Round pipe intersecting line welding seam coordinate system calibration method

Abstract

The invention relates to the technical field of intersecting line track calibration, in particular to a circular pipe intersecting line welding line coordinate system calibration method which comprises the steps that an intersecting line track mathematical model is established, and the coordinate relation of intersecting lines in a main pipe coordinate system and a branch pipe coordinate system is determined; based on the transformation relation between a robot base coordinate system and a master coordinate system, an anti-symmetric matrix is adopted to express an attitude matrix, and a calibration constraint equation for eliminating a translation vector is established; and randomly selecting three teaching points on the intersecting line track, substituting the coordinates of the three teaching points in the two coordinate systems into the constraint equation, solving to obtain an attitude matrix and a translation vector, completing the solving of a conversion matrix, and realizing the calibration of the main coordinate system. According to the method, calibration can be completed only through any three teaching points, auxiliary equipment is not needed, the method is adaptive to all types of intersecting line models, the method has the advantages of being easy and convenient to operate, high in efficiency and precision and wide in application range, and an accurate coordinate system conversion basis can be provided for track planning and interpolation calculation of scenes such as robot intersecting line welding and cutting.

Description

Technical Field

[0001] This invention relates to the field of intersection line trajectory calibration technology, and in particular to a method for calibrating the coordinate system of a circular pipe intersection line weld, which is applicable to scenarios requiring trajectory planning, such as robot intersection line welding and cutting. Background Technology

[0002] The spatial curve formed by the intersection of two circular tubes is called the intersection line. Based on the relative positions of the two tubes, intersection lines are mainly classified into four models: orthogonal, oblique, orthogonal offset, and oblique offset. Figure 1 As shown. In the robot intersection trajectory motion scenario, the robot end effector or gripper needs to move along the intersection trajectory to complete the welding or cutting operation. When the controller's underlying algorithm performs trajectory planning and interpolation calculations for this trajectory, given the modeling characteristics of the intersection line, it usually needs to be performed in the coordinate system of the main pipe (a circular pipe with a large radius), while the robot programming teaching points are often located in the robot's base coordinate system or other coordinate systems, such as... Figure 2 As shown, the point coordinates in the robot's base coordinate system or other coordinate systems must be transformed to the master coordinate system before subsequent velocity planning and trajectory interpolation calculations can be performed.

[0003] In the aforementioned coordinate transformation process, the transformation matrix (i.e., the transformation relationship) between the robot's base coordinate system and the master coordinate system is crucial. How to accurately and efficiently obtain this transformation matrix is ​​a key technical problem in this field. Several existing schemes exist for obtaining this transformation matrix, but all have significant drawbacks: 1. Patent CN114260625A discloses a welding method, welding equipment, and storage medium for the intersection of circular pipes. This scheme obtains contour feature points by scanning the workpiece contour with a laser sensor, fits the common perpendicular line between the axis of the circular pipe and the axes of the two pipes based on the feature points, and then calibrates the relationship between the intersection coordinate system and the user coordinate system of the welding equipment. However, this scheme uses a planar ellipse fitting method, which requires at least 5 points to fit one ellipse. One circular pipe requires two ellipses, for a total of four ellipses that need to be fitted and calculated. The required number of teaching points is too large, making the operation cumbersome and inefficient.

[0004] 2. Patent CN102069267A discloses a general arc welding robot teaching method for cylindrical intersecting weld seams, applicable to all types of intersecting weld seams. It establishes the pose matrix of the workpiece coordinate system relative to the robot's base coordinate system by teaching four feature points on the workpiece online. However, this method does not specify the teaching method for the four feature points. Judging from the attached drawings, the four feature points include two symmetrical points on the branch pipe parallel to the main pipe axis and two points on the branch pipe parallel to the axis. In actual operation, it is difficult to achieve accurate teaching of these four points.

[0005] 3. The paper "Automatic Welding Model and Simulation of Intersecting Curve with Rotating Main Pipe" proposes to determine the relationship between the world coordinate system and the main pipe coordinate system by rotating the main pipe by a certain angle. However, this scheme requires the main pipe equipment to rotate and the welding point to always be at the highest point of the arc, which limits the applicable scenarios and cannot meet the needs of most existing operations.

