Dynamic path planning method and system for multi-axis collaborative welding robot

Abstract

The invention discloses a dynamic path planning method and system for a multi-axis collaborative welding robot, and belongs to the field of robot welding. The method comprises the steps that basic data of a welded workpiece is collected, and a welding basic database is constructed; constructing a geometric model of the welding seam path according to the data in the welding basic database, and parameterizing the geometric model of the welding seam path; on the basis of the parameter result, an initial track is generated between two adjacent weld joint sections of the welding path, time parameterization is conducted on the initial track, and a time-dependent time parameterization spinor track is obtained; and constructing a spinor mapping model based on inverse kinematics and a spinor theory to convert the time parameterized spinor trajectory into a target spinor. The welding quality is improved.

Description

Technical Field

[0001] The present invention relates to the field of robotic welding, and in particular, to a dynamic path planning method and system for a multi-axis collaborative welding robot. Background Art

[0002] In the existing path planning of industrial welding robots, Cartesian space is generally used for welding path planning. Its typical implementation path is as follows: First, discrete path points of the end effector (welding torch) in Cartesian space are determined through 3D modeling or manual teaching. Subsequently, the Cartesian trajectory is converted into a joint space angle sequence through inverse kinematics (IK).

[0003] Although this method is intuitive and easy to implement in engineering, it has the following structural problems in complex welding scenarios: 1. Insufficient geometric adaptability. The Cartesian coordinate system usually adopts a fixed X / Y / Z axis decomposition mode, which is difficult to effectively describe the geometric features of welds with complex curvatures. For example, when the weld presents a spatial helix or a variable curvature surface, the linear interpolation between discrete path points will cause sudden changes in the tangent direction of the weld trajectory, forcing the welding torch to start and stop frequently at the micro scale. In addition, the welding torch attitude (Roll-Pitch-Yaw angles) needs to be planned separately and decoupled from the position trajectory, resulting in difficulty in coordinating the continuity of the spatial movement and attitude movement of the end effector. According to statistics, such attitude mismatch problems will reduce the qualified rate of molten pool formation by 15%-30%. 2. Lack of dynamic compensation mechanism. The existing method optimizes the geometric path planning and process parameters in stages, and it is difficult to compensate in real time for the material deformation caused by the welding thermal process. Even if the thermal expansion amount is predicted through finite element simulation, due to the rigid structure of the Cartesian space trajectory, local correction can only perform translation / rotation compensation on discrete path points, and cannot achieve adaptive adjustment of curve curvature (such as gradient compensation along the normal direction of the weld). This directly leads to the accumulation of trajectory deviations during multi-layer welding, and may cause penetration or insufficient fusion, especially in thin plate welding. 3. Sub-optimal handling of kinematic constraints. The ideal path generated in Cartesian space often ignores physical constraints such as robot joint limits and torque limits. When performing the conversion from Cartesian to joint space, the inverse kinematics solver needs to complete the multi-solution screening within dozens of milliseconds, and often sacrifices path accuracy (such as minimizing joint displacement) or motion smoothness (such as acceleration step) to ensure real-time performance. And this process will cause about 5%-8% of trajectory distortion, which may cause the robotic arm to vibrate or even stall during high-speed welding.

[0004] For example, the patent document with the invention title of "A Welding Robot Path Planning Method" and the publication number of CN106557844A, which was published on April 5, 2017, records a welding robot path planning method based on clustering-guided multi-objective particle swarm optimization technology. This method is based on trajectory planning in Cartesian space; calculates the path length and motion energy consumption between the welding starting point and the welding ending point in the obstacle avoidance path, and performs double-objective path planning on the path length and the motion energy consumption through the clustering-guided multi-objective particle swarm optimization algorithm to obtain the optimized result of path planning. Although this method realizes the multi-objective optimization of the welding robot by using clustering guidance, it still cannot avoid the inherent defects of trajectory planning based on Cartesian space. Summary of the Invention

[0005] One of the purposes of the present invention is to provide a dynamic path planning method for a multi-axis collaborative welding robot to solve the problem in the prior art that the welding path cannot be adaptively adjusted according to the workpiece geometric parameters and welding process parameters.

[0006] The present invention is realized through the following technical solutions. A dynamic path planning method for a multi-axis collaborative welding robot includes the following steps: S100, collecting the basic data of the workpiece to be welded and constructing a welding basic database; S200, constructing a geometric model of the weld path according to the data in the welding basic database and parameterizing the geometric model of the weld path; S300, generating an initial trajectory between two adjacent weld segments of the welding path based on the parameterization result, and performing time parameterization on the initial trajectory to obtain a time-dependent time-parameterized screw trajectory; S400, constructing a screw mapping model based on inverse kinematics and screw theory to convert the time-parameterized screw trajectory into a target screw, and solving the angular velocity component of the target screw to solve the angles and speeds of each joint of the robot, thereby controlling the movement of the robot.

[0007] Furthermore, the basic data includes: the original geometric data of the welding workpiece, the welding process parameter data, and the welding sequence data. Among them, the original geometric data is the detailed three-dimensional point cloud data of the workpiece surface obtained by laser scanning, or the three-dimensional data of the workpiece surface shape obtained by using two or more cameras through image matching and depth calculation; the welding process parameters include: welding current, welding voltage, welding speed, welding shielding gas flow rate, material thermal expansion coefficient, and arc length; the welding sequence data is obtained by combining the original geometric data of the workpiece to be welded and the welding process parameters.

[0008] Furthermore, the geometric model is obtained by fitting point cloud data to obtain a B-spline curve, which represents the position on the welding path. Based on the fitted B-spline curve, the Frenet frame system and the initial screw are defined to realize the parameterization of the geometric model.

