Data-driven robot multi-degree-of-freedom forming force prediction and online control method

Abstract

The present application relates to a kind of robot multi-degree-of-freedom forming force prediction and online control method based on data driving, comprising the following steps: S1, the kinematics relationship between the upper die composite rotary motion and vertical feed motion is established;S2, obtain large-scale simulation domain forming data and experimental domain forming data;S3, simulation domain data and experimental domain data are preprocessed;S4, construct the double-flow neural network consisting of historical feed displacement sequence branch and instantaneous feed speed branch;S5, the forming force prediction model is pre-trained, and then the model is fine-tuned using experimental forming domain data;S6, the forming force prediction model after migration is embedded in online control process, and forming force online control is realized.The present application can solve the problems of lack of process adaptive ability in traditional offline forming force control, dependence on a large number of reliable experimental data in pure data-driven model and difference between simulation and experimental data domain, thereby improving forming force tracking stability and complex component forming precision.

Description

Technical Field

[0001] This invention relates to the field of robot plastic forming control technology, and more specifically, to a data-driven method for predicting and controlling multi-degree-of-freedom forming forces in robots online. Background Technology

[0002] Robotic multi-degree-of-freedom forming processes combine industrial robots with metal plastic forming techniques. They enable complex spatial posture adjustments, localized rolling contact, and continuous material flow through multi-degree-of-freedom motion, making them suitable for the flexible forming of complex structural parts such as spiral bevel gears. Forming force is a key process variable determining the geometric accuracy, surface quality, and equipment load conditions of the component. Insufficient forming force can easily lead to incomplete material filling, uneven local deformation, and increased tooth profile errors; excessive forming force may cause mold wear, equipment overload, folding defects, or excessive work hardening.

[0003] Existing forming force control methods mostly rely on human experience or pre-determined offline motion planning trajectories from finite element simulations, making it difficult to adjust in real time according to changes in material temperature, local contact state, and structural deformation during the actual forming process. While pure data-driven models can avoid oversimplified mechanistic assumptions, in heavy-duty robot multi-degree-of-freedom forming scenarios, high-quality experimental data acquisition is costly, safety constraints are strong, and the number of samples is usually limited. On the other hand, although finite element simulation data is easy to obtain, it has domain differences from the actual experimental process, and direct use for model training can easily lead to prediction bias. Summary of the Invention

[0004] The technical problem to be solved by this invention is to provide a data-driven method for predicting and controlling multi-degree-of-freedom forming forces of robots online. This method can solve the problems of traditional offline forming force control lacking process adaptability, pure data-driven models relying on a large amount of reliable experimental data, and the difference between simulation and experimental data domains, thereby improving the stability of forming force tracking and the forming accuracy of complex components.

[0005] The technical solution adopted by this invention to solve its technical problem is: to construct a data-driven method for predicting and controlling multi-degree-of-freedom forming forces of a robot online, comprising the following steps: S1. Determine the motion form, tool trajectory and key process parameters of the robot's multi-degree-of-freedom forming process, and establish the kinematic relationship between the composite rotational motion of the upper mold and the vertical feed motion. S2. Establish a finite element model of the robot's multi-degree-of-freedom forming process and obtain forming data in a large-scale simulation domain; at the same time, based on the structural characteristics of the heavy-duty forming robot, adopt a distributed force / displacement measurement method to obtain forming data in the experimental domain. S3. Clean, extract, and normalize the simulation domain data and experimental domain data, and analyze the distribution differences between the simulation domain and the experimental domain to provide a data foundation for subsequent transfer learning. S4. Construct a two-stream neural network consisting of historical feed displacement sequence branches and instantaneous feed velocity branches, and introduce the consistency of deformation energy during the forming process as a physical constraint into the model training process; S5. The forming force prediction model is pre-trained using large-scale simulation domain forming data, and then the model is fine-tuned by transfer using experimental forming domain data. S6. Embed the migrated forming force prediction model into the online control process, generate candidate feed speeds based on the real-time forming state, and obtain the optimal feed speed through objective function search to achieve online control of forming force.

[0006] According to the above scheme, the motion form of the multi-degree-of-freedom forming process in step S1 is as follows: The multi-degree-of-freedom forming process of a robot is a local continuous plastic forming process. The blank is placed between an upper mold and a lower mold. The lower mold is fixedly mounted on the machine tool bed, and the upper mold is mounted on the motion platform of a heavy-duty forming robot. During the forming process, the upper mold rotates around the machine tool axis and rotates in the opposite direction around its own axis. At the same time, it is gradually fed in the vertical direction, so that the upper mold and the blank are in continuous local contact, and the blank is driven to undergo plastic flow. The motion of the upper mold includes two rotational degrees of freedom and one vertical feed degree of freedom. The two rotational motions are the revolution around the vertical axis in the machine tool coordinate system and the rotation around the tool's own axis, respectively.

[0007] According to the above scheme, the revolution motion around the vertical axis in the machine tool coordinate system and the rotation motion around the tool's own axis satisfy the constraint relationship that the magnitudes of the angular velocities are equal and the directions are opposite, that is: (1) in, The angular velocity of the upper mold around the machine tool axis. The angular velocity of the upper mold around its own axis; The vertical feed motion of the upper die is used to apply the forming load, and its feed displacement is expressed as: (2) in, For feed displacement, For feed rate, This refers to the forming time.

[0008] According to the above scheme, in step S1, a coupling analysis is performed on the aforementioned composite rotational motion and vertical feed motion, and a point on the upper mold axis is selected. As the research object, based on the principle of kinematic composition, the spatial trajectory equation of this feature point is derived, and the specific expression is as follows: (3) in, It is a point on the upper mold axis. To the cone point The distance; It is a point In coordinate system The initial phase angle is used to determine the initial forming time. The spatial position ensures precise matching between the movement of the upper mold and the positioning of the blank; It is the angle between the two axes of rotation, i.e., the tilt angle.

