A welding device and a welding trace control method thereof

Abstract

The application discloses a welding device and a welding track control method thereof, and the method comprises the following steps: obtaining a desired welding track of a workpiece to be welded; in each welding control period, the following steps are performed: obtaining a current ideal driving torque and a measured driving torque of each joint, estimating a transmission flexibility parameter of each joint and a change amount of an end rotation inertia of the welding robot according to a dynamic residual of each joint; calculating a welding driving torque of each joint according to the desired welding track, the transmission flexibility parameter of each joint and the change amount of the end rotation inertia of the welding robot; and controlling the welding driving torque corresponding to each joint to be applied to each joint. The application considers the change of the end rotation inertia of the welding robot caused by the welding wire consumption and the joint transmission flexibility, and determines the welding driving torque by considering the transmission flexibility parameter of each joint and the change amount of the end rotation inertia of the welding robot, so that the welding driving torque is more suitable for the actual welding working condition, and the welding track tracking error caused by the load change and the flexibility effect is reduced.

Description

Technical Field

[0001] This invention relates to the field of industrial robot control technology, specifically to a welding device and its welding trajectory control method. Background Technology

[0002] Welding is a crucial process in industrial manufacturing, and precise control of the welding trajectory is essential for improving product quality and mechanical properties, as well as reducing energy consumption. During welding, the end-effector load of the welding robot is time-varying due to the consumption of welding wire, and the robot's posture changes during movement, making high-precision welding trajectory tracking difficult. For example, in aerospace, industrial manufacturing, or heavy chemical industries, there are numerous large, complex metal components with three-dimensional curved surfaces, such as rocket fuel tank bottoms, curved hull plates, and large pressure vessel heads. Automated welding of these components is a critical step in the manufacturing process. When welding such components, not only is the end-effector load of the welding robot time-varying due to the consumption of welding wire, but the robot's posture also changes drastically during large-scale spatial movements, triggering significant Coriolis or centrifugal force dynamics, which poses a significant challenge to welding trajectory control. Summary of the Invention

[0003] To address the problems existing in the prior art, the present invention provides a welding device and a welding trajectory control method thereof.

[0004] The first aspect of this invention provides a welding trajectory control method applied to a welding apparatus, the welding apparatus including a welding robotic arm and a welding torch disposed at the end of the welding robotic arm, the welding robotic arm having at least one joint, and the welding trajectory control method comprising:

[0005] Obtain the desired welding trajectory for welding the workpiece;

[0006] In each welding control cycle, perform the following steps:

[0007] Obtain the current ideal driving torque and measured driving torque of each joint, and estimate the transmission flexibility parameters of each joint and the change in end moment of inertia of the welding robot arm based on the dynamic residual of each joint. The dynamic residual is the difference between the measured driving torque and the ideal driving torque.

[0008] Based on the desired welding trajectory, the transmission flexibility parameters of each joint, and the change in the end moment of inertia of the welding robot arm, the welding driving torque of each joint is calculated.

[0009] Control the application of corresponding welding drive torque to each of the joints.

[0010] In some embodiments, estimating the transmission flexibility parameters of each of the joints and the change in end-effector moment of inertia of the welding robot arm based on the dynamic residuals of each of the joints includes:

[0011] Using the transmission flexibility parameters of each joint estimated in the previous welding control cycle, the change in the end-effector moment of inertia of the welding robot arm, and the current motion state of each joint, the dynamic residual of each joint in the current welding control cycle is estimated to obtain the estimated dynamic residual; wherein, in the first welding control cycle, the initial value 0 is used as the transmission flexibility parameters of each joint and the change in the end-effector moment of inertia of the welding robot arm in the previous welding control cycle.

[0012] The dynamic residual error is obtained by differentiating the dynamic residual and the estimated dynamic residual.

[0013] The transmission flexibility parameters of each joint and the change in end-effector moment of the welding robot arm are obtained by correcting the dynamic residual error of the previous welding control cycle. This yields the transmission flexibility parameters of each joint and the change in end-effector moment of the welding robot arm for the current welding control cycle.

[0014] In some embodiments, the welding robotic arm has at least two joints; the motion states include elastic deformation, angular velocity, and angular acceleration;

[0015] The feedforward torque of each joint is calculated based on the motion state of each joint, the transmission flexibility parameters, and the change in the end-effector moment of inertia of the welding robot arm. Specifically, the feedforward torque of each joint is calculated based on the following joint dynamics equations:

[0016] ,

[0017] in, This is the feedforward torque vector composed of the feedforward torques of each joint in the k-th welding control cycle. and These are the angular velocity vector and angular acceleration vector composed of the angular velocity and angular acceleration of each joint in the k-th welding control cycle, respectively. M0 is the nominal inertia matrix, C0 is the Coriolis force and centrifugal force matrix, and g0 is the gravitational torque vector. ,in Let n be the change in the end effector moment of inertia of the welding robot arm during the k-th welding control cycle, and n be the total number of joints. n Let n be the standard basis vectors corresponding to the nth joint and ; ,in These are the equivalent damping values ​​for the first joint to the nth joint in the kth welding control cycle; ,in These represent the equivalent stiffness of the first joint to the nth joint during the k-th welding control cycle. It is the elastic deformation vector composed of the elastic deformation of each joint in the k-th welding control cycle.

[0018] In some embodiments, the cost function of the model predictive control problem is:

[0019]

[0020]

[0021]

[0022] Where k is the cycle number of the current welding control cycle, H is the prediction time domain length, and H is an integer not less than 2, τ(k+i) and τ(k+i-1) represent the driving torque vectors of the k+i and k+i-1 welding control cycles, respectively. ff (k+i) and τ fb (k+i) represent the feedforward torque vector and feedback torque vector of the (k+i)th welding control cycle, respectively; z(k+i) and z(k+i-1) represent the state vectors of the (k+i)th and (k+i-1)th welding control cycles, respectively, and for i = 1, 2, ..., H-1, z(k+i) is predicted based on z(k+i-1) and τ(k+i-1), and f(z(k+i-1), τ(k+i-1)) represents the prediction function of z(k+i) predicted based on z(k+i-1) and τ(k+i-1); e pos (k+i) represents the error between the position of the welding torch in the (k+i)th welding control cycle and the desired welding position obtained based on the desired welding trajectory. The position of the welding torch in the (k+i)th welding control cycle is obtained by reconstructing the state vector z(k+i) through a decoder. Let be the welding heat input rate during the (k+i)th welding control cycle. Let w1(k+i), w2(k+i), and w3(k+i) be the variance of the welding heat input during the (k+i)th welding control cycle; w1(k+i), w2(k+i), and w3(k+i) are the weights during the (k+i)th welding control cycle, respectively. β1 is the thermal stress topological regularization term, and n is the total number of joints. j (k+i) represents the joint angle of the j-th joint during the (k+i)-th welding control cycle, q min and q max These are the upper limit and lower limit of the joint angle, respectively; τ j (k+i) represents the welding driving torque τ of the j-th joint during the (k+i)-th welding control cycle. maxThis represents the upper limit of the welding driving torque.

[0023] In some embodiments, obtaining the desired welding trajectory for welding the workpiece includes:

[0024] Obtain the point cloud of the workpiece to be welded;

[0025] Semantic segmentation is performed on the point cloud of the workpiece to be welded to determine the point cloud belonging to the weld seam in the point cloud of the workpiece to be welded, and the weld seam point cloud is obtained.

[0026] The weld centerline is obtained by fitting the weld point cloud.

[0027] The desired welding trajectory is obtained by non-rigidly registering the weld centerline with the weld reference model.

[0028] In some embodiments, obtaining the weld centerline using the weld point cloud fitting includes:

[0029] A sliding window is used to slide on the weld point cloud. Each time the window slides to a position, the center point within the sliding window is determined. All center points are connected to obtain the initial center line.

[0030] The initial centerline is fitted using the first B-spline function to obtain the weld centerline;

[0031] In some embodiments, the step of non-rigidly registering the weld centerline with a reference model of the weld to obtain the desired weld trajectory includes:

[0032] The desired welding trajectory is obtained by non-rigidly registering the weld centerline with the weld reference model according to the following formula:

[0033]

[0034] Where T(p) represents the coordinates of a point on the desired welding trajectory, p represents the coordinates of a point on the weld centerline, and B d (x) represents the d-th B-spline function of the x-coordinate component, B e (y) represents the e-th B-spline function of the y-coordinate component, B f (z) represents the f-th B-spline function of the z-coordinate component. This represents the displacement of the control points of the first B-spline function, and It can minimize the following energy function:

[0035]

[0036] in, For all The vector formed, S represents the centerline of the weld, wp γ is the weight, Let T(p) be the closest point to the reference model of the weld.

[0037] A second aspect of the present invention provides a welding apparatus, including a welding robotic arm, a welding torch, and a controller;

[0038] The welding robotic arm has at least one joint, and the welding torch is located at the end of the welding robotic arm;

[0039] The controller is used to execute the welding trajectory control method described in the first aspect above, so as to control the welding robot arm to weld the workpiece to be welded.

[0040] The welding trajectory control method and welding apparatus provided in this application take into account the changes in the moment of inertia of the welding robot arm caused by welding wire consumption, as well as the influence of the transmission flexibility of joint movement. It breaks through the limitations of traditional control methods based on fixed parameters and rigidity assumptions. In each welding control cycle, the ideal driving torque and measured driving torque of each joint are obtained to determine the dynamic residual. Based on the dynamic residual, the transmission flexibility parameters of each joint and the change in the moment of inertia of the welding robot arm are estimated. Based on the desired welding trajectory, the transmission flexibility parameters of each joint, and the change in the moment of inertia of the welding robot arm, the welding driving torque of each joint is calculated. This allows for real-time estimation of the transmission flexibility parameters of each joint and the change in the moment of inertia of the welding robot arm. By taking these key parameters into account, the welding driving torque is determined, making the calculation of the welding driving torque more consistent with the actual welding conditions. This effectively suppresses the welding trajectory tracking error caused by load changes and flexibility effects, improves tracking accuracy, and helps ensure the welding trajectory control accuracy under high-speed, large-range movement and when the load at the end of the welding robot arm changes. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of the structure of a welding apparatus according to one embodiment;

[0042] Figure 2 This is a schematic diagram of the structure of a welding robotic arm according to one embodiment;

[0043] Figure 3 This is a flowchart of a welding trajectory control method according to one embodiment;

[0044] Figure 4 This is a flowchart of obtaining the desired welding trajectory for welding workpieces in some embodiments;

[0045] Figure 5 This is a flowchart of semantic segmentation of the point cloud of the workpiece to be welded in some embodiments to determine the point cloud of the workpiece to be welded that belongs to the weld seam, and to obtain the weld seam point cloud.

[0046] Figure 6 This is a flowchart illustrating the fusion of 2D image information and 3D point cloud information in some embodiments;

[0047] Figure 7 This is a flowchart in some embodiments for obtaining the current ideal driving torque and measured driving torque of each joint, estimating the transmission flexibility parameters of each joint and the change in the end-effector rotational inertia of the welding robot arm based on the dynamic residuals of each joint.

[0048] Figure 8 This is a flowchart in some embodiments for calculating the welding driving torque of each joint based on the desired welding trajectory, the transmission flexibility parameters of each joint, and the change in the end-effector rotational inertia of the welding robot arm.

[0049] Figure 9 This is a flowchart in some embodiments for constructing the state vector of the current welding control cycle based on the desired welding trajectory, the transmission flexibility parameters of each joint, and the change in the end-effector moment of inertia of the welding robot.

[0050] Figure 10 This is a comparison diagram of the welding trajectory control method of this application and existing methods. Detailed Implementation

[0051] The present invention will now be described in further detail with reference to specific embodiments and accompanying drawings. Similar elements in different embodiments are referred to by associated similar element reference numerals. In the following embodiments, many details are described to facilitate a better understanding of this application. However, those skilled in the art will readily recognize that some features may be omitted in different situations, or may be replaced by other elements, materials, or methods. In some cases, certain operations related to this application are not shown or described in the specification. This is to avoid obscuring the core parts of this application with excessive description. For those skilled in the art, detailed description of these related operations is not necessary; they can fully understand the related operations based on the description in the specification and general technical knowledge in the art.

[0052] Furthermore, the features, operations, or characteristics described in the specification can be combined in any suitable manner to form various embodiments. At the same time, the steps or actions in the method description can be rearranged or adjusted in a manner obvious to those skilled in the art. Therefore, the various orders in the specification and drawings are only for the clear description of a particular embodiment and do not imply a necessary order, unless otherwise stated that a particular order must be followed.

[0053] The serial numbers assigned to components or physical quantities in this document, such as "first," "second," etc., are used only to distinguish the described objects and have no sequential or technical meaning. They should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. "Multiple" means two or more. Unless otherwise specified, "connection" or "linkage" in this application includes both direct and indirect connections (linkages).

[0054] The inventors researched existing welding trajectory control technologies and found that current technologies still have some limitations, especially for complex spatial components with three-dimensional curved surfaces, where welding quality faces a series of core challenges: ① Complex welding path planning: Due to machining tolerances, clamping deformation, and the complex geometric characteristics of the workpiece itself, there are unavoidable differences between the reference model and the actual workpiece. These minute shape differences make the pre-set welding trajectory based on offline programming poorly adaptable, easily causing the welding torch to deviate from the weld seam, resulting in welding defects. ② High dynamic performance requirements: The inventors believe that during the welding process, the load at the end of the robotic arm is time-varying due to the consumption of welding wire, and the robotic arm's posture changes drastically during large-scale spatial movement, triggering significant Coriolis or centrifugal force dynamic effects. This makes it difficult for traditional control methods based on fixed parameters and rigidity assumptions to maintain high-precision trajectory tracking. ③ Difficulty in heat input control: Welding is a strongly nonlinear, time-varying physicochemical process. Uneven or unstable heat input can directly lead to large residual welding stress and deformation in the workpiece, seriously affecting the dimensional accuracy, mechanical properties, and safety of the product.

[0055] In welding trajectory planning, mainstream methods still heavily rely on offline programming and teach-and-playback. Operators plan the welding trajectory based on a reference model of the workpiece, such as a CAD model, and then perform point-to-point teaching and correction on the actual workpiece. This method is time-consuming, labor-intensive, inflexible, unable to adapt to individual differences in each workpiece, and highly dependent on operator experience. Although some studies have attempted to introduce visual sensors for weld seam tracking, they are mostly limited to two-dimensional or simple weld seams. For complex weld seams on three-dimensional curved surfaces, the online recognition accuracy and trajectory replanning speed are still insufficient to meet the real-time requirements of high-precision welding.