[0009] Furthermore, the Frenet frame system and the initial spinor are obtained through the following sub-steps: S210. The Frenet frame system consists of three parts: the tangent vector, the normal vector, and the binormal vector, which are used to describe the direction of the path, the inclination angle of the welding torch, and the oscillation plane of the path, respectively. The tangent vector, representing the direction of the welding path, is obtained by calculating its first derivative at each point of the B-spline curve. The normal vector is a vector perpendicular to the tangent vector, reflecting the inclination angle of the welding torch, and is obtained by differentiating the tangent vector and normalizing the calculation. The binormal vector is the cross product of the tangent vector and the normal vector, defining the reference of the oscillation plane of the path. The Frenet frame system of the welding path is integrated as {T, N, B}. S220. The initial spinor describes the translational and rotational movements of the welding torch during the welding process and consists of a rotational part and a translational part: The rotational part is controlled by the normal vector, and the magnitude of the rotational part is related to the weld curvature ; The translational part is used to describe the movement of the welding torch along the welding path. The translational speed is the product of the welding speed and the tangent vector, and also includes a component of the helix pitch, which is a parameter related to the welding speed and the inclination angle of the welding torch .

[0010] Furthermore, the tangent vector can be calculated by the following formula:

[0011] , where is the derivative of the path curve at the path point , is the norm (or modulus) of the derivative of the path curve at the path point , reflecting the magnitude of the derivative vector and ensuring the normalization of the tangent vector.

[0012] Furthermore, the normal vector can be calculated by the following formula:

[0013] , where is the derivative of the tangent vector, is the norm of the derivative of the tangent vector.

[0014] Furthermore, the binormal vector can be expressed by the following formula: .

[0015] Furthermore, the rotational part can be dynamically adjusted by the following formula: , where , is the coefficient dynamically adjusted according to the weld curvature . The greater the weld curvature, the greater the rotational angular velocity of the welding torch.

[0016] Furthermore, the translational part can be calculated by the following formula:

[0017] , where ,

[0018] Here is the target inclination angle of the weld normal direction, is to control the helical trajectory of the welding torch along the welding path, is the component of the helix pitch.

[0019] Furthermore, the initial trajectory is generated through the following sub-steps: S310. The starting and ending positions of each path segment are described by the SE(3) transformation matrix, denoted as and , respectively representing the rigid body transformation from the starting point to the ending point. Based on the helical linear interpolation and combined with the B-spline curve fitted through the point cloud data, a smooth transition is generated between adjacent path segments to obtain the first initial trajectory; S320. Add a periodic small-amplitude perturbation to the first initial trajectory to simulate the swinging behavior during the welding process. Using the first initial trajectory as the basic forward trajectory of the robot, the perturbation is superimposed on this trajectory to obtain the final initial trajectory. The superimposed perturbation is realized through the periodic screw superposition and is used for a slight periodic swing on the first initial trajectory to simulate the physical vibration effect during the welding process.

[0020] Furthermore, the first initial trajectory can be calculated by the following formula:

[0021] , where is the rigid body transformation matrix at the path point S defined by the helical linear interpolation, is the rigid body transformation matrix of the starting point. This homogeneous transformation matrix is used to represent the rigid body transformation under the weld segment , and this homogeneous transformation matrix is obtained through the exponential mapping (the conversion from the Lie group to the Lie algebra); , is the screw corresponding to the weld segment , representing the rotation and displacement information of this segment. This screw contains the position and orientation of the robot in the welding path; is the natural exponential function, represents the logarithmic mapping (Lie algebra) between the homogeneous transformation matrix and the homogeneous transformation matrix of the next welding segment, that is, the infinitesimal transformation between the two is obtained, which is realized by calculating their relative transformation; is the inverse matrix of the starting point rigid body transformation matrix, is the rigid body transformation matrix of the ending point. By performing the logarithmic mapping on the combination of these two matrices, the intermediate infinitesimal transformation can be obtained; is the path point parameter, which represents the distance from the weld segment to The transition progress, represents the value of the path point parameter within the interval [0, 1].

[0022] Furthermore, the final initial trajectory can be calculated by the following formula:

[0023] , where is the final trajectory; is the basic forward trajectory of the robot, that is, the trajectory along which the robot advances along the welding path, including the screw part of the robot's movement along the X-axis, describing the basic trajectory of the robot's advancement; is the amplitude of the swing perturbation, used to adjust the intensity of the perturbation; is the sine, is the frequency of the perturbation, determining the period of the perturbation, is the time, , indicating the periodic change of the perturbation over time. This term controls the magnitude and period of the perturbation, making the movement of the end of the welding torch along the welding path not only have a smooth advancement but also be accompanied by a periodic swing; is the swing trajectory of the end of the robot. It is a periodic perturbation around the binormal B-axis, indicating that the specific perturbation is along the B-axis direction, representing the periodic swing of the welding torch during the welding process.

[0024] Furthermore, the dynamic path planning method may further include step S500, an optimization step. This optimization step generates an optimized time-parametrized screw trajectory through an attitude-path coupling optimization model to improve the quality of the time-parametrized screw trajectory. The attitude-path coupling optimization model includes an objective function and constraint conditions. The objective function is used to describe the objective to be optimized, and the best robot trajectory is obtained by minimizing this objective function; the constraint conditions are used to meet physical limitations.

[0025] Furthermore, the objective function includes: a penetration tracking term for ensuring that the robot maintains a constant penetration depth on the path; a spatter suppression term for controlling the droplet detachment speed and avoiding a high spatter rate; and a joint smoothness term for ensuring the smoothness of the robot's movement and avoiding sharp acceleration or speed changes.