[0009] According to the above scheme, a heavy-duty forming robot is used to complete the degree-of-freedom forming process. The heavy-duty forming robot adopts a 6-PSS parallel mechanism configuration. The heavy-duty forming robot includes a fixed platform, a motion platform, and six identical motion chains. Each chain includes one prismatic joint and two ball joints. The six drive sliders are arranged circumferentially along the fixed platform and are driven by servo motors and lead screw transmission mechanisms. Through the coordinated movement of the six drive sliders, the motion platform realizes three-dimensional translation and three-dimensional rotation.

[0010] According to the above scheme, in step S2, a finite element model of the robot's multi-degree-of-freedom forming process is established based on the above kinematic analysis. A three-dimensional model is established, and by changing the key process parameter of feed speed, simulation forming force data under different working conditions is obtained. The simulation data is used to describe the basic mapping relationship between feed displacement, feed speed and forming force during the forming process.

[0011] According to the above scheme, in step S2, a distributed force measurement method is used to obtain the experimental forming force during the acquisition of experimental domain forming data; single-axis force sensors are respectively arranged on multiple drive sliders of the heavy-duty forming robot.

[0012] According to the above scheme, in step S3, the minimum-maximum normalization method is used to map all features to the interval [0,1]. The normalization method is expressed as: (4) in, and These represent the minimum and maximum values ​​for each feature dimension, respectively. The forming force sequence can be divided into multiple local segments, and statistical features such as mean, variance, peak value, and slope can be extracted. Dimensionality reduction methods can be used to analyze the distribution of the simulation domain and experimental domain in the feature space.

[0013] According to the above scheme, in step S4, a physically guided dual-flow neural network is constructed to simultaneously extract historical location information and instantaneous process parameter information. The physically guided dual-stream neural network includes a first input branch, a second input branch, a feature fusion layer, and a forming force output layer. The first input branch is used to process the historical feed displacement sequence, preferably using a gated recurrent unit network to capture the influence of the accumulated deformation history on the current forming force during the forming process. The gated recurrent unit network is represented as follows: (5) in, It is the first Input of time steps, and These are the hidden states of the current and previous time steps, respectively. and These are the update door and the reset door; It is the sigmoid activation function, i.e. This branch encodes the historical feed displacement sequence into a compact time representation. The second input branch processes the current feed rate and uses a multilayer perceptron network, which is represented as follows: (6) in, These are input features. and These are trainable parameters. It is a non-linear activation function; The two feature streams are concatenated and fused before being input into a fully connected regression layer, ultimately outputting the predicted forming force at the current or next time step; the model prediction relationship is expressed as: (7) in, To predict forming force for the model, This represents the neural network model to be trained. Indicates model parameters, This represents a historical feed displacement sequence of length L. Indicates the current feed rate; A deformation energy consistency constraint is introduced during model training; this constraint originates from the external work performed during the effective feed phase; generally, the cumulative external work applied to the deformable system is expressed as: (8) in, and These represent the contact force and contact torque, respectively. and Let these represent the translational velocity vector and the rotational velocity vector, respectively; the cumulative work related to deformation is approximately expressed as: (9) From these cumulative quantities, the incremental energy term can be obtained as follows: (10) To make physical constraints more informative than single-point energy penalties, cumulative consistency and incremental consistency are introduced; a normalized physical guidance loss term is also included. The expression is as follows: (11) in, It is a tiny normal number used to avoid numerical singularity, and This is used to balance the consistency between accumulated energy and incremental energy; Data fitting term Represented as: (12) Therefore, the final training objective function is: (13) in, The contribution of physical guidance regularization is controlled; in this formula, the first term forces the predictor to match the measured or simulated force value, while the second term constrains the predicted force sequence to be consistent with the energy evolution implied by the forming process.

[0014] According to the above scheme, in step S5, the transfer learning process includes a simulation domain pre-training stage and an experimental domain transfer fine-tuning stage. In the simulation domain pre-training stage, physical-guided dual-flow neural network is trained using large-scale simulation domain forming data, enabling the model to learn the forming force variation law under different feed speeds and feed displacements, and to learn the energy consistency characteristics in the forming process through physical constraint loss. In the experimental domain transfer fine-tuning stage, the model parameters obtained from the simulation domain pre-training are used as initial parameters, and the model is fine-tuned using experimental domain forming data. During the fine-tuning process, some low-level feature extraction parameters are kept unchanged, and the network layers related to experimental domain feature adaptation are updated. Alternatively, full parameter fine-tuning or partial parameter fine-tuning can be selected according to the experimental data scale. For cases where it is difficult to obtain complete energy information directly during the experiment, physical constraint terms are frozen or weakened so that the model retains the physical consistency knowledge learned in the simulation stage, while adapting to the data distribution in the real forming process.

[0015] The data-driven robot multi-degree-of-freedom forming force prediction and online control method of the present invention has the following beneficial effects: This invention constructs a model capable of real-time prediction of forming force under limited experimental data and transforms this model into an executable feed rate adjustment strategy. This invention can significantly improve the accuracy of forming force prediction under limited experimental data conditions and effectively reduce forming force control errors in actual robot multi-degree-of-freedom forming processes, demonstrating significant engineering application value. Attached Figure Description

