An intelligent tool path compensation method for robotic incremental forming

Abstract

The application discloses an intelligent tool path compensation method for robot incremental forming. The method firstly constructs a robot forming data set containing position parameters of machining points and corresponding geometric errors of the points; then an intelligent error prediction model based on physical information is established, the model is a neural network model fusing a metal plastic forming physical mechanism, a loss function contains a data loss term and a physical mechanism constraint term, and position parameters are taken as input and corresponding geometric errors are taken as output; finally, a tool path compensation model is established, an initial tool path is corrected point by point according to the predicted geometric errors, and a compensated path is generated. The application considers the accuracy and efficiency of error prediction, and effectively improves the part forming precision and quality of robot incremental forming.

Description

Technical Field

[0001] This invention relates to the field of flexible manufacturing technology for industrial robots, and in particular to an intelligent tool path compensation method for robot incremental forming. Background Technology

[0002] The demand for flexible, low-cost, and short-cycle sheet metal forming technologies in the high-end equipment manufacturing sector continues to upgrade. Robotic incremental forming, as a core technology of moldless flexible manufacturing, does not require dedicated molds and has advantages such as high forming flexibility, short R&D cycle, and high material utilization. It has been gradually applied to high-precision fields such as aerospace, automobile manufacturing, and medical devices, becoming an important technological support for promoting the high-end and intelligent transformation of the manufacturing industry.

[0003] Forming accuracy is a core indicator determining the service performance and product qualification rate of robot-progressive forming parts, and it is also a key prerequisite for the large-scale industrial application of this technology. During the forming process, problems such as insufficient rigidity of the robot body leading to elastic yield, springback effect after plastic deformation of the sheet metal, and uneven thickness reduction can easily cause the actual trajectory of the tool head to deviate from the preset path, resulting in geometric errors exceeding tolerances. Accurate error prediction and path compensation are the core links to ensure forming accuracy.

[0004] In existing precision control schemes, pure physical models based on finite element simulation have low computational efficiency and cannot meet the timeliness requirements of real-time compensation; pure data-driven machine learning models rely on a large number of samples for training, have weak generalization ability and poor interpretability, and cannot simultaneously take into account the accuracy, efficiency and adaptability of error prediction, which seriously restricts the application of robot incremental forming in high-precision manufacturing scenarios. Summary of the Invention

[0005] In view of the above problems, a smart tool path compensation method for robot incremental forming is proposed to overcome or at least partially solve the above problems, including:

[0006] Construct a robot forming dataset, which includes the positional parameters of the processing points during the robot's progressive forming process, as well as the geometric errors of the points corresponding to the positional parameters;

[0007] A smart error prediction model based on physical information is established. The smart error prediction model is a neural network model that integrates the physical mechanism of metal plastic forming. The loss function of the smart error prediction model includes a data loss term and a physical mechanism constraint term. The smart error prediction model takes the position parameters as input and the geometric error of the corresponding point as output.

[0008] A tool path compensation model is established. Based on the geometric error output by the intelligent error prediction model, the tool path compensation model corrects the initial tool path of the robot's progressive forming point by point, and generates a compensated tool path.

[0009] Optionally, the robot forming dataset may also include at least one of the following: material parameters of the metal sheet, geometric parameters of the target forming part, and process parameters of incremental forming; wherein, the material parameters of the metal sheet include at least the elastic modulus, Poisson's ratio, tensile strength, yield strength, material hardening coefficient, and hardening index of the metal sheet; the geometric parameters of the target forming part include at least the wall angle, curvature, and rate of curvature change of the target forming part; and the process parameters of incremental forming include at least the feed rate and depth of step of the incremental forming tool head.

[0010] Optionally, the position parameters may include at least the horizontal distance from the machining point to the metal plate fixture and the forming depth of the machining point.

[0011] Optionally, the intelligent error prediction model embeds the position parameters of the processing point, the material parameters of the metal plate, the geometric parameters of the target forming part, and the process parameters of progressive forming into the calculation process of the neural network model. The data loss term is the mean square error between the geometric error output by the neural network model and the geometric error of the corresponding point in the robot forming dataset. The physical mechanism constraint term is the deviation between the geometric error output by the neural network model and the geometric error calculated by the physical mechanism analysis model of metal plastic forming. The loss function is the total loss value obtained by weighted summation of the data loss term and the physical mechanism constraint term.

[0012] Optionally, the loss function is set with weight coefficients corresponding to the physical mechanism constraint terms. The intelligent error prediction model is trained iteratively using the Adam optimizer. The intelligent error prediction model completes the model performance verification through the coefficient of determination and root mean square error.

[0013] Optionally, the intelligent error prediction model divides the forming area of ​​the metal plate into bending area, sidewall area, contact area and bottom area according to the forming process characteristics. The intelligent error prediction model sets physical mechanism constraint terms that match the deformation mechanism of the corresponding sub-region for each sub-region. The intelligent error prediction model sets independently trained neural network sub-networks for each sub-region.

[0014] Optionally, the intelligent error prediction model sets an overlapping region at the boundary of adjacent sub-regions. The loss function of the intelligent error prediction model also includes a boundary loss function. The boundary loss function is the root mean square of the geometric error difference between the processing points in the overlapping region and the corresponding sub-network outputs of the two adjacent sub-regions. The loss function is the total loss value obtained by weighted summation of the data loss term, the physical mechanism constraint term, and the boundary loss function.

[0015] Optionally, the tool path compensation model obtains the normal vector corresponding to the machining point on the initial tool path, sets the compensation coefficient, multiplies the geometric error output by the intelligent error prediction model with the compensation coefficient to obtain the corrected displacement of the corresponding machining point, and then superimposes the corrected displacement along the normal vector of the corresponding machining point onto the corresponding machining point on the initial tool path to complete the correction of the machining point.

[0016] Optionally, the tool path compensation model performs cubic spline interpolation on the entire sequence of corrected machining points. The cubic spline interpolation ensures that the connection points of the compensated tool path maintain first-order tangential continuity. The initial tool path can be any one of the following: spiral path, contour path, Zigzag path, or fractal path.

[0017] Optionally, the tool path compensation model establishes a UDP communication channel with the robot controller via the RSI communication protocol. The tool path compensation model receives the current processing point information uploaded by the robot controller in real time through the UDP communication channel, and sends the corresponding processing point position correction amount to the robot controller in real time through the UDP communication channel to achieve online real-time compensation.

[0018] This invention constructs a robot forming dataset containing positional parameters and corresponding geometric errors. It uses a neural network that integrates the physical mechanism of metal plastic forming to build an error prediction model. The model is trained by combining a loss function with data loss terms and physical mechanism constraints. This overcomes the shortcomings of pure physical models, such as low computational efficiency and inability to adapt to real-time compensation. It also solves the pain points of pure data-driven models, such as weak generalization ability and poor interpretability. This invention achieves high-precision and high-efficiency prediction of forming geometric errors. By correcting the tool path point by point, it effectively suppresses forming errors, significantly improves the forming accuracy of parts and the product qualification rate, and supports the application of robot progressive forming in high-precision manufacturing scenarios. Attached Figure Description

[0019] To more clearly illustrate the technical solution of the present invention, the accompanying drawings used in the description of the present invention will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a flowchart of an intelligent tool path compensation method for robot progressive forming provided by an embodiment of the present invention;

[0021] Figure 2 This is a schematic diagram of robot progressive forming according to an embodiment of the present invention;

[0022] Figure 3 This is a schematic diagram of an intelligent error prediction model based on physical information provided in an embodiment of the present invention;

[0023] Figure 4 This is a schematic diagram of a tool path compensation model provided in an embodiment of the present invention;

[0024] Figure 5 This is a schematic diagram of a metal plate clamping according to an embodiment of the present invention;

[0025] Figure 6 This is a schematic diagram of a progressive forming spiral path provided in an embodiment of the present invention;

[0026] Figure 7 This is a schematic diagram of the part forming area division provided in an embodiment of the present invention;

[0027] Figure 8 This is a schematic diagram of an online compensation model provided in an embodiment of the present invention. Detailed Implementation

[0028] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0029] This invention provides an intelligent toolpath compensation method for robot progressive forming, which may specifically include:

[0030] Construct a robot forming dataset, which includes the positional parameters of the processing points during the robot's progressive forming process, as well as the geometric errors of the points corresponding to the positional parameters;

[0031] A smart error prediction model based on physical information is established. The smart error prediction model is a neural network model that integrates the physical mechanism of metal plastic forming. The loss function of the smart error prediction model includes a data loss term and a physical mechanism constraint term. The smart error prediction model takes the position parameters as input and the geometric error of the corresponding point as output.