[0056] In terms of dynamic control, most welding robots used in industrial applications employ a fixed-parameter PID (Proportional Integral Derivative) control strategy, failing to adequately consider the impact of dynamic factors such as time-varying loads at the end effector and joint flexibility. Some methods introduce dynamic models to calculate torque, but the parameters of these models are typically identified and fixed offline, making them unable to adapt to load variations caused by wire consumption during welding. This results in decreased system dynamic performance and increased trajectory tracking errors during high-speed, wide-range movements or load changes.

[0057] In terms of process optimization, existing control strategies mostly address robotic arm motion control and welding process quality issues in isolation. Welding engineers are responsible for setting welding current, voltage, and nominal speed, while robotics engineers are responsible for ensuring trajectory accuracy; the two lack collaborative optimization. Although some studies have attempted to ensure quality by monitoring welding parameters, few have directly incorporated the robotic arm's motion state (such as speed smoothness) as a key variable affecting welding heat input into control strategies for optimization objectives, making it difficult to fundamentally guarantee the minimization of welding residual stress and deformation.

[0058] In summary, current technologies lack an integrated solution that can simultaneously coordinate initial adaptive planning of the welding trajectory, online compensation for dynamic disturbances during motion, and collaborative optimization of motion control and welding quality. The independent nature of each stage results in bottlenecks in precision, efficiency, and quality consistency during the welding of workpieces, especially large and complex spatial components.

[0059] Based on the above understanding, this application provides a welding apparatus and a welding trajectory control method. This application provides various embodiments to solve some or all of the problems existing in the prior art. The welding apparatus of this application will be described below.

[0060] Please refer to Figure 1 In some embodiments, the welding apparatus includes a welding robotic arm 1, a welding torch 2, and a controller 3. The welding robotic arm 1 has at least one joint 11 ( Figure 1 Taking three joints as an example (there may be more or fewer joints in different embodiments), the welding torch 2 is located at the end of the welding robotic arm 1 and is driven by the welding robotic arm 1 to different points on the workpiece 4 to be welded to perform welding. The welding robotic arm 1 realizes the free movement of the welding torch 2 in space through the rotation of its various joints.

[0061] In some embodiments, the welding robotic arm 1 is as follows: Figure 2The image shows a 6-DOF welding robot arm, employing a multi-joint serial 6-DOF industrial robot structure. Each degree of freedom, or joint, is driven by an electric servo motor, enabling flexible movement of the end effector in three-dimensional space. The welding robot arm has six joints, arranged as follows:

[0062] ① Base: Fixed to the ground and has rotational freedom, allowing the entire welding robot arm 1 to rotate around the vertical axis.

[0063] ② Base: Connected to the base, it enables the entire welding robotic arm 1 to rotate 360 ​​degrees, providing the maximum rotation range for the welding robotic arm 1.

[0064] ③Shoulder: Connects the first arm and the base, allowing the welded robotic arm 1 to bend freely in the vertical direction.

[0065] ④ Elbow: Allows rotation of the middle section of welding robot arm 1, increasing the working range.

[0066] ⑤ Wrist: A key part that connects to the end effector, allowing for adjustment and control of the end effector's angle to accommodate welding at different angles.

[0067] ⑥ End effector: It fixes the welding torch, wire feeding mechanism and contact tip, and is responsible for completing the welding task.

[0068] The end effector integrates a welding torch, wire feed mechanism, and contact tip, and is responsible for executing the welding operation. The welding torch generates the welding arc and performs the welding operation; its posture is adjustable to accommodate complex curved surfaces and weld orientations. This torch posture adjustment allows for welding at different angles. The wire feed mechanism is responsible for precisely feeding the welding wire into the welding area, controlling the wire feed speed and flow rate. Precise control of the end effector is crucial for ensuring welding quality and stability.

[0069] The controller 3 controls the movement of the welding robot arm 1 to drive the welding torch 2 to weld the workpiece 4. The controller 3 is the executing entity of the welding trajectory control method provided in this application, and can execute the welding trajectory control method of this application to control the welding robot arm 1 to weld the workpiece 4. In some embodiments, the controller 3 employs a real-time operating system, integrating welding trajectory planning, dynamic parameter (including transmission flexibility parameters) identification, and multi-objective optimization algorithms. The controller 3 can use various dedicated controllers for industrial welding robots, such as controllers from KUKA, etc.

[0070] In some embodiments, the welding apparatus also includes a 3D laser scanner, which is fixed to the end of the welding robotic arm 1. The 3D laser scanner is responsible for performing a high-precision non-contact scan of the surface of the workpiece 4 to be welded before welding, acquiring point cloud data of the workpiece 4. The point cloud data provides the basis for subsequent welding trajectory planning and adjustment. Before scanning, the coordinate system of the 3D laser scanner is aligned with the base coordinate system of the welding robotic arm 1 through hand-eye calibration to ensure an accurate welding trajectory is obtained.

[0071] The welding device is also equipped with a sensor system. This system includes dual encoders (one motor-side encoder and one output-side encoder), current sensors, and temperature sensors. The dual encoders are used to monitor joint angles and elastic deformation in real time. Each joint has a corresponding motor-side encoder, typically mounted on the motor rotor, to monitor joint angles for precise control of the welding robot arm 1's various degrees of freedom. The output-side encoder is typically mounted at the joint output end (e.g., at the rear of the reducer) to monitor the actual angles of the welding robot arm 1's end effector and joints, aiding in precise control of the welding position and posture. Current sensors are used to estimate the torque of the joints during welding. Each joint has a corresponding current sensor to acquire the motor current. By monitoring changes in the motor current, the controller 3 can determine load changes in real time and adjust the control strategy accordingly. Temperature sensors are used to compensate for thermal drift caused by the welding process, monitoring the temperature of the welding area and joints in real time.

[0072] The sensor system may also include a six-dimensional force sensor and a robot calibration sensor. The six-dimensional force sensor is used to monitor forces during the welding process. By monitoring changes in forces in various directions, it prevents accidental contact during welding, thus achieving a collision prevention effect. The robot calibration sensor is used to adjust the end-point offset of the welding torch. Before welding, the robot calibration sensor can be used to adjust the offset welding torch tip to a preset position, such as a vertical or horizontal position.

[0073] Controller 3 communicates with the 3D laser scanner, sensors in the sensor system, and end effectors via a high-speed bus, enabling closed-loop control.

[0074] The various hardware components in the welding device work together to provide the hardware foundation for data acquisition, execution, and feedback for the welding trajectory control method.

[0075] The welding trajectory control method provided in this application is described below. This method is applied to the aforementioned welding apparatus and can be executed by controller 3. Please refer to... Figure 3 The welding trajectory control method in some embodiments of this application includes the following steps 100 and 210-230.

[0076] Step 100: Obtain the desired welding trajectory for welding the workpiece.

[0077] The desired welding trajectory is a pre-planned path for the welding torch to move during the welding process. Before welding begins, the desired welding trajectory can be planned using a two-dimensional graphic and / or three-dimensional model of the workpiece. Then, the welding apparatus welds the workpiece according to the desired welding trajectory.

[0078] To complete a weld, multiple welding operations are required on the workpiece to be welded. The time required to complete one welding operation is called a welding control cycle. The controller drives the welding robotic arm to move and complete the welding of the workpiece through multiple welding control cycles. In this application, in each welding control cycle, the controller executes the following steps 210-230.

[0079] Step 210: Obtain the current ideal driving torque and measured driving torque of each joint. Estimate the transmission flexibility parameters of each joint and the change in the end moment of inertia of the welding robot arm based on the dynamic residual of each joint. The dynamic residual is the difference between the measured driving torque and the ideal driving torque.

[0080] The ideal driving torque is determined by the ideal dynamic equations of the robotic arm joints, which refer to various classical robotic arm joint dynamic equations, such as the Lagrange equation and the Newton-Euler equation. The measured driving torque is calculated from the actual current measured by a current sensor.

[0081] The concept of dynamic residual is proposed in this application. The inventors believe that due to the change in end-load and the existence of joint transmission flexibility, there is a difference between the measured driving torque and the ideal driving torque. Therefore, the concept of dynamic residual is proposed to calculate the transmission flexibility parameters of the joint and the change in the end-load rotational inertia of the welding robot arm.

[0082] Step 220: Calculate the welding driving torque for each joint based on the desired welding trajectory, the transmission flexibility parameters of each joint, and the change in the end-effector moment of inertia of the welding robot arm. The welding driving torque is the driving torque applied to each joint to weld the weld seam.

[0083] Step 230: Control the application of the corresponding welding drive torque to each joint.

[0084] Specifically, the corresponding welding drive torque is applied to each joint by controlling the motor. Then, the process returns to step 210 to continue the control of the next welding cycle until the welding is completed.

[0085] The theoretical basis and specific implementation methods of each step are explained in detail below.

[0086] Step 100 involves acquiring the desired welding trajectory. To overcome the problem of uncertain weld trajectories and large geometric deviations leading to path planning failures in complex curved workpieces, an embodiment of this application provides a flexible welding trajectory registration method based on 3D point clouds to determine the desired welding trajectory. The core of this method is: integrating a 3D laser scanner at the end of the welding robotic arm to acquire high-precision three-dimensional point cloud data by scanning the area to be welded; subsequently, using point cloud semantic segmentation technology to accurately distinguish the weld area from the workpiece base material, and using a non-rigid registration algorithm to align the weld point cloud with the reference model with high precision; based on this, the spatial three-dimensional curve of the actual weld is automatically extracted, and the desired welding trajectory is generated accordingly for direct use by the controller. This embodiment, through the fusion of semantic segmentation and non-rigid point cloud registration technologies, achieves accurate perception and adaptive trajectory generation of complex curved welds for controller use, enabling the welding device to initially possess the ability to handle geometric deviations.

[0087] Please refer to Figure 4 In this embodiment, step 100 includes steps 110 to 140, which will be described in detail below.

[0088] Step 110: Obtain the point cloud of the workpiece to be welded.

[0089] Before welding begins, the robotic arm drives a 3D laser scanner to scan the entire or key areas of the workpiece containing the weld seam using a preset multi-angle scanning path, obtaining a point cloud of the workpiece. Prior to scanning, to unify the coordinate systems, the extrinsic parameters between the coordinate system of the 3D laser scanner and the base coordinate system of the robotic arm are calibrated, resulting in a point cloud coordinate transformation matrix. The point cloud obtained by scanning is transformed using the point cloud coordinate transformation matrix. Switch to the base coordinate system of the welding robot arm.

[0090] The obtained point cloud can be represented as:

[0091]

[0092] Where P is the point cloud of the workpiece to be welded, p i This represents the i-th point. Let c be the three-dimensional coordinates of the i-th point. i Let N be the intensity or color information of the i-th point, and N be the number of points.

[0093] Step 120: Perform semantic segmentation on the point cloud of the workpiece to be welded to determine the point cloud belonging to the weld seam in the point cloud of the workpiece to be welded, and obtain the weld seam point cloud.

[0094] Various point cloud semantic segmentation methods can be used for semantic segmentation of the point cloud of the welded workpiece, and this paper does not limit this method. This application also provides a method for semantic segmentation of the point cloud of the welded workpiece; please refer to [reference needed]. Figure 5 This includes steps 121 to 123, which are explained in detail below.

[0095] Step 121: For each point in the point cloud of the workpiece to be welded, extract its feature vector in the neighborhood of different radii, fuse the extracted feature vectors as the feature representation vector token of the point and input it into the Transformer model to obtain the semantic feature vector of the point.

[0096] The number of neighborhoods can be determined according to actual needs. For example, feature vectors can be extracted from neighborhoods with three different radii, and the extracted feature vectors represent the local geometric details of the point. Specifically, local point convolution can be performed in the spherical neighborhoods of each point with three different radii r1, r2, and r3 through a shared multilayer perceptron, and the neighborhood information can be aggregated using the max pooling operator to obtain feature vectors representing local geometric details. By extracting feature vectors in neighborhoods with different radii, multi-scale features can be obtained.

[0097] These feature vectors are fused through concatenation and other methods, and then used as the feature representation vector token for that point. The Transformer model uses its self-attention mechanism to capture the global contextual relationships within the point cloud, fusing local and global information to enhance feature representation capabilities and obtain a 3D semantic feature vector. The Transformer model can be a visual Transformer model, i.e., ViT.

[0098] Step 122: Based on the three-dimensional semantic feature vectors of each point, classify using a first multilayer perceptron to obtain the semantic labels of each point, where the semantic labels include weld seams, i.e., the areas to be welded.

[0099] Semantic tags are used to identify the category of each point and can be set according to the objects present in the actual welding scenario, such as weld, base material, fixture, etc.

[0100] The overall network consisting of the Transformer model and the first multilayer perceptron can be trained using the cross-entropy loss function.

[0101] Step 123: Obtain all points with the semantic label "weld" to form a weld point cloud.

[0102] In one embodiment, the semantically segmented point cloud can be represented as:

[0103]

[0104] in L represents the point cloud after semantic segmentation. i For point p i The corresponding semantic labels, {weld,base,fixture}, represent the set of all possible semantic categories, namely "weld", "base material", and "fixture".

[0105] Based on semantic tags, all points labeled "weld" are selected to form a weld point cloud:

[0106] .

[0107] Step 130: Obtain the weld centerline by fitting the weld point cloud.

[0108] First, a sliding window is used to slide across the weld point cloud. At each position reached, the center point within the sliding window is determined. Connecting all center points yields an initial centerline. The size of the sliding window depends on the size of the workpiece to be welded and the required fitting accuracy. To extract a continuous centerline from the discrete weld point cloud, a specific embodiment uses a sliding window combined with principal component analysis to obtain the initial centerline: the sliding window slides across the weld point cloud, and at each position reached, the center point within the sliding window is determined. Principal component analysis is then performed on the points within the sliding window, and the first principal direction is the tangent direction of the local weld segment within the sliding window. The sliding window slides along this tangent direction. Finally, connecting all center points yields an initial centerline.

[0109] To make the trajectory smoother and meet the kinematic requirements of the robot, the initial centerline is fitted using the first B-spline function to obtain the weld centerline, represented by the arc length s. The weld centerline c(s) is then expressed as:

[0110]

[0111] Among them B b (s) is the b-th first B-spline basis function, Q b Let Q be the b-th control point. Optimize control point Q. b The position can generate a smooth weld centerline c(s) of arbitrary order.

[0112] Step 140: Perform non-rigid registration between the weld centerline and the weld reference model to obtain the desired welding trajectory.