[0006] 4. The journal article "Three-coordinate measurement method for basic parameters of cylinder" discloses a method to determine the axial direction, position and radius of a cylinder based on any set of discrete measurement points on the cylinder. This method uses the least squares method and requires at least 5 measurement points. For two circular tubes, the number of points required is relatively large, and the operation cost is high.

[0007] 5. The journal article "Research on Cylindrical Fitting Algorithm for Sparse Point Measurement of Aviation Conduits" proposes to first project a small number of points, calculate the roundness of the projected points, and select the vector with the smallest roundness as the initial value for fitting the cylinder. However, this scheme still requires 15-20 fitting points, which is too many points and has low efficiency.

[0008] 6. The journal article "6-DOF Industrial Robot Intersection Welding Motion Planning" uses standard tooling to determine the relationship between the workpiece coordinate system and the master coordinate system. However, the tooling has certain accuracy errors and requires special tooling manufacturing, which increases the operating cost and complexity.

[0009] 7. The paper "Research on Intersection Welding Robot System Based on Laser Vision" uses NURBS to fit the intersection line, with a curve degree of 3 and a node number of m+7, requiring a large number of teaching points. The paper "Research on Robot Intersection Welding Trajectory Planning Method" also uses NURBS to fit the intersection line. The interpolation method uses about 50 original data points, while the fitting method requires 20 original points. Both have the problems of many teaching points and complex calculations.

[0010] In addition, there are two other common solutions in the existing technology: one is to use the intersection line trajectory to express the formula, substitute the values ​​of multiple points into a system of equations, and solve for parameters such as the main pipe radius, branch pipe radius, and the intersection angle between the branch pipe axis and the main pipe axis. However, this method requires that the attitude relationship between the main pipe coordinate system and the robot base coordinate system be known. In practical applications, this attitude relationship is often not directly obtainable and requires the main pipe to be fixed by tooling or other auxiliary equipment to ensure that the attitude is fixed and known, thus limiting its applicability. The other is to use a geometric method to calculate the axes of the two pipes. The common perpendicular between the axes is used to obtain the representation of the main coordinate system in the base coordinate system. The conventional approach is to take a circle at each end of the circular tube, teach the points on the circle and fit a circle to obtain the coordinates of the circle center. The axis direction is obtained using the coordinates of the two circle centers. However, this method is difficult to obtain an accurate circumferential plane and requires a large number of teaching points, at least 12 points are needed to complete the axis calculation of the two circular tubes. Even if two points parallel to the axis are taken on the circular tube to determine the direction, although the number of points is reduced, it is difficult to accurately ensure that the straight line determined by the two points is parallel to the axis, which affects the calibration accuracy.

[0011] In summary, existing methods for calibrating the coordinate system of intersecting weld seams of circular pipes generally suffer from problems such as numerous teaching points, cumbersome operation, reliance on auxiliary equipment, narrow applicability, or insufficient calibration accuracy, and cannot meet the requirements for efficient, accurate, and universal calibration. Summary of the Invention

[0012] The purpose of this invention is to overcome the problems of the prior art and provide a method for calibrating the coordinate system of the weld seam of the intersecting line of a circular pipe. This method solves the problems of the existing calibration methods having many teaching points and complicated operation, requiring only a few teaching points to complete the calibration. Secondly, it solves the problems of existing methods relying on auxiliary equipment and having limited applicability. It does not require auxiliary facilities such as sensors and standard tooling, and is compatible with all types of intersecting line models.

