A robot pose-related multi-modal parameter prediction method fusing physical information

Abstract

A method for predicting robot pose-related multimodal parameters by fusing physical information is presented. This method obtains frequency response function data under different poses based on experimental modal analysis. It employs a two-stage identification strategy combining rational fractional polynomial initial value estimation and variable projection weighted nonlinear least squares frequency domain fitting to extract multimodal parameters and construct a training dataset. Then, a deep neural network prediction model fusing physical information is established, including a parameter regression network and a physical reconstruction unit. The frequency response is reconstructed using the multimodal parameters output by the parameter regression network, and the error between the reconstructed response and the measured frequency response is used as a physical constraint in the response domain, which is fused with the parameter domain label error to form a composite loss function. Finally, the Newton-Raphson optimization algorithm is used to complete the hyperparameter optimization training of the model, achieving rapid prediction of multimodal parameters under the target pose. This invention improves the prediction accuracy, physical consistency, and generalization ability of multimodal parameters under different robot poses.

Description

Technical Field

[0001] This invention belongs to the field of robot processing and intelligent manufacturing technology, specifically relating to a method for predicting robot pose-related multimodal parameters by integrating physical information. Background Technology

[0002] Industrial robots have been widely used in various processing and manufacturing scenarios such as milling, grinding and polishing, welding, and spraying in recent years due to their advantages such as large workspace, high flexibility, relatively low deployment cost, and suitability for handling complex curved surfaces and large components. However, compared with traditional CNC equipment, industrial robots typically adopt an open-chain serial structure, resulting in relatively low overall stiffness. Furthermore, their end effector dynamic characteristics change significantly with joint configuration and working posture, exhibiting a clear posture dependence. As the robot's posture changes, its natural frequency, damping, modal stiffness, and vibration response characteristics may all change significantly, thus affecting contact stability, surface quality, and work efficiency. Therefore, accurately acquiring and characterizing the modal parameters of the robot under different postures is of great significance for dynamic analysis, stability assessment, and parameter prediction during robot operation.

[0003] In existing technologies, to obtain the dynamic characteristics of industrial robots under different poses, experimental modal analysis or modal impact tests are typically used to obtain the frequency response function, followed by modal parameter identification. Regarding the prediction of pose-related dynamic characteristics, relevant patents include CN120562173A, which discloses a method for predicting pose-related tool tip dynamics through full admittance matrix measurement, eigenvalue orthogonal decomposition, and multi-output Gaussian process regression; and CN116090171A, which discloses a tool tip dynamic analysis method based on experimental frequency response function, least squares weighted superposition, and modal parameter superposition. Existing methods are mainly divided into analytical modeling methods based on multibody dynamics, finite element analysis, or rigid-flexible coupling, and prediction methods based on regression learning. While existing technologies can reflect the impact of pose changes on system dynamics to some extent, they primarily focus on analytical modeling, admittance matrix processing, frequency response function superposition analysis, or parameter prediction based on sample mapping. Their approach remains largely model approximation or data fitting, failing to effectively integrate the pose-related modal parameter prediction process with the frequency response formation mechanism. This results in a lack of sufficient physical constraints on the prediction results, making it difficult to simultaneously achieve modal parameter identification accuracy, prediction accuracy, and physical consistency. Purely data-driven methods, in particular, rely heavily on the mapping relationship between pose variables and dynamic characteristics, failing to fully utilize the inherent physical connection between modal parameters and frequency response. Furthermore, traditional frequency domain identification methods are sensitive to initial values, easily leading to decreased identification accuracy when modal density, noise interference, or significant residual effects are present. Therefore, it is still necessary to propose a method for predicting robot pose-related multimodal parameters that integrates physical information. This method combines the parameter prediction process with the frequency response physical reconstruction process. By introducing physical constraints in the response domain in addition to the parameter domain constraints, the accuracy, stability, and physical consistency of pose-related modal parameter identification and prediction results can be improved. This is of great significance for realizing high-precision dynamic modeling and performance optimization in robot operation. Summary of the Invention

[0004] To address the problems of low efficiency in acquiring robot pose-related multimodal parameters, insufficient physical constraints in the prediction process, and difficulty in unifying identification and prediction in existing technologies, this invention provides a method for predicting robot pose-related multimodal parameters by fusing physical information. This method acquires sample data through experimental frequency response functions, constructs training labels using two-stage modal parameter identification, and utilizes a deep neural network prediction model that fuses physical information with the Newton-Raphson optimization algorithm to predict multimodal parameters under the target pose.

