A dynamic path planning method and system for multi-axis collaborative welding robots

Abstract

The present invention discloses a dynamic path planning method and system for a multi-axis collaborative welding robot, belonging to the field of robotic welding. The method comprises: collecting basic data of the workpiece to be welded and constructing a basic welding database; constructing a geometric model of the weld path based on the data in the basic welding database and parameterizing the geometric model of the weld path; based on the parameterization results, 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 spinor trajectory; and constructing a spinor mapping model based on inverse kinematics and spinor theory to convert the time-parameterized spinor trajectory into a target spinor. The present invention improves welding quality.

Description

Technical Field

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

[0002] In existing industrial welding robot path planning, Cartesian space is commonly used. A typical implementation involves first determining the discrete path points of the end effector (welding gun) in Cartesian space through 3D modeling or manual teaching. Then, using inverse kinematics (IK), this Cartesian trajectory is converted into a sequence of joint space angles.

[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 makes it difficult to effectively describe the geometric characteristics of welds with complex curvatures. For example, when the weld presents a spatial spiral or a variable curvature surface, the linear interpolation between discrete path points will cause the tangent direction of the weld trajectory to suddenly change, forcing the welding gun to start and stop frequently on a microscopic scale. In addition, the welding gun posture (Roll-Pitch-Yaw angle) needs to be planned separately and decoupled from the position trajectory, making it difficult to coordinate the spatial motion of the end effector and the continuity of the posture motion. According to statistics, this type of posture mismatch problem will reduce the qualified rate of the molten pool formation by 15%-30%. 2. The lack of a dynamic compensation mechanism. The existing method optimizes the geometric path planning and process parameters in stages, which makes it difficult to compensate for the material deformation caused by the welding thermal process in real time. Even if the amount of thermal expansion is predicted through finite element simulation, due to the rigid structure of the Cartesian space trajectory, local corrections can only compensate for the translation / rotation of discrete path points, but cannot achieve adaptive adjustment of the curve curvature (such as gradient compensation along the weld normal). This directly leads to the accumulation of trajectory deviations during multi-layer welding, especially in thin plate welding, which may cause insufficient penetration or fusion. 3. Suboptimal 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 multiple solution screening within tens of milliseconds, often sacrificing path accuracy (such as minimizing joint displacement) or motion smoothness (such as acceleration steps) to ensure real-time performance. This process will result in approximately 5%-8% trajectory distortion, which may cause the robot arm to vibrate or even stall during high-speed welding.

[0004] For example, patent document CN106557844A, published on April 5, 2017, titled "A Welding Robot Path Planning Method" and with publication number CN106557844A, describes a welding robot path planning method based on cluster-guided multi-objective particle swarm optimization. This method, based on trajectory planning in Cartesian space, calculates the path length and motion energy consumption between the welding start and end points in an obstacle avoidance path. Then, using a cluster-guided multi-objective particle swarm optimization algorithm, dual-standard path planning is performed on these path lengths and motion energy consumption, resulting in an optimized path planning result. While this method utilizes clustering guidance to achieve multi-objective optimization for welding robots, it still cannot avoid the inherent drawbacks 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 achieved through the following technical solution, a dynamic path planning method for a multi-axis collaborative welding robot, comprising the following steps: S100, collecting 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, based on the parameterization result, generating an initial trajectory between two adjacent weld segments of the welding path, and time-parameterizing the initial trajectory to obtain a time-dependent time-parameterized spinor 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, solving the angular velocity component of the target spinor to solve the angle and velocity of each joint of the robot, thereby controlling the movement of the robot.

[0007] Furthermore, 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 detailed three-dimensional point cloud data of the workpiece surface obtained by laser scanning, or three-dimensional data of the workpiece surface shape is obtained by image matching and depth inference using two or more cameras; 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 in combination with the original geometric data and welding process parameters of the welded workpiece.

[0008] Furthermore, the geometric model is fitted with a B-spline curve by point cloud data to represent the position on the welding path. Based on the fitted B-spline curve, the Frenet frame system and initial rotation 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, which are respectively used to describe the direction of the path, the inclination of the welding gun and the swing plane of the path; the tangent vector represents the direction of the welding path and is obtained by calculating its first-order derivative at each point of the B-spline curve; the normal vector is a vector perpendicular to the tangent vector, reflecting the inclination 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, which defines the swing plane reference of the path; the Frenet frame system of the welding path is obtained by integration: {T, N, B}; S220, the initial spinor describes the translation and rotational motion of the welding gun during welding, and consists of a rotational part and a translational part: the rotational part is controlled by the normal vector, and the size of the rotational part is related to the curvature of the weld. Related; 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 spiral pitch, which is related to the welding speed and the inclination angle of the welding gun. Related parameters.