[0016] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings: Figure 1 This is a schematic diagram of a multi-degree-of-freedom forming process; Figure 2 This is a diagram showing the motion trajectory of point O1 during the forming process; Figure 3 This is a schematic diagram of the 6-PSS heavy-duty forming robot structure; Figure 4 This is a schematic diagram of a finite element model based on DEFORM-3D; Figure 5 This is a schematic diagram of a distributed force / position measurement method; Figure 6 This is a schematic diagram of the physical-guided dual-flow neural network model structure; Figure 7 This is a framework diagram for transfer learning from simulation to experiment; Figure 8 This is a schematic diagram of the design of an online control method based on a predictive model; Figure 9 This is a simulation diagram of a multi-degree-of-freedom forming process based on DEFORM-3D. Figure 10 It is a hybrid dataset that includes both experiments and simulations; Figure 11 This is a schematic diagram of domain difference analysis based on t-SNE characteristic space and Jensen-Shannon divergence; Figure 12 It is a loss curve plot of the simulation data pre-training; Figure 13 This is a diagram comparing the performance metrics of model training and validation; Figure 14 This is a diagram showing the performance comparison of the models in testing; Figure 15 This is a diagram illustrating the data validity of the fine-tuning strategy; Figure 16 This is a schematic diagram of the experimental design process for spiral bevel gear forming; Figure 17 This is a schematic diagram illustrating the control stability of the spiral bevel gear forming process under different control methods. Figure 18This is a schematic diagram of the surface error of gears manufactured under different control methods. Detailed Implementation

[0017] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0018] The data-driven method for predicting and controlling multi-degree-of-freedom forming forces in robots according to the present invention includes the following steps: S1. Robot multi-degree-of-freedom forming process and kinematic analysis: Determine the motion form, tool trajectory and key process parameters of the robot multi-degree-of-freedom forming process, and establish the kinematic relationship between the composite rotational motion of the upper mold and the vertical feed motion.

[0019] like Figure 1 As shown, the multi-degree-of-freedom forming process of the robot is a local continuous plastic forming process. The blank is placed between the upper mold and the lower mold. The lower mold is fixedly mounted on the machine tool bed, and the upper mold is mounted on the motion platform of the heavy-duty forming robot. During the forming process, the upper mold rotates around the machine tool axis on one hand and rotates in the opposite direction around its own axis on the other hand, while gradually feeding in the vertical direction. This creates continuous local contact between the upper mold and the blank, driving the blank to undergo plastic flow.

[0020] Specifically, the motion of the upper die includes two rotational degrees of freedom and one vertical feed degree of freedom. The two rotational motions are the revolution around the vertical axis of the machine tool coordinate system and the rotation around the tool's own axis. To ensure a stable rolling contact between the tool and the workpiece, the two rotational motions satisfy the constraint relationship that their angular velocities are equal in magnitude and opposite in direction, i.e.: (1) in, The angular velocity of the upper mold around the machine tool axis. This is the angular velocity of the upper mold around its own axis.

[0021] The vertical feed motion of the upper die is used to apply the forming load, and its feed displacement can be expressed as: (2) in, For feed displacement, For feed rate, The forming time is determined by the combined rotary motion and vertical feed motion, which together determine the trajectory of the upper die feature points in space. This trajectory determines the contact position, contact posture, and local material flow state between the tool and the blank, and forms the kinematic basis for subsequent forming force prediction and feed rate control.

[0022] To comprehensively and accurately describe the spatial motion of the upper mold, it is necessary to perform a coupled analysis of the aforementioned composite rotational motion and vertical feed motion. For example... Figure 2 As shown, select a point on the upper mold axis. As the research object, and based on the principle of kinematic composition, the spatial trajectory equation of this feature point can be derived, and the specific expression is as follows: (3) in, It is a point on the upper mold axis. To the cone point The distance; It is a point In coordinate system The initial phase angle is used to determine the initial forming time. The spatial position ensures precise matching between the movement of the upper mold and the positioning of the blank; It is the angle between the two axes of rotation, i.e., the tilt angle.

[0023] This multi-degree-of-freedom forming process is accomplished by a heavy-duty forming robot, which employs a 6-PSS parallel mechanism configuration. For example... Figure 3 As shown, the mechanism includes a fixed platform, a motion platform, and six identical motion chains. Each chain includes one prismatic joint and two ball joints. The six drive sliders are arranged circumferentially along the fixed platform and are driven by servo motors and lead screw transmission mechanisms. Through the coordinated movement of the six drive sliders, the motion platform can achieve three-dimensional translation and three-dimensional rotation, thereby meeting the requirements for complex spatial postures and heavy-load feed motions in multi-degree-of-freedom forming processes.

[0024] S2. Design of a hybrid data acquisition method combining simulation and experimental domains: A finite element model of the robot's multi-degree-of-freedom forming process is established to obtain large-scale forming data in the simulation domain; at the same time, based on the structural characteristics of the heavy-duty forming robot, a distributed force / displacement measurement method is adopted to obtain a small amount of forming data in the experimental domain.

[0025] First, a finite element model of the robot's multi-degree-of-freedom forming process is established based on the above kinematic analysis. For example... Figure 4 As shown, taking the forming of spiral bevel gears as an example, a 3D model is established using UG software based on the geometry of the target gear, blank, upper die, and lower die, and then imported into DEFORM-3D finite element software. Then, by changing the key process parameter of feed rate, simulated forming force data under different working conditions are obtained. To form a large-scale simulation domain sample, the simulation domain forming data needs to cover multiple feed rate conditions at low, medium, and high speeds, with feed rate intervals of 0.1 mm / s, 0.2 mm / s, etc. The simulation data is used to describe the basic mapping relationship between feed displacement, feed rate, and forming force during the forming process, and provides a data foundation for subsequent model pre-training.