[0013] The above objectives are achieved through the following technical solutions: A method for calibrating the coordinate system of a circular pipe intersection weld includes the following steps: Step (1): Establish a mathematical model of the intersection line trajectory in the form of a fixed coordinate system, which includes the main pipe coordinate system {U} (Zu-Xu-Yu) and the branch pipe coordinate system {W} (Zw-Xw-Yw), where the main pipe is the pipe that is passed through and the branch pipe is the pipe that is passed through. Step (2): Based on the transformation relationship between the robot base coordinate system {B} and the master coordinate system {U}, establish calibration constraint equations, wherein the transformation relationship satisfies the following equation; , in, Points under the base coordinate system, For points in the master coordinate system, For the transformation matrix, Let be the attitude matrix. The pose matrix is ​​expressed as a translation vector using an antisymmetric matrix S. ; Step (3): Randomly select no less than 3 points on the intersection line trajectory for teaching, substitute the coordinate values ​​of the obtained points into the calibration constraint equation, and solve to obtain the attitude matrix. Then the attitude matrix Substituting back into the transformation formula, we obtain the translation vector. Complete the transformation matrix Solving for the coordinates enables the calibration of the master coordinate system {U}.

[0014] Furthermore, in step (1), any point on the intersection line The coordinates in the branch pipe coordinate system {W} are: , in, For the branch pipe radius, It is the intersection line at The projection point on the plane and the origin Connecting line segments and The angle formed by the coordinate axes for Point in the branch coordinate system The coordinate values ​​on the axis.

[0015] Furthermore, in step (1), The coordinates of the point in the master coordinate system {U} are: , in: For the supervisor's radius, This is the offset.

[0016] Further, in step (1), the transformation matrix between the main pipe coordinate system {U} and the branch pipe coordinate system {W} is: , Where β is the deflection angle.

[0017] Furthermore, in step (1), the parametric equation of the intersection line in the master coordinate system {U} is: , This parametric equation is obtained by... The solution obtained Substituting the coordinate system transformation matrix into the branch coordinate system It is derived from the expression for the product of point coordinates.

[0018] Furthermore, in step (2), the antisymmetric matrix The expression is: , Attitude matrix pass The calculation shows that, among which It is the identity matrix. , , pose matrix The three independent parameters.

[0019] Furthermore, in step (2), the calibration constraint equations are eliminated by adding point pairs and subtracting the translation vectors. The following derivation reveals the specific details: , in, The coordinates of the points in the robot's base coordinate system. The coordinates of the point in the master coordinate system. =1,2.

[0020] Furthermore, in step (3), the three selected teaching points are distributed on the intersection line trajectory, and there are no special restrictions on the location of the teaching points.

[0021] Furthermore, the intersection line includes four models: orthogonal, oblique, orthogonal offset, and oblique offset.

[0022] Furthermore, the calibration method is used in robot intersection welding or cutting scenarios to provide a coordinate system transformation basis for trajectory planning and interpolation calculation.

[0023] The present invention provides a method for calibrating the coordinate system of a circular pipe intersection weld. This method requires only three randomly selected, dispersed teaching points on the intersection trajectory. It simplifies the attitude matrix calculation using an antisymmetric matrix and establishes calibration constraint equations to eliminate translation vectors. Solving the transformation matrix achieves the calibration of the main coordinate system. No auxiliary equipment is needed, and the method is compatible with all types of intersection models, achieving the advantages of simple operation, high calibration efficiency, and reliable accuracy. Specific advantages are as follows: 1. Fewer teaching points and simpler operation: This invention requires only 3 teaching points to complete the calibration, which is significantly less than the minimum of 5 and up to about 50 teaching points required in the prior art. This greatly reduces the teaching operation steps, shortens the calibration time, and improves the calibration efficiency. Moreover, the teaching points can be arbitrarily selected on the intersection line trajectory without being fixed in a special position. This avoids the strict requirements on the position of the teaching points in the prior art, reduces the difficulty of operation, and allows ordinary operators to complete the calibration work.

[0024] 2. No auxiliary equipment required, wide applicability: This invention does not rely on auxiliary equipment such as laser sensors and standard tooling, requires no additional equipment costs, and does not require special installation conditions such as main pipe rotation, thus reducing the limitations of the operating scenario; it can be adapted to all types of intersection line models such as orthogonal, oblique, orthogonal offset, and oblique offset. Regardless of the relative positional relationship between the two circular pipes, accurate calibration can be completed by this method, solving the problem of limited applicability of existing technologies.