[0026] Furthermore, the objective function can be expressed by the following formula:

[0027]

[0028] where is the path-parametrized trajectory, obtained by converting the time-parametrized trajectory; is the penetration control weight coefficient, which is used to represent the degree of emphasis on penetration control in the objective function. Through this coefficient, the relative influence of penetration error can be adjusted. The greater the weight, the more important the penetration tracking error is; is the helical pitch at any point s on the path. During the welding process, the helical pitch directly affects the penetration depth and is usually closely related to the welding speed. It will vary with different positions on the path, representing the motion characteristics of the multi-axis collaborative robot at this point; is the target penetration value, which is the penetration reference value that the multi-axis collaborative robot is expected to maintain throughout the path. This reference value is usually set based on welding requirements to ensure the weld quality; is the spatter suppression weight coefficient, which is used to represent the degree of emphasis on spatter suppression. By adjusting the value of this coefficient, the importance of spatter suppression in the objective function can be controlled; is the droplet detachment speed. Droplets are the liquid metal that falls from the molten pool during the welding process. Excessive droplet detachment speed will cause spatter and affect the welding quality. The droplet detachment speed is a quantity dynamically related to the welding process and is usually calculated by a spatter mechanics model to ensure that there is no excessive spatter; is the joint smoothness weight coefficient, which is used to control the importance of joint smoothness in the objective function. By adjusting this weight, the influence of joint acceleration on the optimization result can be affected; is the screw Jacobian matrix, which is used to describe the relationship between trajectory changes and robot joint accelerations. Specifically, let be the pose trajectory (position and orientation) of the robot end effector, then connects the relationship between the end effector velocity and the joint velocity, and the inverse of this matrix represents the relationship between the end effector velocity and the joint acceleration; is the acceleration of the robot joint, representing the rate of change of the joint motion.

[0029] Furthermore, the constraint conditions include: joint limit constraints for controlling the range of the robot joints to ensure that the robot's motion does not exceed its physical limits; torque limit constraints for ensuring that the robot does not exceed its torque limit to avoid damaging mechanical components or affecting motion stability; weld tracking accuracy constraints for ensuring that the robot end effector always follows the path and the deviation does not exceed the allowed maximum error.

[0030] Furthermore, the joint limit constraints can be expressed by the following formula:

[0031] , where is the angle or position of the i-th joint. In the multi-axis collaborative motion robot in this embodiment, it is a common industrial six-axis collaborative motion robot, so ; is the minimum angle or position of the i-th joint, is the maximum angle or position of the i-th joint.

[0032] Furthermore, it can be expressed by the following formula:

[0033] , where is the torque of the joint, is the torque of the i-th joint, is the maximum allowable torque of the i-th joint, is the inertia matrix, representing the inertial characteristics of the joint, is the Coriolis force matrix, representing the interaction force between joints, is the gravity term, representing the torque generated by the robot due to gravity.

[0034] Furthermore, it can be expressed by the following formula:

[0035] , where is the rigid body transformation matrix at the path point S, is the origin of the local coordinate system of the robot end effector, is the target weld position at the path point S, is the maximum allowable tracking error, ensuring that the robot end effector always tracks the weld path, and the error does not exceed this threshold.

[0036] On the other hand, the present invention provides a multi-axis collaborative welding robot dynamic path planning system, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, it implements the multi-axis collaborative welding robot dynamic path planning method as described in any one of the above.

[0037] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0038] Through the geometric eigenproperty advantages of the complex space, the present invention fundamentally solves the inherent defects of motion-process decoupling and insufficient dynamic compensation in traditional Cartesian space planning, and provides a new theoretical framework for intelligent welding of high-complexity workpieces. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, form a part of this application, and do not limit the embodiments of the present invention. In the drawings:

[0040] Figure 1 is the flowchart of the method provided in Embodiment 1 of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0041] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Generally, the components of the embodiments of the present invention described and illustrated in the accompanying drawings here can be arranged and designed in various different configurations.

[0042] Embodiment 1

[0043] This embodiment discloses a dynamic path planning method for a multi-axis collaborative welding robot. The dynamic path planning method disclosed in this embodiment abandons the traditional Cartesian space planning paradigm and innovatively adopts a complex space trajectory generation method based on screw theory, achieving a generational breakthrough in Cartesian methods. In this embodiment, the weld path is parameterized as a B-spline curve with differentiable curvature based on the Frenet frame, and the position and attitude changes of the end effector are uniformly described by the rotation component and translation component of the screw, so that the tangent vector (T) naturally corresponds to the main welding movement direction, and the normal vector (N) and the binormal vector (B) form an orthogonal plane for screw rotation, enabling the adjustment of the welding torch inclination (along the N direction) and the swing direction (along the B direction) to be directly realized through the rotation component of the screw. Compared with the decoupled expression of "position + Euler angle" in the Cartesian coordinate system, the complex space model of the present invention integrates six-degree-of-freedom motion into a single coupled operation of rotation and translation, avoiding the geometric singularity of attitude jumps. In the complex space, local deformations caused by material thermal expansion can be smoothed and corrected for the curvature of the screw trajectory through helical linear interpolation. Specifically, the curvature radius of the tangent vector of the Frenet frame can be adjusted in real time with the thermal expansion coefficient as the input, so that the trajectory curvature adaptively compensates for the normal component of the thermal deformation. By defining the basic motion screw and the perturbation screw in the screw space, the swing motion is expressed as a composite screw motion in the time domain. Due to the exponential product property of the screw (the closure property of the SE(3) group), the superposition of the swing and the main motion can ensure the differential smoothness of the motion trajectory without additional coordinate transformation, while avoiding energy loss during joint space calculation. This embodiment converts the multi-dimensional constraint optimization problem of the complex space trajectory into a linear programming problem in Lie algebra through screw mapping, which can effectively improve the solution efficiency compared with the non-linear programming in the Cartesian space. For example, for a common industrial six-axis robot, the Paden-Kahan subproblem decomposition algorithm can be used, and by using the geometric meaning of the screw exponential product, the complex inverse kinematics calculation can be converted into an explicit algebraic operation of the rotation axis, thereby significantly reducing the computational complexity.