[0032] A tool path compensation model is established. Based on the geometric error output by the intelligent error prediction model, the tool path compensation model corrects the initial tool path of the robot's progressive forming point by point, and generates a compensated tool path.

[0033] Robotic incremental forming is a flexible manufacturing process that uses an incremental forming tool head mounted on the end effector of a robot to apply localized, point-by-point loading to a metal sheet, causing plastic deformation to accumulate and form a target shape. During the forming process, the robot controls the incremental forming tool head to move and apply pressure on the surface of the metal sheet according to a predetermined initial tool path. Due to insufficient structural rigidity of the robot body, joint transmission errors, and the springback effect of the metal sheet after forming, there is a deviation between the actual spatial position of the incremental forming tool head at the processing point and the nominal position set by the initial tool path. This deviation manifests as geometric errors at corresponding points of the formed part.

[0034] In practical applications, the first step is to construct a robot forming dataset. This dataset can include the positional parameters of the machining points during the robot's progressive forming process, as well as the geometrical errors corresponding to these parameters. To obtain these positional parameters and geometrical errors, experimental measurement methods can be used to construct the dataset.

[0035] Specifically, a metal plate with an initial thickness ranging from 0.8mm to 4mm can be selected and clamped onto a metal plate fixture. The metal plate fixture includes a base and a movable pressure plate. The base is fixed relative to the ground, and the movable pressure plate is detachably connected to the base. During clamping, the movable pressure plate can be removed first to open the clamping space. After the metal plate is placed in the predetermined position on the base, the movable pressure plate is reinstalled and fixed to achieve clamping of the metal plate. The robot end effector is equipped with a progressive forming tool head with a spherical end, the radius of which ranges from 2mm to 10mm. The robot controls the progressive forming tool head to perform progressive forming processing on the metal plate according to a preset initial tool path.

[0036] After processing, a 3D point cloud data of the surface of the formed part is obtained using a 3D scanning device (such as a laser scanner). The 3D point cloud data is then best fitted and aligned with the 3D model of the target part generated by the computer-aided design tool. The geometric error values ​​at each processing point are extracted by comparison and calculation, and the position parameters of the processing point are stored in correspondence with the corresponding geometric errors, thereby constructing the robot forming dataset.

[0037] The positional parameters include at least the three-dimensional spatial coordinates of the machining point in the robot's base coordinate system or the workpiece coordinate system. To further enrich the dataset, the positional parameters may also include the horizontal distance from the machining point to the metal sheet fixture and the depth coordinates of the machining point along the progressive forming feed direction. The depth coordinates of the machining point along the progressive forming feed direction refer to the spatial position component of the machining point in the direction perpendicular to the initial surface of the metal sheet, reflecting the instantaneous depth of the progressive forming tool head pressing into the metal sheet.

[0038] Furthermore, an intelligent error prediction model based on physical information is established. This model can be a neural network model that integrates the physical mechanisms of metal plastic forming. The input to this model is the position parameters of the processing point, and the output is the geometric error of the point corresponding to those position parameters.

[0039] In the process of building the model, the existing robot forming dataset is first divided into a training set and a test set. The training set is used to train the intelligent error prediction model for parameter optimization, and the test set is used to verify the predictive performance of the model after training. The proportion of the dataset can be determined according to the actual data size. For example, 80% of the total data can be used as the training set, and the remaining 20% ​​as the test set.

[0040] Simultaneously, a physical mechanism analysis model for metal plastic forming is established as a priori physical knowledge model. This physical mechanism analysis model is based on the mechanical principles of incremental forming of metal sheets. For the most significant sidewall springback phenomenon during the robot's incremental forming process, the springback deformation of the sidewall region can be decomposed into a large-deflection bending springback component for the flat plate, a bending beam springback component, and a straight beam springback component, which are calculated separately. The large-deflection bending springback component for the flat plate can be obtained by solving the elastic deformation of the flat plate under large-deflection bending conditions using the KAMAN equation; the bending beam springback component and the straight beam springback component can be calculated based on classical elastic beam theory. By combining the above springback components according to a preset mechanical superposition relationship, the analytical springback calculation value of the corresponding processing point under given process conditions can be obtained. This analytical springback calculation value serves as a reference benchmark for physical mechanism constraints, used to constrain the geometric error value of the model output during subsequent neural network training.

[0041] Then, a framework for an intelligent error prediction model based on physical information is constructed. This framework uses an artificial neural network as its basic network structure. The number of nodes in the network input layer matches the dimension of the input parameters. For example, if the input parameters are the three-dimensional spatial coordinates of the machining point representing the location, the number of input layer nodes can be set to three; if the input parameters also include the horizontal distance from the machining point to the metal plate fixture and the depth coordinates along the progressive forming feed direction, the number of input layer nodes can be set to five; if the input parameters also include the curvature and rate of change of curvature representing the shape of the part, the number of input layer nodes can be set to seven. The number of nodes in the network output layer is one, and the output value is the predicted geometric error value corresponding to the machining point. The intermediate layers of the network can contain several fully connected hidden layers, each containing several neuron nodes. The layers are connected by nonlinear activation functions to enable the network to fit complex nonlinear mapping relationships.

[0042] The loss function of the intelligent error prediction model based on physical information includes a data loss term and a physical mechanism constraint term. The data loss term constrains the model output to approximate the measured data as closely as possible, reflecting data-driven learning capabilities. The physical mechanism constraint term constrains the model output to conform to the basic physical laws of metal plastic forming, enhancing the model's interpretability and generalization ability. The loss function is the total loss value obtained by weighted summation of the data loss term and the physical mechanism constraint term. The physical mechanism constraint term has a preset weight coefficient, which adjusts the proportion of the physical mechanism constraint term in the total loss, achieving a balance between fitting the measured data and adhering to physical laws.

[0043] During the training phase, parameters from the training set are used as input, and the measured geometric error values ​​at corresponding locations are used as supervision labels. Input data is fed batch by batch into the intelligent error prediction model based on physical information. The model performs forward propagation calculations to obtain the predicted geometric error values. Then, the data loss term and the physical mechanism constraint term are calculated separately, and the two terms are weighted and summed according to preset weight coefficients to obtain the total loss value. The parameters in the training set include at least location parameters, and may also include geometric parameters, material parameters, and process parameters.

[0044] During the validation phase, the location parameters from the test set can be used as input to the trained physics-based intelligent error prediction model to obtain the geometric error prediction values ​​for the test set samples. The predicted geometric error values ​​are then compared with the measured geometric error values ​​for the corresponding points in the test set, and two evaluation metrics, the coefficient of determination (COD) and the root mean square error (RMSE), are calculated. It can be understood that the closer the COD is to one, the higher the linear correlation between the model's predicted and measured values; the smaller the RMSE, the smaller the absolute deviation between the model's predicted and measured values. When both the COD and RMSE meet preset thresholds, the model's performance is confirmed to meet the usage requirements.

[0045] Finally, a tool path compensation model is established. Based on the geometric error output by the intelligent error prediction model based on physical information, the tool path compensation model corrects the initial tool path of the robot's progressive forming point by point, generating a compensated tool path.

[0046] Specifically, a 3D solid model of the target part can be generated using computer-aided design tools, and an initial toolpath for robot progressive forming can be generated using the path planning module in computer-aided manufacturing software. The initial toolpath consists of a series of discrete machining points, each containing its nominal position coordinates in space. The computer-aided manufacturing software can then output this initial toolpath as a programming language format file recognizable by the robot controller.

[0047] Then, the position parameters of each processing point in the initial tool path are extracted and sequentially input into the trained intelligent error prediction model based on physical information to calculate the expected geometric error value corresponding to each processing point in batches.

[0048] The toolpath compensation model obtains the normal vector corresponding to each machining point on the initial toolpath. This normal vector refers to the unit direction vector perpendicular to the surface outward at the corresponding machining point of the target part's 3D model surface. This normal vector can be pre-calculated and stored by computer-aided manufacturing software, or it can be calculated in real time during the compensation stage based on the surface mathematical expression of the target part's 3D model.

[0049] The tool path compensation model includes a compensation coefficient. This coefficient is a preset scalar value greater than zero, used to control the strength of the correction. In a typical implementation, the compensation coefficient can be set to one, i.e., a full compensation strategy is employed.

[0050] For each machining point on the initial toolpath, the toolpath compensation model multiplies the geometric error value corresponding to that machining point (output from the intelligent error prediction model based on physical information) with a compensation coefficient to obtain the corrected displacement for that machining point. The direction of the corrected displacement is opposite to the normal vector of the corresponding machining point. That is, the direction of the corrected displacement vector is opposite to the direction of the normal vector. This is because the deviation direction of the actual position of the tool head from its nominal position during the forming process is opposite to the direction of the geometric error. Through reverse compensation, the actual forming position of the tool head after loading and deformation can be made closer to the target position.

