A hand-eye calibration method for line scan 3D cameras

Abstract

The present invention discloses a hand-eye calibration method for a line scan 3D camera, characterized in that the method comprises: solving the coordinates of the feature points in the base coordinate system through the coordinates of the feature points on a single row in the camera coordinate system and the coordinates of the feature points corresponding to the single row in the base coordinate system. The specific steps include: constructing a camera coordinate system; marking the coordinates of a calibration tool; calculating the rotation matrix from the camera coordinate system to the tool coordinate system; calculating the translation matrix from the camera coordinate system to the tool coordinate system; solving the coordinates of any feature point in the base coordinate system. A hand-eye calibration method for a line scan 3D camera, the camera coordinates used for calibration are calculated using a single row of point clouds, and the 6-degree-of-freedom information of the target feature points in the camera coordinate system are all converted to the base coordinate system, solving the problem that the camera coordinate system and the scanning direction are not parallel.

Description

Technical Field

[0001] The present invention belongs to the technical field of hand-eye calibration, and in particular relates to a hand-eye calibration method for a line scan 3D camera. Background Art

[0002] In the eye-in-hand situation, the camera is fixed relative to the end of the robot arm. The robot hand-eye calibration is to calibrate the coordinate transformation relationship between the end of the robot and the camera. There are several coordinate systems: the base coordinate system is the base coordinate system of the robot arm, represented by Base; the end coordinate system is the end coordinate system of the robot arm, represented by End; the camera coordinate system is the coordinate system of the camera fixed on the robot arm, represented by Camera, and the tool coordinate system is the tool coordinate system of the robot arm, represented by t.

[0003] The premise of hand-eye calibration is to obtain complete three-dimensional information of the object surface. The data collected by the laser line scan camera in a single shot is the 3D coordinates of the area illuminated by the laser at an instant, that is, the data generated by the laser uniform scanning needs to be spliced ​​together according to the rules, parallel by default, and constructed into a camera coordinate system. In the actual movement process of the robotic arm, the end of the robotic arm will tilt or the camera will not be parallel to the end of the robotic arm, resulting in different coordinates of the position points. Therefore, a calibration method is needed to solve the problem of the non-parallelism between the camera coordinate system and the scanning direction. Summary of the invention

[0004] In order to solve the above problems, the present invention adopts the following technical solutions:

[0005] A hand-eye calibration method for a line scan 3D camera, the method comprising:

[0006] The coordinates of the feature points on a single row in the camera coordinate system and the coordinates of the feature points corresponding to the single row in the base coordinate system are solved to obtain the coordinates of the feature points in the base coordinate system.

[0007] Furthermore, the method specifically comprises the following steps:

[0008] Construct the camera coordinate system;

[0009] Marking the coordinates of the calibration tool: moving the calibration tool, marking the coordinates of the calibration tool in the base coordinate system, and marking the coordinates of the calibration tool in the camera coordinate system;

[0010] Calculate the rotation matrix from the camera coordinate system to the tool coordinate system;

[0011] Calculate the translation matrix from the camera coordinate system to the tool coordinate system;

[0012] Solve the coordinates of any feature point in the base coordinate system.

[0013] Furthermore, constructing the camera coordinate system includes:

[0014] The direction set by the camera coordinate system is the same as the direction set by the camera scan;

[0015] The X value of the middle point of each row is 0, the X coordinate of each row is the number of points multiplied by the point spacing, and the Y coordinate of each row is the number of rows multiplied by the row spacing.

[0016] Furthermore, the coordinates of the marking calibration tool include: the calibration tool is a sphere and a cone, obtaining the coordinates of the center of the sphere and the vertex of the cone in the base coordinate system; obtaining the coordinates of the center of the sphere and the vertex of the cone in the camera coordinate system.