[0025] 3. High calibration accuracy and complete parameters: This invention establishes a precise mathematical model of the intersection line trajectory, clarifying the coordinate mapping relationship of points on the intersection line; it simplifies the attitude matrix calculation by using antisymmetric matrices, avoiding the defects of traditional methods; it improves the stability and accuracy of the calculation results by solving the parameters through an overdetermined set of equations; finally, it can simultaneously calculate the position parameters (represented by the translation vector Trans) and attitude parameters (represented by the attitude matrix R) of the master coordinate system, providing a precise coordinate system transformation basis for subsequent trajectory planning and interpolation calculations, ensuring the accuracy of the robot's intersection line trajectory motion. Attached Figure Description

[0026] Figure 1 These are the four models in the existing technology: orthogonal, oblique, orthogonal offset, and oblique offset. Figure 2 This is a schematic diagram of a robot in the prior art, where {B} represents the robot's base coordinate system and {U} represents the master coordinate system; Figure 3 This is a flowchart of a method for calibrating the coordinate system of a circular pipe intersection weld as described in this invention; Figure 4 This is a schematic diagram of the mathematical model of the intersection line trajectory in the coordinate system calibration method for the intersection line weld of a circular pipe according to the present invention. Figure 5 This is a schematic diagram of arbitrarily selecting 3 teaching points on the intersection line trajectory in the coordinate system calibration method of the circular pipe intersection line weld described in this invention. Detailed Implementation

[0027] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. The described embodiments are merely some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0028] like Figure 3 As shown, this scheme provides a coordinate system calibration method for the intersection weld of circular pipes. It establishes a mathematical model of the intersection trajectory and calibration constraint equations, and solves the coordinate system transformation matrix using a small number of teaching points. The specific steps include: Step (1): Establish a mathematical model of the intersection line trajectory The trajectory of the intersection line is determined by the main pipe coordinate system and the branch pipe coordinate system, where the main pipe is the pipe that is crossed and the branch pipe is the pipe that is crossed. Zu-Xu-Yu is defined as the main pipe coordinate system {U} and Zw-Xw-Yw is defined as the branch pipe coordinate system {W}.

[0029] Choose any point on the intersection line. The coordinates of this point in the branch pipe coordinate system {W} are expressed as follows: (1), In the formula, For the branch pipe radius, It is the intersection line at The projection point on the plane and the origin Connecting line segments and The angle formed by the coordinate axes for Point in the branch coordinate system The coordinate values ​​on the axis. The coordinate expression of point P in the master coordinate system {U} is: (2), In the formula, (3), For the supervisor's radius, This is the offset.

[0030] There is a fixed transformation relationship between the main pipe coordinate system {U} and the branch pipe coordinate system {W}, and the transformation matrix is: (4), In the formula, This refers to the deflection angle.

[0031] The branch coordinate system in equation (1) is changed to... Multiplying the point coordinates by the transformation matrix of equation (4) yields: (5), From geometric relationships, we can know that The equation can be solved to obtain the solution. The solution process is as follows: right Perform a repositioning process to include... The term with the is placed alone on the left side of the equation, and the remaining terms are moved to the right side of the equation, resulting in: , Divide both sides of the equation by (Requires guarantee) ≠0, if =0, then =90° or 270°, in which case it can be derived separately using special geometric relationships. (To ensure the integrity of the model), the expression is used to solve for: , The solution obtained above Substituting into equation (5), simplifying each term, the parametric equation of the intersection line in the master coordinate system {U} is finally derived: (6), like Figure 4 As shown, this parametric equation completely establishes the coordinates of any point on the intersection line in the main pipe coordinate system and the branch pipe radius. Supervisory radius Offset Deflection angle and included angle The correspondence between them provides a precise mathematical basis for subsequent coordinate transformations.

[0032] Step (2): Establish calibration constraint equations There is a clear transformation relationship between the points in the robot's base coordinate system {B} and the points in the master coordinate system {U}. The expression for this transformation relationship is as follows: (7), In the formula, Let be the point represented in the robot's coordinate system. For points represented in the master coordinate system, This is the transformation matrix between the base coordinate system and the master coordinate system. It is the attitude matrix, used to represent the attitude relationship between two coordinate systems. It is a translation vector used to characterize the positional offset relationship between two coordinate systems.