[0044] Figure 1 The flowchart of the method in this embodiment is shown. It can be seen from the figure that this embodiment includes the following steps: Embodiment

[0045] Step 1: Collect data such as the original geometry, welding process parameters, and welding sequence of the workpieces to be welded, and integrate the data to construct a welding basic database.

[0046] Specifically, detailed three-dimensional point cloud data of the workpiece surface is obtained through laser scanning, so as to accurately capture the geometric shape and surface details of the workpiece. Or two or more cameras can be used to obtain three-dimensional data of the workpiece surface shape through image matching and depth calculation. Thus, the original geometric data of the workpieces to be welded is collected.

[0047] Welding process parameters directly affect the welding quality and the stability of the process. Therefore, they need to be fully considered during the path planning process. By constructing a preset welding process parameter database, the welding process parameters of workpieces with different materials and different original geometric shapes are stored. At least the following should be included in this database: Current (I): The welding current affects the welding heat input and welding speed. Different welding tasks require different current values to ensure the weld quality. Voltage (U): The welding voltage usually determines the stability of the arc and the welding depth. Too high or too low voltage will affect the welding quality, especially the stability of the arc. Welding speed (v): The welding speed determines the distribution of the welding heat input. Too fast a speed may result in an insecure weld, while too slow a speed may lead to overheating and material deformation. Welding gas flow rate: The protective gas flow rate is crucial for the protection during the welding process. Usually, the gas flow rate needs to be adjusted according to different welding materials and processes. Arc length: The arc length has a direct impact on the welding quality. A long arc may cause unstable welding, while a short arc may make the welding temperature too high. The coefficient of thermal expansion of the workpiece material. Different coefficients of thermal expansion of different materials will affect the specific welding path. Therefore, the welding path needs to be compensated by the coefficient of thermal expansion. During path planning, these process parameters need to be comprehensively considered and matched with specific welding tasks and factors such as the material and thickness of the workpiece.

[0048] Combined with the original geometric data and welding process parameters of the workpieces to be welded, determine the welding sequence. The planning of the welding sequence is closely related to the geometric features of the workpiece. A reasonable welding sequence not only helps to ensure the welding quality but also can avoid workpiece deformation caused by uneven thermal stress. Specifically, for complex workpieces, the welding sequence needs to specially consider the geometric features of the workpiece (for example: weld the convex parts first and the concave parts later to prevent deformation caused by uneven thermal expansion).

[0049] By analyzing the original geometry of the workpieces to be welded and the welding area, and comprehensively considering the welding process parameters, the welding sequence is planned. At the same time, the heat input should be evenly distributed as much as possible to reduce the residual stress generated during the welding process. For some areas that are difficult to access, welding can be considered first to ensure that the multi-axis collaborative robot can operate smoothly. On workpieces with different thicknesses, the welding sequence can be optimized according to the thickness change. For example, welding of thick parts can be carried out later to prevent deformation of thin-walled parts due to heat concentration during the welding process.

[0050] Integrate the original geometric data of the workpieces to be welded, welding process parameters, and welding sequence to construct a basic welding database, providing accurate workpiece information for the path planning algorithm. These data will help the robot generate the optimal welding path to ensure the maximization of welding quality and efficiency.

[0051] Step 2: In the planning of the welding path of the multi-axis collaborative robot, constructing an accurate geometric model of the weld path and accurate parameterization of the weld geometric model are the keys to ensuring a smooth and precise welding process. In this step, through a mathematical model based on the Frenet frame, the geometric characteristics of the weld path are constructed and the corresponding screw is defined to achieve accurate parameterization of the weld geometric model, so as to perform precise adjustment and control during subsequent path control and welding execution.

[0052] In this step, point cloud data, material thermal expansion coefficient, and welding speed need to be extracted from the basic welding database for weld geometric parameterization. The point cloud data comes from the original geometric data of the workpiece collected in Step 1. Considering the thermal expansion characteristics of the material, during the welding process, the thermal expansion of the material may affect the geometry of the welding path, so the thermal expansion coefficient is required for compensation. Welding speed: The welding speed is a key parameter in the welding process, affecting the shape of the molten pool and the quality of the weld.

[0053] In this embodiment, in order to construct the geometric model of the weld path, a B-spline curve can be obtained by fitting the point cloud data , representing the position on the welding path. Based on the fitted B-spline curve, we can define the Frenet frame system and the initial screw. The specific sub-steps are as follows:

[0054] 1) The Frenet frame system consists of a tangent vector, a normal vector, and a binormal vector, which are used to describe the direction of the path, the inclination angle of the welding torch, and the oscillation plane of the path, respectively.

[0055] Tangent vector T (welding direction): The tangent vector represents the direction of the welding path and is obtained by calculating its first derivative at each point on the curve. In this embodiment, the tangent vector can be calculated by the following formula:

[0056] ,

[0057] wherein, is the derivative of the path curve at the path point . is the norm (or modulus) of the derivative of the path curve at the path point , reflecting the magnitude of the derivative vector and ensuring the unitization of the tangent vector.

[0058] Normal vector N (indicating the inclination angle of the welding torch): The normal vector is a vector perpendicular to the tangent vector, reflecting the inclination angle of the welding torch, and can be obtained by differentiating the tangent vector T and unitizing the result. In this embodiment, the normal vector can be calculated by the following formula:

[0059] ,

[0060] wherein, is the derivative of the tangent vector, is the norm of the derivative of the tangent vector.

[0061] Binormal vector B (reference for the oscillation plane): The binormal vector is the cross product of the tangent vector and the normal vector, defining the reference for the oscillation plane of the path. In this embodiment, the binormal vector can be expressed by the following formula:

[0062] .

[0063] The Frenet frame system {T, N, B} of the welding path is obtained by integration.

[0064] 2) Construct the initial screw , and the initial screw describes the translational and rotational motions of the welding torch during the welding process. It consists of two parts:

[0065] Rotational part , and the rotational part of the screw is controlled by the normal vector N. Specifically, the magnitude of the rotational part is related to the weld curvature . In this embodiment, it can be dynamically adjusted by the following formula:

[0066] , wherein, , is the coefficient dynamically adjusted according to the weld curvature . The greater the weld curvature, the greater the rotational angular velocity of the welding torch.