[0017] Further, the calculation of the rotation matrix from the camera coordinate system to the tool coordinate system includes:

[0018] The relationship between the coordinates of the sphere center / cone vertex in the base coordinate system and the coordinates in the camera coordinate system is expressed as follows:

[0019] Base 球 =R tb (R ct Camera 球 +T ct )+T tb ,

[0020] As shown in the formula: Base 球 is the coordinate in the base coordinate system of the sphere center / cone vertex; R tb is the rotation matrix from the tool coordinate system to the base coordinate system; R ct The rotation matrix from the camera coordinate system to the tool coordinate system; Camera 球 is the coordinate of the sphere center / cone vertex in the camera coordinate system; T ct is the translation matrix from the camera coordinate system to the tool coordinate system; T tb is the translation matrix from the tool coordinate system to the base coordinate system;

[0021] Move the camera, and subtract the coordinates of the center positions of any two spheres in the base coordinate system from the coordinates in the camera coordinate system to obtain:

[0022] T tb2 -T tb1 =R0·R ct (Camera 球1 -Camera 球2 ),

[0023] Obtain multiple sets of data and use the least squares method to obtain the rotation matrix R from the camera coordinate system to the tool coordinate system ct .

[0024] Furthermore, the calculation of the translation matrix from the camera coordinate system to the tool coordinate system includes: converting the obtained rotation matrix R from the camera coordinate system to the tool coordinate system ct Substitute the coordinates of the sphere center / cone vertex in the base coordinate system and the camera coordinate system into the relationship expression to obtain the translation matrix T from the camera coordinate system to the tool coordinate system: ct .

[0025] Further, it also includes: calculating the rotation angle of the tool coordinate system;

[0026] Calculate the rotation matrix R from the current normal vector to the ideal normal vector according to the Rodriguez rotation formula c , the expression is as follows:

[0027]

[0028] As shown in the formula, E is the third-order unit matrix, θ is the rotation angle from the current vector to the ideal vector position, is the unit vector of the rotation axis from the current vector to the ideal vector position, R c represents the rotation matrix;

[0029] Calculate R c The rotation matrix R in the base coordinate system b , the expression is as follows:

[0030] R b =R tb ×R ct ×R c ,

[0031] Rotation matrix R b The Euler angle is the rotation angle of the tool coordinate system.

[0032] Further, the coordinates of any feature point in the base coordinate system are solved by using the coordinates (X C , Y C , Z C ), the coordinates (X t , Y t , Z t , RX t , R.Y. t , RZ t ), and substitute it into the relationship expression between the coordinates in the base coordinate system and the coordinates in the camera coordinate system to obtain the coordinates of any feature point in the base coordinate system.

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] A hand-eye calibration method for a line scan 3D camera. The line scan 3D camera and a 6-axis robotic arm are in an eye-on-hand hand-eye calibration mode. The camera coordinates used for calibration are calculated using a single-line point cloud, which improves speed and accuracy. The translation matrix is ​​calculated using a direct contact method. After the hand-eye calibration is completed, the 6-degree-of-freedom information of the target feature point in the camera coordinate system is converted to a base coordinate system. Through the coordinate conversion relationship of the target feature point, the problem of the camera coordinate system and the scanning direction not being parallel is solved. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a flow chart of a hand-eye calibration method for a line scan 3D camera of the present invention.

[0036] Figure 2 It is a schematic diagram of multiple line splicing of a laser line scan 3D camera scanning according to a hand-eye calibration method for a line scan 3D camera of the present invention.

[0037] Figure 3 It is a schematic diagram of constructing a camera coordinate system for a hand-eye calibration method for a line scan 3D camera of the present invention.

[0038] Figure 4 It is a schematic diagram of hand-eye calibration of a line scan 3D camera and a robotic arm in a hand-eye calibration method for a line scan 3D camera of the present invention;

[0039] Figure 5 It is a schematic diagram of computing the coordinates of the center of a sphere / vertex of a cone using a single point cloud in a hand-eye calibration method for a line scan 3D camera of the present invention.

[0040] Figure 6 It is another schematic diagram of hand-eye calibration of a line scan 3D camera and a robotic arm in a hand-eye calibration method for a line scan 3D camera of the present invention.

[0041] Figure 7 It is a point cloud data diagram of a cone scanned by a robotic arm moving twice in a hand-eye calibration method for a line-scan 3D camera of the present invention.