[0033] To simplify the formula complexity and reduce the computational difficulty, this invention abandons the traditional Euler angle representation method and uses antisymmetric matrices to express the attitude matrix. Among them, the opposition to the formation The expression is: (8), The attitude matrix R is calculated from the antisymmetric matrix S, and the specific formula is as follows: (9), In the formula, It is the identity matrix. , , pose matrix The attitude matrix can be fully characterized by three independent parameters. Compared to Euler angles, this method effectively reduces parameter redundancy, avoids the gimbal lock problem inherent in Euler angles, and significantly simplifies subsequent calculations.

[0034] To eliminate translation vectors To mitigate the impact on calculations, this invention addresses equation (7) by adding point pairs and subtracting them. Specifically, two sets of corresponding points are selected in the base coordinate system and the master coordinate system. and Substituting the two sets of points into equation (7), we get: (7-1), (7-2), Subtract equation (7-1) from equation (7-2) and shift the vector. The results are canceled out, resulting in: (10), This formula contains only the attitude matrix. The coordinate difference between the two sets of corresponding points effectively simplifies the calculation model.

[0035] Substituting equations (8) and (9) into equation (10), and after a series of matrix operations and algebraic simplification, we obtain the calibration constraint equations: (11), In the formula, These are the coordinates of two points in the robot's base coordinate system. , These represent the coordinates of two corresponding points in the master coordinate system. The calibration constraint equation establishes the attitude matrix. Independent parameters , , The direct correlation between the coordinates of points in the two coordinate systems provides a clear mathematical basis for parameter solving.

[0036] Step (3): Solve for the transformation matrix T like Figure 5 As shown, the first step is to select teaching points and obtain their coordinates: At least three teaching points are arbitrarily selected on the intersection trajectory. To improve calculation accuracy, it is preferable to distribute the teaching points evenly across the intersection trajectory, avoiding calculation errors caused by excessive concentration of teaching points. Through robot teaching operations, the coordinate values ​​of these three teaching points in the robot's base coordinate system are accurately obtained. , , During the teaching process, there is no need to specifically limit the location of the teaching point; it is only necessary to ensure that the teaching point is located on the intersection line trajectory, making the operation convenient and flexible.

[0037] Next, calculate the coordinates of the teaching point in the master coordinate system: based on the parametric equation (6) of the intersection line established in step 1 in the master coordinate system, combined with the known master radius... Branch pipe radius Offset Deflection angle Given the inherent parameters of the workpiece, assign a corresponding included angle to each selected teaching point. value( The value can be flexibly selected based on the position of the teaching point on the intersection line trajectory, without needing to follow a specific rule. , , , and the corresponding Substituting the values ​​into equation (6), the coordinates of each teaching point in the master coordinate system can be obtained through calculation. .

[0038] Then solve for the attitude matrix R: (This involves finding the coordinates of the three corresponding points.) , , By combining pairs of points, we can obtain 3 sets of point-pair combinations, which are as follows: and , and , and Substituting each pair of points into the calibration constraint equation (11) established in step 2, each pair of points generates 3 independent equations, and the 3 pairs of points form a total of 9 equations. Since the independent parameters of the attitude matrix R are... , , There are 3 unsolved parameters and 9 equations forming an overdetermined system of equations. Numerical analysis methods (such as the least squares method) are used to solve this system of equations, yielding the attitude matrix. 3 independent parameters , , The optimal solution. The solution obtained... , , Substituting into equations (8) and (9), the complete attitude matrix can be calculated. .

[0039] Finally, solve for the translation vector Trans and determine the transformation matrix. The attitude matrix obtained by solving Substitute back into equation (7), and select any set of coordinate values ​​for the teaching points (e.g. and Substituting into equation (7), and after rearranging the terms, the translation vector can be obtained. The specific calculation process is as follows: Depend on , Rearranging the terms, we get: , Will coordinates, attitude matrix as well as Substituting the coordinates into the above formula, the translation vector can be obtained through matrix-vector multiplication and vector subtraction. The specific value.