[0051] The toolpath compensation model superimposes the calculated corrected displacement vector onto the nominal position coordinates of the corresponding machining points in the initial toolpath, obtaining the compensated machining point coordinates. This correction operation is then performed sequentially on all machining points in the initial toolpath sequence to generate the compensated toolpath machining point sequence.

[0052] To ensure the smoothness of the compensated tool path during robot motion and avoid impacts on robot movement caused by local abrupt changes introduced by the discrete correction amount, the tool path compensation model can perform cubic spline interpolation on the entire sequence of machining points after correction. Cubic spline interpolation ensures that the compensated tool path maintains first-order tangential continuity at the connection points between adjacent machining points, that is, the first derivative of the path curve is continuous at the connection points, thereby ensuring a smooth transition in the velocity direction of the robot's end effector as it moves along the compensated tool path.

[0053] Finally, the generated compensated toolpath is converted into program instructions executable by the robot controller. The robot controls the progressive forming tool head to perform progressive forming machining on the metal sheet along the compensated toolpath.

[0054] In one or more embodiments of the present invention, an error perturbation term for actual factors is added to the loss function of the intelligent error prediction model based on physical information. This error perturbation term characterizes the influence of random disturbance factors present in the actual machining process of robot incremental forming on geometric errors. These random disturbance factors include positioning fluctuations caused by robot joint transmission clearances, deformation differences caused by uneven local thickness of the metal plate, changes in friction conditions between the incremental forming tool head and the metal plate, and minor changes in material properties caused by fluctuations in ambient temperature. These random disturbance factors are difficult to accurately describe using a deterministic analytical model, but by introducing an error perturbation term into the loss function, the intelligent error prediction model can learn robust adaptability to these disturbance factors during training.

[0055] The specific construction method of the error perturbation term is as follows: In each training iteration, a random perturbation variable following a preset probability distribution is superimposed on the geometric error prediction value output by the neural network model. The superimposed perturbation geometric error prediction value replaces the original geometric error prediction value in the calculation of the data loss term. The preset probability distribution can be a normal distribution with a mean of zero and a preset small variance, or a random variable uniformly distributed within a preset symmetrical interval. Since the random perturbation variable superimposed in each iteration is sampled independently, the data loss term during training will include a penalty effect on the uncertainty of the model prediction, so that the intelligent error prediction model after training convergence can still output stable geometric error prediction results when facing random disturbances in the actual processing environment.

[0056] In one or more embodiments of the present invention, the robot forming dataset further includes at least one of the material parameters of the metal sheet, the geometric parameters of the target forming part, and the process parameters of incremental forming; wherein, the material parameters of the metal sheet include the elastic modulus, the material hardening coefficient, and the hardening index of the metal sheet; the geometric parameters of the target forming part include the wall angle, curvature, and rate of change of curvature of the target forming part; and the process parameters of incremental forming include the feed rate and step depth of the incremental forming tool head.

[0057] Material parameters of a metal sheet can be used to describe its mechanical response characteristics during plastic deformation. These parameters include the elastic modulus, material hardening factor, and hardening exponent. The elastic modulus reflects the stress-strain ratio during elastic deformation; the material hardening factor and hardening exponent are constitutive parameters describing the relationship between flow stress and plastic strain after the sheet enters the plastic deformation stage, following a power-law hardening model. These material parameters can be obtained through uniaxial tensile tests. When constructing the robot forming dataset, the elastic modulus, material hardening factor, and hardening exponent values ​​measured by uniaxial tensile tests are used as material attribute fields and associated with the corresponding forming test samples for storage.

[0058] The geometric parameters of the target formed part can be used to describe its spatial geometric features. These parameters include the wall angle, curvature, and rate of curvature change. The wall angle is the angle between the sidewall surface of the target formed part and the horizontal reference plane; the curvature is the degree of bending of the target formed part's surface along a given direction at a specified machining point, and is the reciprocal of the radius of curvature; the rate of curvature change is the derivative of the curvature along the tangential direction of the surface at the machining point, used to measure the drastic change in curvature. These geometric parameters can be obtained by analyzing the computer-aided design 3D model of the target formed part. For each machining point on the surface of the target formed part, the corresponding wall angle, curvature, and rate of curvature change values ​​are calculated based on the point's spatial position in the 3D model, and these values ​​are stored as geometric parameter fields in the robot forming dataset.

[0059] The process parameters for incremental forming can be used to describe the operating conditions set during the robotic incremental forming process. These parameters include the feed rate and depth of step of the incremental forming tool head. The feed rate is the linear velocity of the incremental forming tool head as it moves along the surface of the metal sheet, and the depth of step is the minimum interlayer distance between two adjacent layers of the incremental forming tool head's trajectory. When constructing the robotic forming dataset, the feed rate and depth of step values ​​set for each forming experiment are recorded as process parameter fields, along with the corresponding position parameters and geometric error data.

[0060] In embodiments of the present invention, the position parameters include at least the horizontal distance from the processing point to the metal plate fixture and the forming depth of the processing point.

[0061] The horizontal distance from the machining point to the metal sheet fixture refers to the shortest straight-line distance from the machining point to the clamping boundary of the metal sheet fixture in a plane parallel to the initial surface of the metal sheet. This distance reflects the strength of the constraint effect of the fixture on the machining point. The forming depth of the machining point refers to the vertical distance of the machining point relative to the initial surface of the metal sheet along the progressive forming feed direction, that is, the instantaneous depth of the progressive forming tool head pressing into the metal sheet at that point.

[0062] The two positional parameters mentioned above can be obtained as follows: First, use computer-aided manufacturing software to obtain the three-dimensional spatial coordinates of the designed part in the base coordinate system. Then, calculate the planar projection distance between these coordinates and the fixed coordinate position of the metal plate fixture to obtain the horizontal distance from the machining point to the metal plate fixture. Next, calculate the difference between the component of this coordinate perpendicular to the initial surface and the height of the reference plane of the initial surface of the metal plate to obtain the forming depth of the machining point. The calculated horizontal distance and forming depth values ​​correspond one-to-one with the machining points and can be stored as positional parameter fields in the robot forming dataset.

[0063] In one or more embodiments of the present invention, the intelligent error prediction model embeds the position parameters of the processing point, the material parameters of the metal plate, the geometric parameters of the target forming part, and the process parameters of progressive forming into the calculation process of the neural network model. The data loss term is the mean square error between the geometric error output by the neural network model and the geometric error of the corresponding point in the robot forming dataset. The physical mechanism constraint term is the deviation between the geometric error output by the neural network model and the geometric error calculated by the physical mechanism analysis model of metal plastic forming. The loss function is the total loss value obtained by weighted summation of the data loss term and the physical mechanism constraint term.

[0064] Specifically, the intelligent error prediction model includes a neural network model with an input layer, several hidden layers, and an output layer. The input layer contains multiple input nodes, each receiving different types of input parameters. Specifically, the first set of input nodes receives the position parameters of the machining point, which include at least the three-dimensional spatial coordinates of the machining point in the robot's base coordinate system or the workpiece's coordinate system; the second set of input nodes receives the material parameters of the metal plate, including the elastic modulus, material hardening coefficient, and hardening index; the third set of input nodes receives the geometric parameters of the target part, including the wall angle, curvature, and rate of change of curvature at the machining point; and the fourth set of input nodes receives the incremental forming process parameters, including the feed rate and depth of step of the incremental forming tool head.

[0065] During each forward propagation calculation of the neural network model, all the aforementioned input parameters are simultaneously fed into the network according to their connection relationships with their respective input nodes. The values ​​received by each node in the input layer are weighted and summed before being passed to each neuron node in the first hidden layer. Each neuron node in the first hidden layer applies a nonlinear activation function transformation to the received weighted sum and passes the transformation result to the next hidden layer. The nonlinear activation function can be any one of the hyperbolic tangent function, modified linear unit function, or sigmoid function, so that the neural network model has the ability to fit the complex nonlinear mapping relationship between the input and output. After forward propagation and transformation through several hidden layers, a scalar value is finally output by a single neuron node in the output layer. This scalar value is the geometric error prediction value of the neural network model for the input processing point. Through the above embedding method, the material parameters of the metal plate, the geometric parameters of the target forming part, and the process parameters of incremental forming participate in the forward calculation process of the neural network model as part of the input features, enabling the neural network model to learn the variation law of geometric error of processing point under different material properties, different part geometric features, and different process conditions.