[0010] Furthermore, the tangent vector can be calculated as follows:

[0011] ,in, For the path curve at the path point The derivative at For the path curve at the path point The norm (or modulus) of the derivative at , reflects the size of the derivative vector and ensures the unitization of the tangent vector.

[0012] Furthermore, the normal vector can be calculated as follows:

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

[0014] Furthermore, the binormal can be expressed as follows: .

[0015] Furthermore, the rotating part It can be dynamically adjusted by the following formula: ,in, , According to the weld curvature Dynamic adjustment coefficient, the greater the weld curvature, the greater the rotation angular velocity of the welding gun.

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

[0017] ,in, ,

[0018] here, is the target inclination angle of the weld normal, To control the spiral trajectory of the welding gun along the welding path, is the component of the helical pitch.

[0019] Furthermore, the initial trajectory is generated by the following sub-steps: S310, the starting and ending positions of each path segment are described by the SE (3) transformation matrix, which is recorded as and , respectively representing the rigid body transformation from the starting point to the end point, based on spiral linear interpolation combined with the point cloud data fitting to obtain a B-spline curve, generate a smooth transition between adjacent path segments, and obtain a first initial trajectory; S320, add periodic small-amplitude disturbances to the first initial trajectory to simulate the swinging behavior during the welding process, take the first initial trajectory as the basic forward trajectory of the robot, superimpose disturbances on the trajectory, and thus obtain the final initial trajectory. The superimposed disturbance is realized by periodic spinor superposition, and is used to perform slight periodic swings 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] ,in, is the rigid body transformation matrix at the path point S defined by spiral linear interpolation, The rigid body transformation matrix of the starting point is used to represent the homogeneous transformation matrix in the weld segment. The rigid body transformation under , the homogeneous transformation matrix is ​​obtained by exponential mapping (conversion from Lie group to Lie algebra); , Weld segment The corresponding rotation quantity represents the rotation and displacement information of the segment. This rotation quantity contains the position and orientation of the robot in the welding path. is the natural exponential function, Represent the logarithmic mapping (Lie algebra) from the homogeneous transformation matrix to the homogeneous transformation matrix of the next welding segment, that is, to obtain the infinitesimal transformation between the two, which is achieved by calculating the relative transformation between the two; is the inverse matrix of the rigid body transformation matrix of the starting point, is the rigid body transformation matrix of the end point. By performing logarithmic mapping on the combination of these two matrices, the infinitesimal transformation in the middle can be obtained. is the path point parameter, which means the distance from the weld segment to the weld segment in this formula. arrive The transition progress, Indicates the value of the path point parameter in the interval [0, 1].

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

[0023] ,in, For the final trajectory; is the basic forward trajectory of the robot, that is, the trajectory of the robot moving along the welding path, which includes the rotation part of the robot moving along the X-axis and describes the basic trajectory of the robot; is the amplitude of the oscillating disturbance, which is used to adjust the intensity of the disturbance; is a sine, is the frequency of the disturbance, which determines the period of the disturbance. For time, , which represents the periodic variation of the disturbance in time. This term controls the magnitude and period of the disturbance, making the movement of the welding gun tip along the welding path not only smooth but also accompanied by periodic oscillations; is the swing trajectory of the robot end, which is a periodic disturbance around the binormal B-axis, indicating that the specific disturbance is along the B-axis direction, representing the periodic swing of the welding gun during the welding process.

[0024] Furthermore, the dynamic path planning method may also include step S500, an optimization step, which 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 to be optimized, and the optimal robot trajectory is obtained by minimizing the objective function; the constraints 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 along the path; a spatter suppression term for controlling the droplet detachment speed to avoid an excessively high spatter rate; and a joint smoothness term for ensuring the smoothness of the robot's motion to avoid sudden acceleration or speed changes.