[0005] A method for predicting robot pose-related multimodal parameters by fusing physical information, comprising the following steps: Step S1: Construct a set of sampled poses in the robot's workspace, obtain the pose description vector corresponding to each sampled pose, perform experimental modal analysis on the robot system under multiple sampled poses, and obtain the frequency response function data under the corresponding poses; Step S2: Based on rational fractional polynomial initial value estimation and variable projection weighted nonlinear least squares frequency domain fitting, perform two-stage modal parameter identification on the frequency response function data to obtain the multimodal parameter labels corresponding to each sampling pose; construct a pose-multimodal parameter training dataset based on the pose description vector of each sampling pose and the multimodal parameter labels. Step S3: Establish a deep neural network prediction model that integrates physical information, including a parametric regression network and a physical reconstruction unit; Step S4: Construct a composite loss function consisting of a parameter domain error term and a response domain physical error term; Step S5: Use the pose-multimodal parameter training dataset and the Newton-Raphson optimization algorithm to optimize the hyperparameters of the deep neural network prediction model and complete the training of the deep neural network prediction model. Step S6: Input any target pose into the trained deep neural network prediction model and output the multimodal parameters under the target pose.

[0006] Further, the steps are as follows: The pose description vector in step S1 includes at least one of the following: joint angle vectors of each joint of the robot; position parameters of the tool center point in the base coordinate system and tool axis attitude parameters; redundant angle parameters characterizing different joint configurations of the same tool position; the sampled pose set is constructed according to the spatial distribution and attitude change range of the area to be processed, using one or more of the following methods: spatial grid layout, trajectory key point selection, or typical workstation selection. The experimental modal analysis includes: arranging acceleration sensors along the orthogonal X, Y, and Z directions at the robot spindle base or flange position, obtaining frequency response functions in one or more measurement directions through modal impact excitation, and averaging the time-domain signals obtained from repeated measurements to obtain the frequency response function matrix corresponding to the robot's low-frequency structural modes; the frequency response function matrix includes a direct frequency response term on the main diagonal, and may further include cross-frequency response terms between different measurement directions.

[0007] Further, step S2 includes: establishing an analytical model of the frequency response function containing modal terms, conjugate modal terms, low-frequency residual terms, and high-frequency residual terms; using rational fractional polynomials to perform initial value estimation on the frequency response function data to obtain initial parameters for complex poles, natural frequencies, and damping ratios; then using variable projection weighted nonlinear least squares frequency domain fitting to separate and solve the nonlinear parameters related to poles and the linear parameters related to residuals, and obtaining the multimodal parameters of each sampling pose through iterative updates, wherein the multimodal parameters include at least one or more of natural frequencies, modal stiffness, and modal damping. Further, the deep neural network prediction model that integrates physical information in step S3 includes a parameter regression network and a frequency response function physical reconstruction unit. The parameter regression network includes an input layer, at least one trainable hidden layer, and an output layer. The input layer is used to receive the normalized pose description vector. The at least one trainable hidden layer is used to extract the nonlinear mapping features between the pose description vector and the multimodal parameters. The output layer is used to output the predicted values ​​of the multimodal parameters under the corresponding pose. The frequency response function physical reconstruction unit is connected to the output end of the parameter regression network and does not contain trainable parameters. It is used to substitute the predicted values ​​of the multimodal parameters into a preset frequency response function analytical model to calculate the reconstructed frequency response function under the corresponding pose, so as to introduce the frequency response function formation mechanism into the deep neural network prediction model.

[0008] Further, the composite loss function in step S4 includes a parameter domain data error term and a response domain physical error term; wherein, the parameter domain data error term is used to measure the difference between the multimodal parameter prediction values ​​output by the parametric regression network and the multimodal parameter labels, and the response domain physical error term is used to measure the difference between the reconstructed frequency response function calculated by the frequency response function physical reconstruction unit and the experimental frequency response function; during training, the weight parameters of the parametric regression network are updated according to the composite loss function through backpropagation, so that the multimodal parameter prediction process is simultaneously constrained by the parameter labels and the physical laws of the frequency response function.

