to each position in {C} Substituting into formula (1), expanding and subtracting from the formula corresponding to the first position, we can get:

[0010] in

[0011] In the matrix M, is the coordinate of the center of the sphere A under {C}, which is geometrically equivalent to the space vector from the origin of {C} to A. Since the posture of {C} remains unchanged during the linear movement of the robot, the Can be directly added (subtracted) to obtain a new space vector and

[0012] because is a vector with three rows and one column. The number of positions where the robot moves linearly must be at least 4, that is, n ≥ 4, so that the number of columns in M ​​is greater than or equal to 3. If there are three collinear positions in the process of the robot's linear movement, such as position 1, position 2 and position 3, then and Must be linearly related; if the robot has four coplanar positions during linear movement, such as position 1, position 2, position 3 and position 4, then and Any vector in can be linearly represented by the other two vectors.

[0013] When the number of positions of the robot's linear movement is n=4, the obtained M and N are both 3X3 square matrices. In order to avoid M singularity, any three positions of the robot's linear movement cannot be collinear and the four positions cannot be coplanar.

[0014] When the number of positions n of the robot's linear movement is greater than 4, the obtained M and N are both 3×(n-1) matrices, not square matrices, and the posture matrix to be calibrated The least squares method can be used for calculation, but it is necessary to ensure that at least four positions are not coplanar and at least three positions are not colinear.

[0015] Calibration position matrix When the standard ball is kept in place, the robot end moves in different positions and postures, and the line laser is ensured to illuminate the surface of the standard ball. Record the position of the coordinate system {E} in {B} corresponding to each position and posture. and posture Calculate the coordinates of the sphere center A in {C} corresponding to each posture Substituting into formula (1), expanding and subtracting from the formula corresponding to the first pose, we can get: in

[0016] Each row of P is equal to the terminal posture matrix of the robot in other postures minus the terminal posture matrix of the first posture. Since the posture matrix is ​​a rotation matrix, and the determinant of the difference between two rotation matrices is 0, if the robot moves only 2 postures, P will be singular. Therefore, the robot must move at least 3 times in different postures, that is, m ≥ 3. At this time, the matrix P is not a square matrix, and the position matrix It can be calculated by the least squares method, calculate.

[0017] Beneficial effects:

[0018] The present invention proposes a hand-eye calibration data collection and processing method that avoids singularity, which can effectively and accurately obtain the posture matrix and position matrix of the hand-eye calibration matrix, and is of great significance to improving the collaborative working effect of industrial robots and line laser sensors. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 Schematic diagram of the hand-eye calibration process for industrial robots and line laser sensors;

[0020] Figure 2 It is a schematic diagram of measuring the space vector from the origin of the coordinate system {C} to the center of the sphere A when the robot moves linearly;

[0021] Figure 3 To calibrate the attitude matrix Schematic diagram of the method for determining the position point of the robot linear movement to avoid singularity;

[0022] Figure 4 is the calibration position matrix Schematic diagram of the method for determining the moving position point to avoid the singular robot posture change;

[0023] In order to enable those skilled in the art to better understand the solution of the present application, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application.

[0024] Figure 1 The figure is a schematic diagram of the hand-eye calibration process for industrial robots and line laser sensors. The base of the industrial robot is fixed on the ground or on a mounting platform. Its base coordinate system is represented by {B}. Its end is connected to the base through multiple joints in turn. The end coordinate system is represented by {E}. The measurement coordinate system of the line laser sensor is represented by {C}. The line laser sensor is fixed on the end of the robot. A standard sphere with a known radius is fixed on the ground or on a mounting platform in the robot's workspace. The center position of the sphere is recorded as A. The position matrix of A in {B} is recorded as (x, y, z represent the three spatial coordinate components, and the T in the upper right corner represents transposition). Similarly, the position matrix of A in {C} is recorded as The pose transformation relationship from {E} to {B} is given by the pose matrix and the position matrix The joint representation is that the pose transformation relationship from {C} to {E} is represented by the pose matrix and the position matrix Joint representation. can be read by the robot controller, This constitutes the required hand-eye calibration matrix.

[0025] The robot drives the sensor to move to different positions, and at each position the sensor emits a laser to illuminate the standard sphere. By collecting the robot's posture information and the outer contour information of the standard sphere, the hand-eye relationship matrix is ​​calculated. The posture matrix and position matrix are calibrated in two steps.