[0066] The data loss term is the mean squared error between the geometric error prediction value output by the neural network model and the measured geometric error value of the corresponding point in the robot forming dataset. The specific calculation method for the mean squared error is as follows: For a training batch containing several samples, extract the geometric error prediction value output by the neural network model for each sample, and read the measured geometric error value of the corresponding point in the robot forming dataset; calculate the difference between the geometric error prediction value and the measured geometric error value; square this difference to obtain the squared error value for a single sample; sum the squared error values ​​of all samples in the training batch; divide the sum by the total number of samples in the training batch, and the resulting arithmetic mean is the data loss term value for that training batch. The data loss term measures the degree of agreement between the predicted output of the neural network model and the actual measurement result. The smaller the data loss term value, the stronger the fitting ability of the neural network model to the existing measured data.

[0067] The physical mechanism constraint term is the deviation between the geometric error prediction value output by the neural network model and the analytical geometric error value calculated by the physical mechanism analysis model of metal plastic forming. The physical mechanism analysis model of metal plastic forming is an analytical calculation model based on the mechanical theory of metal plastic forming. This analytical model uses the same input parameters as the neural network model as independent variables, namely, the position parameters of the processing point, the material parameters of the metal sheet, and the process parameters of incremental forming. It calculates the theoretical springback amount of the processing point under given conditions based on the analytical formula of elastic springback mechanics, and outputs this theoretical springback amount as the analytical geometric error value.

[0068] For the springback deformation of the sidewall region during the incremental forming process of a robot, the physical mechanism analysis model of metal plastic forming can decompose the sidewall springback into flat plate large deflection bending springback component, bending beam springback component, and straight beam springback component, and solve them analytically respectively. The flat plate large deflection bending springback component is solved using shell analysis theory, while the bending beam springback component and the straight beam springback component are calculated based on classical elastic beam theory. Finally, the springback components are combined according to a preset mechanical superposition relationship to obtain the geometric error analytical value of the corresponding processing point. The deviation value of the physical mechanism constraint term can be calculated in the form of mean square error, that is, for all samples in the training batch, the arithmetic mean of the squares of the differences between the geometric error prediction value output by the neural network model and the geometric error analytical value output by the physical mechanism analysis model of metal plastic forming is calculated. The physical mechanism constraint term is used to constrain the output of the neural network model to not deviate from the basic physical laws of metal plastic forming, so that the neural network model can still give prediction results that conform to the physical mechanism when extrapolated to processing areas or process conditions that were not trained.

[0069] The loss function is the total loss value obtained by weighted summation of the data loss term and the physical mechanism constraint term. The expression for the weighted summation is: the total loss value equals the data loss term multiplied by the first weight coefficient plus the physical mechanism constraint term multiplied by the second weight coefficient. Alternatively, the first weight coefficient can be implicitly set to one, and only the second weight coefficient can be set as a weight adjustment factor for the physical mechanism constraint term relative to the data loss term. In this case, the total loss value equals the data loss term plus the product of the physical mechanism constraint term and the weight coefficient. The weight coefficient is a preset hyperparameter, determined by the operator based on experience or through hyperparameter search methods before the neural network model training begins. The value of the weight coefficient determines the relative proportion of the physical mechanism constraint term in the total loss: when the weight coefficient is set larger, the training process will focus more on ensuring that the output of the neural network model conforms to the calculation results of the physical mechanism analysis model; when the weight coefficient is set smaller, the training process will focus more on making the output of the neural network model approximate the measured geometric error value in the robot forming dataset.

[0070] In one or more embodiments of the present invention, the loss function sets the weight coefficients corresponding to the physical mechanism constraint terms, the intelligent error prediction model uses the Adam optimizer for iterative training, and the intelligent error prediction model completes the model performance verification through the coefficient of determination and root mean square error.

[0071] The loss function sets the weight coefficients corresponding to the physical mechanism constraint terms. These weight coefficients can be preset positive real numbers. In each training iteration, the calculated result of the physical mechanism constraint terms is multiplied by the weight coefficients, and then added to the data loss term to form the total loss value used for backpropagation calculation.

[0072] Intelligent error prediction models can be iteratively trained using the Adam optimizer. The Adam optimizer is a gradient-based first-order optimization algorithm that maintains an independent adaptive learning rate for each trainable parameter in the neural network model during training. The Adam optimizer dynamically scales the learning rate for each parameter by calculating the first-order and second-order moment estimates of the gradient.

[0073] During the training phase, the hyperparameters of the Adam optimizer are first set, including the learning rate, first-order moment decay coefficient, second-order moment decay coefficient, and numerical stability constant. In each training batch, after the intelligent error prediction model completes forward propagation and calculates the total loss value, the Adam optimizer is invoked to calculate the gradient of the total loss value with respect to the connection weights and bias terms of each layer in the neural network model, and the network parameters are updated based on the gradient values ​​and historical moment estimates. The training process continues for multiple iterations until the total loss value converges to a preset condition or reaches a preset maximum number of iterations.

[0074] The intelligent error prediction model is validated using the coefficient of determination (COD) and root mean square error (RMSE). After model training, the model is validated using test set data that was not used in the training. The location parameters of the processing points, the material parameters of the metal sheet, the geometric parameters of the target formed part, and the process parameters of incremental forming are input into the intelligent error prediction model to obtain the geometric error prediction values ​​for each test sample. The geometric error prediction values ​​are compared with the measured geometric error values ​​of the corresponding points in the test set, and the COD and RMSE values ​​are calculated respectively. The closer the COD is to one, the higher the explanatory power of the model's predictions on the measured values. The smaller the RMSE, the smaller the absolute deviation between the model's predictions and the measured values. When the COD is greater than a preset threshold and the RMSE is less than a preset threshold, the performance of the intelligent error prediction model is confirmed to meet the usage requirements.

[0075] In one or more embodiments of the present invention, the intelligent error prediction model divides the forming area of ​​the metal plate into a bending area, a sidewall area, a contact area, and a bottom area according to the forming process characteristics. The intelligent error prediction model sets physical mechanism constraint terms that match the deformation mechanism of the corresponding sub-region for each sub-region. The intelligent error prediction model sets independently trained neural network sub-networks for each sub-region.

[0076] The intelligent error prediction model can divide the forming area of ​​a metal sheet into a bending region, a sidewall region, a contact region, and a bottom region based on the forming process characteristics. The bending region is the area where the metal sheet undergoes bending deformation and film stretching deformation during the progressive forming process, located at the curved transition section of the target formed part. The sidewall region is the sidewall surface area of ​​the metal sheet with a certain tilt angle, where the metal sheet simultaneously experiences the coupled effects of bending and stretching deformation. The contact region is the instantaneous area where the ball end of the progressive forming tool head directly contacts and loads the metal sheet. The bottom region is the bottom planar area of ​​the target formed part, which is subjected to the final flattening effect of the tool head in the later stages of the forming process.

[0077] Specifically, the regions can be divided as follows: Based on the computer-aided design 3D model of the target forming part, analyze the curvature characteristics, tilt angle, and relative positional relationship with the motion trajectory of the progressive forming tool head at each processing point on the model surface. Points that meet the dominant characteristic criteria of bending deformation are assigned to the bending region, points that meet the sidewall characteristic criteria are assigned to the sidewall region, points located within the projection contact range of the progressive forming tool head in the current processing layer are assigned to the contact region, and points in the bottom plane region are assigned to the bottom region.

[0078] The intelligent error prediction model sets physical mechanism constraints for each sub-region, matching the deformation mechanism of that sub-region. For the bending region, the physical mechanism constraints are constructed based on a simplified membrane deformation springback model. For the sidewall region, the physical mechanism constraints are further superimposed on the cumulative springback value in the bending region, consisting of a combination of analytical components for large-deflection bending springback of the flat plate and analytical components for bending springback of the straight beam of the sidewall. The analytical component for large-deflection bending springback of the flat plate is solved using shell analysis theory to determine the elastic recovery of the metal plate under bending-dominant deformation, while the analytical component for bending springback of the straight beam of the sidewall is calculated based on classical elastic beam theory to determine the angular springback of the sidewall section under bending moment. For the contact region, the physical mechanism constraints are further superimposed on the physical mechanism constraints for the sidewall region, consisting of a locally indented springback analytical component, calculated based on Hertzian contact theory and a simplified membrane deformation springback model. For the bottom region, the physical mechanism constraints are constructed by combining analytical components for bending springback of the bottom plane and analytical components for unloading springback. The physical mechanism constraints of each sub-region take the location parameters of the processing point, the material parameters of the metal plate, and the process parameters of incremental forming as inputs, and output the geometric error analysis value corresponding to the processing point in that sub-region.

[0079] The intelligent error prediction model sets up an independently trained neural network subnetwork for each sub-region. Each subnetwork has the same basic network structure, including an input layer, several hidden layers, and an output layer, but each subnetwork has independent connection weight parameters and bias parameters, and they do not share parameters with each other.