[0009] Furthermore, the Newton-Raphson optimization algorithm used in step S5 includes: defining a hyperparameter vector to be optimized, wherein the hyperparameter vector includes at least one of the following: number of network layers, number of hidden layer nodes, learning rate, random deactivation coefficient, and physical constraint weight coefficient; taking the minimum value of the composite loss function on the validation set as the optimization objective; initializing a candidate hyperparameter set; calculating the fitness corresponding to each candidate hyperparameter; iteratively updating the positions of the candidate hyperparameters according to the Newton-Raphson search rule, and combining boundary checks and trap avoidance operators to suppress local optima; and outputting the optimal hyperparameter combination after reaching the preset termination condition to complete the final training of the deep neural network prediction model that integrates physical information.

[0010] Compared with existing technologies, this invention has at least the following beneficial effects: First, by combining rational fractional polynomial initial value estimation with variable projection weighted nonlinear least squares frequency domain fitting, the sensitivity of traditional nonlinear frequency domain fitting to initial values ​​can be reduced, the parameter identification stability under multimodal dense regions and noise conditions can be improved, and the training reliability of subsequent prediction models can be enhanced. Second, by embedding physical reconstruction units after the parameter regression network and constructing a composite objective function with joint constraints of the parameter domain and response domain, the fitting quality of formants, anti-resonance regions, and cross-coupling terms can be strengthened simultaneously, thereby avoiding the problem of "small parameter error but significant frequency response peak deviation" that may occur when only optimizing the mean square error of parameters, and improving the physical consistency of pose-related multimodal parameter prediction results. Third, by introducing the Newton-Raphson optimization algorithm to jointly optimize the model hyperparameters, the computational burden caused by manual trial and error and grid search can be reduced, and the generalization ability of the model in high-dimensional coupled parameter prediction scenarios can be improved. Fourth, this invention can realize the rapid prediction of multimodal parameters under arbitrary target poses during robot operation. Attached Figure Description

[0011] Figure 1 This is a schematic diagram of the overall process of the robot pose-related multimodal parameter prediction method based on Newton-Raphson optimization according to the present invention.

[0012] Figure 2 This is a schematic diagram of the two-stage modal parameter identification process in this invention.

[0013] Figure 3 This is a schematic diagram illustrating the construction of the deep neural network prediction model that integrates physical information and the composite loss function in this invention.

[0014] Figure 4 This is a schematic diagram of the hyperparameter optimization process of the Newton-Raphson optimization algorithm in this invention.

[0015] Figure 5 This is a comparison diagram of the experimental frequency response function under the target pose and the frequency response function obtained by reconstructing from the predicted multimodal parameters in this invention. Detailed Implementation

[0016] The present invention will be further described below with reference to the accompanying drawings and embodiments. It should be understood that the following embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit the scope of protection of the present invention. Equivalent substitutions or modifications made by those skilled in the art to the implementation steps, parameter forms, network structure forms, and optimization processes without departing from the spirit and substance of the present invention should all fall within the scope of protection of the present invention.

[0017] like Figure 1 As shown, the present invention provides a method for predicting robot pose-related multimodal parameters by fusing physical information, comprising the following steps: Step S1: Construct a set of sampled poses in the robot's workspace, obtain the pose description vector corresponding to each sampled pose, perform experimental modal analysis on the robot system under multiple sampled poses, and obtain the frequency response function data under the corresponding poses; Step S2: Based on rational fractional polynomial initial value estimation and variable projection weighted nonlinear least squares frequency domain fitting, perform two-stage modal parameter identification on the frequency response function data to obtain the multimodal parameter labels corresponding to each sampling pose; construct a pose-multimodal parameter training dataset based on the pose description vector of each sampling pose and the multimodal parameter labels. Step S3: Establish a deep neural network prediction model that integrates physical information, including a parametric regression network and a physical reconstruction unit; Step S4: Construct a composite loss function consisting of a parameter domain error term and a response domain physical error term; Step S5: Use the pose-multimodal parameter training dataset and the Newton-Raphson optimization algorithm to optimize the hyperparameters of the deep neural network prediction model and complete the training of the deep neural network prediction model. Step S6: Input any target pose into the trained deep neural network prediction model and output the multimodal parameters under the target pose.