[0026] Furthermore, the objective function can be expressed as follows:

[0027]

[0028] in, is the path parameterized trajectory, which is obtained by converting the time parameterized trajectory; The penetration control weight coefficient is used to indicate the importance of penetration control in the objective function. The coefficient can be used to adjust the relative influence of the penetration error. The larger the weight, the more important the error of penetration tracking is. The spiral pitch at any point s on the path directly affects the penetration depth during welding and is usually closely related to the welding speed. It will change with different positions on the path, indicating the motion characteristics of the multi-axis collaborative robot at that point; The target penetration value is the penetration reference value that the multi-axis collaborative robot hopes to maintain throughout the entire path. This reference value is usually set based on welding requirements to ensure weld quality. is the splash suppression weight coefficient, which is used to indicate the importance of splash suppression. By adjusting the value of this coefficient, the importance of splash suppression in the objective function can be controlled; The droplet detachment rate is the liquid metal that falls from the molten pool during welding. A too high droplet detachment rate can cause spatter, affecting weld quality. The droplet detachment rate is a variable that is dynamically related to the welding process and is usually calculated using a spatter mechanics model to ensure that excessive spatter does not occur. 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 spinor Jacobian matrix, which is used to describe the relationship between trajectory change and robot joint acceleration. Specifically, let is the pose trajectory (position and attitude) of the robot end effector, then Connects the relationship between the end effector velocity and the joint velocity, and the inverse of this matrix It represents the relationship between the end effector velocity and the joint acceleration; is the acceleration of the robot joint, which represents the rate of change of joint motion.

[0029] Furthermore, the constraints include: joint limit constraints used to control the range of the robot joints and ensure that the robot's movement does not exceed its physical limitations; torque limit constraints used to ensure that the robot does not exceed its torque limit to avoid damaging mechanical parts or affecting the stability of movement; weld tracking accuracy constraints used to ensure that the robot's end effector always follows the path and the deviation does not exceed the maximum allowable error.

[0030] Furthermore, the joint limit constraint can be expressed as follows:

[0031] ,in, is the angle or position of the i-th joint. In this embodiment, the multi-axis cooperative motion robot is a common industrial six-axis cooperative 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] ,in, 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, which represents the inertia characteristics of the joint, is the Coriolis force matrix, which represents the interaction force between joints. is the gravity term, which represents the torque generated by the robot due to gravity.

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

[0035] ,in, 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 path point S, The maximum allowed tracking error ensures that the robot end effector always tracks the weld path with an error not exceeding this threshold.

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

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

[0038] The present invention fundamentally solves the inherent defects of motion-process decoupling and insufficient dynamic compensation in traditional Cartesian space planning by taking advantage of the geometric intrinsic properties of complex space, and provides a new theoretical framework for intelligent welding of highly complex 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, constitute a part of this application, and do not constitute a limitation of the embodiments of the present invention. In the drawings:

[0040] Figure 1 This is a flow chart of the method provided in Example 1 of the present invention. DETAILED DESCRIPTION

[0041] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0042] Example 1

[0043] This embodiment discloses a dynamic path planning method for a multi-axis collaborative welding robot. This method abandons the traditional Cartesian space planning paradigm and innovatively employs a complex space trajectory generation method based on spinor theory, achieving a generational breakthrough over the Cartesian method. In this embodiment, the weld path is parameterized as a curvature-differentiable B-spline curve based on the Frenet frame. The position and posture changes of the end effector are uniformly described using the rotational and translational components of the spinor. This ensures that the tangent vector (T) naturally corresponds to the main welding motion direction, and the normal vector (N) and the binormal (B) form orthogonal planes for the spinor rotation. This allows the welding gun tilt angle (along the N direction) and swing direction (along the B direction) to be adjusted directly using the spinor's rotational components. Compared to the "position + Euler angle" decoupled representation of the Cartesian coordinate system, the complex space model of this invention integrates six degrees of freedom motion into a single coupled rotation and translation operation, avoiding the geometric singularities of posture jumps. In complex space, local deformation caused by material thermal expansion can be smoothly corrected for the curvature of the spinor trajectory using helical linear interpolation. Specifically, the tangent vector curvature radius of the Frenet frame can be adjusted in real time by taking the thermal expansion coefficient as input, so that the trajectory curvature can adaptively compensate for the normal component of thermal deformation. By defining the basic motion spinor and the perturbation spinor in the spinor space, the swinging motion is expressed as a composite spinor motion in the time domain. Due to the exponential product characteristics of the spinor (SE(3) group closure), 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 solution. This embodiment converts the multi-dimensional constrained optimization problem of the complex space trajectory into a linear programming problem in Lie algebra through spinor mapping, which can effectively improve the solution efficiency compared to nonlinear programming in Cartesian space. For example, for common industrial six-axis robots, the Paden-Kahan subproblem decomposition algorithm can be used to utilize the geometric meaning of the spinor exponential product to convert complex inverse kinematics calculations into explicit algebraic operations of the rotation axis, thereby significantly reducing the computational complexity.