[0026] Secondly, experimental forming data is acquired. Since the multi-degree-of-freedom forming process of the robot is a heavy-duty forming process, directly installing high-range multi-axis force sensors at the tool end would place high demands on the sensor's stiffness, overload resistance, thermal stability, and installation space, leading to significant engineering challenges. Therefore, this invention employs a distributed force measurement method to obtain the experimental forming force. For example... Figure 5 As shown, single-axis force sensors are arranged on multiple drive sliders of the heavy-duty forming robot. During the forming process, the forming force acting on the upper mold is transmitted to the drive sliders through the branches of the parallel mechanism, and each single-axis force sensor collects the force information in the corresponding slider direction. Simultaneously, to improve the position measurement accuracy under heavy-duty conditions, this invention employs a dual-source position distribution measurement method combining a motor encoder and a linear grating ruler. The motor encoder is used to obtain the position estimate on the transmission side, while the linear grating ruler is used to directly measure the displacement of the drive slider. The data from the two types of sensors are fused using a Kalman filter method to obtain estimates of the displacement, velocity, and acceleration states of the drive slider. Finally, based on the robot's digital twin model, a mapping relationship is established between the motion and force states of the slider and the motion and force states of the tool end, thereby reconstructing the overall forming force and motion acting on the upper mold or motion platform.

[0027] S3. Data Preprocessing and Domain Difference Analysis: The simulation domain data and the experimental domain data are cleaned, staged, and normalized, and the distribution differences between the simulation domain and the experimental domain are analyzed to provide a data foundation for subsequent transfer learning.

[0028] Robotic multi-degree-of-freedom forming processes typically include a preparation stage, a feeding stage, and a holding stage. In the preparation stage, the tool has not yet made effective contact with the workpiece, and there is no forming force. In the holding stage, the feeding motion stops, and it is mainly used for tooth profile trimming and material filling. The feeding stage is the critical stage where the material undergoes major plastic deformation, the forming force changes rapidly, and it directly affects the forming quality. Therefore, this invention preferably extracts data from the feeding stage as the main data source for model training and online control.

[0029] To ensure the data can be effectively used for subsequent model training, we performed systematic preprocessing to improve data quality. First, invalid values, outliers, and irrelevant data from non-target stages were removed. Then, considering that inconsistencies in the dimensions and numerical ranges of different physical quantities may lead to gradient imbalance, we adopted a min-max normalization method to map all features to the interval [0,1]. This method preserves the relative magnitude of features while adapting to the distribution characteristics of the formed data. The normalization method can be expressed as: (4) in, and These represent the minimum and maximum values ​​for each feature dimension, respectively.

[0030] Furthermore, to analyze the differences between the forming data in the simulation domain and the forming data in the experimental domain, feature extraction and distribution visualization can be performed on both types of data. For example, the forming force sequence can be divided into multiple local segments, and statistical features such as mean, variance, peak value, and slope can be extracted. Dimensionality reduction methods can then be used to analyze the distribution of the simulation domain and the experimental domain in the feature space. If there is a significant distribution shift between the simulation domain and the experimental domain, it indicates that directly using the simulation training model in the experimental process will produce prediction bias, and it is necessary to introduce transfer learning methods for cross-domain adaptation.

[0031] S4. Physically Guided Construction of Dual-Stream Neural Network Prediction Model: A dual-stream neural network consisting of historical feed displacement sequence branches and instantaneous feed velocity branches is constructed, and the consistency of deformation energy during the forming process is introduced as a physical constraint into the model training process.

[0032] The forming force of a robot with multiple degrees of freedom is related not only to the current feed rate, but also to the previously occurring plastic deformation of the material, local contact states, and material flow history. Therefore, it is difficult to accurately describe the variation law of forming force using only the current process parameters. This invention constructs a physically guided dual-flow neural network to simultaneously extract historical position information and instantaneous process parameter information.

[0033] like Figure 6 As shown, the physically guided dual-stream neural network includes a first input branch, a second input branch, a feature fusion layer, and a forming force output layer. The first input branch is used to process the historical feed displacement sequence, preferably employing a gated recurrent unit network to capture the influence of accumulated deformation history on the current forming force during the forming process. The gated recurrent unit network can be represented as: (5) in, It is the first Input of time steps, and These are the hidden states of the current and previous time steps, respectively. and These are the update door and the reset door. It is the sigmoid activation function, i.e. This branch encodes the historical feed displacement sequence into a compact time representation.

[0034] The second input branch processes the current feed rate, preferably using a multilayer perceptron network to extract the impact of the feed rate on the instantaneous load level. This design avoids unnecessary timing modeling and stably represents instantaneous process effects. The multilayer perceptron can be represented as: (6) in, These are input features. and These are trainable parameters. It is a non-linear activation function.

[0035] The two feature streams are concatenated and fused before being input into a fully connected regression layer, ultimately outputting the predicted forming force at the current or next time step. The model's prediction relationship can be represented as: (7) in, To predict forming force for the model, This represents the neural network model to be trained. Indicates model parameters, This represents a historical feed displacement sequence of length L. This indicates the current feed rate.

[0036] To improve the physical plausibility of the model's predictions, this invention introduces a deformation energy consistency constraint during model training. This constraint originates from the external work performed during the effective feed phase. Generally, the cumulative external work applied to the deformable system can be expressed as: (8) in, and These represent the contact force and the contact torque, respectively. and Let represent the translational velocity vector and the rotational velocity vector, respectively. Under the current process settings, the rotational motion is preset and remains fixed under given operating conditions, while the main contribution to the change related to the evolving deformation state is the work done in the feed direction. Therefore, the cumulative work related to deformation can be approximated as: (9) From these cumulative quantities, the incremental energy term can be obtained as follows: (10) To make physical constraints more informative than single-point energy penalties, cumulative consistency and incremental consistency are introduced. A normalized physical guidance loss term is also included. This can be expressed as: (11) in, It is a tiny positive constant used to avoid numerical singularity, and This is used to balance the consistency between accumulated energy and incremental energy.

[0037] Data fitting term Represented as: (12) Therefore, the final training objective function is: (13) in, The contribution of physics-guided regularization is controlled. In this formula, the first term forces the predictor to match the measured or simulated force values, while the second term constrains the predicted force sequence to be consistent with the energy evolution implied by the forming process. Through this training method, the model not only learns the statistical mapping relationships in the data but is also constrained by the physical laws of the forming process, thereby improving the model's generalization ability under small sample sizes and across operating conditions.