[0018] In step S1: To characterize the pose-related dynamic characteristics of the robot system, its dynamic equations are first established in the Cartesian coordinate system. Let the equivalent mass matrix, equivalent damping matrix, and equivalent stiffness matrix of the robot system in the current pose be respectively... , and The displacement response vector of the robot system is The external excitation force vector is Then the dynamic equations of the robot system can be expressed as: in, , and Let J represent the equivalent mass matrix, equivalent damping matrix, and equivalent stiffness matrix of the robot system in the current pose. Since the robot is a multi-joint connected structure, there is a pose-dependent mapping relationship between its Cartesian space dynamic parameters and its joint space dynamic parameters. Let J be the Jacobian matrix in the current pose, and let J be the inertia matrix, damping matrix, and stiffness matrix in joint space. , and Then we have: As can be seen from the above equation, since the Jacobian matrix J changes with the pose, the dynamic parameters of the robot system also change with the pose. Taking a Laplace transform of equation (1) yields the frequency response function matrix in the current pose. : For a three-dimensional vibration description, the frequency response function matrix is ​​preferably written as a full-frequency response matrix including direct frequency response terms and cross-frequency response terms, i.e. , , as well as , , By simultaneously considering direct and cross terms, the coupling effects of the robot structure in different directions can be more completely characterized, thus providing a foundation for subsequent multimodal parameter identification and prediction.

[0019] In a preferred embodiment, the experimental modal analysis employs an industrial robot platform, an electric spindle, a cutting tool, an impact hammer, and a multi-channel vibration acquisition system to form an experimental modal analysis platform. For each sampling pose, accelerometers are arranged along the orthogonal X, Y, and Z directions at the spindle base or flange position to acquire low-frequency structural modes; if necessary, a triaxial accelerometer can be arranged at the cutting tool tip to assist in acquiring high-frequency modes. To reduce the influence of random errors and environmental noise, multiple impact tests are repeated at each sampling pose, and the sampled signals are averaged to obtain a stable frequency response function.

[0020] In constructing the sampled pose set, it is preferable to select the tool center point as the main input variable of the task space in the robot base coordinate system, and combine it with redundant angle parameters to describe different joint configurations under the same tool position. The pose description vector of a sampled pose can be represented as: in, and These represent the position coordinates of the tool center point in the plane of the base coordinate system. This represents the redundant angle parameters corresponding to the tool position. In actual implementation, based on the spatial distribution and attitude variation range of the area to be processed, a set of sampled poses can be constructed using one or more methods, such as gridded point layout, selection of trajectory key points, or selection of typical workstations. Multiple redundant angles can be set at each tool position to obtain a set of sampled poses covering different stiffness configurations.