[0080] During the training phase, sample data belonging to the bending region is input into the first sub-network for training, sample data belonging to the sidewall region is input into the second sub-network for training, sample data belonging to the contact region is input into the third sub-network for training, and sample data belonging to the bottom region is input into the fourth sub-network for training. Each sub-network constructs its loss function by invoking the physical mechanism constraints of its corresponding sub-region during training, and independently updates its network parameters using the error backpropagation algorithm. After training, for any given processing point, the sub-region to which the processing point belongs is first determined, and then the corresponding trained neural network sub-network for that sub-region is invoked to predict the geometric error of that processing point.

[0081] In one or more embodiments of the present invention, the intelligent error prediction model sets an overlapping region at the boundary of adjacent sub-regions. The loss function of the intelligent error prediction model also includes a boundary loss function. The boundary loss function is the root mean square of the geometric error difference between the processing points in the overlapping region and the corresponding sub-network outputs of the two adjacent sub-regions. The loss function is the total loss value obtained by weighted summation of the data loss term, the physical mechanism constraint term, and the boundary loss function.

[0082] The intelligent error prediction model sets overlapping regions at the boundaries of adjacent sub-regions. An overlapping region refers to a transitional strip-shaped area with a certain spatial extension located on both sides of the boundary line between two adjacent sub-regions. The overlapping region is set as follows: after dividing the metal sheet forming area into sub-regions, for each boundary curve between adjacent sub-regions, a preset distance is extended outwards in both directions along the normal direction of the boundary curve. The area enclosed by the extended boundary line is defined as the overlapping region. Processing points located within the overlapping region are simultaneously assigned the region identifiers of both adjacent sub-regions; that is, the processing point belongs to both the first and second sub-regions.

[0083] The loss function of the intelligent error prediction model also includes a boundary loss function. This boundary loss function is the root mean square of the difference between the predicted geometric errors of the processing points within the overlapping region and the corresponding sub-network outputs of two adjacent sub-regions. The specific calculation process is as follows:

[0084] For each processing point within the overlapping region, the position parameters of the processing point, the material parameters of the metal plate, the geometric parameters of the target forming part, and the process parameters of progressive forming are input to the first sub-network corresponding to the adjacent first sub-region and the second sub-network corresponding to the adjacent second sub-region, respectively. The first geometric error prediction value output by the first sub-network and the second geometric error prediction value output by the second sub-network are obtained. The difference between the first geometric error prediction value and the second geometric error prediction value is calculated. The difference is squared to obtain the squared difference value corresponding to the processing point. The arithmetic mean of the squared differences corresponding to all processing points within the overlapping region is calculated, and the square root of the arithmetic mean is taken. The result is the value of the boundary loss function.

[0085] The boundary loss function is used to constrain the prediction outputs of adjacent sub-networks to be consistent in the overlapping region, thereby ensuring the continuous transition of prediction results of different sub-regions at the boundary and avoiding abrupt changes in the geometric error prediction values ​​at the boundary caused by independent training of partitions.

[0086] The loss function is the total loss value obtained by weighted summation of the data loss term, the physical mechanism constraint term, and the boundary loss function. The specific weighted summation method is as follows: the total loss value equals the data loss term multiplied by the first weight coefficient, plus the physical mechanism constraint term multiplied by the second weight coefficient, plus the boundary loss function multiplied by the third weight coefficient. The first, second, and third weight coefficients can all be preset positive real-valued hyperparameters, which can be determined by the operator based on experience or selected through a hyperparameter search method before training begins.

[0087] The relative magnitudes of the weighting coefficients determine the proportions of the data loss term, physical mechanism constraint term, and boundary loss function in the total loss. In each iteration of the training phase, the values ​​of the data loss term, physical mechanism constraint term, and boundary loss function corresponding to the current training batch are simultaneously calculated. The total loss value is then calculated using the weighted summation formula described above, and backpropagation and network parameter updates are performed based on the total loss value. By introducing the boundary loss function and incorporating it into the total loss for joint optimization, the intelligent error prediction model synchronously learns the error distribution patterns within each sub-region and the prediction consistency at the boundaries of adjacent sub-regions during training, thereby obtaining continuous and accurate geometric error prediction results within the entire formed region.

[0088] In one or more embodiments of the present invention, the tool path compensation model obtains the normal vector corresponding to the machining point on the initial tool path, sets a compensation coefficient, multiplies the geometric error output by the intelligent error prediction model with the compensation coefficient to obtain the corrected displacement of the corresponding machining point, and superimposes the corrected displacement along the normal vector of the corresponding machining point to the corresponding machining point on the initial tool path to complete the correction of the machining point.

[0089] Specifically, the normal vector can be obtained as follows: Using the geometric analysis function of computer-aided manufacturing software, the computer-aided design 3D model of the target part is read. For each machining point in the initial toolpath sequence, the surface normal vector at the projection position of the machining point on the surface of the 3D model is calculated, and the normal vector is normalized to a unit length to obtain the normal vector corresponding to the machining point. The normal vector contains three directional components in the robot base coordinate system or workpiece coordinate system: the component of the normal vector in the direction of the first coordinate axis, the component of the normal vector in the direction of the second coordinate axis, and the component of the normal vector in the direction of the third coordinate axis.

[0090] The tool path compensation model sets a compensation coefficient. This compensation coefficient is a preset scalar value used to adjust the magnitude of the corrected displacement. The value range of the compensation coefficient is typically [0, 1.5]. When the compensation coefficient is set to one, it indicates a full compensation strategy, meaning all geometric errors predicted by the intelligent error prediction model are converted into corrected displacement. When the compensation coefficient is set to a positive number less than one, it indicates a partial compensation strategy, converting only a certain proportion of the geometric error into corrected displacement. When the compensation coefficient is set to a positive number greater than one, it indicates an overcompensation strategy, meaning the corrected displacement is greater than the predicted geometric error to offset any additional springback that may occur after compensation. The specific value of the compensation coefficient can be determined comprehensively based on the stability of the actual forming process, the repeatability accuracy of the robot system, and the springback characteristics of the metal sheet material.

[0091] The toolpath compensation model multiplies the geometric error output by the intelligent error prediction model with a compensation coefficient to obtain the corrected displacement for the corresponding machining point. For each machining point on the initial toolpath, the trained intelligent error prediction model is first invoked, inputting the position parameters of the machining point, the corresponding metal sheet material parameters, the geometric parameters of the target forming part, and the incremental forming process parameters to obtain the predicted geometric error value for that machining point. The predicted geometric error value is a scalar value with a positive and negative sign. A positive value indicates that the dimension of the machining point is too large in the direction of the normal vector, and a negative value indicates that the dimension of the machining point is too small in the opposite direction of the normal vector. After taking the opposite sign of the predicted geometric error value, it is multiplied with the compensation coefficient, and the resulting product is the modulus of the corrected displacement for that machining point. The direction of the corrected displacement is opposite to the direction of the normal vector.

[0092] The toolpath compensation model superimposes the corrected displacement along the normal vector of the corresponding machining point onto the corresponding machining point of the initial toolpath, thus completing the correction of the machining point. The specific superposition operation can be as follows:

[0093] Multiplying the magnitude of the corrected displacement by the unit direction vector of the normal vector yields a corrected displacement vector with both magnitude and direction, the direction of which is opposite to that of the normal vector. The nominal position coordinates of the machining point in the initial toolpath are then added to the components of the corrected displacement vector along the three coordinate axes to obtain the compensated machining point coordinates. The compensated machining point coordinates are spatially offset from their nominal position towards the interior of the metal plate by a certain distance, equal to the product of the absolute value of the predicted geometric error and the compensation coefficient. By sequentially performing the above normal vector acquisition, corrected displacement calculation, and coordinate superposition operations on all machining points in the initial toolpath sequence, a complete compensated toolpath point sequence can be obtained.

[0094] The compensated tool path can pre-counteract springback deformation and robot retreat deformation during the forming process, so that the surface shape of the final formed part after progressive forming is close to the design surface shape of the target formed part.

[0095] In one or more embodiments of the present invention, the tool path compensation model performs cubic spline interpolation on the corrected sequence of all machining points. The cubic spline interpolation ensures that the connection points of the compensated tool path maintain first-order tangential continuity. The initial tool path adopts any one of the following: spiral path, contour path, Zigzag path, or fractal path.

[0096] The cubic spline interpolation process is a numerical fitting method used to construct a continuous and smooth spatial curve between given discrete machining points, such that the curve satisfies a preset continuity condition at each machining point. Before performing the cubic spline interpolation process, the compensated machining point coordinate sequence has been obtained through the aforementioned correction steps. These points are arranged in space according to the machining order of the initial tool path.