[0113] To associate the generated weld centerline with the weld reference model and further correct systematic deviations, it is necessary to register the weld centerline with the weld reference model. The reference model is a pre-constructed 3D model of the weld, such as a CAD model, which represents the theoretical weld curve. This step uses non-rigid registration to align the weld centerline with the theoretical weld curve in the reference model. Specifically, based on the first B-spline basis function, a displacement is applied to the control points using the same B-spline fitting approach. This displacement is obtained by minimizing an energy function, thereby minimizing the deviation between the weld centerline and the theoretical weld curve. In other words, the desired welding trajectory is obtained by non-rigid registration of the weld centerline with the weld reference model according to the following formula:

[0114]

[0115] Where T(p) represents the coordinates of a point on the desired welding trajectory, p represents the coordinates of a point on the weld centerline, and B d (x) represents the d-th B-spline function of the x-coordinate component, B e (y) represents the e-th B-spline function of the y-coordinate component, B f (z) represents the f-th B-spline function of the z-coordinate component. This represents the displacement of the control points of the first B-spline function. The goal of registration is to find the optimal displacement. This is achieved by constructing the following energy function, namely It can minimize the following energy function:

[0116] ,

[0117] in, For all The vector consists of S, which represents the weld centerline, and w p Let γ be the weight corresponding to point p, whose value can be determined by the location distance of point p and the semantic classification probability of point p during semantic segmentation, and γ be a preset weight. Let T(p) be the closest point on the reference model of the weld. This energy function can characterize the deviation between the weld centerline and the reference model of the weld.

[0118] Based on the above energy function, an iterative solution is performed to finally obtain the optimal displacement. This achieves accurate registration of the weld point cloud to the reference model, reducing geometric deviations.

[0119] In some embodiments, to eliminate outliers and measurement noise generated during the scanning process and to preserve key edge features, the method further includes smoothing the point cloud of the workpiece to be welded according to the following formula before step 120:

[0120]

[0121] in, N represents the coordinates of the point after smoothing, p represents the coordinates of the point before smoothing, and N represents the coordinates of the point before smoothing. r (p) represents the first neighborhood of point p, and q is a point within the first neighborhood. For spatial weighting functions, W is the range weight function. i The normalization factor can be the sum of the weights of all points in the first neighborhood, used to ensure that the new position is a weighted average of the coordinates of points in the first neighborhood. Let I(p) represent the Euclidean distance between points p and q, and let I(p) and I(q) represent the eigenvalues ​​of points p and q, respectively. This represents the absolute difference between the eigenvalues ​​of points p and q.

[0122] For each point p i The eigenvalues ​​can be taken from their second neighborhood. Calculate the covariance matrix:

[0123]

[0124] Where C i p represents the i-th point i The corresponding covariance matrix, Represents the points within the second neighborhood. Let the centroid of a point in the second neighborhood be . This represents the number of points in the second neighborhood. The second neighborhood can be the same as or different from the first neighborhood. Usually, the second neighborhood is greater than or equal to the first neighborhood. For C... i Perform eigenvalue decomposition, and the eigenvector corresponding to the smallest eigenvalue is the point p. i normal vector n i The minimum eigenvalue is point p. i eigenvalues.

[0125] In some embodiments, after smoothing, the point cloud can be voxel downsampled or farthest point sampled to maintain a uniform distribution of the point cloud.

[0126] The above smoothing process combines spatial proximity and feature similarity of point clouds to achieve the filtering effect. While filtering out noise, it effectively preserves the sharp features of weld bevels and other areas. After processing, the original point cloud is transformed into a smooth enhanced point cloud.

[0127] Due to self-occlusion caused by the geometry of the workpiece to be welded or the high reflectivity of the metal surface, the point cloud obtained by scanning may have holes or missing data. In order to obtain a complete geometric model of the workpiece to be welded, some embodiments also use a generative network based on a diffusion model to complete the smoothed point cloud.

[0128] The diffusion model learns the data distribution through a forward noise addition process and a backward noise reduction process. During the training phase, the diffusion model learns how to progressively recover the structure of the original point cloud from pure Gaussian noise. The training loss function of the diffusion model in this embodiment is... for:

[0129]

[0130] in Let x be the time step, and x represent the sample point cloud used for training. To add realistic noise to the sample point cloud, z t This refers to the noisy latent variables obtained after adding noise to the sample point cloud. For time step The diffusion model is based on the noisy latent variable z t Predicted noise.

[0131] The smoothed point cloud is used as a conditional input to the trained diffusion model. The diffusion model generates new points in the missing regions that conform to the surrounding geometric continuity through an iterative denoising process, and finally outputs a complete point cloud without holes.

[0132] In some embodiments, to further improve the segmentation accuracy in details such as weld edges and reflective areas, multimodal fusion of 2D image information and 3D point cloud information is introduced. Specifically, in this embodiment, step 122 includes... Figure 6 Steps 151-154 are shown.

[0133] Step 151: Project the point cloud of the workpiece to be welded onto a two-dimensional plane to obtain a depth map.

[0134] For example, a panoramic depth map D(u,v) can be obtained through spherical projection, and the corresponding 2D color image can also be obtained. The spherical coordinate relationship in spherical projection is as follows:

[0135]

[0136] Where (u,v) are the coordinates of a point on the depth map, and D(u,v) is the depth value of point (u,v). W and H are the width and height of the depth map, respectively. u,v , Y u,v Z u,v) represents the coordinates of the 3D point in the point cloud corresponding to point (u,v).

[0137] Step 152: Extract features from the depth map to obtain two-dimensional semantic feature vectors for each point on the depth map. The two-dimensional semantic feature vectors are used to perform semantic segmentation on the depth map to obtain the semantic labels of each point on the depth map.

[0138] Various semantic segmentation methods can be used to extract features from depth maps and perform semantic segmentation based on the extracted feature vectors, which are then used as two-dimensional semantic feature vectors. In one embodiment of this application, the SAM model is used to automatically segment and obtain the semantic labels L of each point on the depth map. 2D (u,v) uses the high-dimensional feature vector extracted by the SAM model as the two-dimensional semantic feature vector of each point.

[0139] Step 153: Backproject the two-dimensional semantic feature vectors of each point on the depth map to the corresponding points in the point cloud, and fuse the three-dimensional semantic feature vectors of each point in the point cloud with the two-dimensional semantic feature vectors obtained by backprojection to obtain the global information of that point.

[0140] For a 3D point p in a point cloud i Assuming its corresponding point on the depth map is (u,v), and its semantic label is L 2D (u,v), the two-dimensional semantic feature vector is f 2D (u,v), backprojected to point p i The two-dimensional semantic feature vector is denoted as: The three-dimensional semantic feature vector is denoted as f. 3D (i) In one embodiment, the two can be concatenated and then input into a second multilayer perceptron to obtain point p. i Global information :

[0141]

[0142] MLP2 represents the second multilayer perceptron.

[0143] Step 154: Input the global information of each point into the first multilayer perceptron for classification to obtain the semantic label of each point.

[0144] This embodiment also introduces consistency loss to constrain the learning of the Transformer model, making the segmentation more accurate at weld edges and reflective areas. The consistency loss function is... as follows:

[0145]

[0146] After non-rigid registration, the desired welding trajectory is still represented by c(s), which is now in the same coordinate system as the reference model and is a continuous curve. In some embodiments, it is discretized into a robot-executable trajectory, that is, the desired welding trajectory is discretized into multiple trajectory points. The desired welding pose of each trajectory point is calculated according to the curve c(s), forming a pose point. Each pose point has a corresponding desired welding pose. Therefore, the discretized desired welding trajectory consists of multiple pose points, that is, the desired welding trajectory is a discrete pose sequence. The desired welding pose of a trajectory point includes the desired welding position and the desired welding posture at that point. The desired welding position can be represented by position coordinates or position vectors, and the desired welding posture can be represented by a rotation matrix.

[0147] Specifically, the arc length is first parameterized based on c(s) to obtain the arc length parameterized reference trajectory:

[0148]

[0149] Where s is the arc length, which represents the cumulative path length along the curve from the starting point. This represents the desired welding position at arc length s, where L is the total weld length. Arc length parameterization is crucial; the arc length parameterization reference trajectory satisfies:

[0150]

[0151] This ensures the decoupling of speed control and trajectory geometry, given a constant... This corresponds to a constant welding torch linear speed, simplifying the control of welding heat input.

[0152] Based on the arc length corresponding to each pose point, The desired welding position can then be obtained. Construct the Frenet frame field:

[0153]

[0154] For space curves Its Frenet frame field consists of three orthogonal unit vectors:

[0155] Tangent vector: ;

[0156] Normal vector: ,in For curvature;

[0157] Binormal vector: .

[0158] This frame describes the local spatial orientation of the weld at each point, which is crucial for welding: the welding torch posture needs to be adjusted according to n(s) or b(s) to ensure molten pool symmetry and weld formation quality. In regions with zero or near-zero curvature, the classic Frenet frame exhibits singularities; therefore, parallel transport frames can be used for smooth transitions to ensure global frame continuity.

[0159] The rotation matrix is ​​constructed using the Frenet frame: The matrix satisfies And det(R)=1, belonging to the special orthogonal group SO(3).

[0160] To unify the above geometric information into a pose sequence that can be directly used in robot kinematics, position and attitude are fused into a single SE(3) Lie group element:

[0161]

[0162] The homogeneous transformation matrix is ​​the pose matrix of the pose point, which describes the expected welding pose of the welding torch at each point on the weld.

[0163] To overcome the problems of time-varying load at the end of the welding robot arm due to continuous consumption of welding wire and inaccurate dynamic model caused by joint transmission flexibility, which in turn leads to a decrease in trajectory tracking accuracy, this application introduces the concept of dynamic residual. In step 210, the transmission flexibility parameters of each joint and the change in the end-effector moment of inertia of the welding robot arm are estimated using the dynamic residual of each joint. These key parameters are taken into account when calculating the welding driving torque of the joint, which can reduce the welding trajectory tracking error caused by load changes and joint transmission flexibility, and improve tracking accuracy.

[0164] This application proposes a dynamic model considering time-varying load and joint transmission flexibility in some embodiments. The core of this dynamic model lies in the explicit introduction of a time-varying term for the end-effector's moment of inertia caused by welding wire consumption, and elastic deformation and damping torque terms resulting from the joint's transmission flexibility, based on the traditional ideal rigid-body dynamic model of a robotic arm. This constructs a more realistic "rigid-flexible-time-varying load" coupled dynamic model, accurately transforming the ideal rigid-body dynamic model of the robotic arm into a practical flexible-time-varying load disturbance dynamic model. Furthermore, in some embodiments, based on this dynamic model, by constructing dynamic residuals and identifying the change in end-effector's moment of inertia and transmission flexibility parameters online, real-time adaptive estimation of key time-varying dynamic parameters such as the change in end-effector's moment of inertia, the equivalent stiffness of the joint, and the equivalent damping is achieved. This data is then used by the controller to calculate the welding drive torque, enabling the welding device to perceive and adaptively compensate for load changes and joint transmission flexibility online.

[0165] The following section will introduce the improved dynamic model and the estimation principles of key parameters such as the change in end-effector moment of the welding robot and the transmission flexibility parameters of the joints.

[0166] Consider a series welding robot arm with n joints, where n is an integer not less than 1, and the nth joint is the end effector joint. Typically, welding robots have at least two joints, and the following description is based on this. Under the assumption of ideal rigid bodies, all links of the welding robot arm are absolutely rigid bodies, the joints have no elastic deformation, and the end effector load is constant. Therefore, its dynamic behavior can be described by various classical robot arm joint dynamics equations. This paper uses the Lagrange equation as an example. In different implementations, other classical robot arm joint dynamics equations can be used based on the same principle. The Lagrange equation is as follows:

[0167]

[0168] in, Represent real numbers, The joint angle vector, composed of the joint angles of each joint (the unit can be rad), represents the current configuration of the welding robot arm. These are the angular velocity vector and angular acceleration vector, respectively, composed of the angular velocity (units can be rad / s) and angular acceleration (units can be rad / s²) of each joint; τ rigid The ideal torque vector (units can be expressed as follows) consists of the ideal driving torques required to maintain the motion of each joint. ); The nominal inertia matrix is ​​positive definite and symmetric, reflecting the resistance of the link's mass distribution to accelerated motion, and is determined by the joint angle vector q. The matrix represents the Coriolis force and centrifugal force, whose elements depend on the joint angle vector q and the angular velocity vector. ,satisfy It is an antisymmetric matrix; It is the gravitational torque vector, which is determined by the potential energy gradient of the center of mass of each link in the gravitational field and depends on the joint angle vector q.

[0169] As mentioned above, in actual welding operations, there are two main factors that cause the actual dynamics to deviate significantly from the rigid body dynamics model of the robotic arm: the flexibility of joint transmission represented by the harmonic reducer and the real-time change in end-load mass caused by the continuous consumption of welding wire. These will be analyzed separately below.

[0170] ① Flexible joint transmission, represented by harmonic reducers

[0171] Modern industrial robotic arms commonly use harmonic reducers as joint transmission mechanisms. Although they offer high transmission ratios and precision, the internal flexible gears have limited torsional stiffness, which affects the accuracy of the motor-side angle vector q measured by the motor-side encoder. m There is a small but not negligible elastic deformation between the output-side angle vector q measured by the output-side encoder and the output-side angle vector q:

[0172]

[0173] Where t represents time, q m q(t) and q(t) are the joint angle vector composed of the motor-side angles measured by the motor-side encoder at time t and the output-side angle vector composed of the actual joint angles measured by the output-side encoder, respectively. Let be the elastic deformation vector composed of the elastic deformation of each joint at time t. This deformation induces two types of torques: elastic restoring torque and viscous damping torque.

[0174] The elastic restoring torque can be expressed as ,in is the time-varying equivalent stiffness matrix. These represent the equivalent stiffness (units can be N·m / rad) of the first to nth joints at time t, specifically the equivalent torsional stiffness of the drive train (usually a harmonic reducer + motor shaft + connecting rod) of that joint. The equivalent stiffness is not constant and is affected by factors such as temperature rise, lubrication conditions, wear levels, and changes in assembly preload, potentially decreasing by 10%–30% during prolonged welding. Furthermore, during high-acceleration motion, the flexibility effect caused by the equivalent stiffness significantly amplifies trajectory tracking errors, especially during the high-speed oscillation phase at the end of the trajectory.

[0175] The viscous damping torque can be expressed as ,in The time-varying equivalent damping matrix mainly originates from internal friction of the reducer, oil film damping, bearing resistance, and structural internal losses. These represent the equivalent damping (units can be N·m·s / rad) for the first to nth joints at time t, specifically the equivalent viscous friction coefficient. Damping exhibits nonlinear characteristics (e.g., a mixture of Coulomb friction and viscous friction), but under small-signal excitation, it can be approximated as a linear time-varying parameter. Therefore, online damping identification helps suppress high-frequency vibrations and improve trajectory smoothness.