[0021] In step S2: as follows Figure 2As shown, for each sampling pose, the corresponding multi-directional frequency response function is acquired, and a two-stage modal parameter identification strategy is used to extract multi-mode parameters. The first stage uses a rational fractional polynomial initial value estimation method to quickly obtain the initial values ​​of complex poles, natural frequencies, and damping ratios for each mode within the analysis frequency band. The second stage uses a variable projection weighted least squares frequency domain fitting method. During the second stage frequency domain refinement, a Levenberg-Marquardt nonlinear iterative framework is used for solution. In each iteration, nonlinear parameters are first separated from linear parameters based on the variable projection idea; then, given the nonlinear parameters, the corresponding optimal linear parameters are obtained through inner-layer linear least squares solution; and finally, the nonlinear parameters related to the poles are updated by outer-layer nonlinear iteration. When the change in the objective function between two adjacent iterations is less than a preset threshold, or the number of iterations reaches a preset upper limit, the iteration is considered converged, and a high-precision multimodal parameter set is output. The complex poles of the r-th mode can be expressed as: in, Let be the natural frequency of the r-th mode. To correspond to the damping ratio, and to characterize the modal features within the finite analysis frequency band and the truncation effect of modes outside the analysis band, a partially fractional expansion model with upper and lower residual terms is preferred to represent the frequency response function: in, Indicates in Apply incentives in the direction, The frequency response function obtained from the direction acquisition response; and These represent the response direction and the excitation direction, respectively. ; Indicates angular frequency; The imaginary unit; This indicates the order of the modes involved in the fitting within the analysis frequency band; Indicates the modal order number; Indicates the direction of measurement , The corresponding number Modal complex residues; express The complex conjugate; Indicates the direction of measurement , The corresponding number First-order mode complex poles; express The complex conjugate; For measuring direction , Corresponding to the low-frequency residual term, For measuring direction , Corresponding to high-frequency residual terms; superscript This represents the complex conjugate operation. By introducing the above residual term, the fitting accuracy under finite bandwidth conditions can be improved, and the physical interpretability of the identified multimodal parameters can be enhanced. To further improve the fitting robustness in the resonance and anti-resonance regions, a weighted error objective function can be constructed: in, Indication and measurement direction , The corresponding set of nonlinear parameters preferably includes modal complex poles, or natural frequencies and damping ratios equivalently represented by modal complex poles; Indication and measurement direction , The corresponding set of linear parameters preferably includes modal complex residues, low-frequency residuals, and high-frequency residuals; This indicates the number of frequency points within the analyzed frequency band; Indicates the frequency point number; Indicates the first The angular frequency corresponding to each frequency point; Indicates the first Frequency domain weighting coefficients for each frequency point; Indicates the direction of measurement , The corresponding number Measured frequency response function at each frequency point; To represent the first frequency response function calculated by the analytical model Fitting the frequency response function at each frequency point. Preferably, higher weights are assigned to the resonance region, and the weights are appropriately reduced in the noise-dominated anti-resonance region to enhance the algorithm's sensitivity to high signal-to-noise ratio modal regions. For the joint solution of linear and nonlinear parameters, a variable projection strategy is preferred to transform the original high-dimensional fitting problem into a dimensionality reduction optimization problem only concerning the nonlinear parameters. Let the matrix form of the theoretical frequency response function be written as: in, Represents a set of nonlinear parameters Constructed basis function matrix.

[0022] The optimal linear parameter can then be expressed as: in, For Moore-Penrose generalized inverse; This is a diagonal weighted matrix composed of the weighting coefficients for each frequency point; Indicates the direction of measurement , The corresponding measured frequency response function vector; After substituting the optimal linear parameter expression back into the weighted objective function, the optimized pole parameters and residue parameters can be solved using Levenberg-Marquardt nonlinear iteration, and further, the set of multi-mode parameters for each sampling pose can be obtained. For the ... For each sampled pose, its multimodal parameter labels can be denoted as: in, It includes at least one or more of the natural frequencies, modal stiffness, and modal damping of the r-th order mode. Based on the pose description vectors of multiple sampled poses and their corresponding multimodal parameter labels, a pose-multimodal parameter training dataset can be constructed. in, For the first A pose description vector for each sampled pose. This represents the number of sampled poses used to construct the training dataset; The pose-multimodal parameter training dataset takes the robot pose description vector as input and the identified multimodal parameter set as output. The pose description vector can be composed of the position parameters and redundant angle parameters of the tool center point in the base coordinate system, or it can be composed of joint angle parameters. The multimodal parameter set includes at least one or more of natural frequencies, modal stiffness, and modal damping. By selecting representative sample poses within the workspace, a training sample set covering both high-stiffness and low-stiffness configurations can be constructed.

[0023] In step S3: after completing the construction of the training dataset, a deep neural network prediction model incorporating physical information is established. For example... Figure 3 As shown, the deep neural network prediction model that integrates physical information consists of a parameter regression network and a physical reconstruction unit. The parameter regression network establishes a nonlinear mapping between the pose description vector and multimodal parameters; its input is the normalized pose description vector, and its output is the multimodal parameters under the target pose. The physical reconstruction unit does not contain trainable parameters; instead, it substitutes the predicted multimodal parameters into the aforementioned analytical frequency response model to reconstruct the theoretical frequency response function under the target pose, thus embedding the dynamic physical laws into the prediction process.