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

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

[0046] Specifically, laser scanning is used to obtain detailed 3D point cloud data of the workpiece surface, accurately capturing the workpiece's geometry and surface details. Alternatively, two or more cameras can be used to obtain 3D data of the workpiece's surface shape through image matching and depth estimation. This allows the acquisition of the original geometric data of the workpiece being welded.

[0047] Welding process parameters directly impact weld quality and process stability, and therefore require careful consideration during path planning. A pre-defined welding process parameter database is constructed to store welding process parameters for different materials and workpiece geometries. This database should at least include the following: Current (I): Welding current affects welding heat input and welding speed. Different welding tasks require different current values ​​to ensure weld quality. Voltage (U): Welding voltage generally determines arc stability and weld depth. Excessively high or low voltage can affect weld quality, particularly arc stability. Welding speed (V): Welding speed determines the distribution of heat input. Excessively high speeds can result in a weak weld, while excessively low speeds can lead to overheating and material deformation. Welding gas flow rate: Shielding gas flow rate is crucial for shielding the weld and is typically adjusted based on the welding material and process. Arc length: Arc length directly impacts weld quality. Long arcs can lead to unstable welds, while short arcs can result in excessively high welding temperatures. The thermal expansion coefficient of the workpiece material. The differences in thermal expansion coefficients of different materials affect the specific direction of the welding path, so the welding path needs to be compensated by the thermal expansion coefficient. In path planning, these process parameters need to be comprehensively considered and matched to the specific welding task and factors such as the material and thickness of the workpiece.

[0048] The welding sequence is determined by combining the original geometric data of the workpiece and the welding process parameters. The planning of the welding sequence is closely related to the geometric characteristics of the workpiece. A reasonable welding sequence not only helps to ensure weld quality but also prevents workpiece deformation caused by uneven thermal stress. Specifically, for complex workpieces, the welding sequence needs to take special consideration of the workpiece's geometric characteristics (for example, welding protruding parts first and concave parts later to prevent deformation caused by uneven thermal expansion).

[0049] By analyzing the original geometry of the workpieces and the weld area, and taking into account the welding process parameters, the welding sequence can be planned, while also ensuring that the heat input is evenly distributed to minimize residual stresses generated during welding. For areas that are difficult to access, welding can be performed first to ensure smooth operation of the multi-axis collaborative robot. For workpieces of varying thickness, the welding sequence can be optimized based on the thickness variation. For example, welding of thicker sections can be performed later to prevent deformation of thinner sections due to heat concentration during welding.

[0050] The basic welding database is constructed by integrating the original geometric data of the welded workpiece, welding process parameters and welding sequence, providing accurate workpiece information for the path planning algorithm. This data will help the robot generate the optimal welding path to ensure maximum welding quality and efficiency.

[0051] Step 2: When planning the welding path for a multi-axis collaborative robot, constructing a precise geometric model of the weld path and accurately parameterizing the weld geometry are key to ensuring a smooth and precise welding process. In this step, a mathematical model based on the Frenet frame is used to construct the geometric characteristics of the weld path and define the corresponding rotations, thereby achieving accurate parameterization of the weld geometry. This allows for 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 are extracted from the welding basic database to parameterize the weld geometry. The point cloud data is derived from the original workpiece geometry data collected in Step 1. The material thermal expansion coefficient is used to compensate for the material's thermal expansion characteristics, which can affect the geometry of the weld path during welding. Welding speed is a key parameter in the welding process, influencing 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. , represents the position on the welding path. Based on the fitted B-spline curve, we can define the Frenet frame system and the initial spin. The specific steps include the following:

[0054] 1) The Frenet frame consists of three parts: the tangent vector, the normal vector, and the 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.

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

[0056] ,

[0057] in, For the path curve at the path point The derivative at For the path curve at the path point The norm (or modulus) of the derivative at reflects the size of the derivative vector and ensures that the tangent vector is normalized.

[0058] Normal vector N (guiding the welding gun inclination angle): The normal vector is a vector perpendicular to the tangent vector, reflecting the inclination angle of the welding gun. It can be obtained by differentiating the tangent vector T and normalizing it. In this embodiment, the normal vector can be calculated using the following formula:

[0059] ,

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

[0061] Binormal B (swing plane reference): The binormal is the cross product of the tangent vector and the normal vector, defining the swing plane reference of the path. In this embodiment, the binormal can be expressed as follows:

[0062] .