[0176] ② Real-time changes in end-load mass caused by continuous consumption of welding wire

[0177] During welding, the welding wire is fed into the molten pool at a constant rate and melts, causing the total mass of the end effector (including the welding torch and remaining welding wire) to decrease monotonically over time, and its center of mass to drift slowly. Although the change in the total mass of the end effector during a single welding operation is small (typically <5%), ignoring this change in high-precision trajectory tracking (such as thin-walled aerospace components) will introduce unacceptable phase lag.

[0178] set up Let be the total mass of the end effector at time t, and r(t) be the distance (approximately constant) from the center of mass of the end effector to the rotation axis of the end joint. Then, the equivalent moment of inertia of the end effector about the last joint (the nth axis) at time t is:

[0179]

[0180] because The change in terminal moment of inertia is slow (typical rate of change < 1 g / s). It is a slow time-varying positive scalar and satisfies:

[0181]

[0182] in Let be the initial terminal rotational inertia.

[0183] This change only significantly affects the last row / column of the inertia matrix because the inertia of the other links is much greater than the change in the end-effector's moment of inertia. Therefore, the inertia disturbance matrix caused by the change in the end-effector's moment of inertia can be approximated as:

[0184]

[0185] in It is the standard basis vector corresponding to the nth joint, which means that only the acceleration term of the nth joint is subject to additional inertia perturbation.

[0186] In summary, the measured torque vector is composed of the measured driving torques of each joint. satisfy:

[0187] ,

[0188] This is the true dynamic model that takes into account time-varying loads and the flexibility of joint transmission. Among them, The additional inertial force caused by the change in the equivalent moment of inertia of the end effector. and The elastic torque and damping generated by the flexible joint. This represents noise, including sensor noise, higher-order nonlinear friction, modeling truncation error, etc.

[0189] In control systems, the deviation between the dynamic model and the actual welding conditions is a major cause of performance degradation and even instability. To detect and compensate for these deviations online, this application introduces a core concept: Dynamic Residual, also known as Torque Residual. The dynamic residual vector is composed of the dynamic residuals of each joint. Defined as:

[0190] ,

[0191] In a servo drive system, the dynamic residual vector Typically, the torque constant can be derived from the motor current measured by the current sensor, providing high real-time performance. and These are the measured torque vector and the ideal torque vector at time t, respectively.

[0192] During the movement of the welding robotic arm, the angular velocity vector and angular acceleration vector It is also changing, and Represented in time-varying form and Substituting the actual dynamic model and the Lagrange equations, we get:

[0193]

[0194] in, This represents a real-time estimate of the elastic deformation.

[0195] inertia perturbation matrix Substituting into the calculation formula, we get:

[0196]

[0197] in The change in terminal moment of inertia at time t is defined as follows:

[0198] ,

[0199] This is a scalar time-varying parameter with an initial value of 0, which decreases monotonically as the welding wire is consumed.

[0200] In step 210, the change in end-effector moment of inertia is a parameter to be estimated. Simultaneously, the transmission flexibility parameters of each joint also need to be estimated. This introduces two key parameter vectors to be estimated: the equivalent stiffness vector... and equivalent damping vector ,in:

[0201] , .

[0202] Using a diagonal structure, matrix-vector multiplication can be simplified to element-wise multiplication:

[0203]

[0204]

[0205] in This represents the Hadamard (element-by-element) product.

[0206] Therefore, the dynamic residual equation can be rewritten in explicit parametric form:

[0207] .

[0208] Expanding and analyzing it according to joint indices j = 1, 2, ..., n, for the first n-1 non-terminal joints we have:

[0209] ,

[0210] in, This represents the dynamic residual of the j-th joint at time t. , , , and Let represent the equivalent damping, angular velocity, equivalent stiffness, elastic deformation, and noise of the j-th joint at time t, respectively. The first n-1 non-end-effector joints are unaffected by changes in end-effector load mass, and their dynamic residuals are determined solely by their local flexibility characteristics. This implies that the parameter identification of each non-end-effector joint is essentially an independent one-dimensional linear regression problem.

[0211] For the nth joint, i.e., the terminal joint:

[0212] ,

[0213] in, This represents the dynamic residual of the end joint at time t. , , , , and Let represent the equivalent damping, angular velocity, equivalent stiffness, elastic deformation, angular acceleration, and noise of the end joint at time t, respectively. and It is a flexible item. It is the inertia change term.

[0214] Define the estimated parameter vector Then all the time-varying physical parameters to be identified can be organized as follows:

[0215]

[0216] Among these, the ultimate goal is to estimate the equivalent moment of inertia at the end point. However, in this embodiment, the object of identification is its deviation relative to the nominal value I0. This refers to the change in terminal moment of inertia, which helps improve numerical stability and simplify initial condition settings. Then, the equivalent moment of inertia at the end point can be obtained from the initial moment of inertia I0. .

[0217] Based on the estimated parameter vector Dynamic residual vector It can be represented as:

[0218]

[0219] The regression matrix H(t) is determined by the motion state of each joint and has the following sparse block structure:

[0220]

[0221] Each row of this matrix corresponds to the dynamic residual equation of a joint, and each column corresponds to the excitation channel of a parameter to be estimated. Based on the above principle, ignoring uncertain noise, the dynamic residual vector can be used to... And regression matrix H(t) estimation .

[0222] Where the estimated parameter vector It is time-varying; the equivalent stiffness gradually decreases with temperature rise, the consumption of welding wire causes the effective moment of inertia at the end to continuously decrease, and the damping coefficient may also be slightly adjusted with lubrication conditions. Therefore, in order to estimate the transmission flexibility parameters of each joint and the change in the moment of inertia of the welding robot arm in a timely and accurate manner within each welding control cycle, this application proposes an online parameter estimation method that can converge quickly and track parameter drift. Specifically, step 210 includes... Figure 7 Steps 211 to 213 shown below will be explained in detail.

[0223] Step 211: Using the transmission flexibility parameters of each joint estimated in the previous welding control cycle, the change in the end moment of inertia of the welding robot arm, and the current motion state of each joint, estimate the dynamic residuals of each joint in the current welding control cycle, and obtain the estimated dynamic residuals.

[0224] In the first welding control cycle, due to a lack of prior knowledge, the initial value of 0 is usually used as the transmission flexibility parameters of each joint and the change in end-effector moment of inertia of the welding robot arm in the previous welding control cycle; that is, the end-effector equivalent moment of inertia is equal to the nominal value. Let's consider... Let represent the estimated parameter vector consisting of the transmission flexibility parameters of each joint and the change in the end-effector moment of inertia of the welding robot arm in the k-th (k is a positive integer) welding control cycle. Then we have This setting aligns with actual operating conditions, namely, when the welding device is cold-started, the welding wire is fully loaded and the reducer is at room temperature.

[0225] As analyzed above, the dynamic residual can be obtained from the regression matrix and the estimated parameter vector. Therefore, based on the current motion state of each joint, a regression matrix can be constructed, and the estimated dynamic residual can be obtained using the estimated parameter vector from the previous welding control cycle.

[0226] ,

[0227] in Let H(k) be the estimated dynamic residual vector composed of the estimated dynamic residuals of each joint in the k-th welding control cycle, and let H(k) be the regression matrix representing the motion state of each joint in the k-th welding control cycle. This represents the estimated parameter vector consisting of the transmission flexibility parameters of each joint and the change in the end-effector moment of the welding robot arm during the (k-1)th welding control cycle.

[0228] In some embodiments, the motion state of non-end-effector joints includes elastic deformation and angular velocity, while the motion state of end-effector joints includes elastic deformation, angular velocity, and angular acceleration. Based on the analysis above, we can conclude that:

[0229]

[0230] in, and These represent the elastic deformation of the first joint and the end joint during the k-th welding control cycle, respectively. and These are the angular velocities of the first joint and the end joint in the k-th welding control cycle, respectively. Let be the angular acceleration of the joint at the end of the k-th welding control cycle. This matrix consists entirely of known physical quantities and does not include any unknown quantities, ensuring the feasibility of the algorithm.

[0231] In addition, the dynamic residual vector of the current welding control cycle is obtained:

[0232]

[0233] in, and These are the measured driving torque and the ideal driving torque for the k-th welding control cycle, respectively. , and These are the joint angle vector, angular velocity vector, and angular acceleration vector for the k-th welding control cycle, respectively.

[0234] The quality of the dynamic residual vector directly determines the performance of parameter identification; therefore, in some embodiments... Appropriate filtering (such as low-pass filtering or using a state observer) is employed to suppress differential noise; and the measured driving torque can be... Compensation driver delay and static friction.

[0235] Step 212: Difference the dynamic residual and the estimated dynamic residual to obtain the dynamic residual error, i.e.

[0236] .

[0237] Step 213: Use dynamic residual error to correct the transmission flexibility parameters of each joint and the change in end-effector moment of the welding robot obtained from the previous welding control cycle, and obtain the transmission flexibility parameters of each joint and the change in end-effector moment of the welding robot in the current welding control cycle.

[0238] For example, the dynamic residual error can be multiplied by a coefficient and then compared with... Summation yields In one embodiment of this application, a gain matrix K(k) is set to adjust the magnitude of the correction:

[0239]

[0240] In some embodiments, a parameter estimation error covariance matrix P(k) is set to reflect the uncertainty of the estimated parameter vector, and its initial value is P(0) = α1I, where I is the identity matrix with dimension 2n+1, and α1 > 1. Here, α1 can take a value much greater than 1, for example, 10. 4 This allows the initial parameter estimation error covariance matrix to be a large numerical diagonal matrix, meaning that the parameters to be estimated are all unknown. This allows early data to have a strong influence on the estimation results, accelerating convergence. Based on this, the gain matrix K(k) is...

[0241]

[0242] Where P(k-1) is the parameter estimation error covariance matrix of the (k-1)th welding control cycle, λ is the forgetting factor and λ < 1, the forgetting factor λ is a key hyperparameter; numerator Measuring the potential impact of prior data on the parameters to be estimated; scalars in the denominator. It serves as a normalization mechanism to prevent excessive gain from causing instability. This gain matrix can adaptively adjust the correction magnitude, with a larger correction magnitude when the uncertainty is high (large P(k-1)) or the excitation is strong (large H(k)).

[0243] In each welding control cycle, the parameter estimation error covariance matrix is ​​also updated synchronously according to the following formula:

[0244]

[0245] Here, P(k) is the parameter estimation error covariance matrix for the k-th welding control cycle. This update ensures that the parameter estimation error covariance matrix always reflects the reliability of the current estimated parameter vector. As data accumulates, P(k) typically decreases gradually (the estimation becomes more certain), but because λ < 1, it will not tend to zero, always retaining sensitivity to new changes.

[0246] In some embodiments, to ensure the reasonableness of the estimation results, physical boundaries are forcibly imposed on the estimation results of each parameter, and a lower limit value of equivalent stiffness is preset. The lower limit of equivalent damping c min and the lower limit of the terminal moment of inertia I min Then, after step 213, the following steps are also included:

[0247] After estimating the equivalent stiffness of each joint, it is compared with a preset lower limit value for equivalent stiffness. The larger of the two values ​​is taken as the final equivalent stiffness of the joint; after estimating the equivalent damping of each joint, it is compared with the preset lower limit value c of the equivalent damping. min The larger of the two values ​​is taken as the final equivalent damping of the joint. After estimating the change in end-effector moment of inertia of the welding robot arm, the current end-effector moment of inertia is calculated based on the initial end-effector moment of inertia and the change in end-effector moment of inertia. The current end-effector moment of inertia is then compared with the preset lower limit value I of the end-effector moment of inertia. min The two are compared, and the larger one is taken as the final current end moment of inertia. Based on this, the final change in end moment of inertia is obtained.

[0248] Expressed as a formula:

[0249]

[0250] in, This represents the estimated equivalent stiffness of the j-th joint during the k-th welding control cycle. This represents the estimated equivalent damping of the j-th joint in the k-th welding control cycle. This represents the estimated change in end-effector moment of inertia during the k-th welding control cycle. This is because joint stiffness cannot be negative or zero (otherwise the structure would be unstable), and typical values ​​are 30% to 50% of the nominal value; similarly, damping is non-negative, hence c min >0 can be set to a very small positive number; I min >0 can be set to the inertia corresponding only to the mass of the welding torch.

[0251] The final output is the complete estimated parameter vector:

[0252]

[0253] in, These are the equivalent stiffnesses of the first to nth joints estimated during the k-th welding control cycle. These are the equivalent damping values ​​for the first to nth joints estimated during the k-th welding control cycle.

[0254] The online parameter estimation method described in the above embodiments constructs a complete closed loop: physical mechanism modeling → linear regression reconstruction → online parameter identification with forgetting factor → physical constraint projection. This achieves efficient, robust, and physically interpretable online estimation of key time-varying dynamic parameters of the welding robot arm, such as transmission flexibility parameters and end-effector moment of inertia. These key time-varying dynamic parameters can be updated in real time during each welding control cycle for subsequent welding drive torque calculation, significantly improving welding trajectory tracking accuracy.

[0255] Step 220 involves determining the welding driving torque that drives the joint movement. In some embodiments of this application, the welding driving torque of each joint is determined based on model predictive control (MPC). Specifically, step 220 includes... Figure 8 Steps 221 to 223 shown below will be explained in detail.

[0256] Step 221: Based on the motion state of each joint, the transmission flexibility parameters, and the change in the end-effector moment of the welding robot, calculate the feedforward torque of each joint.

[0257] The feedforward torque can be calculated based on the modified joint dynamics equation of the robotic arm. The modified joint dynamics equation is obtained by adding a compensation term determined by the transmission flexibility parameters of each joint and the change in the end-effector moment of the welding robotic arm to the classic joint dynamics equation.

[0258] In some embodiments, the motion states of each joint include elastic deformation, angular velocity, and angular acceleration; based on the analysis above, the modified joint dynamics equations are as follows:

[0259] ,

[0260] in, This is the feedforward torque vector composed of the feedforward torques of each joint in the k-th welding control cycle. , , It is the elastic deformation vector composed of the elastic deformation of each joint in the k-th welding control cycle.

[0261] Step 222: Based on the desired welding trajectory, the transmission flexibility parameters of each joint, and the change in the end-effector moment of inertia of the welding robot, construct the state vector for the current welding control cycle. Using the desired welding trajectory as the reference trajectory and the driving torque vector composed of the welding driving torques of each joint as the control input vector, solve the model predictive control problem to obtain the feedback torque of each joint. The welding driving torque is expressed as the sum of the feedforward torque and the feedback torque.