[0097] The specific method of cubic spline interpolation is as follows: Two adjacent points in the compensated processing point sequence are taken as the two endpoints of the interpolation interval. Within each interpolation interval, a cubic polynomial function with respect to the arc length parameter is constructed. This cubic polynomial function describes the spatial coordinates corresponding to any arc length position within the interval. All cubic polynomial functions on adjacent point intervals together constitute a piecewise cubic polynomial curve. To ensure the smoothness of the curve, a continuity constraint is set at the common endpoint of two adjacent cubic polynomial functions: the first derivative of the cubic polynomial function in the preceding interval at the endpoint is required to be equal to the first derivative of the cubic polynomial function in the following interval at the starting point. This constraint ensures that the entire piecewise cubic polynomial curve has a continuous first derivative at all processing point connections, meaning the tangent direction of the curve does not change abruptly at the connection points, thus achieving first-order tangential continuity. For the first and last endpoints of a non-closed path, natural boundary conditions can be set, i.e., the second derivative values ​​at the first and last endpoints are set to zero.

[0098] After completing cubic spline interpolation, the interpolation curve can be resampled at equal arc length intervals or according to the interpolation cycle of the robot control system to generate a dense path point sequence that can be directly executed by the robot controller. The first-order tangential continuity ensures a smooth transition in velocity direction during the movement of the robot's end-effector progressive forming tool head along the compensated tool path, avoiding the impact load on the robot joints caused by sudden changes in motion direction, and also helps maintain the stability of the contact state between the tool head and the metal plate during the forming process.

[0099] The initial toolpath can be any one of the following: spiral path, contour path, zigzag path, or fractal path. A spiral path is a continuous spatial trajectory that starts from the center or edge of the forming area and expands outwards or inwards in an involute spiral pattern. The path appears spiral-shaped on the horizontal projection plane and gradually moves downwards with each layer in the vertical direction. Its characteristics are continuous path without breaks and fewer tool head lifts. A contour path involves horizontally slicing the 3D model of the target part according to a preset layer height. Within each layer, the tool head moves along the contour line of that layer. After completing one layer, it moves down one step depth along the feed direction to enter the next layer for processing. Its characteristics are clear layer boundaries and suitability for parts with relatively uniform sidewall inclination angles. A zigzag path involves the tool head reciprocating along a set of parallel straight lines within each processing layer. Adjacent straight line trajectories are connected by arcs or straight lines. Its characteristics are simple path planning algorithms and high computational efficiency. Fractal paths are spatial filling curves with self-similar properties generated based on fractal geometry principles. When the tool head moves along the fractal curve, it can achieve uniform coverage within a limited space. Its characteristic is that it is highly adaptable to complex boundary shapes.

[0100] The selection of the initial tool path type depends on factors such as the geometric complexity of the target part, the forming characteristics of the sheet metal, and the constraints of the robot's workspace. Those skilled in the art can choose according to their actual needs.

[0101] In one or more embodiments of the present invention, the tool path compensation model establishes a UDP communication channel with the robot controller through the RSI communication protocol. The tool path compensation model receives the current processing point information uploaded by the robot controller in real time through the UDP communication channel, and sends the position correction amount of the corresponding processing point to the robot controller in real time through the UDP communication channel, thereby realizing online real-time compensation.

[0102] Specifically, the tool path compensation model can establish a User Datagram Protocol (UDP) communication channel with the robot controller through the robot sensor interface communication protocol. The robot sensor interface communication protocol is a real-time data interaction interface provided by the robot control system, allowing external computing devices to exchange data with the robot controller at fixed communication intervals during the robot's motion program execution. The User Datagram Protocol (UDP) is a connectionless network transmission protocol characterized by low transmission latency and high data packet transmission efficiency, making it suitable for industrial control scenarios with high real-time requirements.

[0103] The specific method for establishing a User Datagram Protocol (UDP) communication channel is as follows: Enable the robot sensor interface communication protocol function on the robot controller, configure the communication mode to UDP, and set the Internet Protocol address and port number on the robot controller. On the external computing device, run the tool path compensation model program and bind it to an Internet Protocol address and corresponding port number on the same network segment as the robot controller. The robot controller and the external computing device are physically connected via network cable or industrial Ethernet. After completing the above configuration, a bidirectional UDP communication channel is established between the robot controller and the external computing device, allowing both parties to send data packets to each other during the communication cycle.

[0104] The tool path compensation model receives the current machining point information uploaded by the robot controller in real time via a User Datagram Protocol (UDP) communication channel. During the robot's execution of the initial tool path program, the robot controller sends status data such as the actual spatial coordinates of the robot's end effector in the Cartesian coordinate system, the current path segment number, and the interpolation progress ratio to an external computing device according to a preset communication cycle. After receiving this data, the external computing device parses it to obtain the position parameters of the current machining point.

[0105] The tool path compensation model sends position correction values ​​for the corresponding machining points to the robot controller in real time via a User Datagram Protocol (UDP) communication channel. The external computing device, based on the received current machining point position parameters, invokes the pre-trained intelligent error prediction model, inputting the position parameters of the machining point, the corresponding metal sheet material parameters, the geometric parameters of the target forming part, and the incremental forming process parameters to obtain the geometric error prediction value for that machining point. Subsequently, it obtains the normal vector corresponding to the machining point, multiplies the geometric error prediction value by a preset compensation coefficient, and applies it in the opposite direction along the normal vector to calculate the corrected displacement vector for that machining point. The corrected displacement vector is decomposed in the robot's base coordinate system into a first position correction value along the first coordinate axis, a second position correction value along the second coordinate axis, and a third position correction value along the third coordinate axis. The external computing device encapsulates these three position correction values ​​into a UDP datagram and sends it to the robot controller through the established communication channel.

[0106] After receiving the position correction, the robot controller superimposes it onto the target position of the current motion command at the servo control level, adjusting the motion angles of each joint axis in real time to change the actual motion trajectory of the progressive forming tool head. The above-mentioned receiving, calculation, sending, and superimposing processes are executed once per communication cycle, forming a closed-loop online real-time compensation process.

[0107] This invention constructs a robot forming dataset containing positional parameters and corresponding geometric errors. It uses a neural network that integrates the physical mechanism of metal plastic forming to build an error prediction model. The model is trained by combining a loss function with data loss terms and physical mechanism constraints. This overcomes the shortcomings of pure physical models, such as low computational efficiency and inability to adapt to real-time compensation. It also solves the pain points of pure data-driven models, such as weak generalization ability and poor interpretability. This invention achieves high-precision and high-efficiency prediction of forming geometric errors. By correcting the tool path point by point, it effectively suppresses forming errors, significantly improves the forming accuracy of parts and the product qualification rate, and supports the application of robot progressive forming in high-precision manufacturing scenarios.

[0108] The above is the overall concept of the present invention. For ease of understanding, the present invention also provides the following embodiments:

[0109] This invention provides an intelligent toolpath compensation method for robot progressive forming, such as... Figure 1 As shown, the method includes the following basic steps:

[0110] Step S10: Obtain the geometric error data of the metal sheet during the robot's incremental forming process. A schematic diagram of the robot's incremental forming process is shown below. Figure 2 As shown;

[0111] Step S20: Establish an intelligent error prediction model based on physical information. The basic framework is as follows: Figure 3 As shown;

[0112] Step S30: Establish the tool path compensation model, the basic framework of which is as follows: Figure 4 As shown;

[0113] Step S40: Experimental verification.

[0114] Specifically, step S20 includes the following steps:

[0115] Step S201: Construct the dataset and divide it into training and test sets;

[0116] Step S202: Establish a physical prior knowledge model;

[0117] Step S203: Build a framework for an intelligent error prediction model based on physical information;

[0118] Step S204: Train a physical information-based intelligent error prediction model using the training set;

[0119] Step S205: Verify model performance using a test set.

[0120] Specifically, step S40 includes the following steps:

[0121] Step S401: Use CAD design tools to generate a 3D model of the target part;

[0122] Step S402: Generate the tool trajectory in the robot programming language;

[0123] Step S403: Predict geometric errors using a physically based intelligent error prediction model;

[0124] Step S404: Optimize the tool trajectory using the tool path compensation model;

[0125] Step S405: The robot controls the progressive forming tool head to form the shape;

[0126] Step S406: Detect the error of the formed part.