[0024] in, For the first The output feature vector of the hidden layer For the first Layer network weight matrix, For bias vectors, is the activation function. Preferably, the prediction model employs a multi-layer feedforward neural network structure, combined with a random deactivation mechanism to suppress overfitting.

[0025] In step S4: To simultaneously ensure the accuracy of multimodal parameter prediction and the consistency of frequency response, this invention constructs a composite loss function with joint constraints in the parameter domain and response domain: in, This is the parameter domain data error term, used to characterize the difference between the predicted multimodal parameters and the identified labels; The physical reconstruction error term in the response domain is used to characterize the difference between the frequency response function reconstructed from the predicted multimodal parameters and the measured frequency response function. These are the weight coefficients for physical constraints. During training, both the parameter domain data error term and the response domain physical reconstruction error term are calculated simultaneously, and the trainable parameters in the parameter regression network are updated synchronously through backpropagation to ensure that the output matches the training labels and satisfies the dynamic constraints. Preferably, the parameter domain error term adopts the mean squared error form: in, Indicates the first Each sample is a multimodal parameter prediction vector output by a parametric regression network. Indicates the first The multimodal parameter labels corresponding to each sample; Indicates the number of samples in the training batch; The physical error term in the response domain preferably adopts a logarithmic magnitude range error form to balance the influence of the resonant and anti-resonant regions on the training process, thereby improving the fitting ability to the overall shape of the frequency response function. in, To indicate the first Each sample in the measurement direction , The following is the first result obtained from the reconstruction of predicted multimodal parameters. Frequency response function at each frequency point; Indicates the first Each sample in the measurement direction , The experimental measurement of the first Frequency response function at each frequency point; This is used to avoid small positive numbers with unstable values ​​in logarithmic operations; In step S5: as follows Figure 4As shown, the performance of the prediction model depends not only on the network weight parameters but also on hyperparameters such as the number of network layers, the number of hidden layer nodes, the learning rate, the random deactivation coefficient, and the physical constraint weight coefficients. Since this optimization problem typically exhibits non-convex, high-dimensional, and black-box characteristics, traditional manual trial-and-error or conventional search methods are insufficient to efficiently obtain a globally optimal solution. Therefore, this invention introduces the Newton-Raphson optimization algorithm to jointly optimize one or more sets of hyperparameters, including the number of network layers, the number of hidden layer nodes, the learning rate, the random deactivation coefficient, and the physical constraint weight coefficients. Let the set of hyperparameters to be optimized be: in, For network layers, This represents the number of hidden layer nodes. For learning rate, This is the random inactivation coefficient; The optimal hyperparameter solution problem, evaluated based on the composite objective function value on the validation set, can be written as: in, For the validation set, This represents the feasible region for hyperparameters. By introducing the Newton-Raphson search rule and trap avoidance mechanism, the search efficiency and global optimization capability in high-dimensional hyperparameter spaces can be improved.

[0026] The basic process of the Newton-Raphson optimization algorithm includes: initializing multiple candidate hyperparameter individuals within the feasible region of hyperparameters, and using each candidate hyperparameter individual as a set of network training configurations to be evaluated; for each candidate hyperparameter individual, constructing a corresponding deep neural network prediction model that integrates physical information, and training the deep neural network prediction model using the training set; calculating the composite objective function value on the validation set, and using the composite objective function value as the fitness evaluation result of the corresponding candidate hyperparameter individual; determining the current better individual based on the fitness evaluation results of each candidate hyperparameter individual, and then performing a search based on the Newton-Raphson search algorithm. The positions of candidate hyperparameter individuals are then updated. The Newton-Raphson search rule is used to estimate the update direction and step size based on the difference information of the objective function within the neighborhood of the candidate hyperparameter individuals. During the update process, boundary checks are performed on the updated candidate hyperparameter individuals to keep them within the feasible region of the hyperparameters. When a preset trigger condition is met, a trap avoidance operator is executed to perturb or reorganize some candidate hyperparameter individuals to reduce the probability of the search process getting trapped in local optima. When the maximum number of iterations is reached, the fitness change is less than a preset threshold, or other preset termination conditions are met, the globally optimal hyperparameter combination is output. Preferably, the individual position update rule can be expressed as: in, The objective function value, As a scaling factor, For finite difference perturbations, NRSR represents the Newton-Raphson search rule. Using this position update rule, position updates can be performed in the hyperparameter space by incorporating local curvature information, thereby improving search efficiency. To avoid premature convergence to local suboptimal solutions under a multimodal objective function, random perturbations or boundary bounce strategies can be applied to some candidate individuals.