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

[0064] 2) Construct the initial spinor , the initial rotation describes the translation and rotational motion of the welding gun during the welding process. It consists of two parts:

[0065] Rotating part , the rotation part of the screw is controlled by the normal vector N. Specifically, the size of the rotation part is related to the curvature of the weld. In this embodiment, dynamic adjustment can be made by the following formula:

[0066] ,in, , According to the weld curvature Dynamic adjustment coefficient, the greater the weld curvature, the greater the rotation angular velocity of the welding gun.

[0067] Translation part The translation part is used to describe the movement of the welding gun along the welding path. The translation speed is the welding speed The product of the tangent vector T, which also includes the component of the helical pitch , the spiral pitch is related to the welding speed and the inclination angle of the welding gun Related parameters. In this embodiment, the translation part can be calculated by the following formula:

[0068] ,

[0069] in, ,

[0070] here, is the target inclination angle of the weld normal, To control the spiral trajectory of the welding gun along the welding path.

[0071] Step 3: Based on the Frenet frame system of the welding path, the logarithmic and exponential mapping of Lie groups and Lie algebras are realized in combination with spiral linear interpolation to generate an initial trajectory between two adjacent weld segments of the welding path.

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

[0073] As a result, the final generated path is not just a straight line path, but a trajectory that includes process disturbances and periodic actions, making the welding process more refined and in line with requirements.

[0074] Specifically, the following sub-steps may be included:

[0075] 1) The first initial trajectory for transition between adjacent path segments is smoothly generated by spiral linear interpolation to ensure that the robot moves smoothly along the welding path.

[0076] The starting and ending positions of each path segment are described by the SE(3) transformation matrix, denoted as and , which represent the rigid body transformation from the starting point to the end point respectively. 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.

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

[0078] ,

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

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

[0081] It should be noted that spiral linear interpolation is used to smoothly generate transitions between adjacent path segments, ensuring that the robot's welding gun tip 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 making the robot move from the weld segment to the weld segment, the robot can move from the weld segment to the weld segment. Smooth transition to These two path segments can be transformed by the and to represent the linear interpolation by spiral, that is, and is the SE(3) transformation matrix representing the starting point and the end point of the path segment, where each transformation matrix includes information of rotation and translation. In the formula disclosed in this embodiment, and denote the exponential and logarithmic maps, respectively, for converting between Lie groups (SE(3)) and Lie algebras; by The difference between the transformations (i.e. the difference between the rotation and translation) can be obtained by A smooth trajectory can be generated. The final trajectory of the robot welding gun end has a smooth transition between each adjacent path segment, which prevents sudden changes in the translation and rotation of the trajectory in space. The interpolation result is usually a transformation matrix in SE(3) space, which is used to describe the position and posture of the robot.

[0082] 2) After obtaining the first initial trajectory, periodic small-amplitude perturbations are added to it to simulate the oscillation behavior during welding. The first initial trajectory serves as the robot's basic forward trajectory, and perturbations are superimposed on it to obtain the final trajectory. This simulates the periodic small-amplitude oscillations during welding and improves welding quality.

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

[0084] ,

[0085] in, For the final trajectory; is the basic forward trajectory of the robot, that is, the trajectory of the robot moving along the welding path, which includes the rotation part of the robot moving along the X-axis and describes the basic trajectory of the robot; is the amplitude of the oscillating disturbance, which is used to adjust the intensity of the disturbance; is a sine, is the frequency of the disturbance, which determines the period of the disturbance. For time, , which represents the periodic variation of the disturbance in time. This term controls the magnitude and period of the disturbance, making the movement of the welding gun tip along the welding path not only smooth but also accompanied by periodic oscillations; is the swing trajectory of the robot end, which is a periodic disturbance around the binormal B-axis, indicating that the specific disturbance is along the B-axis direction, representing the periodic swing of the welding gun during the welding process.

[0086] It's important to note that in the actual welding process, in addition to maintaining a stable trajectory, the robot also needs to incorporate process-related perturbations to simulate the oscillation or vibration experienced during welding, ensuring more consistent welding quality. Oscillation perturbations are achieved through periodic spinor superposition. This superposition ensures that the robot not only follows a basic trajectory but also experiences slight periodic oscillations along the trajectory, simulating the physical vibration effects of welding.