[0042] Figure 8 It is a schematic diagram of the coordinates of any feature point in the camera coordinate system of a hand-eye calibration method for a line scan 3D camera of the present invention. DETAILED DESCRIPTION

[0043] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. It should be understood that the present application is not limited to the example embodiments disclosed herein. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0044] like Figure 2 As shown in the figure, the scanning process of the laser line scan 3D camera is line by line, and multiple lines are spliced ​​together. When the end of the robotic arm moves at an angle or the camera is not parallel to the end of the robotic arm, the line splicing will be misaligned, resulting in inaccurate position data. Therefore, a hand-eye calibration method for a line scan 3D camera is proposed. The coordinates of the feature points on a single line in the camera coordinate system and the coordinates of the single line corresponding to the feature point in the base coordinate system are solved to obtain the coordinates of the feature points in the base coordinate system.

[0045] like Figure 1 As shown, a hand-eye calibration method for a line scan 3D camera specifically comprises the following steps:

[0046] S1 builds the camera coordinate system;

[0047] S2 marks the coordinates of the calibration tool: moves the calibration tool, marks the coordinates of the calibration tool in the base coordinate system, and marks the coordinates of the calibration tool in the camera coordinate system;

[0048] S3 calculates the rotation matrix from the camera coordinate system to the tool coordinate system;

[0049] S4 calculates the translation matrix from the camera coordinate system to the tool coordinate system;

[0050] S5 solves the coordinates of any feature point in the base coordinate system.

[0051] This method calculates the calibration parameters through S1-S4, and can realize scanning the object through the camera, calculate the coordinates of the object in the base coordinate system, and let the end of the robot arm accurately move to the position of the object. S5 explains how to use the calibration parameters to realize the function of guiding the robot arm with the camera. The method of calculating the characteristic coordinates of the calibration information of the present invention calculates the coordinates of the center of the sphere / vertex of the cone in the base coordinate system and the coordinates of the center of the sphere / vertex of the cone in the camera coordinate system through a single point cloud. This method can effectively avoid the problem that the scanning direction is not parallel to the Y-axis of the camera when it is not calibrated, and improve the calibration accuracy.

[0052] In this embodiment, if Figure 3As shown, S1 constructs the camera coordinate system including: the direction set by the camera coordinate system is the same as the direction set by the camera scanning. Specifically, the camera scans a single line along the X axis, then moves along the Y axis to scan a number of lines, and finally moves to another plane along the Z axis, continues to scan a single line along the X axis, and then moves along the Y axis to scan a number of lines. The X value of the middle point of each row is 0, the X coordinate of each row is the number of points multiplied by the point spacing, and the Y coordinate of each row is the number of rows multiplied by the row spacing.

[0053] In this embodiment, the scanning camera for constructing the camera coordinate system is a laser line scanning 3D camera. The images scanned by the laser line scanning 3D camera are line by line and strip by strip.

[0054] In this embodiment, if Figure 4 As shown in , the coordinates of the S2 marking calibration tool include: the calibration tools are a sphere and a cone. The sphere is used to calibrate the rotation matrix and is fixed. The cone is used to calibrate the translation matrix and is also fixed. The point cloud coordinate system is a set of coordinates used to describe the position and direction of a point in the point cloud, including the Cartesian coordinate system and the polar coordinate system. Figure 5 As shown, the coordinates of the center of the circle are calculated through a single point cloud. The coordinates of the center of the sphere and the vertex of the cone in the base coordinate system are obtained; the coordinates of the center of the sphere and the vertex of the cone in the camera coordinate system are obtained.

[0055] In this embodiment, S3 calculates the rotation matrix from the camera coordinate system to the tool coordinate system, including:

[0056] The relationship between the coordinates of the center of the S31 sphere / cone vertex in the base coordinate system and the coordinates in the camera coordinate system is expressed as follows:

[0057] Base 球 =R tb (R ct Camera 球 +T ct )+T tb ,

[0058] Among them, Base 球 :The coordinates of the center of the sphere / cone vertex in the base coordinate system. During the calibration process, the sphere / cone does not move, so this coordinate is an unknown constant. The coordinates of a certain point in the base coordinate system. During the actual calibration, the vertex of the cone is selected, and the end of the robot arm is allowed to contact the vertex of the cone. The coordinates of the tool coordinate system in the base coordinate system at this time are obtained, which is the Base 球 .

[0059] R tb : The rotation matrix from the tool coordinate system to the base coordinate system. This parameter can be obtained in the robot arm teach pendant.

[0060] R ct: The rotation matrix from the camera coordinate system to the tool coordinate system. This parameter is the unknown number to be solved, that is, one of the results of hand-eye calibration.