[0262] The inventors believe that, to better handle welding tasks on complex spatial curved surfaces, the controller's decisions cannot rely solely on raw sensor data or low-dimensional error signals. Instead, they must integrate two fundamentally different types of prior knowledge: geometric priors and physical priors. The geometric prior, derived from the desired welding trajectory obtained in step 100, provides weld shape information and, based on the current welding time and / or the welding torch position, can determine the desired welding pose of the welding torch for the current welding control cycle. The physical prior, derived from dynamic parameters such as transmission flexibility parameters and end-effector moment of inertia changes estimated in real-time in step 210, integrates these two types of prior knowledge for predicting the feedback torque. Together with the feedforward torque calculated based on the transmission flexibility parameters and end-effector moment of inertia changes, the welding driving torque is determined, thereby improving the welding trajectory tracking accuracy and welding quality of complex spatial curved surface components.

[0263] Therefore, in this embodiment, a state vector is constructed by combining the expected welding pose of the welding torch in the current welding control cycle, the transmission flexibility parameters of each joint, and the change in the end moment of inertia of the welding robot arm. These vectors can be fused into a single vector as the state vector, or they can be fused after feature extraction as the state vector.

[0264] The cost function of model predictive control can be constructed according to the optimization objectives that need to be controlled in the welding task. The optimization objectives include at least minimizing the error between the welding torch position and the desired welding trajectory, and may also include optimization objectives such as minimizing energy consumption.

[0265] In the cost function, the welding driving torque is expressed as the sum of the feedforward torque and the feedback torque. Since the feedforward torque has been obtained in step 221, the feedback torque can be obtained by performing MPC optimization based on the cost function. The feedback torque is used to compensate for model mismatch, external disturbances, and unmodeled dynamics.

[0266] Step 223: Calculate the sum of the feedforward torque and feedback torque of each joint to obtain the welding driving torque of each joint.

[0267] The inventors argue that geometric priors and physical priors naturally exist in mathematical spaces of different properties. Geometric priors are inherent in nonlinear Lie group manifolds, while physical priors belong to Euclidean vector spaces. Directly concatenating or simply weighting these priors can easily lead to the loss of structural information and confusion in the optimization direction. Therefore, some embodiments of this application propose a dual-manifold embedding mechanism, which maps these two heterogeneous types of information to a unified but structurally preserved latent representation space to construct state vectors, laying the foundation for subsequent coupled prediction and multi-objective optimization.

[0268] Please refer to Figure 9 In this embodiment, the process of constructing the state vector of the current welding control cycle based on the desired welding trajectory, the transmission flexibility parameters of each joint, and the change in the end moment of inertia of the welding robot arm includes the following steps 222a to 222e, wherein steps 222a to 222b are for obtaining the geometric manifold embedding, steps 222c to 222d are for obtaining the dynamic manifold embedding, and step 222e is for splicing the two types of embedding results to form a unified joint potential state.

[0269] Step 222a: Based on the desired welding trajectory, obtain the desired welding pose of the welding torch in the current welding control cycle, and map it to the tangent space to obtain the geometric feature vector.

[0270] The desired welding pose of the welding torch in the current welding control cycle can be obtained from the pose sequence parameterized by the arc length.

[0271]

[0272] Where s(k) is the arc length parameter of the kth welding control cycle, obtained through the actual speed of the integral end effector:

[0273]

[0274] Where tk is the time corresponding to the k-th welding control cycle. This represents the actual speed of the end effector.

[0275] Next, we use Lie algebraic projection to map the group elements to their tangent space, which has good vector space properties. We define the Lie algebraic logarithmic mapping:

[0276]

[0277] , for the desired welding position. Let the axis angle of rotation be represented, satisfying , It is an antisymmetric matrix operator.

[0278] Based on the above Lie algebra logarithmic mapping, the desired welding pose is mapped to the tangent space to obtain the geometric feature vector.

[0279] Step 222b: Perform feature encoding on the geometric feature vectors to obtain the geometric latent vectors.

[0280] In some embodiments, to further extract higher-order geometric features, a graph neural network is used as a geometric encoder to encode the geometric feature vectors to obtain the geometric latent vectors.

[0281]

[0282] It is A low-dimensional vector is used to compactly and structurally encode the local and global geometric features of the weld position of the welding torch at the current moment. It is a more generalized geometric encoder symbol. This represents a graph neural network. Instead of operating on a traditional graph structure, this graph neural network treats the neighboring points (e.g., pose points) of the current desired welding position obtained along the desired welding trajectory as nodes, and the geometric feature vectors of the neighboring points as the feature vectors of the nodes, constructing a local spatiotemporal graph. Edge weights are defined by the arc distance and curvature similarity between two nodes on the desired welding trajectory. This is achieved through a message passing mechanism. It can capture the local differential geometric properties of the weld and its global orientation consistency. Final output. It is a structure-aware geometric latent vector that retains the pose information of SE(3) and also contains the semantic features of the weld shape.

[0283] Step 222c: Calculate the equivalent modal frequency based on the equivalent stiffness and equivalent moment of inertia of each joint; calculate the damping ratio based on the equivalent stiffness, equivalent moment of inertia and equivalent damping of each joint; calculate the rate of change of end moment of inertia based on the change in end moment of inertia of the welding robot arm; and form a dynamic characteristic vector from the equivalent modal frequency, damping ratio and rate of change of end moment of inertia of each joint.

[0284] If the estimated parameter vector is directly used Inputting the data into a neural network can be difficult for the network to understand, as the network struggles to comprehend the physical coupling relationships. Therefore, in this embodiment, it is first transformed into a more physically meaningful dynamic feature vector. Here, the equivalent modal frequency of the j-th joint is... ,in Let be the equivalent rotational inertia of the j-th joint; damping ratio. This characterizes the rate of vibration decay; while the rate of change of the terminal moment of inertia... It can be based on the change in the moment of inertia at the end. The terminal equivalent moment of inertia is calculated from the nominal value I0. Then, it was estimated using a sliding window difference method, which reflects the rate of welding wire consumption.

[0285] The above transformation can be achieved using a differentiable analytical feature extraction function. express:

[0286] .

[0287] Step 222d: Perform feature encoding on the dynamic feature vector to obtain the dynamic potential vector.

[0288] In some embodiments, a fully connected network (e.g., a multilayer perceptron) is used as a differentiable physical encoder, and the dynamic feature vector is input into the fully connected network to obtain the dynamic latent vector. , can be represented as:

[0289]

[0290] Where, d d MLP represents the dimension of the dynamic latent vector. d Represents a multilayer perceptron. Dynamic latent vector. It is a compressed and information-rich dynamic state representation that reflects the current dynamic properties of the robotic arm.

[0291] This fully connected network, trained end-to-end, can automatically learn which modal features have the greatest impact on welding trajectory tracking error, energy consumption, and / or thermal stress. Because It is a differentiable function, and the entire embedding process supports gradient backpropagation, which facilitates joint optimization with the upper-level controller.

[0292] Step 222e: Concatenate the geometric latent vector and the dynamic latent vector to obtain the state vector for the current welding control cycle. This can be represented as:

[0293] ,

[0294] State vector It contains the complete context.

[0295] In order to indirectly ensure the uniformity of welding heat input by constraining the rate of change of welding speed, thereby reducing thermal stress and deformation, minimizing trajectory tracking error, and reducing energy consumption, an embodiment of this application designs an optimal trajectory prediction control strategy based on the fusion of multiple objectives of "accuracy-energy consumption-thermal stress". A core aspect of this control strategy lies in using a state vector that integrates geometric and dynamic prior information (e.g., the dual-manifold embedding mechanism in the above embodiment, which couples heterogeneous geometric and physical priors in a unified latent space for prediction). It employs cross-manifold neural differential equations (Neural ODEs) for state prediction and introduces a thermal stress topology regularization term based on continuous homology. In some embodiments, a causal-aware multi-objective weight generator dynamically adjusts the optimization weights of three optimization objectives: welding trajectory tracking error, welding driving torque, and thermal input uniformity. Causal analysis and topological data analysis techniques are used to intelligently balance conflicting control objectives, representing another core innovation of this control strategy. Ultimately, within the model predictive control framework, a finite-time optimal control problem integrating multi-objective optimization, causal awareness, and thermal stress topology regularization is solved in a rolling manner. This achieves high-precision trajectory tracking while actively mitigating thermal input fluctuations, optimizing energy consumption, and fundamentally suppressing welding residual stress and deformation, thereby significantly improving the overall quality, accuracy, and process consistency of welding complex spatial curved surface components.

[0296] In this embodiment, the cost function for the model predictive control problem is:

[0297]

[0298]

[0299]

[0300] Where k is the cycle number of the current welding control cycle, H is the prediction time domain length, and H is an integer not less than 2, τ(k+i) and τ(k+i-1) represent the driving torque vectors of the k+i and k+i-1 welding control cycles, respectively. ff (k+i) and τ fb(k+i) represent the feedforward torque vector and feedback torque vector of the (k+i)th welding control cycle, respectively; z(k+i) and z(k+i-1) represent the state vectors of the (k+i)th and (k+i-1)th welding control cycles, respectively, and for i = 1, 2, ..., H-1, z(k+i) is predicted based on z(k+i-1) and τ(k+i-1), and f(z(k+i-1), τ(k+i-1)) represents the prediction function of z(k+i) predicted based on z(k+i-1) and τ(k+i-1); e pos (k+i) represents the error between the position of the welding torch and the desired welding position obtained based on the desired welding trajectory during the (k+i)th welding control cycle, characterizing the welding trajectory tracking error. The position of the welding torch during the (k+i)th welding control cycle is obtained by reconstructing the state vector z(k+i) through a decoder. Let be the welding heat input rate during the (k+i)th welding control cycle. Let w1(k+i), w2(k+i), and w3(k+i) be the variance of the welding heat input during the (k+i)th welding control cycle; w1(k+i), w2(k+i), and w3(k+i) are the weights during the (k+i)th welding control cycle, respectively. q represents the thermal stress topological regularization term, with β1 being its coefficient; j (k+i) represents the joint angle of the j-th joint during the (k+i)-th welding control cycle, q min and q max These are the upper limit and lower limit of the joint angle, respectively; τ j (k+i) represents the welding driving torque τ of the j-th joint during the (k+i)-th welding control cycle. max This represents the upper limit of the welding driving torque.

[0301] For the prediction function f(z(k+i-1), τ(k+i-1)), one embodiment constructs a cross-manifold neural differential equation, which incorporates state vectors from both the geometric and dynamical manifolds. It is viewed as a unified but heterogeneous system state, serving as the initial state and evolutionary basis for the cross-manifold neural differential equation, and is transmitted through a parameterized, learnable vector field. Describe its continuous-time evolution:

[0302]

[0303] Where t represents time. The inputs are the state vector z(t) and the driving torque vector τ(t) at time t, and the parameter set is... The neural network. The entire equation defines a continuous-time dynamic system, whose solution z(t) describes how the "geo-dynamic joint state" evolves with time and control action.

[0304] Therefore, assuming the current time is t0, given the state vector z(t0) at the current time t0 and the future driving torque vector τ(t), the state vector after time Δt can be predicted through numerical integration:

[0305]

[0306] Therefore, we can obtain

[0307]

[0308] Some embodiments employ the Runge-Kutta-Fehlberg method with adaptive step size for efficient integration, ensuring automatic dense sampling in curvature abrupt change regions and sparse computation in straight sections, balancing accuracy and efficiency.

[0309] Traditional ODE (Ordinary Differential Equations) solvers struggle with backpropagation of gradients. Therefore, in some embodiments of this application, the adjoint method is employed, defining adjoint variables. L is the final loss, and the accompanying variables satisfy the inverse ODE:

[0310]

[0311] By simultaneously integrating the state vector With inverse integrals and associated variables It can efficiently calculate the loss gradient. This enables end-to-end training of the entire transmanifold neural differential equation.

[0312] For neural networks To capture asymmetric, context-dependent interaction conditional dependencies, it is explicitly decomposed into two sub-networks, and a bidirectional cross-attention mechanism is introduced to construct an attention-coupled network model:

[0313]

[0314] in, , which is the first sub-neural network used to update the geometric latent vector; , which is the second sub-neural network used to update the dynamic potential vector; and Let be the geometric latent vector and the dynamic latent vector at time t, respectively; and It is a learnable attention weight matrix that enables dynamic information routing between manifolds.

[0315] To achieve dynamic information routing between manifolds, some embodiments set

[0316]

[0317]

[0318] in, and These are the learnable first query weight matrix and the second query weight matrix, respectively. and These are the learnable first and second bond weight matrices, d k The key / query dimension, consistent with the state vector dimension, is used for scaling to avoid gradient saturation. The Softmax function is used for row normalization, ensuring that each geometric feature dimension focuses on a weighted combination of dynamic features.

[0319] This embodiment achieves collaborative optimization of "shape-guided dynamic response and dynamic constraint geometric feasibility" by using a cross-attention mechanism between manifolds, where geometric and dynamic prior information interact dynamically during the prediction process.

[0320] Using the above prediction function, z(k+i) can be predicted from z(k), and then the position p of the welding torch at the (k+i)th welding control cycle can be obtained by a decoder. ee (k+i). Therefore, the future welding trajectory of the welding torch can be predicted. The decoder can employ various existing decoder networks, which will not be elaborated upon here. The position error is then... ,in, This refers to the desired welding position obtained based on the desired welding trajectory.

[0321] In the cost function This indicates the magnitude of the motor torque, and

[0322]

[0323] It reflects the total strength of the motor output torque at each joint, and is highly positively correlated with instantaneous power consumption and joint heating. It is a proxy indicator of energy consumption and mechanical stress.

[0324] Within each welding control cycle, the controller iteratively searches for the optimal torque evolution trajectory (including the torque at future moments) in the search space, making the future welding trajectory predicted by Neural ODE as close as possible to the desired welding trajectory. Based on the optimal torque evolution trajectory, the controller uses continuous-time evolution Neural ODE to predict the future welding trajectory, and then obtains the feedforward torque for the future welding control cycle through inverse dynamics.

[0325] Welding heat input rate Where I(k+i) and V(k+i) are the welding current and arc voltage during the (k+i)th welding control cycle, respectively, and η is the thermal efficiency constant. Welding heat input variance The welding heat input rate can be estimated by setting a sliding window and utilizing the rate within the sliding window. The variance of the welding heat input characterizes the uniformity of the heat input.