[0087] 3) Time parameterize the generated final trajectory to obtain a time-dependent time-parameterized spinor trajectory ,The screw trajectory describes how the robot moves smoothly from the starting point to the end point during the ,whole welding process so that the robot can move smoothly along the trajectory ,according to the time sequence.

[0088] It should be noted that the resulting time-parameterized spinor trajectory must not only meet the requirements of smooth progress but also take into account the periodic perturbations of the process. In the process of generating the time-parameterized spinor trajectory, the two components of spiral linear interpolation and the spinor superposition of the swinging process complement each other: spiral linear interpolation ensures smooth transitions between different path segments and provides the basic trajectory for the time-parameterized spinor trajectory, that is, the robot moves smoothly along the welding path. The spinor superposition of the swinging process periodically perturbs this basic trajectory to simulate the periodic movements required in the welding process (such as swinging), increasing the complexity and detail of the trajectory.

[0089] Step 4: Step 3 ultimately yields a time-parameterized spinor trajectory in complex space. This trajectory is generated based on the basic workpiece structure and dynamic constraints. This trajectory provides a preliminary path planning tool for the multi-axis collaborative robot, but it cannot fully meet all the precise requirements of the welding process, such as controlling penetration depth, suppressing spatter, and ensuring smooth joints.

[0090] In order to ensure that the final trajectory can fully meet all the precise requirements of the welding process, in this embodiment, the posture-path coupling optimization model is used to further improve the trajectory quality, and finally an optimized time-parameterized spinor trajectory is generated to meet the specific requirements of 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 posture-path coupled optimization model, which is used to describe the goal to be optimized, and the optimal robot trajectory is obtained by minimizing the objective function.

[0093] In this embodiment, the objective function may include three parts: 1. A penetration tracking term for ensuring that the robot maintains a constant penetration depth along the path; 2. A spatter suppression term for controlling the droplet detachment speed to avoid excessive spattering; and 3. A joint smoothness term for ensuring smooth robot motion and avoiding sudden acceleration or velocity changes. In this embodiment, the objective function can be expressed as follows:

[0094]

[0095] in, is the path parameterized trajectory, which is obtained by converting the time parameterized trajectory; The penetration control weight coefficient is used to indicate the importance of penetration control in the objective function. The coefficient can be used to adjust the relative influence of the penetration error. The larger the weight, the more important the error of penetration tracking is. The spiral pitch at any point s on the path directly affects the penetration depth during welding and is usually closely related to the welding speed. It will change with different positions on the path, indicating the motion characteristics of the multi-axis collaborative robot at that point; The target penetration value is the penetration reference value that the multi-axis collaborative robot hopes to maintain throughout the entire path. This reference value is usually set based on welding requirements to ensure weld quality.

[0096] is the splash suppression weight coefficient, which is used to indicate the importance of splash suppression. By adjusting the value of this coefficient, the importance of splash suppression in the objective function can be controlled; The droplet detachment velocity is the liquid metal that falls from the molten pool during welding. A too high droplet detachment velocity can cause spatter, affecting welding quality. The droplet detachment velocity is a variable dynamically related to the welding process and is usually calculated using a spatter mechanics model to ensure that excessive spatter does not occur. In this embodiment, it can be calculated using the following formula:

[0097] ,

[0098] in, is the dynamic coupling coefficient, which is obtained by testing and calibrating 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 gun; The critical detachment velocity is the maximum velocity at which the droplet remains stable. It depends on the surface tension, density and droplet radius of the welding material of different materials and 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 spinor Jacobian matrix, which is used to describe the relationship between trajectory change and robot joint acceleration. Specifically, let is the pose trajectory (position and attitude) of the robot end effector, then Connects the relationship between the end effector velocity and the joint velocity, and the inverse of this matrix It represents the relationship between the end effector velocity and the joint acceleration; is the acceleration of the robot joint, which represents the rate of change of joint motion.

[0101] It should be noted that It is the penetration tracking item. It is the square difference between the spiral 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 to maintain the stability of the penetration depth, thereby improving the welding quality. is the splash suppression term, It is the square of the droplet detachment speed, which measures the speed of the droplet detachment. By minimizing this item, spattering can be suppressed, ensuring stable droplet detachment, thereby improving welding quality. is the joint smoothness term, This is the size of the robot joint acceleration. By minimizing this value, the robot movement is ensured to be smooth, excessive joint acceleration is avoided, and the robot can operate smoothly during welding, reducing wear or overload of mechanical components.