[0061] Camera 球 : The coordinates of the center of the sphere / cone vertex in the camera coordinate system. This parameter needs to be calculated in the point cloud by the visual software.

[0062] T ct : The translation matrix from the camera coordinate system to the tool coordinate system. This parameter is the unknown number to be solved, that is, the second result of the hand-eye calibration.

[0063] T tb : Translation matrix from tool coordinate system to base coordinate system. This parameter can be obtained in the robot arm teach pendant.

[0064] According to the relationship between the coordinates in the base coordinate system and the coordinates in the camera coordinate system, what needs to be solved is R ct and T ct , other parameters can be obtained. Therefore, by moving the end position of the robot twice, bringing in two sets of robot rotation and translation parameters and tool coordinates in the camera coordinate system, subtracting them can eliminate Base 球 At the same time, we ensure that the two movements of the robot arm are pure translations without rotation, so R tb1 and R tb2 are equal, both are recorded as R0, and subtracting them can also eliminate T ct , only R is left ct A parameter, solve to get R ct .like Figure 6-7 As shown, the robot arm drives the camera to scan the cone and obtain Figure 7 The specific steps are as follows:

[0065] S32 moves the laser line scan 3D camera, the relative position of the sphere center / cone vertex and the base coordinates remains unchanged, and two sets of robot arm and camera coordinates are obtained.

[0066] Base 球 =R tb1 (R ct1 Camera 球1 +T ct )+T tb1 ,

[0067] Base 球 =R tb2 (R ct1 Camera 球2 +T ct )+T tb2 ,

[0068] S33 The coordinates of the center positions of any two spheres in the base coordinate system are subtracted from the coordinates in the camera coordinate system to obtain:

[0069] T tb2 -T tb1 =R0·R ct (Camera 球1 -Camera 球2 );

[0070] S34 obtains multiple sets of data and uses the least squares method to obtain the rotation matrix R from the camera coordinate system to the tool coordinate system ct .

[0071] In this embodiment, since the unknown quantity R has been obtained above ct , we can substitute a set of real cone vertex coordinates to find another unknown quantity T ct .

[0072] S4 calculates the translation matrix from the camera coordinate system to the tool coordinate system. The specific steps are as follows: Convert the obtained rotation matrix R from the camera coordinate system to the tool coordinate system ct and a set of cone vertex coordinates, and bring them into the relationship expression between the coordinates of the sphere center / cone vertex in the base coordinate system and the coordinates in the camera coordinate system to obtain the translation matrix T from the camera coordinate system to the tool coordinate system ct .

[0073] A unified explanation of steps S1-S4: All of them aim to solve the equation and find R ct and T ct .

[0074] Formula Base 球 =R tb (R ct Camera 球 +T ct ) is the mathematical basis of the entire calibration, which includes known quantities and unknown quantities; by substituting two sets of known quantities and then subtracting the two equations, we get the formula T tb2 -T tb1 =R0·R ct (Camera 球1 -Camera 球2 ).

[0075] Formula T tb2 -T tb1 =R0·R ct (Camera 球1 -Camera 球2 ) has only one unknown quantity R ct , can be solved normally; bring in R ct Base球 =R tb (R ct Camera 球 +T ct ), then the formula Base 球 =R tb (R ct Camera 球 +T ct ) has only one unknown quantity T ct , and then substitute a set of known quantities to solve this equation.

[0076] In this embodiment, it also includes: S41 calculating the rotation angle of the tool coordinate system. The purpose is to calculate the coordinates of the feature point in the base coordinate system. This coordinate includes 6 degrees of freedom, X, Y, Z, RX, RY, RZ. Steps S1-S4 can only calculate X, Y, Z, so it is necessary to calculate the rotation angle of the tool coordinate system. The specific steps are as follows:

[0077] S411 calculates the rotation matrix R from the current normal vector to the ideal normal vector according to the Rodriguez rotation formula c , the expression is as follows:

[0078]

[0079] S412 Calculate R c The rotation matrix R in the base coordinate system b , the expression is as follows:

[0080] R b =R tb ×R ct ×R c ,

[0081] Rotation matrix R b The Euler angle is the rotation angle of the tool coordinate system.