[0067] Translational part , and the translational part is used to describe the motion of the welding torch along the welding path. The translational speed is the product of the welding speed and the tangent vector T, and also includes the component of the helix pitch , and the helix pitch is related to the welding speed and the inclination angle of the welding torch The relevant parameters. In this embodiment, the translation part can be calculated by the following formula:

[0068] ,

[0069] where, ,

[0070] Here, is the target inclination angle of the weld normal, is to control the helical trajectory of the welding torch along the welding path.

[0071] Step 3: Based on the Frenet frame system of the welding path, combined with helical linear interpolation to realize the logarithmic and exponential mappings of Lie groups and Lie algebras, and generate an initial trajectory between two adjacent weld segments of the welding path.

[0072] At the same time, in order to ensure that the generated final path adapts to the specific workpiece structure, by introducing process constraints, the basic forward trajectory is combined with periodic perturbations (such as a swinging trajectory), so that the movement of the end of the welding torch includes both smooth forward movement and periodic perturbations, in order to meet the process requirements during welding.

[0073] Thus, the finally generated path is not just a straight path, but a trajectory that includes process perturbations and periodic actions, making the welding process more precise and meeting the requirements.

[0074] Specifically, it can include the following sub-steps:

[0075] 1) Smoothly generate a first initial trajectory for the transition between adjacent path segments through helical linear interpolation to ensure that the robot moves smoothly along the welding path.

[0076] Describe the starting and ending positions of each path segment by the SE(3) transformation matrix, denoted as and , which respectively represent the rigid body transformation from the starting point to the ending point. Based on helical linear interpolation and combined with the B-spline curve fitted by point cloud data, a smooth transition is generated between adjacent path segments to obtain the first initial trajectory.

[0077] In this embodiment, the initial trajectory is generated by helical linear interpolation. The helical linear interpolation can be calculated by the following formula:

[0078] ,

[0079] where, is the rigid body transformation matrix at the path point S defined by helical linear interpolation, is the rigid body transformation matrix of the starting point. This homogeneous transformation matrix is used to represent at the weld segment The rigid body transformation below is obtained through the exponential mapping (the conversion from Lie group to Lie algebra) of the homogeneous transformation matrix; , is the weld segment The corresponding twist represents the rotation and displacement information of this segment. This twist contains the position and orientation of the robot in the welding path.

[0080] is the natural exponential function, represents the logarithmic mapping (Lie algebra) from the homogeneous transformation matrix to the homogeneous transformation matrix of the next welding segment, that is, obtaining the infinitesimal transformation between the two, which is achieved by calculating their relative transformation; is the inverse matrix of the starting rigid body transformation matrix, is the rigid body transformation matrix of the end point. By performing the logarithmic mapping on the combination of these two matrices, the intermediate infinitesimal transformation can be obtained; is the path point parameter, which represents the transition progress from the weld segment to in this formula, represents the value range of the path point parameter between [0, 1].

[0081] It should be noted that the screw linear interpolation is used to smoothly generate the transition between adjacent path segments to ensure that the end of the robot's welding torch moves smoothly along the welding path. It is based on the B-spline path and is used to generate continuous transformations between points on the path. Specifically, by enabling the robot to smoothly transition from the weld segment to These two path segments can be represented by the transformation matrices and Through the screw linear interpolation, that is, and are the SE(3) transformation matrices representing the starting point and the end point of the path segment, and each transformation matrix includes the information of rotation and translation. In the formula disclosed in this embodiment, and respectively represent the exponential and logarithmic mappings for converting between the Lie group (SE(3)) and the Lie algebra; through the difference between the transformations (i.e., the difference in rotation and translation) can be obtained, and through a smooth trajectory can be generated. Finally, the trajectory of the end of the robot's welding torch smoothly transitions between each adjacent path segment, which makes the translation and rotation of the trajectory in space not change suddenly. The result of the interpolation is usually a transformation matrix in the SE(3) space, which is used to describe the position and orientation of the robot.

[0082] 2) After obtaining the first initial trajectory, add small periodic perturbations to the first initial trajectory to simulate the swinging behavior during the welding process. Use the first initial trajectory as the basic forward trajectory of the robot, and superimpose the perturbations on this trajectory to obtain the final trajectory, thereby simulating the small periodic swinging during the welding process and enhancing the welding quality.

[0083] In this embodiment, the final initial trajectory can be calculated by the following formula:

[0084] ,

[0085] where, is the final trajectory; is the basic forward trajectory of the robot, that is, the trajectory along which the robot advances along the welding path, including the screw part of the robot's movement along the X-axis, describing the basic trajectory of the robot's advance; is the amplitude of the swinging perturbation, used to adjust the intensity of the perturbation; is the sine, is the frequency of the perturbation, which determines the period of the perturbation, is the time, , indicating the periodic change of the perturbation over time. This term controls the magnitude and period of the perturbation, so that the movement of the end of the welding torch along the welding path not only has a smooth advance, but also is accompanied by periodic swinging; is the swinging trajectory of the robot end, which is a periodic perturbation around the binormal B-axis, indicating that the specific perturbation is along the B-axis direction, representing the periodic swinging of the welding torch during the welding process.

[0086] It should be noted that during the actual welding process, in addition to advancing along a smooth trajectory, the robot also needs to incorporate process requirements. By adding process perturbations to the robot, the swinging or vibration during the welding process is simulated, making the welding quality more uniform. The swinging perturbation is achieved through the superposition of periodic screws. Through such superposition, the robot will not only advance along the basic trajectory, but also perform slight periodic swinging on the trajectory, simulating the physical vibration effect during the welding process.