[0326] The heat input rate is affected by the end-effector speed of the welding robot. The controller predicts the thermal stress on the future welding trajectory. If thermal stress concentration is predicted to occur on the future trajectory, the controller will adjust the future input torque and change the end-effector speed of the welding robot, thereby changing the future heat input rate and obtaining the heat input rate for the future welding control cycle.

[0327] For the weights w1(k+i), w2(k+i), and w3(k+i) of each item, fixed or dynamic decision weights can be set according to the actual needs of the optimization objectives of each item under the actual welding conditions.

[0328] To balance the three optimization objectives, one embodiment of this application uses kernel space Granger causality analysis to dynamically evaluate the impact of each optimization objective on overall performance and adaptively generate the weights of each objective. Furthermore, considering that the changes in position error, motor torque amplitude, and welding heat input rate are nonlinear dynamic processes, kernel ridge regression is used to fit the nonlinear relationship in the regeneration kernel Hilbert space, overcoming the limitations of linear Granger causality in modeling nonlinear dynamics. The causal strength is calculated as follows:

[0329]

[0330] in, This represents the causal contribution of variable m to variable l. The closer the value is to 1, the more crucial the historical information of variable l is to predict variable m, indicating the existence of a strong causal chain. This represents the mean squared error of the baseline model using the kernel-space Granger causality method to predict the future value of variable m without introducing variable l. This represents the mean squared error in predicting the future value of variable m when variable l is introduced as a prior condition. The formula expresses the ratio of the mean squared error differences when using historical information of variable l to predict variable m. In this embodiment, variables 1, 2, and 3 are the location errors, respectively. Motor torque amplitude and welding heat input variance .

[0331] Let matrix This represents the causal graph between the three variables mentioned above. Using the causal graph, the weights of each optimization objective can be dynamically adjusted based on the performance of each objective in the (k+i)th welding control cycle. Let...

[0332] ,

[0333] Treating the causal graph C as an influence propagation matrix, we can perform causal diffusion of each cost:

[0334] .

[0335] Finally, by using temperature parameters The Softmax function generates normalized weights:

[0336]

[0337] Wherein, α2 is a preset temperature coefficient used to reflect the weight of heat input rate; the larger α2 is, the greater the weight of heat input rate. for The h-th element.

[0338] For the (k+i)th welding control cycle, the weights w1(k+i), w2(k+i), and w3(k+i) are determined by the above formula.

[0339] Thermal stress topological regularization term It can characterize the degree of residual stress or deformation caused by thermal stress. In one embodiment of this application, the thermal stress topological regularization term is obtained by analyzing the thermal stress field of a pre-constructed weld using a continuous homology method. .

[0340] To estimate the thermal stress on the weld surface in real time, a thermal stress field of the weld needs to be constructed. In some embodiments, the thermal stress at position x at time t can be approximately calculated based on the pre-constructed weld temperature field T(x,t) and the linear elastic thermal stress relationship, thus obtaining the thermal stress field. :

[0341]

[0342] Where D is the elastic tensor. Let T be the coefficient of thermal expansion, T0 be the ambient temperature, and T(x,t) be the temperature at position x at time t.

[0343] The weld temperature field T(x,t) can be any temperature field suitable for describing the heat conduction in the weld during welding. In one embodiment, a lightweight but physically consistent weld temperature field T(x,t) is constructed to obtain real-time thermal stress estimates, avoiding reliance on time-consuming finite element simulations. This weld temperature field T(x,t) is determined by the following equation:

[0344]

[0345] Where x represents position, T(x,t) represents the temperature at position x at time t, and k T (x,t) represents the thermal conductivity that varies with space and time. This is the volumetric heat source term (units can be W / m³), which is determined by the motion state of the welding torch and the arc parameters.

[0346] Thermal conductivity is not constant; it is modulated by the curvature at position x on the desired welding trajectory, specifically:

[0347]

[0348] Where s(x) is the arc length corresponding to position x. Let k0 be the curvature of the desired welding trajectory at arc length s, and k0 be the reference thermal conductivity. These are preset coefficients.

[0349] In one embodiment, the motion state of the welding torch includes the position and speed of the welding torch, and the heat source The distribution is not uniform; it is determined by both the motion of the welding torch and the arc parameters.

[0350]

[0351] in, Let I(t) be the Gaussian heat source distribution function, and let I(t) and V(t) be the welding current and arc voltage at time t, respectively, derived from real-time feedback from the welding power source. and The positions and speeds of the welding torch at time t are respectively.

[0352] In some embodiments, the thermal stress field can be Sampling is performed at discrete grid point x to form a spatiotemporal thermal stress point cloud. Based on this thermal stress field, for the (k+i)th welding control cycle, a family of lower level sets is defined. :

[0353]

[0354] Where, x i For the i-th discrete grid point, For maximum stress, This is the thermal stress threshold.

[0355] Make the thermal stress threshold As the stress increases from 0 to the maximum, the low-stress regions (regions below the thermal stress threshold) gradually grow and connect; this process constitutes a filtered complex. The connections and cancellations of topological features (such as "hole" structures) in the thermal stress field are recorded. Whenever a new low-stress region (denoted as the i-th low-stress region) appears, a connected component is created, and the thermal stress threshold at this time is recorded. When two connected components merge, one of them cancels out the other. The thermal stress threshold at which the i-th low-stress region disappears is recorded. The final thermal stress topological regularization term is:

[0356]

[0357] in The longest survival interval or longest lifetime is the length of the topological features in the thermal stress field obtained based on the thermal stress field of the weld at the (k+i)th welding control cycle. The larger this value is, the more stable and wide-ranging the low-stress region is, meaning that the high-stress region is effectively compressed into a few connected blocks, or even a single region. Conversely, if this value is very small, it means that the low-stress region is fragmented and the high-stress region is distributed in a spot-like pattern, which is prone to multi-point failure.

[0358] To ensure that control commands are executable and safe, this embodiment also applies hard constraints to the joint position and the magnitude of the motor torque, including joint limit constraints: Motor torque saturation constraint: These constraints are strictly satisfied during optimization to avoid mechanical collisions or motor drive overload.

[0359] For the joint angle, in each welding control cycle, the controller performs continuous-time evolution based on Neural ODE to predict the state vector of the future welding control cycle, and then uses the integral result of the future time domain integration to obtain the future joint angle using inverse kinematics.

[0360] In each welding control cycle, the controller performs a finite-time rolling optimization based on the aforementioned cost function to solve for the optimal feedback torque sequence for the next H welding control cycles. The optimal feedback torque from the first step (i=0) is obtained as the feedback torque for the current welding control cycle, and the rest are discarded. In the next welding control cycle, the state is re-observed, the costs and weights of each term are updated, and the thermal stress topology regularization term is adjusted again for optimization. Therefore, the control command ultimately sent to the motor driver in the current welding control cycle is:

[0361]

[0362] The following detailed description of a specific embodiment further illustrates this application. The welding robotic arm is a six-degree-of-freedom industrial welding robotic arm, widely used in welding production lines for automobile bodies, etc., featuring high repeatability (±0.05 mm) and a maximum load capacity of 16 kg. A 3D laser scanner is installed at the end effector of the welding robotic arm. The sensor system includes dual encoders (including a motor-side encoder and an output-side encoder), a current sensor, a temperature sensor, a six-dimensional force sensor, and a robot calibration sensor.

[0363] This embodiment illustrates a repair welding scenario for the leading edge of an engine turbine blade. The blade is a metal component with a complex three-dimensional curved surface, and the area to be welded is an irregular weld seam distributed along the leading edge of the blade. Due to thermal deformation during long-term service, the actual geometry of the blade deviates from the original CAD design model by approximately 0.5mm to 2.0mm.

[0364] Before welding begins, hand-eye calibration is first performed to obtain the homogeneous transformation matrix from the scanner coordinate system S to the robot base coordinate system B. The calibration results are as follows:

[0365]

[0366] The first three rows of the last column form a translation vector, representing the coordinates of the optical center of the 3D laser scanner in the robot's base coordinate system as (1500.5, -200.2, 850.8) mm. The welding robotic arm drives the 3D laser scanner, following a preset "Z"-shaped trajectory, to scan the weld seam and its surrounding area at a distance of approximately 150 mm from the blade surface, obtaining the original point cloud data of the blade. The coordinates of each data point are then transformed using a homogeneous transformation matrix. After transforming to the robot's base coordinate system, we obtain the original point cloud data P in a unified coordinate system, containing N=856320 points, with the data format as follows: .

[0367] Calculate the normal vector and eigenvalue for each point in the original point cloud data P. For any point p in the point cloud... i For example, p i =(1206.50, -352.80, 651.00), take its value. The second neighborhood is formed by the 20 nearest neighbors. Calculate the centroid of the second neighborhood. = (1206.53, -352.75, 650.91). Calculate the covariance matrix using the formula:

[0368]

[0369] The result is C. i = [ 0.025 0.001 -0.089 ] [ 0.001 0.152 0.003 ] [ -0.089 0.003 0.320 ]. For C i Eigenvalue decomposition yields three eigenvalues. =0.345, =0.151, =0.001. Minimum eigenvalue The corresponding eigenvector is the normal vector n of that point.i n i = [0.785, 0.021, -0.619], This is the characteristic value of that point.

[0370] The original point cloud data is then smoothed based on eigenvalues ​​to effectively preserve sharp features such as weld bevels while filtering out noise, resulting in smoothed coordinates. :

[0371] .

[0372] Subsequently, voxel downsampling was used, with the voxel size set to 0.5 mm, to downsample the smoothed point cloud and obtain a more uniformly distributed dataset with lower computational cost. Finally, a smooth and uniform enhanced point cloud was obtained. The number of points has decreased to 182,450.

[0373] There is shadow obscuring the root of the weld seam on the blade. There are two obvious holes in the data, with a total loss of about 5%. The point cloud containing these holes... As a condition, the data is input into a pre-trained point cloud completion diffusion model for completion. This model uses a loss function to process a large amount of data on similar curved surface components. The training process was conducted. The point cloud completion diffusion model generates new points in the hole regions through an iterative denoising process. These new points maintain geometric continuity and smoothness with the surrounding point cloud. Finally, a complete point cloud without holes is output, with the number of points increased to 191,580.

[0374] For each point, its feature vector is extracted in three neighborhoods with radii r1=5mm, r2=10mm, and r3=20mm. These feature vectors are then fused by concatenation and other methods to serve as the feature representation vector token of that point, which is then input into the Transformer model to obtain a three-dimensional semantic feature vector.

[0375] Subsequently, using the optical center of the 3D laser scanner as the center, the 3D point cloud is converted into a panoramic 2D depth map through spherical projection. On the 2D depth map, models such as SAM are used to automatically segment and obtain the 2D semantic feature vector f of each point. 2D (u,v), then backprojected to the corresponding 3D point p i : Finally, in the segmentation network, the 3D semantic feature vector f of the 3D points is... 3D (i) The two-dimensional semantic feature vector obtained by its back projection The fusion process yields the fused global information. :

[0376]

[0377] The global information of each point is input into the first multilayer perceptron for classification to obtain the semantic label of each point. The statistics of each type of point after segmentation are as follows:

[0378] quantity 15230 172850 3500

[0379] By back-projecting two-dimensional features to three-dimensional points and fusing them with three-dimensional features, approximately 3% of boundary misclassification points were corrected, making segmentation more accurate at weld edges and reflective areas. Finally, a more accurate semantic segmentation point cloud optimized by two-dimensional and three-dimensional multimodal information was output.

[0380] All weld points were selected to form a weld point cloud:

[0381] .

[0382] The point cloud contains a total of 15,230 points.

[0383] To extract continuous centerlines from a discrete set of weld points, a sliding window combined with principal component analysis (PCA) is used. A 10mm wide window is set on the weld point cloud and slid along the approximate direction of the weld point cloud, capturing the center point within the window. For example, within a window containing 150 weld points, PCA is performed, calculating the first principal component direction (i.e., the local tangent direction) as v1 = [0.08, 0.99, -0.12], and the geometric center of the points within the window is c. win =(1206.10, -360.50, 652.30), then slide along this tangent direction to the next window. Connect the geometric centers of all windows to obtain an initial centerline containing approximately 200 points. To smooth it, fit it using a first-order B-spline function of degree 3 to obtain the weld centerline:

[0384]

[0385] Among them, control points There are 30 control points in total. The positions of these 30 control points were obtained through optimization calculation using the least squares method. The first 3 control points are: = (1205.15, -348.90, 650.18) = (1205.42, -355.23, 651.05) = (1205.80, -361.48, 652.41).

[0386] The average deviation between the obtained weld centerline and the blade CAD model is approximately 1.2 mm. Non-rigid registration is then performed between the weld centerline and the blade CAD model. The energy function is then iteratively optimized. Find the optimal displacement of the control points for the first B-spline function. This allows the deformed point cloud T(p) to be closest to the point on the CAD model. The distance is minimized. After 30 iterations, the energy function converges, registration is completed, and the desired welding trajectory is obtained. The desired welding trajectory is precisely aligned to the CAD model coordinate system. The average residual after registration is reduced to 0.15mm, achieving precise correlation between the desired welding trajectory and the reference model of the blade design.

[0387] After completing the non-rigid registration, the desired welding trajectory is obtained as a smooth B-spline curve c(s) aligned with the CAD model coordinate system of the blade, accurately describing the geometric center of the actual weld, where the parameter s ranges from [0, 1]. This continuous geometric curve is then converted into a timestamped discrete pose sequence that the controller can execute. The target welding speed v of the welding torch is set to 8.0 mm / s, and the discretization step size of the desired welding trajectory is set... The value is 0.05. A robot tool coordinate system is constructed at the tip of the welding torch, and the robot tool coordinate system {Tool} is defined as follows:

[0388] Z-axis (t): points in the welding direction, i.e., the tangent direction of the curve;

[0389] X-axis (n): The direction pointing to the normal to the weld surface, used to control the tilt angle of the welding torch;

[0390] Y-axis (b): Determined by t and n using the right-hand rule. ).

[0391] First, the robot tool coordinate system is calibrated using a robot calibration sensor.

[0392] The robot calibration sensor has multiple laser points, for example, four. First, the welding torch rotates once around the center point within the robot calibration sensor. When it passes a laser point, the robot calibration sensor emits an I / O signal. At this time, the controller records the position of the current point in the robot's tool coordinate system {Tool} at the rising and falling edges of the I / O signal emitted by the robot calibration sensor for each laser point. Then, the welding torch is lowered by a certain height. Then, rotate around the center point again and record the position of each laser point when it is triggered by the rising edge and the falling edge. Calculate the rotational offset of the welding torch around the x-axis and y-axis based on the 16 positions.