[0082] like Figure 4-5 As shown in the figure, during the calibration of the rotation matrix, the contour can be selected at will, and the operation is simple. When obtaining multiple sets of sphere center coordinates, the position of the tool coordinates needs to remain unchanged to eliminate the translation matrix from the camera to the tool coordinates.

[0083] In this embodiment, since the parameters in the relationship expression between the coordinates in the base coordinate system and the coordinates in the camera coordinate system have been solved, the coordinates of any feature point in the camera coordinate system can be converted to the coordinates of the feature point in the base coordinate system. Figure 8 As shown, the specific steps of S5 to solve the coordinates of any feature point in the base coordinate system are as follows:

[0084] The coordinates of the starting point and end point of each line collected by the S51 robot are known, and the time and uniform motion parameters of the robot are known. Therefore, the coordinates of the feature points in this single line at a certain time are obtained based on the time and speed. That is, the coordinates of the feature points on the single line in the camera coordinate system (X C , Y C , Z C ).

[0085] S52 The coordinates of any feature point corresponding to a single row in the base coordinate system (X t , Y t , Z t , RX t , R.Y. t , RZ t ), this row is the known Y row. Substitute it into the relationship expression between the coordinates in the base coordinate system and the coordinates in the camera coordinate system to obtain the coordinates of any feature point in the base coordinate system.

[0086] In order to better accommodate more usage scenarios when using calibration parameters. Because when the robot arm movement direction and the laser line angle change, the line spacing will also change, which will cause the feature points (X C , Y C , Z C ) coordinates are distorted, enter the formula Base 球 =R tb (R ct Camera 球 +T ct )+T tb The coordinates are the starting point and feature point of the scanning robot. However, since the line spacing will change, the relative relationship between the starting point and the feature point of the scanning robot is not fixed, and the actual coordinate error of the feature point calculated in the end will be large. Therefore, we can change our thinking and choose to enter the formula Base 球 =R tb (R ct Camera 球 +T ct )+T tb The coordinates of the feature point (X C , 0, Z C ) and the coordinates of the base coordinate system corresponding to the feature point (X t , Y t , Z t , RX t , R.Y. t , RZ t ), which avoids the Y coordinate in the point cloud stitching being affected by the row spacing. The stitching point cloud is only used when extracting features, and the Y of the row where the feature point is located is taken as 0 by default when calculating the coordinates.

[0087] Feature point (XC , 0, Z C ) is the formula Base 球 =R tb (R ct Camera 球 +T ct )+T tb Camera 球 , the coordinates of the base coordinate system corresponding to the feature point (X t , Y t , Z t , RX t , R.Y. t , RZ t ), where (X t , Y t , Z t ) corresponds to formula R tb (R ct Camera 球 +T ct )+T tb T tb , (RX t , R.Y. t , RZ) corresponds to the formula R tb (R ct Camera 球 +T ct )+T tb R tb .

[0088] Substitute the above coordinates into the formula Base 球 =R tb (R ct Camera 球 +T ct ), where the translation is written as a column vector and the rotation is written as a 3x3 rotation matrix. Solve for the coordinates of the feature point in the robot base coordinate system.

[0089] A hand-eye calibration method for a line scan 3D camera. The line scan 3D camera and a 6-axis robotic arm are in an eye-on-hand hand-eye calibration mode. The camera coordinates used for calibration are calculated using a single-line point cloud, which improves speed and accuracy. The translation matrix is ​​calculated using a direct contact method. After the hand-eye calibration is completed, the 6-degree-of-freedom information of the target feature point in the camera coordinate system is converted to a base coordinate system. Through the coordinate conversion relationship of the target feature point, the problem of the camera coordinate system and the scanning direction not being parallel is solved.

[0090] It should also be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the statement "including a ..." do not exclude the presence of other identical elements in the process, method, article or device including the elements.