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

[0103] Joint limit constraints are used to control the range of the robot's joints and ensure that the robot's movement does not exceed its physical limitations. In this embodiment, the joint limit constraints can be expressed as follows:

[0104] ,

[0105] in, is the angle or position of the i-th joint. In this embodiment, the multi-axis cooperative motion robot is a common industrial six-axis cooperative 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] The torque limit constraint is used to ensure that the robot does not exceed its torque limit, avoid damaging mechanical parts or affecting the stability of movement. In this embodiment, the torque limit constraint can be expressed as follows:

[0107] ,

[0108] in, 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, which represents the inertia characteristics of the joint, is the Coriolis force matrix, which represents the interaction force between joints. is the gravity term, which represents the torque generated by the robot due to gravity.

[0109] The seam 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 allowed error. In this embodiment, the seam tracking accuracy constraint can be expressed as follows:

[0110] ,

[0111] in, 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 path point S, The maximum allowed tracking error ensures that the robot end effector always tracks the weld path with an error not exceeding this threshold.

[0112] It should be noted that the time-parameterized spinor trajectory is further optimized using the posture-path coupling optimization model in this step to ensure that it can meet these more refined and specific welding requirements. This avoids problems such as uneven penetration and reduced weld quality caused by trajectory errors during welding. The posture-path coupling optimization model can optimize the dynamic characteristics of the welding process. For example, by adjusting the acceleration of the robot joints to ensure a smooth trajectory, it avoids excessive vibration or jerky motion during welding, which can affect welding quality or even damage the robot. It also suppresses spatter and droplet detachment, controls the droplet detachment speed, and reduces spatter, preventing metal from splashing to areas where it should not splash during welding, thereby affecting the quality of the weld joint. By meeting physical and engineering constraints, for example, ensuring that the range of motion and torque limits of each robot joint are not violated, it avoids joints exceeding physical limits during welding. The posture-path coupling optimization model not only optimizes the trajectory geometry to enable it to better track the target weld path, but also adds fine-grained control over dynamic smoothness and weld quality. In this way, the final trajectory can better meet the specific requirements of the welding process while meeting physical constraints.

[0113] Step 5: The optimization process in Step 4 yields an optimized time-parameterized spinor trajectory. This trajectory is smooth and satisfies all constraints, representing the spatial state of the robot end effector at each moment. This trajectory allows us to determine the target state of the robot end effector at each moment during the welding process.

[0114] However, in actual operation, industrial robot control systems typically only understand commands in joint space. Therefore, time-parameterized screw trajectories must be converted into joint angles to drive the robot. By mapping screws to joint angles, the optimized screw trajectories are converted into joint space commands (i.e., robot joint angles) for multi-axis collaborative motion robots.

[0115] In this embodiment, the optimized time parameterized spinor trajectory (i.e., ) is converted into the angles of each joint of the robot and speed , so as to be able to control the robot movement. The specific steps include the following:

[0116] 1) Optimized time-parameterized spinor trajectory It includes the position, posture, linear velocity and angular velocity of the end effector at each moment. The screw trajectory reflects the motion state of the robot's end effector (such as a welding gun).

[0117] 2) First, the spinor trajectory is converted into a joint angle command through inverse kinematics calculation using a spinor mapping model. In this embodiment, the spinor mapping model can be expressed as follows:

[0118] ,

[0119] in, is a logarithmic mapping, is a natural constant, The intrinsic rotation of each joint of the multi-axis cooperative motion robot is pre-calibrated according to different types of robot structures. These rotations represent the kinematic parameters of this type of multi-axis cooperative motion robot. is the angle of the joint, indicating the actual position of each joint of the robot; is the target rotation, which represents the desired posture of the robot end effector.

[0120] It should be noted that spinor is a mathematical object that describes spatial position and posture (including translation and rotation). It is a 6-dimensional vector, which consists of a 3-dimensional angular velocity (describing rotation) and a 3-dimensional linear velocity (describing translation). It is a bridge between Lie group and Lie algebra, which can effectively express the translation and rotation of space. The rotation of each joint of the robot contains the displacement and rotation information of the joint in space. It is the target that needs to be calculated. In the inverse kinematics solution, by solving the rotation trajectory, we get the angle of each joint. These angle instructions 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 spinor is mapped by the exponential mapping ( ) to represent the rotation state of a joint at a certain moment. Specifically, It is the exponential mapping of the spinor, which is used to convert the displacement and rotation represented by the spinor into the rotation matrix or displacement of the joint. It is used to represent the composite effect of the rotation and displacement described by the spinor. This mapping helps to describe the motion state of the robot joint through the spinor and control the rotation of each joint through the angle. ) is a key step in the inverse kinematics of spinors, which transforms the spinors into elements of Lie algebra. Through logarithmic mapping, we can map the exponentials of multiple spinors ( ) is converted into the representation of the robot joint angle. Thus, the target rotation of the final position and posture that the robot end effector is expected to reach is finally obtained. The target rotation includes the target position and target attitude of the end effector, that is, the spatial displacement and rotation of the end effector. The target rotation is the final goal that the end effector of the robot wants to achieve, which provides a reference for calculating the angle of each joint.