[0040] Attitude matrix Translation vector Once determined, the transformation matrix between the robot's base coordinate system and the master coordinate system... That is, the transformation matrix is ​​completely determined. This fully encompasses the attitude and position offset relationships between the two coordinate systems, thus completing the calibration of the master coordinate system. Subsequent robot trajectory movements along the intersection line can be performed using a transformation matrix. The coordinates of the programming teaching points under the robot's base coordinate system are accurately converted to the master coordinate system, providing a reliable basis for the controller's underlying algorithm to perform trajectory planning and interpolation calculations.

[0041] The above description is merely illustrative of the embodiments of the present invention and is not intended to limit the present invention. For those skilled in the art, any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calibrating the coordinate system of a circular pipe intersection weld, characterized in that, Includes the following steps: Step (1): Establish a mathematical model of the intersection line trajectory in the form of a fixed coordinate system, which includes the main pipe coordinate system {U} and the branch pipe coordinate system {W}, where the main pipe is the pipe that is passed through and the branch pipe is the pipe that is passed through. Step (2): Based on the transformation relationship between the robot base coordinate system {B} and the master coordinate system {U}, establish calibration constraint equations, wherein the transformation relationship satisfies the following equation; ， in, Points under the base coordinate system, For points in the master coordinate system, For the transformation matrix, Let be the attitude matrix. The pose matrix is ​​expressed as a translation vector using an antisymmetric matrix S. ; Step (3): Randomly select no less than 3 points on the intersection line trajectory for teaching, substitute the coordinate values ​​of the obtained points into the calibration constraint equation, and solve to obtain the attitude matrix. Then the attitude matrix Substituting back into the transformation formula, we obtain the translation vector. Complete the transformation matrix Solving for the coordinates enables the calibration of the master coordinate system {U}.

2. The method for calibrating the coordinate system of a circular pipe intersection weld according to claim 1, characterized in that, In step (1), any point on the intersection line The coordinates in the branch pipe coordinate system {W} are: ， in, For the branch pipe radius, It is the intersection line at The projection point on the plane and the origin Connecting line segments and The angle formed by the coordinate axes for Point in the branch coordinate system The coordinate values ​​on the axis.

3. The method for calibrating the coordinate system of a circular pipe intersection weld according to claim 2, characterized in that, In step (1), The coordinates of the point in the master coordinate system {U} are: ， in: ， For the supervisor's radius, This is the offset.

4. The method for calibrating the coordinate system of a circular pipe intersection weld according to claim 3, characterized in that, In step (1), the transformation matrix between the main pipe coordinate system {U} and the branch pipe coordinate system {W} is: ， Where β is the deflection angle.

5. The method for calibrating the coordinate system of a circular pipe intersection weld according to claim 4, characterized in that, In step (1), the parametric equation of the intersection line in the master coordinate system {U} is: ， This parametric equation will be obtained by... The solution obtained Substituting the coordinate system transformation matrix into the branch coordinate system It is derived from the expression for the product of point coordinates.

6. The method for calibrating the coordinate system of a circular pipe intersection weld according to claim 1, characterized in that, In step (2), the antisymmetric matrix The expression is: ， Attitude matrix pass The calculation shows that, among which It is the identity matrix. , , pose matrix The three independent parameters.

7. The method for calibrating the coordinate system of a circular pipe intersection weld according to claim 6, characterized in that, In step (2), the calibration constraint equations are eliminated by adding point pairs and subtracting the translation vectors. The following derivation reveals the specific details: ， in, The coordinates of the points in the robot's base coordinate system. The coordinates of the point in the master coordinate system. =1,2.

8. The method for calibrating the coordinate system of a circular pipe intersection weld according to claim 1, characterized in that, In step (3), the three selected teaching points are distributed on the intersection line trajectory, and there are no special restrictions on the location of the teaching points.

9. The method for calibrating the coordinate system of a circular pipe intersection weld according to claim 1, characterized in that, The intersection line includes four models: orthogonal, oblique, orthogonal offset, and oblique offset.

10. A method for calibrating the coordinate system of a circular pipe intersection weld according to any one of claims 1-9, characterized in that, The calibration method is used in robot intersection welding or cutting scenarios to provide coordinate system transformation basis for trajectory planning and interpolation calculation.

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