[0087] 3) Perform time parameterization on the generated final trajectory to obtain a time-dependent time-parameterized screw trajectory , which describes how the robot smoothly advances from the starting point to the ending point during the entire welding process so that the robot can move smoothly along the trajectory according to the time sequence.

[0088] It should be noted that the finally obtained time - parameterized spinor trajectory not only needs to meet the requirements of smooth advancement, but also needs to consider the periodic disturbances of the process. During the generation of the time - parameterized spinor trajectory, the two parts of helical linear interpolation and spinor superposition of the weaving process complement each other: helical linear interpolation ensures smooth transitions between different path segments, providing a basic trajectory for the time - parameterized spinor trajectory, that is, the robot travels smoothly along the welding path. The spinor superposition of the weaving process then perturbs periodically on this basic trajectory, simulating the periodic actions (such as weaving) required during the welding process and increasing the complexity and details of the trajectory.

[0089] Step 4: Through Step 3, a time - parameterized spinor trajectory in the complex space is finally obtained. This time - parameterized spinor trajectory is generated based on the basic workpiece structure and dynamic constraints. This trajectory can provide a preliminary path planning for the multi - axis collaborative motion robot, but it cannot fully meet all the precise requirements during the welding process, such as the control of penetration depth, the suppression of spatter, and the smoothness of joints.

[0090] In order to make the final trajectory fully meet all the precise requirements during the welding process, in this embodiment, through the attitude - path coupling optimization model, the trajectory quality is further improved, and finally an optimized time - parameterized spinor trajectory is generated to meet the specific requirements during the welding process.

[0091] In this embodiment, the attitude - path coupling optimization model includes an objective function and constraint conditions.

[0092] Specifically, the objective function is the core of the entire attitude - path coupling optimization model, used to describe the objective to be optimized, and the best robot trajectory is obtained by minimizing this objective function.

[0093] In this embodiment, the objective function can include three parts: 1. The penetration - depth tracking term for ensuring that the robot maintains a constant penetration depth on the path; 2. The spatter - suppression term for controlling the droplet detachment speed and avoiding a high spatter rate; 3. The joint - smoothness term for ensuring the smoothness of the robot motion and avoiding sharp acceleration or speed changes. In this embodiment, the objective function can be expressed by the following formula:

[0094]

[0095] Among them, is the path - parameterized trajectory, obtained by converting the time - parameterized trajectory; is the penetration - depth control weight coefficient, used to represent the degree of emphasis on penetration - depth control in the objective function. Through this coefficient, the relative influence of the penetration - depth error can be adjusted. The greater the weight, the more important the penetration - depth tracking error is; is the helix pitch at any point s on the path. During the welding process, the helix pitch directly affects the penetration depth and is usually closely related to the welding speed. It will vary with different positions on the path, indicating the motion characteristics of the multi-axis collaborative robot at that point. is the target penetration depth value, which is the reference penetration depth value that the multi-axis collaborative robot is expected to maintain throughout the path. This reference value is usually set based on welding requirements to ensure the weld quality.

[0096] is the splash suppression weight coefficient, which is used to represent the degree of emphasis on splash suppression. By adjusting the value of this coefficient, the importance of splash suppression in the objective function can be controlled. is the droplet detachment speed. Droplets are the liquid metal that falls from the molten pool during the welding process. Excessive droplet detachment speed will cause splashes and affect the welding quality. The droplet detachment speed is a quantity dynamically related to the welding process and is usually calculated by a splash mechanics model to ensure that there are no excessive splashes. In this embodiment, it can be calculated by the following formula:

[0097] ,

[0098] where, is the dynamic coupling coefficient, which can be obtained by experimental calibration for welding materials of different materials.

[0099] is the arc force, which describes the pulling force of the arc on the droplet. is the distance from the welding point to the welding torch. is the critical detachment speed, which is the maximum speed at which the droplet remains stable and depends on the surface tension, density, and droplet radius of welding materials of different materials. It can usually be obtained by experimental calibration.

[0100] is the joint smoothness weight coefficient, which is used to control the importance of joint smoothness in the objective function. By adjusting this weight, the influence of joint acceleration on the optimization result can be affected. is the screw Jacobian matrix, which is used to describe the relationship between the trajectory change and the robot joint acceleration. Specifically, let be the pose trajectory (position and orientation) of the robot end effector, then connects the relationship between the end effector speed and the joint speed, and the inverse of this matrix represents the relationship between the end effector speed and the joint acceleration. is the acceleration of the robot joint, which represents the rate of change of the joint motion.

[0101] It should be noted that, is the penetration depth tracking term, is the square difference between the helical pitch and the target penetration depth, which is used to measure the error between the actual penetration depth and the target penetration depth. Minimizing this value helps maintain the stability of the penetration depth, thereby improving the welding quality. is the splash suppression term, is the square of the droplet detachment velocity, which measures the magnitude of the droplet detachment velocity. By minimizing this term, splash is suppressed, ensuring stable droplet detachment and thus improving the welding quality. is the joint smoothness term, is the magnitude of the robot joint acceleration. By minimizing this value, the robot's motion is ensured to be smooth, avoiding excessive joint acceleration, ensuring that the robot can operate stably during welding, and reducing wear or overload of mechanical components.

[0102] In this embodiment, the following constraint conditions may be included:

[0103] is used to control the range of the robot joints, ensuring the joint limit constraint that the robot's motion does not exceed its physical limits. In this embodiment, the joint limit constraint can be expressed by the following formula:

[0104] ,

[0105] where, is the angle or position of the i-th joint. In the multi-axis coordinated motion robot in this embodiment, it is a common industrial six-axis coordinated motion robot, so ; is the minimum angle or position of the i-th joint, is the maximum angle or position of the i-th joint.