[0038] S5. Design of transfer learning method from simulation domain to experimental domain: The forming force prediction model is pre-trained using large-scale simulation domain forming data, and then the model is fine-tuned using limited experimental domain forming data to adapt the model to the actual robot multi-degree-of-freedom forming process.

[0039] Finite element simulation data is relatively inexpensive to acquire and can cover a wide range of feed rate conditions. However, it differs from real experimental processes in terms of material models, friction conditions, boundary constraints, and on-site disturbances. Experimental data, on the other hand, better reflects the actual forming process, but it is costly to acquire and has a limited sample size. Transfer learning has gradually become an effective mechanism to bridge this gap, as it can apply knowledge embedded in low-cost simulation data to resource-scarce experimental domains. Therefore, this invention employs a combination of simulation domain pre-training and experimental domain transfer fine-tuning to improve the applicability of the forming force prediction model in actual forming processes.

[0040] like Figure 7 As shown, the transfer learning process consists of two stages. The first stage is the simulation domain pre-training stage, where a physical-guided dual-stream neural network is trained using large-scale simulation domain forming data. This allows the model to learn the forming force variation under different feed rates and feed displacements, and to learn the energy consistency characteristics during the forming process through physical constraint loss. The second stage is the experimental domain transfer fine-tuning stage, where the model parameters obtained from the simulation domain pre-training are used as initial parameters, and the model is fine-tuned using a small amount of experimental domain forming data. During fine-tuning, some low-level feature extraction parameters can be kept unchanged, with a focus on updating network layers related to experimental domain feature adaptation; alternatively, full parameter fine-tuning or partial parameter fine-tuning can be selected based on the scale of the experimental data. For situations where complete energy information is difficult to obtain directly during the experiment, physical constraint terms can be frozen or weakened, allowing the model to retain the physical consistency knowledge learned in the simulation stage while adapting to the data distribution in the real forming process.

[0041] Through the above transfer learning method, the model can learn general forming rules using forming data from the simulation domain, and then use forming data from the limited experimental domain to correct the deviation between simulation and experiment, thereby obtaining high forming force prediction accuracy when there are few experimental samples.

[0042] To facilitate subsequent evaluation of model performance, this invention employs three common metrics: (1) Fitting coefficient R²: (14) (2) Mean Absolute Error (MAE): (15) (3) Root Mean Square Error (RMSE): (16) in, It is the actual value. It is a predicted value. It is the length of the dataset.

[0043] S6. Design of online control method based on prediction model: The transferred forming force prediction model is embedded into the online control process. Candidate feed speeds are generated according to the real-time forming state, and the optimal feed speed is obtained by searching the objective function to realize online control of forming force.

[0044] In the multi-degree-of-freedom forming process of robots, the feed rate is a crucial controllable parameter affecting the magnitude and trend of the forming force. This invention uses a forming force prediction model derived from transfer learning as the prediction core of the online controller, optimizing the feed rate for the next control cycle based on the real-time collected forming status.

[0045] like Figure 8 As shown, the online control process includes real-time data acquisition, status updates, candidate feed rate generation, forming force prediction, objective function evaluation, and control command issuance. First, the industrial computer reads the current feed displacement, current feed rate, and current forming force in real time. Then, based on the actuator's allowed speed range and the maximum speed change between adjacent control cycles, a set of candidate feed rates is generated. (17) in, and These are the minimum and maximum allowable feed rates, respectively. The current feed rate, This represents the maximum allowable speed change between adjacent control cycles.

[0046] For each candidate feed rate in the candidate set, first predict the feed displacement at the next moment based on the sampling period: (18) Then, the updated historical feed displacement sequence and candidate feed rate are input into the forming force prediction model to obtain the corresponding predicted forming force for the next moment: (19) in, Indicates the candidate number Each feed rate.

[0047] Furthermore, an objective function is constructed to evaluate the merits of candidate feed rates: (20) in, For the desired forming force, To ensure the upper limit of the forming force for safety, As the weighting factor for forming force tracking error, As a weight for feed rate smoothness, The overload penalty weight is used. The first term of the objective function is used to reduce the deviation between the predicted forming force and the desired forming force, the second term is used to avoid drastic fluctuations in the feed rate, and the third term is used to prevent the forming force from exceeding the upper limit of the equipment's safe load.

[0048] The controller uses a grid search method to select the feed rate that minimizes the objective function from the set of candidate feed rates as the control command for the next control cycle. (twenty one) Finally, the industrial computer will optimize the feed rate. The data is sent to the control card, which then drives the servo motor and hydraulic actuator via fieldbus to adjust the feed speed online during the robot's multi-degree-of-freedom forming process. Simultaneously, sensors continue to collect forming force and displacement data for the next moment and feed it back to the industrial computer, forming a closed-loop control process of "perception-prediction-optimization-execution-feedback".

[0049] To avoid frequent adjustments to the feed rate during the low-load initial stage of forming, this invention also incorporates a threshold triggering strategy. When the real-time forming force is less than or equal to the desired forming force threshold, the robot executes according to a preset reference feed rate; when the real-time forming force exceeds the desired forming force threshold, feed rate optimization control based on a predictive model is initiated. This strategy reduces unnecessary control intervention and improves the stability and engineering feasibility of online control.

[0050] The present invention also provides specific examples as follows: (1) Data acquisition and analysis like Figure 9As shown, in the data acquisition stage, the finite element simulation model of the robot's multi-degree-of-freedom forming process is first simulated. In the simulation model, the billet material is set to 15Cr14Co12Mo5Ni2WA, and the die material is set to H13; the initial temperature of the billet is 1100℃, and the initial temperature of the die is 300℃; the friction factor is set to 0.3; the upper die tilt angle is set to 1.5°; the angular velocity of the upper die around the machine tool axis is set to 6.28 rad / s, and the angular velocity around its own axis is set to -6.28 rad / s. Using this finite element model, the forming process under different feed rates is simulated, and forming force data in the simulation domain is obtained.