[0393] Modify the attitude offset of the current robot tool coordinate system {Tool} based on the rotation offset. Rotate the new robot tool coordinate system {Tool1} around the robot calibration sensor to obtain the positions of the laser point when it is triggered by the rising edge and the falling edge. Calculate the midpoint O of the robot tool coordinate system {Tool1} using these 8 points, and find the vertex of the welding torch tip on the vertical line of this midpoint. Record its position in the current robot tool coordinate system and calculate the welding torch. Position offset in direction.

[0394] Modify the position offset of the current robot tool coordinate system {Tool1} based on the position offset to obtain the final robot tool coordinate system {Tool2} at the end of the welding torch.

[0395] The following example, using the initial part of the curve, illustrates the process of generating pose points.

[0396] At the starting point of the desired welding trajectory, generate pose point 0, at which point the arc length parameter s0 = 0.0, and the timestamp... =0.0, the position coordinates of pose point 0 are calculated from the B-spline curve c(s). = c(0.0) = [1205.15, -348.90, 650.18] (unit: mm). Attitude calculation is as follows:

[0397] Tangent vector (Z-axis): ;

[0398] Normal vector (X-axis): Obtain the normal vector of this point from the registered B-spline curve or the surface model of the blade. To ensure the robot tool coordinate system is strictly orthogonal, the normal vector is projected onto a plane perpendicular to the tangent vector to eliminate the attitude error introduced by the surface tilt.

[0399]

[0400] Right now

[0401] After normalization, we get: ;

[0402] Binormal vector (Y-axis): .

[0403] Construct a rotation matrix using n0, b0, and t0 as column vectors. and with position vector The homogeneous transformation matrix is ​​obtained by combination. The pose matrix for pose point 0:

[0404]

[0405] Based on discretization step size To determine the position of the next pose point 1, the pose point 1 (timestamp) can be obtained in the same way. homogeneous transformation matrix :

[0406]

[0407] Similarly, the homogeneous transformation matrix of pose point 2 can be obtained. :

[0408]

[0409] Repeat the above process until s=1.0 to obtain the entire pose sequence, which contains multiple (timestamp, pose matrix) pairs, i.e.:

[0410]

[0411] Where F is the total number of timestamps or pose points.

[0412] Welding begins after the desired welding trajectory is obtained. In this embodiment, the nominal link parameters (including mass, center of mass position, inertia tensor, etc.) of the welding robotic arm are all obtained based on the factory CAD model and pre-calibrated using the dynamic identification tool provided by the manufacturer. Based on this, the parameters required for calculating the feedforward torque can be obtained. The end effector uses a standard MIG welding torch, integrating a wire feed mechanism and a contact tip. The initial wire spool mass is 0.8 kg, which is consumed at an average rate of 0.5 g / s during continuous welding, causing the end effector's moment of inertia to decrease monotonically over time. The welding device's controller is equipped with a high-performance real-time operating system. An incremental photoelectric encoder (20-bit resolution) is installed on the motor side, and an absolute multi-turn encoder (17-bit resolution) is installed on the output side. Simultaneously, the current loop sampling frequency reaches 10 kHz, enabling high-precision reconstruction of the welding drive torque for each joint. This hardware configuration allows for precise joint angle... Motor angle angular velocity angular acceleration Both the torque signal and the welding control signal can be acquired in real time during the welding control cycle, providing the necessary data foundation for the online identification of key time-varying parameters.

[0413] Before powering on the welding equipment or before starting a welding task, perform the following initialization steps:

[0414] The robotic arm's degrees of freedom, or number of joints, is n=6;

[0415] Nominal terminal equivalent moment of inertia (Fully loaded welding wire condition), this value is calculated by integration from the CAD model and verified by offline experiments;

[0416] Initial estimated parameter vector (Because the total number of parameters to be estimated is 2n+1, including 6 equivalent stiffnesses, 6 equivalent dampings and 1 change in end moment of inertia).

[0417] Initial covariance matrix This indicates that there is a high degree of uncertainty about all parameters at the initial time, allowing for rapid correction of estimates based on early data;

[0418] Forgetting factor This value has been verified in a large number of simulations and actual tests as the optimal compromise parameter that balances tracking speed and noise robustness;

[0419] Physical constraint boundaries:

[0420] Lower limit of equivalent stiffness This is approximately 25% of the new machine's nominal stiffness of 2000 N·m / rad, to prevent excessive underestimation of stiffness due to temperature rise or wear.

[0421] Equivalent damping lower limit This ensures that the damping coefficient is non-negative and avoids physically unrealizable solutions.

[0422] Lower limit of terminal moment of inertia This corresponds to the minimum inertia when only the welding torch body is without welding wire;

[0423] Welding control cycle Synchronized with the underlying servo control, ensuring that the algorithm can run in real time on standard industrial controllers (such as KUKA KRC5).

[0424] Assuming the welding device is executing a typical arc welding trajectory, the trajectory control process of a welding control cycle is illustrated below using the k=1000th welding control cycle (i.e., welding time t=2.0s) as an example.

[0425] The following filtered data was collected during this welding control cycle:

[0426] Joint angle: ;

[0427] Angular velocity: ;

[0428] Angular acceleration: ;

[0429] Motor side angle: ;

[0430] Actual driving torque: .

[0431] First, the elastic deformation of each joint is directly obtained by using the difference between the two encoders:

[0432]

[0433] Although the deformation is small, it is sufficient to generate stiffness-related torques, which is the key excitation source for identifying equivalent stiffness.

[0434] The ideal driving torque is calculated by calling the nominal dynamic model provided by the manufacturer, inputting the current motion state of each joint, and then calling the model.

[0435]

[0436] The dynamic residuals reflecting model mismatch were then calculated:

[0437]

[0438] Construct a 6×13 dimensional regression matrix H(k):

[0439]

[0440] Calculate the gain vector K(k) based on the regression matrix H(k) and the covariance matrix P(k-1) of the previous time step, and update the estimated parameter vector:

[0441] .

[0442] This indicates that the stiffness of each joint is slightly lower than the nominal value due to the temperature rise, the damping is within the normal range, and the equivalent moment of inertia at the end has decreased by 0.003 kg·m².

[0443] Verify compliance with physical constraints: All , keep; all Retain; terminal equivalent moment of inertia ,reserve.

[0444] The estimated parameters not only form the basis for calculating the feedforward torque, but also provide key physical constraints for subsequent state prediction.

[0445] Assuming the current arc length parameter s = 0.35, the desired welding position can be obtained from the pose sequence Trajectory.

[0446] ,

[0447] and the corresponding rotation matrix And the SE(3) Lie group pose matrix formed by the combination of the two:

[0448]

[0449] The desired welding position has been converted to the International System of Units (SI) to match the dimensional consistency requirements of the subsequent dynamic model.

[0450] Then, by transforming to the tangent space through the Lie algebra-logarithmic mapping, a six-dimensional geometric eigenvector is obtained:

[0451]

[0452] The last three digits correspond to a 45° rotation around the Y-axis. This geometric feature vector is then fed into a pre-trained graph neural network containing three graph convolutional layers. Each layer aggregates neighborhood control point information, ultimately outputting a 32-dimensional geometric latent vector. It can concisely express the local curvature, trend, and global contextual dependencies of the current position.

[0453] The equivalent modal frequencies are calculated based on the equivalent stiffness and equivalent moment of inertia of each joint. The damping ratios are also calculated based on the equivalent stiffness, equivalent moment of inertia, and equivalent damping of each joint. For example, for the third joint:

[0454]

[0455]

[0456] Simultaneously calculate the rate of change of the terminal moment of inertia. The equivalent modal frequencies and damping ratios of the six joints, as well as the rate of change of end moment of inertia, were calculated. The concatenated dynamic feature vectors are fed into a three-layer fully connected network (with output dimensions of 64→32→16 for each layer) to obtain a 16-dimensional dynamic latent vector. Ultimately, and The vectors are concatenated to form a 48-dimensional state vector. This serves as the initial condition for cross-manifold prediction.

[0457] Subsequently, the system performs cross-manifold neural differential equation prediction. Using z(k) as the initial value, over the next 20 control steps (prediction time domain length H=20, sampling period T),... s Within 2ms (total 40ms), the state vector undergoes continuous-time evolution through a learnable neural differential equation:

[0458]

[0459] The vector field of this differential equation is parameterized by a deep neural network, enabling implicit modeling of the coupling between geometric deformation and dynamic response. The prediction results are then reconstructed by a lightweight decoder, outputting a sequence of future welding torch positions. This is used for subsequent optimization.

[0460] Based on the predictions, the costs of various tasks, as well as the weight allocation and thermal stress topology regularization term based on causal perception, are calculated simultaneously. Taking the current welding control cycle as an example, the measured position error in the current welding control cycle is... The amplitude of the total joint torque is Welding heat input rate (Based on typical process parameters: current 220A, voltage 28V, thermal efficiency 0.8), the welding heat input variance (100ms window) is: .

[0461] By using kernel space Granger causality analysis, the impact of each optimization objective on the overall performance is dynamically evaluated, and the weights of each optimization objective are adaptively generated.

[0462] ,

[0463] The three items correspond to position error, total joint torque amplitude, and welding heat input rate, respectively.

[0464] In addition, considering the current weld curvature We construct the weld temperature field T(x,t) and the thermal stress field. Using the continuous homology method, we extract the "hole" structure features of the thermal stress field and obtain the length of the longest survival interval. Then the thermal stress topological regularization term is:

[0465] ,

[0466] Used to suppress areas of thermal stress concentration that may lead to crack initiation.

[0467] Perform multi-objective MPC optimization based on the following cost function:

[0468]

[0469]

[0470] An efficient quadratic programming solver (such as OSQP) is used online to obtain the optimal feedback torque. Simultaneously, using the previously identified time-varying parameters, a high-precision feedforward torque is calculated. The final control command torque is the sum of the feedforward torque and the feedback torque.

[0471] ,

[0472] The control command is sent to the servo driver in real time to complete the closed-loop adjustment of this welding control cycle.

[0473] The welding trajectory control method and welding device based on the above embodiments take into account the changes in the rotational inertia of the welding robot arm end effect caused by the consumption of welding wire, as well as the influence of the transmission flexibility of joint movement. It breaks through the limitations of traditional control methods based on fixed parameters and rigidity assumptions, and innovatively proposes the concept of dynamic residual. It uses the dynamic residual to estimate key time-varying parameters such as joint stiffness, damping and end effector inertia in real time online. This enables the controller to perform feedforward compensation based on an accurate time-varying dynamic model, making the calculation of welding driving torque more consistent with the actual welding conditions. It effectively suppresses the welding trajectory tracking error caused by load changes and flexibility effects, and ensures the welding trajectory control accuracy under high speed, large range of motion and when the load at the end of the welding robot arm changes.

[0474] In some embodiments, by integrating a 3D laser scanner with point cloud processing technology to complete diffusion model completion, semantic segmentation, and non-rigid registration, the desired welding trajectory is obtained. This enables real-time online and high-precision extraction of the three-dimensional trajectory of the actual weld, and automatic generation of a robot motion program that perfectly matches the actual object, thus solving the problem of welding torch deviation caused by geometric deviation.

[0475] In some embodiments, welding trajectory tracking accuracy, joint drive energy consumption, welding heat input rate, and welding thermal stress are simultaneously incorporated into the optimization objectives for the first time. By introducing methods such as causal perception-based weight allocation and thermal stress topology regularization, energy consumption is actively optimized and welding deformation and residual stress are minimized while ensuring welding trajectory tracking accuracy, thus achieving a simultaneous improvement in welding quality and efficiency.

[0476] Furthermore, in some embodiments, step 220 can seamlessly connect the high-precision geometric reconstruction result of step 100 with the real-time dynamic identification output of step 210. Through the integrated architecture of "perception-modeling-prediction-optimization", the synergistic optimization of geometric accuracy, energy efficiency and thermal stress management in complex curved surface welding is realized, which fully demonstrates the technological advancement, engineering practicality and scalability of the present invention in the field of intelligent repair of high-end equipment.

[0477] Please refer to Figure 10 Actual welding experiments have verified that the welding trajectory control method proposed in this application improves weld uniformity by about 45%, reduces thermal deformation by 20%, reduces trajectory tracking error by 35%, and reduces welding energy consumption by 18%, which is significantly better than traditional PID control or MPC strategy that only considers a single objective.

[0478] Those skilled in the art will understand that all or part of the functions of the various methods in the above embodiments can be implemented by hardware or by computer programs. When all or part of the functions in the above embodiments are implemented by computer programs, the program can be stored in a computer-readable storage medium, which may include: read-only memory, random access memory, disk, optical disk, hard disk, etc., and the program is executed by a computer to achieve the above functions. For example, the program can be stored in the memory of a device, and when the program in the memory is executed by the processor, all or part of the above functions can be achieved. In addition, when all or part of the functions in the above embodiments are implemented by computer programs, the program can also be stored in a server, another computer, disk, optical disk, flash drive, or external hard drive, etc., and can be downloaded or copied to the memory of a local device, or the system of the local device can be updated. When the program in the memory is executed by the processor, all or part of the functions in the above embodiments can be achieved.

[0479] The above examples illustrate the present invention only to aid in understanding it and are not intended to limit the scope of the invention. Those skilled in the art can make various simple deductions, modifications, or substitutions based on the principles of this invention.

Claims

1. A welding trajectory control method, applied to a welding apparatus, the welding apparatus comprising a welding robotic arm and a welding torch disposed at the end of the welding robotic arm, the welding robotic arm having at least one joint, characterized in that, The welding trajectory control method includes: Obtain the desired welding trajectory for welding the workpiece; In each welding control cycle, perform the following steps: Obtain the current ideal driving torque and measured driving torque of each joint, and estimate the transmission flexibility parameters of each joint and the change in end moment of inertia of the welding robot arm based on the dynamic residual of each joint. The dynamic residual is the difference between the measured driving torque and the ideal driving torque. Based on the desired welding trajectory, the transmission flexibility parameters of each joint, and the change in the end moment of inertia of the welding robot arm, the welding driving torque of each joint is calculated. Control the application of corresponding welding driving torque to each of the joints; The step of estimating the transmission flexibility parameters of each joint and the change in end-effector moment of inertia of the welding robot arm based on the dynamic residuals of each joint includes: Using the transmission flexibility parameters of each joint estimated in the previous welding control cycle, the change in the end-effector moment of inertia of the welding robot arm, and the current motion state of each joint, the dynamic residual of each joint in the current welding control cycle is estimated to obtain the estimated dynamic residual; wherein, in the first welding control cycle, the initial value 0 is used as the transmission flexibility parameters of each joint and the change in the end-effector moment of inertia of the welding robot arm in the previous welding control cycle. The dynamic residual error is obtained by differentiating the dynamic residual and the estimated dynamic residual. The transmission flexibility parameters of each joint and the change in end-effector moment of the welding robot arm are estimated and obtained from the previous welding control cycle by using the dynamic residual error correction, so as to obtain the transmission flexibility parameters of each joint and the change in end-effector moment of the welding robot arm in the current welding control cycle. The transmission flexibility parameters of each joint and the change in end-effector moment of inertia of the welding robot arm in the kth welding control cycle are determined by the following formula: ， in, This represents an estimated parameter vector consisting of the transmission flexibility parameters of each joint and the change in the end-effector moment of inertia of the welding robot arm during the k-th welding control cycle. This represents the estimated parameter vector, r, consisting of the transmission flexibility parameters of each joint estimated in the (k-1)th welding control cycle and the change in the end-effector moment of inertia of the welding robot. D H(k) is the dynamic residual vector composed of the dynamic residuals of each joint in the k-th welding control cycle, H(k) is the regression matrix representing the motion state of each joint, K(k) is the gain matrix, and k is a positive integer.