[0091] The above-mentioned sequence of the embodiments of the present invention is only for description and does not represent the advantages and disadvantages of the embodiments. The processes depicted in the accompanying drawings do not necessarily require the specific order or continuous order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0092] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present application. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A hand-eye calibration method for a line scan 3D camera, characterized in that: The method comprises: The coordinates of the feature points on a single line in the camera coordinate system and the coordinates of the feature points corresponding to the single line in the base coordinate system are solved to obtain the coordinates of the feature points in the base coordinate system; specifically including: Construct the camera coordinate system; the direction set by the camera coordinate system is the same as the direction set by the camera scanning; the camera scans a single line along the X axis, then moves along the Y axis to scan several lines, and finally moves to another plane along the Z axis, continues to scan a single line along the X axis, and then moves along the Y axis to scan several lines; the X value of the middle point of each row is 0, the X coordinate of each row is the number of points multiplied by the point spacing, and the Y coordinate of each row is the number of rows multiplied by the row spacing; Marking the coordinates of the calibration tool: moving the calibration tool, marking the coordinates of the calibration tool in the base coordinate system, and marking the coordinates of the calibration tool in the camera coordinate system; Calculate the rotation matrix from the camera coordinate system to the tool coordinate system; Calculate the translation matrix from the camera coordinate system to the tool coordinate system; Solve the coordinates of any feature point in the base coordinate system; by knowing the coordinates of any feature point on a single line in the camera coordinate system (X c ,Y c ,Z c ), the coordinates (X t ,Y t ,Z t ,RX t ,RY t ,RZ t ), bring it into the relationship expression between the coordinates in the base coordinate system and the coordinates in the camera coordinate system, and get the coordinates of any feature point in the base coordinate system; The coordinates of the marking calibration tool include: when the calibration tool is a sphere and a cone, obtaining the coordinates of the center of the sphere and the vertex of the cone in the base coordinate system; obtaining the coordinates of the center of the sphere and the vertex of the cone in the camera coordinate system; The calculation of the rotation matrix from the camera coordinate system to the tool coordinate system includes: The relationship between the coordinates of the sphere center / cone vertex in the base coordinate system and the coordinates in the camera coordinate system is expressed as: Base 球 =R tb (R ct ·Camera 球 +T ct )+T tb ; As shown in the formula: Base 球 is the coordinate in the base coordinate system of the sphere center / cone vertex; R tb is the rotation matrix from the tool coordinate system to the base coordinate system; R ct The rotation matrix from the camera coordinate system to the tool coordinate system; Camera 球 is the coordinate of the sphere center / cone vertex in the camera coordinate system; T ct is the translation matrix from the camera coordinate system to the tool coordinate system; T tb is the translation matrix from the tool coordinate system to the base coordinate system; Move the camera, the relative position of the sphere center / cone vertex and the base coordinates remain unchanged, and obtain two sets of robot arm and camera coordinate points as follows: Base 球 =R tb1 (R ct1 ·Camera 球1 +T ct )+T tb1 ; Base 球 =R tb2 (R ct1 ·Camera 球2 +T ct )+T tb2 ; Among them, to ensure that the two movements of the robot arm are pure translations without rotation, then R tb1 With R tb2 Equal, denoted as R0; Subtract the coordinates of the center positions of any two spheres in the base coordinate system from the coordinates in the camera coordinate system to obtain: T tb2 -T tb1 =R0·R ct (Camera 球1 -Camera 球2 ); Obtain multiple sets of data and use the least squares method to obtain the rotation matrix R from the camera coordinate system to the tool coordinate system ct .

2. The hand-eye calibration method for a line scan 3D camera according to claim 1, characterized in that: The calculation of the translation matrix from the camera coordinate system to the tool coordinate system includes: converting the obtained rotation matrix R from the camera coordinate system to the tool coordinate system ct Substitute the coordinates of the sphere center / cone vertex in the base coordinate system and the camera coordinate system into the relationship expression to obtain the translation matrix T from the camera coordinate system to the tool coordinate system: ct .

3. The hand-eye calibration method for a line scan 3D camera according to claim 2, characterized in that: Also includes: Calculate the rotation angle of the tool coordinate system; Calculate the rotation matrix R from the current normal vector to the ideal normal vector according to the Rodriguez rotation formula c , the expression is as follows: As shown in the formula, E is the third-order unit matrix, θ is the rotation angle from the current vector to the ideal vector position, R is the unit vector of the rotation axis from the current vector to the ideal vector position; c represents the rotation matrix; Calculate R c The rotation matrix R in the base coordinate system b , the expression is as follows: R b =R tb ×R ct ×R c ; Rotation matrix R b The Euler angle θ is the rotation angle of the tool coordinate system.

Images