[0051] In the simulation domain forming data acquisition, the feed rate was set from 1.5 mm / s to 6.5 mm / s, with a step size of 0.1 mm / s, resulting in 51 sets of simulation trajectory data. Each set of data recorded the changes in feed displacement, feed rate, and forming force during the corresponding feeding process, which were used for pre-training of the subsequent forming force prediction model. Figure 10 As shown in (a), the simulation domain forming data covers a wide range of feed rates and can provide richer samples of forming force evolution.

[0052] In acquiring forming data in the experimental domain, a distributed sensing approach was used for data collection. Three representative feed rates of 2 mm / s, 4 mm / s, and 6 mm / s were selected for the experimental domain forming data, used for model transfer fine-tuning and verification of the actual forming process. Figure 10 As shown in (b), the number of experimental domain forming data samples is significantly less than that of simulation domain forming data, reflecting the actual scarcity of heavy-load forming experimental data.

[0053] To analyze the differences between finite element simulation data and experimental data, this embodiment extracts features from the preprocessed forming force sequences of the simulation and experimental domains, and uses feature dimensionality reduction and distribution distance analysis methods to compare the two types of data. Figure 11 As shown in (a), the simulation domain and experimental domain samples form relatively independent distribution regions in the feature space, indicating a significant domain difference between them. Figure 11 As shown in (b), the Jensen-Shannon divergence was further used to quantitatively analyze the forming data of the simulation domain and the experimental domain under the same feed rate conditions. The divergences between the simulation domain and the experimental domain were 0.334, 0.350, and 0.349 for the three working conditions of 2 mm / s, 4 mm / s, and 6 mm / s, respectively. This result indicates that directly using the model trained in the simulation domain for the actual experimental process will produce a large prediction bias. Therefore, transfer learning methods are needed to adapt the model to the experimental domain.

[0054] (2) Model training and validation In this invention, the model hyperparameters are obtained through Bayesian optimization. The final network and training parameters are as follows: GRU input dimension is 1, hidden layer dimension is 64, and the number of GRU layers is 2; the MLP branch includes two fully connected layers with dimensions of 1 to 64 and 64 to 64 respectively, and the activation function is ReLU; the dimensions of the fused fully connected layers are 64 to 32, and the output layer dimensions are 32 to 1; the batch size is set to 32, the window length is set to 5, the number of training epochs is 100, the optimizer is Adam, and the learning rate is 6.6 × 10⁻⁶. -4 The physical constraint weights were set to 0.4. The simulation domain forming data were divided into training, validation, and test sets according to the operating conditions, with 43 sets used for training, 5 sets for validation, and 3 sets for testing, in order to avoid evaluation bias caused by data leakage under the same operating condition.

[0055] like Figure 12 As shown, during model training, both training loss and validation loss decrease rapidly and gradually converge, with a small difference between them, indicating that the model has good training stability and generalization ability. Loss decomposition results show that both data fitting loss and physical constraint loss gradually decrease during training, demonstrating that the described physical-guided dual-stream neural network can simultaneously balance the accuracy of forming force prediction and the consistency of energy evolution.

[0056] like Figure 13 As shown, the model of this invention is compared with support vector machines, multilayer perceptrons, and gated recurrent unit networks. The results show that the model of this invention performs better in terms of prediction accuracy and stability. On the simulation domain test set, the coefficient of determination R of the model of this invention is [value missing]. 2 The result shows a forming force prediction capability of 0.993, a root mean square error (RMSE) of 0.117MN, and a mean absolute error (MAE) of 0.059MN. In contrast, the support vector machine model exhibits lower overall prediction performance, while the multilayer perceptron and gated recurrent unit network models show insufficient generalization under certain conditions. These results demonstrate that simultaneously incorporating historical feed displacement, current feed rate, and deformation energy physical constraints can effectively improve the forming force prediction capability.

[0057] To verify the model's generalization performance under unseen operating conditions, this embodiment further selected three feed rate conditions of 2.2 mm / s, 3.0 mm / s, and 5.5 mm / s—which were not involved in the training—for testing. Figure 14 As shown, the predicted forming force curve of the proposed model maintains good consistency with the actual forming force curve, with peak absolute errors below 1.4MN, 0.8MN, and 0.75MN under the three test conditions, respectively. This result demonstrates that the physically guided dual-flow network constructed in this invention can effectively describe the nonlinear relationship between feed motion and forming force, and possesses strong cross-condition generalization ability.

[0058] like Figure 15As shown, if the pre-trained model from the simulation domain is directly deployed to the experimental domain, its forming force prediction MAE is 1.4172MN, indicating that the domain difference between the simulation domain and the experimental domain significantly reduces the model's prediction accuracy. After using transfer tuning, the model's prediction error is significantly reduced. Table 1 shows the performance of the transfer-tuned model under different experimental data ratios.

[0059] Table 1 Performance of the transfer fine-tuning model under different experimental data proportions

[0060] The above results demonstrate that the proposed transfer learning method can effectively utilize simulation domain knowledge and a small amount of experimental domain data, significantly reducing the prediction bias from simulation to experiment.

[0061] (3) Forming control and precision improvement In the online forming force control implementation phase, the migrated forming force prediction model is embedded into the robot's multi-degree-of-freedom forming control system.