2. The welding trajectory control method as described in claim 1, characterized in that, Wherein, P(k-1) is the parameter estimation error covariance matrix of the (k-1)th welding control cycle, which is used to reflect the uncertainty of the estimated parameter vector, and P(0)=α1I, I is the identity matrix, α1>1, λ is the forgetting factor and λ<1.

3. The welding trajectory control method as described in claim 2, characterized in that, Also includes: Update the parameter estimation error covariance matrix according to the following formula: Where P(k) is the parameter estimation error covariance matrix for the k-th welding control cycle.

4. The welding trajectory control method as described in claim 1, characterized in that, The welding robotic arm has at least two joints; the motion states of the non-end joints include elastic deformation and angular velocity, and the motion states of the end joints include elastic deformation, angular velocity, and angular acceleration. Where n is the total number of joints. and These represent the elastic deformation of the first joint and the end joint during the k-th welding control cycle, respectively. and These are the angular velocities of the first joint and the end joint in the k-th welding control cycle, respectively. Let be the angular acceleration of the joint at the end of the k-th welding control cycle.

5. The welding trajectory control method as described in claim 1, characterized in that, The transmission flexibility parameters include equivalent stiffness and equivalent damping; The welding trajectory control method further includes: After estimating the equivalent stiffness of each joint, it is compared with a preset lower limit value for equivalent stiffness. The two values ​​are compared, and the larger one is taken as the final equivalent stiffness of the joint. After estimating the equivalent damping of each joint, it is compared with a preset lower limit value c of equivalent damping. min The two values ​​are compared, and the larger one is taken as the final equivalent damping of the joint. After estimating the change in end-effector moment of inertia of the welding robot arm, the current end-effector moment of inertia is calculated based on the initial end-effector moment of inertia and the change in end-effector moment of inertia. The current end-effector moment of inertia is then compared with a preset lower limit value I for end-effector moment of inertia. min The two are compared, and the larger one is taken as the final current end moment of inertia. Based on this, the final change in end moment of inertia is obtained.

6. The welding trajectory control method as described in claim 1, characterized in that, The step of calculating the welding driving torque of each joint based on the desired welding trajectory, the transmission flexibility parameters of each joint, and the change in the end-effector moment of inertia of the welding robot arm includes: Based on the motion state of each joint, the transmission flexibility parameters, and the change in the end moment of inertia of the welding robot arm, the feedforward torque of each joint is calculated. Based on the desired welding trajectory, the transmission flexibility parameters of each joint, and the change in the end-effector moment of inertia of the welding robot, a state vector for the current welding control cycle is constructed. The desired welding trajectory is used as a reference trajectory, and the driving torque vector composed of the welding driving torques of each joint is used as the control input vector. The model predictive control problem is solved to obtain the feedback torque of each joint. The welding driving torque is expressed as the sum of the feedforward torque and the feedback torque. The sum of the feedforward torque and the feedback torque of each joint is calculated to obtain the welding driving torque of each joint.

7. The welding trajectory control method as described in claim 6, characterized in that, The welding robotic arm has at least two joints; the motion states include elastic deformation, angular velocity, and angular acceleration. The feedforward torque of each joint is calculated based on the motion state of each joint, the transmission flexibility parameters, and the change in the end-effector moment of inertia of the welding robot arm. Specifically, the feedforward torque of each joint is calculated based on the following joint dynamics equations: ， in, This is the feedforward torque vector composed of the feedforward torques of each joint in the k-th welding control cycle. and These are the angular velocity vector and angular acceleration vector composed of the angular velocity and angular acceleration of each joint in the k-th welding control cycle, respectively. M0 is the nominal inertia matrix, C0 is the Coriolis force and centrifugal force matrix, and g0 is the gravitational torque vector. ,in Let n be the change in the end effector moment of inertia of the welding robot arm during the k-th welding control cycle, where n is the total number of joints, and e is the end effector moment of inertia. n Let n be the standard basis vectors corresponding to the nth joint and ; ,in These are the equivalent damping values ​​for the first joint to the nth joint in the kth welding control cycle; ,in These represent the equivalent stiffness of the first joint to the nth joint during the k-th welding control cycle. It is the elastic deformation vector composed of the elastic deformation of each joint in the k-th welding control cycle.

8. The welding trajectory control method as described in claim 6, characterized in that, The transmission flexibility parameters include equivalent stiffness and equivalent damping; The state vector for the current welding control cycle, constructed based on the desired welding trajectory, the transmission flexibility parameters of each joint, and the change in the end-effector moment of inertia of the welding robot, includes: Based on the desired welding trajectory, the desired welding pose of the welding torch in the current welding control cycle is obtained and mapped to the tangent space to obtain the geometric feature vector; The geometric feature vector is encoded to obtain the geometric latent vector; The equivalent modal frequency is calculated based on the equivalent stiffness and equivalent moment of inertia of each joint. The damping ratio is calculated based on the equivalent stiffness, equivalent moment of inertia and equivalent damping of each joint. The end moment of inertia rate is calculated based on the change in end moment of inertia of the welding robot arm. The equivalent modal frequency, damping ratio and end moment of inertia rate of each joint form a dynamic characteristic vector. The dynamic feature vector is encoded to obtain the dynamic potential vector; By concatenating the geometric potential vector and the dynamic potential vector, the state vector of the current welding control cycle is obtained.

9. The welding trajectory control method as described in claim 8, characterized in that, The step of encoding the geometric feature vector to obtain the geometric latent vector includes: using a graph neural network to encode the geometric feature vector to obtain the geometric latent vector; The step of performing feature encoding on the dynamic feature vector to obtain the dynamic potential vector includes: inputting the dynamic feature vector into a fully connected network to obtain the dynamic potential vector.

10. The welding trajectory control method as described in claim 6, characterized in that, The cost function for the model predictive control problem is: Where k is the cycle number of the current welding control cycle, H is the prediction time domain length, and H is an integer not less than 2, τ(k+i) and τ(k+i-1) represent the driving torque vectors of the k+i and k+i-1 welding control cycles, respectively. ff (k+i) and τ fb (k+i) represent the feedforward torque vector and feedback torque vector of the (k+i)th welding control cycle, respectively; z(k+i) and z(k+i-1) represent the state vectors of the (k+i)th and (k+i-1)th welding control cycles, respectively, and for i = 1, 2, ..., H-1, z(k+i) is predicted based on z(k+i-1) and τ(k+i-1), and f(z(k+i-1), τ(k+i-1)) represents the prediction function of z(k+i) predicted based on z(k+i-1) and τ(k+i-1); e pos (k+i) represents the error between the position of the welding torch in the (k+i)th welding control cycle and the desired welding position obtained based on the desired welding trajectory. The position of the welding torch in the (k+i)th welding control cycle is obtained by reconstructing the state vector z(k+i) through a decoder. Let be the welding heat input rate during the (k+i)th welding control cycle. Let w1(k+i), w2(k+i), and w3(k+i) be the variance of the welding heat input during the (k+i)th welding control cycle; w1(k+i), w2(k+i), and w3(k+i) are the weights during the (k+i)th welding control cycle, respectively. β1 is the thermal stress topological regularization term, and n is the total number of joints. j (k+i) represents the joint angle of the j-th joint during the (k+i)-th welding control cycle, q min and q max These are the lower limit and upper limit of the joint angle, respectively; τ j (k+i) represents the welding driving torque τ of the j-th joint during the (k+i)-th welding control cycle. max This represents the upper limit of the welding driving torque.

11. The welding trajectory control method as described in claim 10, characterized in that, Where t represents time. This represents the state vector z(t) and driving torque vector τ(t) at time t, with parameters as follows: Neural networks.

12. The welding trajectory control method as described in claim 11, characterized in that, The state vector includes the geometric potential vector z. g (t) and dynamic potential vector z d (t); Among them, A gd and A dg This is a learnable attention weight matrix. For the first sub-neural network used to update the geometric latent vector, This is a second sub-neural network used to update the dynamic latent vector; and These are the learnable first query weight matrix and the second query weight matrix, respectively. and These are the learnable first and second bond weight matrices, d k For the key / query dimension, the Softmax function is used for row normalization.

13. The welding trajectory control method as described in claim 10, characterized in that, The weights w1(k+i), w2(k+i), and w3(k+i) are determined by the following formula: Where α2 is the temperature coefficient. for The h-th element, and in, This represents the mean squared error of the baseline model using the kernel-space Granger causality method to predict the future value of variable m without introducing variable l. This represents the mean squared error in predicting the future value of variable m when variable l is introduced as a prior condition; variables 1, 2, and 3 are respectively... , and .

14. The welding trajectory control method as described in claim 10, characterized in that, ,in The longest survival interval length of the topological features in the thermal stress field obtained by the continuous homology method based on the thermal stress field of the weld at the (k+i)th welding control cycle. The thermal stress field is obtained based on the pre-constructed weld temperature field T(x,t), and the weld temperature field T(x,t) is determined by the following equation: Where x represents position, t represents time, T(x,t) represents the temperature at position x at time t, and k T (x,t) is the thermal conductivity, and it is modulated by the curvature at position x on the desired welding trajectory. This is a volumetric heat source term, determined by the motion state of the welding torch and the arc parameters.

15. The welding trajectory control method as described in claim 1, characterized in that, The process of obtaining the desired welding trajectory for welding the workpiece includes: Obtain the point cloud of the workpiece to be welded; Semantic segmentation is performed on the point cloud of the workpiece to be welded to determine the point cloud belonging to the weld seam in the point cloud of the workpiece to be welded, and the weld seam point cloud is obtained. The weld centerline is obtained by fitting the weld point cloud. The desired welding trajectory is obtained by non-rigidly registering the weld centerline with the weld reference model.

16. The welding trajectory control method as described in claim 15, characterized in that, Before performing semantic segmentation on the point cloud of the workpiece to be welded to determine the point cloud belonging to the weld seam in the point cloud of the workpiece to be welded, and obtaining the weld seam point cloud, the welding trajectory control method further includes: The point cloud of the workpiece to be welded is smoothed according to the following formula: in, W represents the coordinates of the point after smoothing, p represents the coordinates of the point before smoothing, and W represents the coordinates of the point before smoothing. i N is the normalization factor. r (p) represents the first neighborhood of point p, and q is a point within the first neighborhood. For spatial weighting functions, For the range weight function, Let I(p) represent the Euclidean distance between points p and q, and let I(p) and I(q) represent the eigenvalues ​​of points p and q, respectively. This represents the absolute difference between the eigenvalues ​​of points p and q; The diffusion model is used to complete the smoothed point cloud.

17. The welding trajectory control method as described in claim 15, characterized in that, The step of semantically segmenting the point cloud of the workpiece to be welded to determine the point cloud belonging to the weld seam, thereby obtaining the weld seam point cloud, includes: For each point in the point cloud of the workpiece to be welded, its feature vector is extracted in the neighborhood of different radii. The extracted feature vectors are fused together as the feature representation vector token of the point and input into the Transformer model to obtain the three-dimensional semantic feature vector of the point. Based on at least the three-dimensional semantic feature vectors of each point, a first multilayer perceptron is used for classification to obtain semantic labels for each point, and the semantic labels include weld seams. All points with the semantic label "weld" are obtained to form a weld point cloud.

18. The welding trajectory control method as described in claim 15, characterized in that, The semantic labels for each point, obtained by classifying the at least three-dimensional semantic feature vectors based on each point using a first multilayer perceptron, include: The point cloud of the workpiece to be welded is projected onto a two-dimensional plane to obtain a depth map; Feature extraction is performed on the depth map to obtain a two-dimensional semantic feature vector of each point on the depth map. The two-dimensional semantic feature vector is a feature vector used to perform semantic segmentation on the depth map to obtain the semantic label of each point on the depth map. The two-dimensional semantic feature vectors of each point on the depth map are back-projected to the corresponding points in the point cloud. The three-dimensional semantic feature vectors of each point in the point cloud are fused with the two-dimensional semantic feature vectors obtained by back-projection to obtain the global information of the point. The global information of each point is input into the first multilayer perceptron for classification to obtain the semantic label of each point.

19. The welding trajectory control method as described in claim 15, characterized in that, The process of obtaining the weld centerline by fitting the weld point cloud includes: A sliding window is used to slide on the weld point cloud. Each time the window slides to a position, the center point within the sliding window is determined. All center points are connected to obtain the initial center line. The initial centerline is fitted using the first B-spline function to obtain the weld centerline; The step of non-rigidly registering the weld centerline with the weld reference model to obtain the desired welding trajectory includes: The desired welding trajectory is obtained by non-rigidly registering the weld centerline with the weld reference model according to the following formula: Where T(p) represents the coordinates of a point on the desired welding trajectory, p represents the coordinates of a point on the weld centerline, and B d (x) represents the d-th B-spline function of the x-coordinate component, B e (y) represents the e-th B-spline function of the y-coordinate component, B f (z) represents the f-th B-spline function of the z-coordinate component. This represents the displacement of the control points of the first B-spline function, and It can minimize the following energy function: in, For all The vector formed, S represents the centerline of the weld, w p γ is the weight, Let T(p) be the closest point to the reference model of the weld.

20. A welding apparatus, characterized in that, Includes a welding robotic arm, welding torch, and controller; The welding robotic arm has at least one joint, and the welding torch is located at the end of the welding robotic arm; The controller is used to execute the welding trajectory control method as described in any one of claims 1 to 19 to control the welding robotic arm to weld the workpiece to be welded.

Images