[0106] is used to ensure that the robot does not exceed its torque limit, avoiding damage to mechanical components or affecting the motion stability, the torque limit constraint. In this embodiment, the torque limit constraint can be expressed by the following formula:

[0107] ,

[0108] where, is the torque of the joint, is the torque of the i-th joint, is the maximum allowable torque of the i-th joint, is the inertia matrix, representing the inertial characteristics of the joint, is the Coriolis force matrix, representing the interaction forces between joints, is the gravity term, representing the torque generated by the robot due to gravity.

[0109] The weld tracking accuracy constraint is used to ensure that the robot end effector (TCP) always follows the path and the deviation does not exceed the maximum allowable error. In this embodiment, the weld tracking accuracy constraint can be expressed by the following formula:

[0110] ,

[0111] where, is the rigid body transformation matrix at the path point S, is the origin of the local coordinate system of the robot end effector, is the target weld position at the path point S, is the maximum allowable tracking error, ensuring that the robot end effector always tracks the weld path and the error does not exceed this threshold.

[0112] It should be noted that through the pose-path coupling optimization model in this step, the time-parameterized screw trajectory is further optimized to ensure that the time-parameterized screw trajectory can meet these more refined and specific welding requirements. Avoid problems such as uneven penetration and decreased welding quality caused by trajectory errors during welding. The pose-path coupling optimization model can optimize the dynamic characteristics during welding. For example, by adjusting the robot joint acceleration, it ensures a smooth trajectory and avoids excessive vibration or unstable movement during welding, which may affect the welding quality and even damage the robot. Suppress spatter and droplet detachment, control the detachment speed of droplets, reduce spatter, and avoid metal splashing to places where it should not splash during welding, thus affecting the quality of the welded joint. By being able to meet physical and engineering limitations, for example, ensuring that the motion range and torque limitations of each robot joint are not violated, avoiding the situation where joints exceed physical limitations during welding. Through the pose-path coupling optimization model, not only the geometric shape of the trajectory is optimized to better track the target weld path, but also fine control of dynamic smoothness, welding quality, etc. is added on this basis. In this way, the final trajectory can better meet the specific requirements during welding while meeting physical limitations.

[0113] Step 5: An optimized time-parameterized screw trajectory is obtained through the optimization step in Step 4. This trajectory is a smooth and constraint-satisfying trajectory, representing the spatial state of the robot end effector at each moment. Through this trajectory, the target state of the robot end at each moment during welding can be known.

[0114] However, in the actual operation process, the control system of the industrial robot usually only understands the commands in the joint space. Therefore, it is necessary to convert the time-parameterized screw trajectory into joint angles to drive the robot to move. Through the mapping relationship from screw to joint angles, the optimized screw trajectory is converted into the joint space commands (i.e., the angles of the robot joints) of the multi-axis collaborative robot.

[0115] In this embodiment, the screw mapping model constructed based on inverse kinematics and screw theory is used to convert the optimized time-parameterized screw trajectory obtained in step 4 (i.e., ) into the angles and speeds of each joint of the robot, so as to be able to control the movement of the robot. Specifically, it includes the following sub-steps:

[0116] 1) The optimized time-parameterized screw trajectory contains the position, attitude, linear velocity, and angular velocity of the end effector at each moment. This screw trajectory reflects the motion state of the end effector (such as a welding gun) of the robot.

[0117] 2) First, through the screw mapping model, this screw trajectory is converted into joint angle commands through the calculation of inverse kinematics. In this embodiment, the screw mapping model can be expressed by the following formula:

[0118] ,

[0119] where is the logarithmic mapping, is the natural constant, is the intrinsic screw of each joint of the multi-axis collaborative robot, which is pre-calibrated according to different types of robot structures. These screws represent the kinematic parameters of this type of multi-axis collaborative robot; is the angle of the joint, representing the actual position of each joint of the robot; is the target screw, representing the expected attitude of the robot end effector.

[0120] It should be noted that a screw is a mathematical object that describes spatial position and attitude (including translation and rotation). A screw is a 6D vector, which consists of a 3D angular velocity (describing rotation) and a 3D linear velocity (describing translation). It is a bridge between Lie groups and Lie algebras and can effectively express the translation and rotation in space, while the intrinsic screw is the screw corresponding to each joint of the robot. The screw of each joint contains the displacement information and rotation information of the joint in space. The angle of each joint is the target to be calculated. In the inverse kinematics solution, by solving the screw trajectory, we obtain the angles of each joint, and these angle commands ultimately drive the movement of the robot is the angle of the i-th joint, which describes the rotation state of the robot joint. The twist represents the rotation state of a joint at a certain moment through the exponential map ( ). Specifically, is the exponential map of the twist, which is used to convert the displacement and rotation represented by the twist into the rotation matrix or displacement of the joint, and is used to represent the combined effect of the rotation and displacement described by the twist. This map helps to describe the motion state of the robot joint through the twist and control the rotation of each joint through the angle. The logarithmic map ( ) is a key step in the inverse kinematics of the twist. It converts the twist into an element of the Lie algebra. Through the logarithmic map, we can convert the composite trajectory composed of the exponential maps of multiple twists ( ) into the representation of the robot joint angles, and finally obtain the target twist that the end effector of the robot is expected to reach. The target twist includes the target position and target attitude of the end effector, that is, the spatial displacement and rotation of the end effector. The target twist is the final target that the end effector of the robot is desired to reach, and it provides a reference for calculating the angles of each joint.

[0121] In addition, it should be noted that: in this embodiment, a 6-axis industrial robot is exemplified. Therefore, the product symbol represents the product of the exponential maps of the twists from the first joint to the sixth joint of the industrial six-axis collaborative robot. Those skilled in the art should know that the collaborative robot in this embodiment is not limited to the 6-axis collaborative robot. The solution provided in this application is universal, and those skilled in the art can adjust the joints according to the actual situation. The formulas in this embodiment are only used for illustration.

[0122] 3) Finally, solve the angular velocity component of the target twist to solve the angle of each joint. This step can select existing algorithms to solve the angular velocity component in the twist space and solve the joint angles of the robot through these components.