[0127] Example 1

[0128] In step S10, this embodiment acquires the dataset through experimental data collection. The experiment uses AISI304 stainless steel sheet with a thickness of 1.0 mm. The initial sheet shape is a square with a side length of 300 mm. The target shape is a regular square frustum with a top side length of 120 mm, a forming height of 30 mm, and sidewall inclination angles of 30°, 40°, and 50° to the horizontal. The fixture fixing area 4 is adjacent to the edge of the forming area 31, i.e., L is 0 mm. A schematic diagram of the metal sheet 3 clamping is shown below. Figure 5 A spiral-type constant residual height feed method is selected, and the path diagram is shown below. Figure 6 As shown. The forming speeds were selected as 0.01 m / s, 0.02 m / s, and 0.03 m / s, and the step depths for each layer were selected as 0.1 m, 0.2 m, and 0.3 m. After each set of experiments, a laser scanner was used to acquire the surface three-dimensional point cloud data of the formed part. By comparing it with the design model, the geometric error values ​​of each point were extracted.

[0129] In step S201, the raw data collected in step S10 is cleaned and normalized. In this embodiment, the training set and test set are divided according to the shape of the part: the data of formed parts with 8 different geometric shape parameters are selected as the training set, and the data of formed parts with geometric parameters that do not overlap with the first 8 sets of formed parts are selected as the test set, so as to verify the generalization ability of the model in unknown geometric shapes.

[0130] In step S202, this embodiment addresses the most significant sidewall springback problem in progressive forming by introducing an analytical model as a physical constraint. The forming force application point is set to the position of the last forming point at the bottom during calculation. The springback in the sidewall region is decomposed into a flat plate springback calculation. Calculation of springback in bending beams Calculation of springback in straight beam Three parts. Among them... The large deflection bending of the plate is obtained by solving the KAMAN equation. and Calculated based on classical elastic beam theory. Total elastic deflection in the sidewall region. The approximate expression is

[0131]

[0132] The analytical calculation result is not used as the final predicted value, but as a physical constraint term, which is used in subsequent model training to constrain the output of the neural network so that it conforms to the laws of mechanics.

[0133] In step S203, this embodiment uses an Artificial Neural Network (ANN) as the base network. The network input layer has five nodes: the predicted point coordinates (x, y, z), the tool head feed speed v, and the step depth Δz. The output layer has one node, representing the geometric error value at that point. The loss function consists of two parts: a data loss function and a physical information loss function. Material parameters are set in the analytical model; the inputs are the predicted point coordinates, the coordinates of the forming force application point, the forming speed, and the step depth; the output is the longitudinal deviation. The loss function (Loss) is composed of two weighted components:

[0134]

[0135] in, The mean squared error (MSE) is the difference between the network's predicted values ​​and the training set labels. The deviation between the network predicted value and the value calculated by the analytical model in step S202, These are the weighting coefficients for the physical constraint terms.

[0136] In step S204, the training set data is input into the network for iterative training using the Adam optimizer. After training, the test set data is input into the model, the prediction error is compared with the measured error, and the coefficient of determination (R²) and root mean square error (RMSE) are calculated.

[0137] In step S30, for each tool path point Calculate the normal vector of the point based on its position on the surface. Prediction error The deviation that needs to be compensated is considered to be the corrected displacement vector of the tool path point, determined according to the principle of "error reverse compensation". Where k is the compensation coefficient (in this embodiment, k=1.0, i.e., full compensation). The correction vector is superimposed on the initial toolpath point to obtain the compensated new toolpath point. Since this embodiment uses a spiral tool path, the path is continuous and the Z-axis continuously decreases. Cubic spline interpolation is performed on the compensated tool path point sequence to eliminate local abrupt changes that may be introduced by the discreteness of error prediction, ensuring that the compensated path is first-order continuous (tangentially continuous) at the connection point, thus avoiding impacts when robot 1 moves.

[0138] In step S401, this embodiment uses SolidWorks to create a three-dimensional solid model of the target square truncated pyramid and exports an STL format copy for subsequent error comparison benchmarks.

[0139] In step S402, the CAM module selects the "spiral constant residual height" feed strategy, sets the residual height to 0.01m, generates the initial toolpath, and outputs it as a G-code file. This file contains a series of discrete toolpath point coordinates.

[0140] In step S403, the tool path point coordinates and corresponding process parameters from S402 are extracted and input into the intelligent error prediction model trained in step S20 to calculate the expected forming geometry error at each tool path point in batches. .

[0141] In step S404, the result calculated in step S403 is... relative to the initial tool path point Input the data into the compensation model established in step S30, and calculate the compensated tool path points. After smoothing the compensated point sequence, it is converted into a dedicated control program (.src format) for KUKA robots using a Python program. The program contains instructions for tool head start / stop, feed speed, trajectory interpolation mode, etc.

[0142] In step S405, the robot program generated in step S404 is imported into the KUKA robot controller. The end effector of robot 1 is equipped with a spherical progressive forming tool head 2, which performs single-point progressive forming on a 1.0mm thick 304 stainless steel plate according to the compensated optimized trajectory until the part is processed.

[0143] In step S406, after the forming is completed, a laser scanner is used to scan the part to obtain 3D point cloud data of the actual formed contour. The point cloud data and the design model in step S401 are imported into the comparison software, and after best fitting and alignment, the geometric error distribution of the entire part surface is calculated.

[0144] Example 2

[0145] The overall process of this embodiment is basically the same as that of embodiment 1. The difference is that in step S20 (establishing an intelligent error prediction model based on physical information), a partitioned modeling and prediction strategy is adopted for different geometric feature regions to further improve the prediction accuracy.

[0146] In step S10, the specific implementation method is the same as in Example 1. AISI304 stainless steel sheet is used, with a thickness of 1.0 mm. The target shape is a regular square frustum, and the distance L between the fixture fixing area 4 and the forming area 31 is 50 mm. The remaining process parameter settings and data acquisition methods are consistent with Example 1 and will not be repeated here.

[0147] In step S20, this embodiment introduces a partitioning modeling method, as follows:

[0148] In step S201, the selection method for the training set and test set in this embodiment is the same as in embodiment 1. The part 3 is divided into a bending area 32, a sidewall area 33, a contact area 34, and a bottom area 35. Since the fixture fixing area 4 is 50mm away from the forming area, and the bending area 32 is relatively large with a large overlap with the sidewall, the specific classification in this embodiment is as shown in the appendix. Figure 7 As shown. Bending region 32 is the flat top area of ​​the part, where deformation is mainly membrane stretching and bending, coupled with large deflection deformation of the plate; sidewall region 33 is the inclined wall area, where bending and stretching are coupled; contact region 34 is the connection between the bottom surface and the sidewall, the contact area between the tool and the sheet metal at the end of progressive forming. Labels are added based on the region where the points are located to distinguish the datasets corresponding to different subdomains. Simultaneously, to avoid discontinuities in prediction results at partition boundaries, an overlapping area with a width of 2mm is set near the boundary and marked as boundary points.

[0149] In step S202, this embodiment establishes corresponding physical prior knowledge models based on the four forming regions (bending region 32, sidewall region 33, contact region 34, and bottom region 35) mentioned in step S201. This physical prior knowledge model mainly consists of three core calculations: bending region springback calculation based on membrane analysis, sidewall springback calculation based on the equivalent mapping method, and contact region springback calculation based on membrane analysis. The forming force loading point is set to the position of the last forming point at the bottom. The physical prior knowledge models for each region are combined by superimposing the above calculations. Specifically, the bending region physical prior knowledge model includes bending region springback and large deflection deviation calculations for the flat plate; the sidewall region model is the sum of bending region springback calculations and sidewall springback calculations; the contact region model is the sum of bending region springback calculations, sidewall springback calculations, and contact region springback calculations; and the bottom region model is the sum of bending region springback calculations, sidewall springback calculations, and contact region springback calculations.

[0150] In step S203, this embodiment uses four parallel sub-networks corresponding to four partitions, each with the same structure (6-input, 1-output ANN), but trained independently. The loss function is a weighted average of data loss, physical loss, and boundary loss. The data loss function is the same as that in S203 of embodiment 1. Similarly, the physical loss term for each partition calls the analytical model calculation results of the corresponding partition in step S202, and the boundary loss function. This is the root mean square of the difference between the predicted values ​​of the boundary point in two adjacent regions. The total loss function is...

[0151]

[0152] in , , These are the weighting coefficients for the data loss, physical loss, and boundary loss components, respectively.

[0153] In step S204, the training sets of each partition are input into the corresponding sub-networks for training, and the training parameters (optimizer, learning rate, number of iterations) are the same as in Example 1. After training, the test set is used for overall prediction verification.

[0154] In step S30, the construction and implementation of the compensation model are exactly the same as in Example 1, that is, the normal bias method is used to correct the tool path points point by point, which will not be repeated here.

[0155] In step S40, the specific operation methods of each sub-step (S401~S406) of the experimental verification are the same as those in Example 1. The difference is that the prediction model used in step S403 is replaced by the partition prediction model trained in this example.