[0121] It should be noted that: the example in this embodiment is a 6-axis industrial robot, so the product symbol , represents the product of the spin index mapping from the first joint to the sixth joint of the industrial six-axis collaborative motion robot. Those skilled in the art should know that the collaborative motion robot in this embodiment is not limited to a six-axis collaborative motion robot. The solution provided in this application is universal, and those skilled in the art can adjust the joints according to actual conditions. The formula in this embodiment is only for illustration.

[0122] 3) Finally, the angular velocity components of the target spinor are calculated to determine the angles of each joint. In this step, existing algorithms can be used to calculate the angular velocity components in spinor space and use these components to determine the robot's joint angles.

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

[0124] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection 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 includes: S100, collecting basic data of the welded workpiece and building 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, The geometric model of the weld path is parameterized by constructing the geometric characteristics of the weld path and defining the corresponding rotation. The mathematical model based on the Frenet frame obtains a B-spline curve by fitting the point cloud data to represent the position on the welding path, and defines the Frenet frame system and the initial spin based on the fitted B-spline curve; 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 spinor trajectory, 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 point cloud data fitting to obtain the B-spline curve, generate a smooth transition between adjacent path segments, and obtain the first initial trajectory, The first initial trajectory is calculated by the following formula: ， in, is the rigid body transformation matrix at the path point S defined by spiral linear interpolation, The rigid body transformation matrix of the starting point is used to represent the weld segment The rigid body transformation under is the natural exponential function; is the inverse matrix of the rigid body transformation matrix of the starting point, is the rigid body transformation matrix of the end point, Is the path point parameter, indicating the distance from the weld segment arrive transition progress; 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, and superimposing the disturbances on the trajectory to obtain a final initial trajectory; The final initial trajectory is calculated by the following formula: ， in, For the final trajectory; is the basic forward trajectory of the robot, is the amplitude of the oscillating disturbance, which is used to adjust the intensity of the disturbance; is a sine, is the frequency of the disturbance, which determines the period of the disturbance. For time, is the swing trajectory of the robot end; S400. Construct a spinor mapping model based on inverse kinematics and spinor theory to convert the time parameterized spinor trajectory into a target spinor, and solve the angular velocity component of the target spinor to solve the angle and velocity of each joint of the robot.

2. The dynamic path planning method for a multi-axis collaborative welding robot 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 original geometric data of the welded workpieces and welding process parameters.

3. The dynamic path planning method for a multi-axis collaborative welding robot according to claim 1, characterized in that: The Frenet frame system and initial spinor are obtained by the following sub-steps: The S210 and Frenet frames are composed of three parts: the tangent vector, the normal vector, and the 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 of the welding gun during the welding process, which consists of a rotational part and a translational 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 spiral pitch, which is related to the welding speed and the inclination angle of the welding gun. Related parameters.

4. The dynamic path planning method for a multi-axis collaborative welding robot 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.

5. The dynamic path planning method for a multi-axis collaborative welding robot 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, thereby improving the quality of the time parameterized spinor trajectory. The attitude-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 optimal robot trajectory is obtained by minimizing the objective function; Constraints are used to satisfy physical limitations.

6. The dynamic path planning method for a multi-axis collaborative welding robot according to claim 5, characterized in that: The objective function includes: Depth tracking to ensure the robot maintains a constant depth of penetration along its 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 robot motion and avoid sudden acceleration or velocity changes.

7. The dynamic path planning method for a multi-axis collaborative welding robot according to claim 5, 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 used to ensure that the robot does not exceed its torque limits to avoid damaging 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.

8. A dynamic path planning system for a multi-axis collaborative welding robot, characterized in that: The dynamic path planning system includes: processor; The memory stores a computer program, and when the computer program is executed by the processor, the dynamic path planning method of the multi-axis collaborative welding robot according to any one of claims 1 to 7 is implemented.

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