[0027] In step S6: after obtaining the optimal hyperparameter combination, the deep neural network prediction model fusing physical information is reconstructed or updated based on the optimal hyperparameter combination, and the deep neural network prediction model fusing physical information is finally trained using all training samples. After training, for any target pose U By inputting this into the trained model, the corresponding multimodal parameter prediction result K can be output. Therefore, this invention enables the rapid acquisition of multimodal parameters under the target pose.

[0028] In one specific embodiment, the XY plane of the robot's base coordinate system is used as the sampling plane. Grid points covering the task area are selected at 200mm intervals, and three redundant angles of -10°, 50°, and 150° are set at each grid point to form 189 sampled poses. Three impact tests are performed on each sampled pose to obtain the frequency response functions in the X, Y, and Z directions, and these functions are averaged. Using rational fractional polynomial initial value estimation and variable projection weighted nonlinear least squares frequency domain fitting, the natural frequencies, modal stiffness, and modal damping of each sampled pose are identified, forming a pose-multimodal parameter training dataset. During training, the pose description vector is first normalized, and then the samples are divided into training and validation sets. The Newton-Raphson optimization algorithm is used to optimize the number of network layers, the number of hidden layer nodes, the learning rate, the random deactivation coefficient, and the physical constraint weight coefficients. For target poses that are not involved in training, their pose description vectors are input into the trained prediction model, which outputs the corresponding multimodal parameters. The frequency response function under the target pose is then reconstructed through a physical reconstruction unit. To verify the effectiveness of the method of this invention, multiple target poses that were not involved in training were selected as verification poses. The pose description vectors of each verification pose were input into the trained prediction model to obtain the corresponding multimodal parameter prediction values. The frequency response function under the verification pose was then reconstructed using a frequency response function physical reconstruction unit. The reconstructed frequency response function was compared with the measured frequency response function obtained from experimental modal analysis under the same verification pose. The results are as follows: Figure 5As shown. Within the frequency range including the robot's low-frequency structural modes, the reconstructed frequency response function and the measured frequency response function maintain consistency in terms of resonant frequency, resonant peak amplitude variation trend, and cross-coupling response characteristics. This indicates that the method of the present invention can effectively predict multimodal parameters in the target pose without training, and can improve the physical consistency of the prediction results through physical reconstruction constraints in the response domain. The above description is only a preferred embodiment of the present invention, used to illustrate the technical solution of the present invention, and not to limit the scope of protection of the present invention. The technical features described in different embodiments can be combined with each other without contradicting each other. Equivalent substitutions, modifications, or improvements made by those skilled in the art based on the technical ideas disclosed in the present invention should all fall within the scope of protection defined by the claims of the present invention.

Claims

1. A method for predicting robot pose-related multimodal parameters by fusing physical information, characterized in that, The steps are as follows: Step S1: Construct a set of sampled poses in the robot's workspace, obtain the pose description vector corresponding to each sampled pose, perform experimental modal analysis on the robot system under multiple sampled poses, and obtain the frequency response function data under the corresponding poses; Step S2: Based on rational fractional polynomial initial value estimation and variable projection weighted nonlinear least squares frequency domain fitting, perform two-stage modal parameter identification on the frequency response function data to obtain the multimodal parameter labels corresponding to each sampling pose; construct a pose-multimodal parameter training dataset based on the pose description vector of each sampling pose and the multimodal parameter labels. Step S3: Establish a deep neural network prediction model that integrates physical information, including a parametric regression network and a physical reconstruction unit; Step S4: Construct a composite loss function consisting of a parameter domain error term and a response domain physical error term; Step S5: Use the pose-multimodal parameter training dataset and the Newton-Raphson optimization algorithm to optimize the hyperparameters of the deep neural network prediction model and complete the training of the deep neural network prediction model. Step S6: Input any target pose into the trained deep neural network prediction model and output the multimodal parameters under the target pose.