[0123] In this embodiment, considering that it is a 6-axis collaborative robot, the Paden-Kahan subproblem decomposition algorithm is used to convert the target twist into the corresponding joint angles. This algorithm can effectively solve the joint angles of a 6-degree-of-freedom robot.

[0124] The specific embodiments described above further elaborate on the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only the specific embodiments of the present invention and is not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A dynamic path planning method for a multi-axis collaborative welding robot, characterized in that: The dynamic path planning method comprises: S100, collecting basic data of the welded workpiece and building a welding basic database; S200, constructing a geometric model of a weld path according to data in a welding basic database, and parameterizing the geometric model of the weld path; S300, based on the parameterization result, generating an initial trajectory between two adjacent weld segments of the welding path, and performing time parameterization on the initial trajectory to obtain a time-dependent time-parameterized screw trajectory; S400, constructing a spinor mapping model based on inverse kinematics and spinor theory to convert the time parameterized spinor trajectory into a target spinor, and solving the angular velocity component of the target spinor to solve the angle and velocity of each joint of the robot.

2. The multi-axis collaborative welding robot dynamic path planning method according to claim 1, characterized in that: The basic data includes: original geometric data of the welding workpiece, welding process parameter data and welding sequence data, wherein: The original geometric data is the detailed three-dimensional point cloud data of the workpiece surface obtained by laser scanning. Or use two or more cameras to obtain three-dimensional data of the workpiece surface shape through image matching and depth estimation; The welding process parameters include: welding current, welding voltage, welding speed, welding shielding gas flow rate, material thermal expansion coefficient and arc length; The welding sequence data is obtained by combining the original geometric data of the welded workpieces and the welding process parameters.

3. The multi-axis collaborative welding robot dynamic path planning method according to claim 1, characterized in that: The geometric model is fitted with point cloud data to obtain a B-spline curve, which represents the position on the welding path. Based on the fitted B-spline curve, the Frenet frame system and initial spinor are defined to realize the parameterization of the geometric model.

4. The multi-axis collaborative welding robot dynamic path planning method according to claim 3, characterized in that: The Frenet frame system and the initial spinor are obtained by the following sub-steps: S210, Frenet frame system consists of three parts: tangent vector, normal vector and binormal, which are used to describe the direction of the path, the inclination angle of the welding gun and the swing plane of the path respectively; The tangent vector, representing the direction of the welding path, is obtained by calculating the first-order derivative at each point of the B-spline curve; The normal vector is a vector perpendicular to the tangent vector, reflects the inclination angle of the welding gun, and is obtained by differentiating the tangent vector and normalizing it; The binormal is the cross product of the tangent vector and the normal vector, defining the swing plane reference of the path; S220, initial rotation describes the translation and rotation movement of the welding gun during welding, which consists of a rotation part and a translation part: The rotation part is controlled by the normal vector, and the size of the rotation part is related to the curvature of the weld; The translation part is used to describe the movement of the welding gun along the welding path. The translation speed is the product of the welding speed and the tangent vector. It also includes the component of the helical pitch, which is related to the welding speed and the inclination angle of the welding gun. Related parameters.

5. The multi-axis collaborative welding robot dynamic path planning method according to claim 1, characterized in that: The initial trajectory is generated by the following sub-steps: S310, describe the starting and ending positions of each path segment by SE (3) transformation matrix, denoted as and , respectively represent the rigid body transformation from the starting point to the end point, based on the spiral linear interpolation combined with the B-spline curve obtained by fitting the point cloud data, a smooth transition is generated between adjacent path segments to obtain the first initial trajectory; S320, adding periodic small-amplitude disturbances to the first initial trajectory to simulate the swinging behavior during the welding process, taking the first initial trajectory as the basic forward trajectory of the robot, superimposing the disturbance on the trajectory, and thus obtaining the final initial trajectory.

6. The multi-axis collaborative welding robot dynamic path planning method according to claim 1, characterized in that: The spinor mapping model is: ， in, is a logarithmic mapping, is a natural constant, is the intrinsic rotation of each joint of the multi-axis cooperative motion robot, and n is the number of joints of the multi-axis cooperative motion robot; is the angle of the joint, is the target spinor.

7. The multi-axis collaborative welding robot dynamic path planning method according to claim 1, characterized in that: The dynamic path planning method may further include step S500, an optimization step, wherein the optimization step generates an optimized time parameterized spinor trajectory through a posture-path coupling optimization model to improve the quality of the time parameterized spinor trajectory. The posture-path coupling optimization model includes an objective function and constraints. The objective function is used to describe the goal that you want to optimize, and the best robot trajectory is obtained by minimizing the objective function. Constraints are used to satisfy physical limitations.

8. The multi-axis collaborative welding robot dynamic path planning method according to claim 7, characterized in that: The objective function includes: A penetration tracking option to ensure that the robot maintains a constant penetration depth along the path; A spatter suppression item used to control the droplet detachment speed and avoid excessive spatter rate; And the joint smoothness term is used to ensure the smoothness of the robot motion and avoid sharp acceleration or velocity changes.

9. The multi-axis collaborative welding robot dynamic path planning method according to claim 7, characterized in that: The constraints include: Joint limit constraints used to control the range of the robot's joints and ensure that the robot's movement does not exceed its physical limitations; Torque limit constraints to ensure that the robot does not exceed its torque limits, thereby avoiding damage to mechanical parts or affecting motion stability; Seam tracking accuracy constraint used to ensure that the robot end effector always follows the path and does not deviate by more than the maximum allowed error.

10. A dynamic path planning system for a multi-axis collaborative welding robot, characterized in that: The dynamic path planning system comprises: processor; A memory stores a computer program, and when the computer program is executed by a processor, the multi-axis collaborative welding robot dynamic path planning method as described in any one of claims 1 to 9 is implemented.

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