[0026] Figure 2 Represents the spatial vector from the origin of the coordinate system {C} to the center of the sphere A when the robot moves linearly in a fixed posture The figure shows four moving positions, namely n = 1…4. Since the posture of {C} remains unchanged during the linear movement of the robot, the Can be directly added (subtracted) to obtain a new space vector and

[0027] Figure 3 Represents the calibration attitude matrix To avoid singularity, the robot moves linearly in a fixed posture to determine the 4 positions when collecting data. The first position must satisfy the requirement that the sensor can effectively obtain the standard ball line profile information at this position; the second position is obtained by the robot driving the sensor to translate a certain distance along the x-axis of the robot base coordinate system {B}; the third position is obtained by the robot driving the sensor to translate a certain distance along the y-axis of the coordinate system {B}; the fourth position is obtained by the robot driving the sensor to translate a certain distance along the z-axis of the coordinate system {B}. Record the position of the coordinate system {E} in {B} corresponding to each position and posture Calculate the coordinates of the sphere center A corresponding to each position in {C} Since the robot's posture remains fixed during movement, The data collected at the 4 locations form a matrix Since the direction vectors from position 1 to position 2, from position 2 to position 3, and from position 3 to position 4 are orthogonal to each other, these four positions are neither collinear nor coplanar. This ensures that the matrix M is non-singular, and the attitude matrix According to calculate.

[0028] If the robot continues to move linearly to the fifth position along the straight line x=y=z in {B} (or other directions that are not coplanar with positions 1, 2, 3, and 4) in the current posture, the data collected from the five positions will form the matrix Pose Matrix The least squares method can be used to calculate,

[0029] Figure 4 Represents the calibration position matrix To avoid singularity, the robot moves in three different postures during data collection. From posture 1 to posture 2 and from posture 2 to posture 3, the position and posture of the robot end have changed. The position of the coordinate system {E} in {B} corresponding to each posture is recorded. and posture Calculate the coordinates of the sphere center A in {C} corresponding to each posture The data collected from the three pose points form a matrix Position Matrix It can be calculated according to the least squares method, that is,

[0030] Of course, the present invention may have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art may certainly make various corresponding changes and modifications based on the present invention, but these corresponding changes and modifications should all fall within the scope of protection of the claims attached to the present invention.

Claims

1. A method for collecting and processing hand-eye calibration data to avoid singularity, wherein the method uses a standard sphere with a known radius as a calibration tool, and the robot drives the sensor to move. The hand-eye relationship matrix between the robot and the sensor is calibrated by collecting the robot's terminal posture information and the outer contour information of the standard sphere. In order to avoid the occurrence of a singular matrix in the calculation process, the number of robot movements and the location points of data collection are set according to S1-S5, and the calibration result is obtained by data processing. The hand-eye relationship matrix is ​​composed of the posture matrix and the position matrix Together they constitute, The base coordinate system is represented by {B}, the terminal coordinate system is represented by {E}, the measurement coordinate system of the line laser sensor is represented by {C}, and the center position of the sphere is recorded as A. The calibration is to calibrate the attitude matrix and the position matrix respectively. The data acquisition and processing method includes: S1: Calibration attitude matrix When the robot drives the sensor to move linearly to n different positions with a fixed posture, n ≥ 4, and collects the posture information of the robot end relative to its base coordinate system at each position. The pose information is expressed as a pose matrix and the position matrix Indicates that the outer contour information of the standard ball is collected. Process the external contour information to obtain the coordinates of the sphere center A in the sensor measurement coordinate system And ensure that at least four positions are not coplanar, and at least three positions are not colinear; S2: The data collected by the method described above form a matrix matrix M, N and The relationship is: S3: When n=4, it is necessary to ensure that the four positions are not coplanar and at least three positions are not colinear. The obtained M and N are both 3X3 square matrices and M is non-singular. The attitude matrix According to calculate; S4: When n>4, it is necessary to ensure that at least four positions are not coplanar and at least three positions are not colinear. The obtained M and N are both 3×(n-1) matrices, and the posture matrix The least squares method can be used to calculate, S5: Calibration position matrix When the robot drives the sensor to move to m different positions with varying postures, m ≥ 3, the posture information of the robot end relative to its base coordinate system is collected at each position. The posture information is expressed by the posture matrix and the position matrix Indicates that the outer contour information of the standard ball is collected and the outer contour information is processed to obtain the coordinates of the ball center A in the sensor measurement coordinate system. The data collected by the method described above constitute a matrix matrix P, Q and The relationship is: Each row of P is the difference between two rotation matrices, and its determinant is 0. Therefore, when m=2, P is singular. In order to avoid singularity during calculation, the robot must move to at least three positions with different postures, that is, m≥3. At this time, the matrix P is not a square matrix, and the position matrix It can be calculated according to the least squares method, that is,

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