2. The method for predicting robot pose-related multimodal parameters by fusing physical information according to claim 1, characterized in that, The steps are as follows: The pose description vector in step S1 includes at least one of the following: joint angle vectors of each joint of the robot; position parameters of the tool center point in the base coordinate system and tool axis posture parameters; redundant angle parameters characterizing different joint configurations of the same tool position; the sampled pose set is constructed according to the spatial distribution and posture change range of the area to be processed, using one or more of the following methods: spatial grid layout, trajectory key point selection, or typical station selection; the experimental modal analysis includes: arranging acceleration sensors along the orthogonal X, Y, Z directions at the robot spindle base or flange position, obtaining frequency response functions in one or more measurement directions through modal impact excitation, and averaging the time-domain signals obtained from repeated measurements to obtain the frequency response function matrix corresponding to the robot's low-frequency structural modes; the frequency response function matrix includes a direct frequency response term on the main diagonal, and may further include cross frequency response terms between different measurement directions.

3. The method for predicting robot pose-related multimodal parameters by fusing physical information according to claim 1, characterized in that, The steps are as follows: Step S2 includes: An analytical model of the frequency response function, including modal terms, conjugate modal terms, low-frequency residual terms, and high-frequency residual terms, is established. Rational fractional polynomials are used to perform initial value estimation on the frequency response function data to obtain the initial parameters of complex poles, natural frequency, and damping ratio. Then, variable projection weighted nonlinear least squares frequency domain fitting is used to separate and solve the nonlinear parameters related to the poles and the linear parameters related to the residuals. The multimodal parameters of each sampling pose are obtained through iterative updates. The multimodal parameters include at least one or more of natural frequency, modal stiffness and modal damping.

4. The method for predicting robot pose-related multimodal parameters by fusing physical information according to claim 1, characterized in that, The deep neural network prediction model that integrates physical information in step S3 includes a parameter regression network and a frequency response function physical reconstruction unit. The parameter regression network includes an input layer, at least one trainable hidden layer, and an output layer. The input layer is used to receive the normalized pose description vector. The at least one trainable hidden layer is used to extract the nonlinear mapping features between the pose description vector and the multimodal parameters. The output layer is used to output the predicted values ​​of the multimodal parameters under the corresponding pose. The frequency response function physical reconstruction unit is connected to the output end of the parameter regression network and does not contain trainable parameters. It is used to receive the predicted values ​​of the multimodal parameters and calculate the reconstructed frequency response function under the corresponding pose according to a preset frequency response function analytical model, so as to introduce the frequency response function formation mechanism into the deep neural network prediction model.

5. The method for predicting robot pose-related multimodal parameters by fusing physical information according to claim 1, characterized in that, The composite loss function in step S4 includes a parameter domain data error term and a response domain physical error term. The parameter domain data error term measures the difference between the predicted multimodal parameters output by the parametric regression network and the multimodal parameter labels. The response domain physical error term measures the difference between the reconstructed frequency response function calculated by the frequency response function physical reconstruction unit and the experimental frequency response function. During training, the weight parameters of the parametric regression network are updated according to the composite loss function through backpropagation, so that the multimodal parameter prediction process is simultaneously constrained by the parameter labels and the physical laws of the frequency response function.

6. The method for predicting robot pose-related multimodal parameters by fusing physical information according to claim 1, characterized in that, The Newton-Raphson optimization algorithm used in step S5 includes: defining a hyperparameter vector to be optimized, wherein the hyperparameter vector includes at least one of the following: number of network layers, number of hidden layer nodes, learning rate, random deactivation coefficient, and physical constraint weight coefficient; taking the minimum value of the composite loss function on the validation set as the optimization objective; initializing a candidate hyperparameter set; calculating the fitness of each candidate hyperparameter; iteratively updating the positions of the candidate hyperparameters according to the Newton-Raphson search rule, and combining boundary checks and trap avoidance operators to suppress local optima; and outputting the optimal hyperparameter combination after reaching the preset termination condition to complete the final training of the deep neural network prediction model that integrates physical information.

Images