[0062] like Figure 16 As shown, this embodiment uses an aerospace spiral bevel gear and its corresponding mold for forming control experiments. After forming, the geometric accuracy of the formed part was evaluated using a Zeiss coordinate measuring machine. In the control experiment, the upper mold tilt angle was 1.5°, the angular velocity of the upper mold around the machine tool axis was 6.28 rad / s, and the angular velocity around its own axis was -6.28 rad / s; the initial feed rate was 6.5 mm / s, and the feed displacement was 10.75 mm; the initial temperatures of the billet and the mold were 1100℃ and 300℃, respectively; the maximum load capacity of the equipment was 8MN, and the desired forming force was set to 5MN.

[0063] like Figure 17 As shown in (a), in the traditional offline control method, the feed rate is executed according to a pre-planned fixed trajectory and cannot be adjusted according to the actual changes in forming force. Therefore, significant overshoot and fluctuation of forming force occur during the forming process, with the average absolute error of forming force reaching 0.727MN.

[0064] like Figure 17 As shown in (b), the feed rate can be adjusted online according to the real-time forming state after adopting the method of the present invention. In the experiment, the optimized feed rate was gradually adjusted from the initial 6.5 mm / s to gradually stabilize the forming force near the target load. Finally, the average absolute error of the forming force under the method of the present invention was reduced to 0.126 MN, which is about 82.6% lower than that of the traditional offline control method. This result shows that the method of the present invention can effectively suppress the fluctuation of forming force and improve the online control accuracy of the heavy-duty forming process.

[0065] To further evaluate the impact of the method of this invention on the forming quality, the surface error of the formed spiral bevel gear is detected. For example... Figure 18 As shown, the maximum surface error of the gear formed using the traditional offline control method is 440 μm; after using the method of the present invention, the maximum surface error of the gear is reduced to 263 μm, a reduction of approximately 40.2%. This result demonstrates that the method of the present invention can not only improve the forming force control accuracy, but also improve the material flow state by stabilizing the load and optimizing the feed rate, thereby improving the forming accuracy of the spiral bevel gear.

[0066] In summary, this embodiment verifies the effectiveness of the method of the present invention through finite element simulation data acquisition, distributed measurement in the experimental domain, domain difference analysis, physical-guided dual-stream network training, simulation-to-experiment transfer fine-tuning, and online predictive control experiments. The implementation results show that the present invention can significantly improve the accuracy of forming force prediction under limited experimental data conditions, and effectively reduce forming force control errors and gear surface errors in actual robot multi-degree-of-freedom forming processes, demonstrating good engineering application value.

[0067] This invention combines a physics-guided transfer learning forming force prediction model with online feed rate optimization control, ultimately reducing the mean absolute error of forming force in the multi-degree-of-freedom forming process of a robot from 0.727MN to 0.126MN, a reduction of approximately 82.6%; and reducing the maximum surface error of machining spiral bevel gears from 440μm to 263μm, a reduction of approximately 40.2%. Simultaneously, the transfer learning strategy reduces the mean absolute error of forming force prediction from 1.4172MN under direct deployment to 0.1271MN, a reduction of approximately 91.0%. These results demonstrate the efficiency and feasibility of this invention's method in multi-degree-of-freedom forming force control and precision forming for heavy-duty robots.

[0068] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A data-driven method for predicting and controlling multi-degree-of-freedom forming forces in robots, characterized in that, Includes the following steps: S1. Determine the motion form, tool trajectory and key process parameters of the robot's multi-degree-of-freedom forming process, and establish the kinematic relationship between the composite rotational motion of the upper mold and the vertical feed motion. S2. Establish a finite element model of the robot's multi-degree-of-freedom forming process and obtain forming data in a large-scale simulation domain; at the same time, based on the structural characteristics of the heavy-duty forming robot, adopt a distributed force / displacement measurement method to obtain forming data in the experimental domain. S3. Clean, extract, and normalize the simulation domain data and experimental domain data, and analyze the distribution differences between the simulation domain and the experimental domain to provide a data foundation for subsequent transfer learning. S4. Construct a two-stream neural network consisting of historical feed displacement sequence branches and instantaneous feed velocity branches, and introduce the consistency of deformation energy during the forming process as a physical constraint into the model training process; S5. The forming force prediction model is pre-trained using large-scale simulation domain forming data, and then the model is fine-tuned by transfer using experimental forming domain data. S6. Embed the migrated forming force prediction model into the online control process, generate candidate feed speeds based on the real-time forming state, and obtain the optimal feed speed through objective function search to achieve online control of forming force.

2. The data-driven method for predicting and controlling multi-degree-of-freedom forming forces in robots according to claim 1, characterized in that, The motion form of the multi-degree-of-freedom forming process in step S1 is as follows: The multi-degree-of-freedom forming process of a robot is a local continuous plastic forming process. The blank is placed between an upper mold and a lower mold. The lower mold is fixedly mounted on the machine tool bed, and the upper mold is mounted on the motion platform of a heavy-duty forming robot. During the forming process, the upper mold rotates around the machine tool axis and rotates in the opposite direction around its own axis. At the same time, it is gradually fed in the vertical direction, so that the upper mold and the blank are in continuous local contact, and the blank is driven to undergo plastic flow. The motion of the upper mold includes two rotational degrees of freedom and one vertical feed degree of freedom. The two rotational motions are the revolution around the vertical axis in the machine tool coordinate system and the rotation around the tool's own axis, respectively.

3. The data-driven method for predicting and controlling multi-degree-of-freedom forming forces in robots according to claim 2, characterized in that, The revolution around the vertical axis of the machine tool coordinate system and the rotation around the tool's own axis satisfy the constraint that their angular velocities are equal in magnitude and opposite in direction, that is: （1） in, The angular velocity of the upper mold around the machine tool axis. The angular velocity of the upper mold around its own axis; The vertical feed motion of the upper die is used to apply the forming load, and its feed displacement is expressed as: （2） in, For feed displacement, For feed rate, This refers to the forming time.