[0156] Example 3

[0157] The overall process of this embodiment is basically the same as that of embodiment 2. The difference is that in step S30, an online compensation model based on RobotSensorInterface (RSI) communication is used to realize real-time correction of the tool trajectory during the forming process.

[0158] In step S10, the same as in Example 2, stainless steel sheet with grade AISI304 is used, with a thickness of 1.0 mm. The forming target is a regular square truncated pyramid. The process parameter settings and data acquisition methods are the same as in Example 2, and will not be repeated here.

[0159] In step S20, the specific implementation method is exactly the same as in Example 2, including a geometric feature-based partitioning strategy (bending region 32, sidewall region 33, contact region 34, and bottom region 35), the design of physical constraints for each partition, the construction of the partitioned neural network framework, and the training and verification of the model. The trained partitioned prediction model can output the expected geometric error at any tool path point within the forming region 31. The only difference is that in the physical prior knowledge model, the force loading position used for calculation is calculated based on the current forming point.

[0160] In step S30, in this embodiment, the tool path compensation model is implemented using an online real-time correction method, as follows: Figure 8 As shown, the details are as follows:

[0161] S301: Basic Path Generation

[0162] Similar to Example 1, an initial toolpath (spiral fixed residual height) is first generated by CAM software and converted into a basic path program executable by robot 1. This program contains a series of nominal toolpath points. And corresponding feed rate and other instructions. Unlike offline compensation, the points in the basic path program in this embodiment are nominal values ​​that have not been compensated.

[0163] S302: Setting up an RSI communication environment

[0164] Enable RSI real-time communication in the KUKA robot controller, set the communication period to 4ms, and establish a UDP communication channel for receiving external correction commands in real time. The robot controller runs the basic path program and simultaneously sends information such as the current actual position and speed outwards at 4ms intervals through the RSI interface, while receiving position corrections returned by an external computer.

[0165] S303: Online Error Compensation Algorithm

[0166] An external computer (or industrial control computer) runs the following compensation logic in real time:

[0167] Receive current status: Obtain the current path segment and corresponding parameters of robot 1 via RSI (such as the start and end points of the current segment and the interpolation ratio).

[0168] Query prediction error: Based on the current position of robot 1, quickly query (or interpolate and calculate) the prediction geometric error corresponding to that point from the prediction model in step S20. .

[0169] Calculate the correction amount: Calculate the correction vector according to the normal offset principle. r, where The theoretical normal vector of the current point (pre-calculated and stored by the CAM model or calculated in real time based on the surface equation), and the compensation coefficient. Take 1.0.

[0170] Send correction command: Calculate the correction vector The position offset (Δx, Δy, Δz) is converted into the robot's base coordinate system and sent to the robot controller via the RSI interface at 4ms intervals, and then superimposed on the current motion command.

[0171] S304: Real-time trajectory overlay and smoothing

[0172] After receiving the correction values, the robot controller superimposes them onto the position commands of each axis in real time at the servo level, enabling online fine-tuning of the trajectory. Because the correction values ​​are updated at a high frequency (250Hz) and only a small offset is applied in each cycle, robot 1's motion remains smooth and shock-free. To ensure the stability of the compensation, a first-order low-pass filter (cutoff frequency 5Hz) is applied to the correction value sequence to filter out possible high-frequency noise.

[0173] In step S40, steps S401-S402 are the same as in Example 2, using SolidWorks to model and generate a spiral-shaped, fixed-residual-height basic path, outputting the robot's basic program (uncompensated). In step S403, the intelligent error prediction model based on physical information constructed in S20 of this example is used to predict geometric errors in real time. In step S404, the robot's basic path program is started, and the external industrial control computer's compensation program is started simultaneously. Robot 1 uploads its status in real time via RSI, and the industrial control computer calculates the correction amount and sends it back. Throughout the forming process, the actual motion trajectory of robot 1 is the superposition of the initial path and the real-time correction amount, achieving online compensation for forming errors.

[0174] Steps S405-S406 are the same as in Example 2. Robot 1 completes the progressive forming of a 1.0mm thick 304 stainless steel sheet according to the actual trajectory after online compensation. After forming, a laser scanner is used to acquire the point cloud of the part and compare it with the design model.

[0175] Through the above steps, this embodiment achieves online path compensation based on the partition prediction model and real-time communication with RSI, further improving forming accuracy and process adaptability.

[0176] The above provides a detailed description of an intelligent tool path compensation method for progressive forming of robots. Specific examples have been used to illustrate the principles and implementation methods of the invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the invention. Therefore, the content of this specification should not be construed as a limitation of the invention.

Claims

1. A smart tool path compensation method for robot progressive forming, characterized in that, The method includes: Construct a robot forming dataset, which includes the position parameters of the processing points during the robot's progressive forming process, as well as the geometric errors of the points corresponding to the position parameters; A smart error prediction model based on physical information is established; wherein, the smart error prediction model is a neural network model that integrates the physical mechanism of metal plastic forming, the loss function of the smart error prediction model includes a data loss term and a physical mechanism constraint term, and the smart error prediction model takes the position parameter as input and the geometric error of the point corresponding to the position parameter as output. A tool path compensation model is established. Based on the geometric error output by the intelligent error prediction model, the tool path compensation model corrects the initial tool path of the robot's progressive forming point by point, and generates a compensated tool path. The intelligent error prediction model embeds the processing point location parameters, metal plate material parameters, target forming part geometric parameters, and progressive forming process parameters into the calculation process of the neural network model. The data loss term is the mean square error between the geometric error output by the neural network model and the geometric error of the corresponding point in the robot forming dataset. The physical mechanism constraint term is the deviation between the geometric error output by the neural network model and the geometric error calculated by the metal plastic forming physical mechanism analysis model. The loss function is the total loss value obtained by weighted summation of the data loss term and the physical mechanism constraint term. The intelligent error prediction model divides the forming area of ​​the metal plate into bending area, sidewall area, contact area and bottom area according to the forming process characteristics. The intelligent error prediction model sets physical mechanism constraint terms that match the deformation mechanism of the corresponding sub-region for each sub-region. The intelligent error prediction model sets independently trained neural network sub-networks for each sub-region.

2. The method according to claim 1, characterized in that, The robot forming dataset also includes at least one of the following: material parameters of the metal sheet, geometric parameters of the target forming part, and process parameters of incremental forming; wherein, the material parameters of the metal sheet include at least the elastic modulus, Poisson's ratio, tensile strength, yield strength, material hardening coefficient, and hardening index of the metal sheet; the geometric parameters of the target forming part include at least the wall angle, curvature, and rate of change of curvature of the target forming part; and the process parameters of incremental forming include at least the feed rate and depth of step of the incremental forming tool head.

3. The method according to claim 2, characterized in that, The positional parameters include at least the horizontal distance from the processing point to the metal plate fixture and the forming depth of the processing point.

4. The method according to claim 1, characterized in that, The loss function sets the weight coefficients corresponding to the physical mechanism constraint terms. The intelligent error prediction model is trained iteratively using the Adam optimizer. The intelligent error prediction model completes the model performance verification through the coefficient of determination and root mean square error.

5. The method according to claim 4, characterized in that, The intelligent error prediction model sets an overlapping region at the boundary of adjacent sub-regions. The loss function of the intelligent error prediction model also includes a boundary loss function. The boundary loss function is the root mean square of the geometric error difference between the processing points in the overlapping region and the corresponding sub-network outputs of the two adjacent sub-regions. The loss function is the total loss value obtained by weighted summation of the data loss term, the physical mechanism constraint term, and the boundary loss function.

6. The method according to claim 5, characterized in that, The tool path compensation model obtains the normal vector corresponding to the machining point on the initial tool path. The tool path compensation model sets a compensation coefficient. The tool path compensation model multiplies the geometric error output by the intelligent error prediction model with the compensation coefficient to obtain the corrected displacement of the corresponding machining point. The tool path compensation model superimposes the corrected displacement along the normal vector of the corresponding machining point to the corresponding machining point on the initial tool path to complete the correction of the machining point.

7. The method according to claim 6, characterized in that, The tool path compensation model performs cubic spline interpolation on all the corrected processing point sequences. The cubic spline interpolation ensures that the point connections of the compensated tool path maintain first-order tangential continuity. The initial tool path can be any one of the following: spiral path, contour path, Zigzag path, or fractal path.

8. The method according to claim 1, characterized in that, The tool path compensation model establishes a UDP communication channel with the robot controller through the RSI communication protocol. The tool path compensation model receives the current processing point information uploaded by the robot controller in real time through the UDP communication channel, and sends the position correction amount of the corresponding processing point to the robot controller in real time through the UDP communication channel to achieve online real-time compensation.

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