4. The data-driven method for predicting and controlling multi-degree-of-freedom forming forces in robots according to claim 3, characterized in that, In step S1, a coupled analysis is performed on the aforementioned composite rotary motion and vertical feed motion, and a point on the upper mold axis is selected. As the research object, based on the principle of kinematic composition, the spatial trajectory equation of this feature point is derived, and the specific expression is as follows: （3） in, It is a point on the upper mold axis. To the cone point The distance; It is a point In coordinate system The initial phase angle is used to determine the initial forming time. The spatial position ensures precise matching between the movement of the upper mold and the positioning of the blank; It is the angle between the two axes of rotation, i.e., the tilt angle.

5. The data-driven method for predicting and controlling multi-degree-of-freedom forming forces in robots according to claim 2, characterized in that, A heavy-duty forming robot is used to complete the degree-of-freedom forming process. The heavy-duty forming robot adopts a 6-PSS parallel mechanism configuration. The heavy-duty forming robot includes a fixed platform, a motion platform, and six identical motion chains. Each chain includes one prismatic joint and two ball joints. The six drive sliders are arranged circumferentially along the fixed platform and are driven by servo motors and lead screw transmission mechanisms. Through the coordinated movement of the six drive sliders, the motion platform realizes three-dimensional translation and three-dimensional rotation.

6. The data-driven method for predicting and controlling multi-degree-of-freedom forming forces in robots according to claim 1, characterized in that, In step S2, a finite element model of the robot's multi-degree-of-freedom forming process is established based on the above kinematic analysis. A three-dimensional model is established, and by changing the key process parameter of feed speed, simulated forming force data under different working conditions are obtained. The simulation data is used to describe the basic mapping relationship between feed displacement, feed speed and forming force during the forming process.

7. The data-driven method for predicting and controlling multi-degree-of-freedom forming forces in robots according to claim 5, characterized in that, In step S2, a distributed force measurement method is used to obtain the experimental forming force during the acquisition of experimental forming data; single-axis force sensors are respectively arranged on multiple drive sliders of the heavy-duty forming robot.

8. The data-driven method for predicting and controlling multi-degree-of-freedom forming forces in robots according to claim 5, characterized in that, In step S3, a min-max normalization method is used to map all features to the interval [0,1]. The normalization method is expressed as: （4） in, and These represent the minimum and maximum values ​​for each feature dimension, respectively. The forming force sequence can be divided into multiple local segments, and statistical features such as mean, variance, peak value, and slope can be extracted. Dimensionality reduction methods can be used to analyze the distribution of the simulation domain and experimental domain in the feature space.

9. The data-driven method for predicting and controlling multi-degree-of-freedom forming forces in robots according to claim 5, characterized in that, In step S4, a physically guided dual-flow neural network is constructed to simultaneously extract historical location information and instantaneous process parameter information; The physically guided dual-stream neural network includes a first input branch, a second input branch, a feature fusion layer, and a forming force output layer. The first input branch is used to process historical feed displacement sequences, preferably employing a gated recurrent unit network to capture the influence of accumulated deformation history on the current forming force during the forming process. The gated recurrent unit network is represented as follows: （5） in, It is the first Input of time steps, and These are the hidden states of the current and previous time steps, respectively. and These are the update door and the reset door; It is the sigmoid activation function, i.e. This branch encodes the historical feed displacement sequence into a compact time representation. The second input branch processes the current feed rate and uses a multilayer perceptron network, which is represented as follows: （6） in, These are input features. and These are trainable parameters. It is a non-linear activation function; The two feature streams are concatenated and fused before being input into a fully connected regression layer, ultimately outputting the predicted forming force at the current or next time step; the model prediction relationship is expressed as: （7） in, To predict forming force for the model, This represents the neural network model to be trained. Indicates model parameters, This represents a historical feed displacement sequence of length L. Indicates the current feed rate; A deformation energy consistency constraint is introduced during model training; this constraint originates from the external work performed during the effective feed phase; generally, the cumulative external work applied to the deformable system is expressed as: （8） in, and These represent the contact force and contact torque, respectively. and Let these represent the translational velocity vector and the rotational velocity vector, respectively; the cumulative work related to deformation is approximately expressed as: （9） From these cumulative quantities, the incremental energy term can be obtained as follows: （10） To make physical constraints more informative than single-point energy penalties, cumulative consistency and incremental consistency are introduced; a normalized physical guidance loss term is also included. The expression is as follows: （11） in, It is a tiny positive constant used to avoid numerical singularity, and This is used to balance the consistency between accumulated energy and incremental energy; Data fitting term Represented as: （12） Therefore, the final training objective function is: （13） in, The contribution of physical guidance regularization is controlled; in this formula, the first term forces the predictor to match the measured or simulated force value, while the second term constrains the predicted force sequence to be consistent with the energy evolution implied by the forming process.

10. The data-driven method for predicting and controlling multi-degree-of-freedom forming forces in robots according to claim 1, characterized in that, In step S5, the transfer learning process includes a simulation domain pre-training stage and an experimental domain transfer fine-tuning stage. In the simulation domain pre-training stage, physical-guided dual-flow neural networks are trained using large-scale simulation domain forming data, enabling the model to learn the forming force variation law under different feed speeds and feed displacements, and to learn the energy consistency characteristics in the forming process through physical constraint loss. In the experimental domain transfer fine-tuning stage, the model parameters obtained from the simulation domain pre-training are used as initial parameters, and the model is fine-tuned using the experimental domain formed data. During the fine-tuning process, some low-level feature extraction parameters are kept unchanged, and the network layers related to the adaptation of experimental domain features are updated. Alternatively, full parameter fine-tuning or partial parameter fine-tuning can be selected according to the experimental data scale. For situations where it is difficult to obtain complete energy information directly during the experiment, the physical constraints are frozen or weakened so that the model retains the physical consistency knowledge learned in the simulation stage, while adapting to the data distribution in the actual forming process.

Images