A segmented modeling and physical parameter identification method for asymmetric hysteresis characteristics of a robot joint

Abstract

The application discloses a kind of segmented modeling and physical parameter identification method of robot joint asymmetric hysteresis characteristics, belong to robot transmission system modeling and parameter identification technical field.Step 1: determine dynamic direction identification and initial value;Step 2: based on the initial value determined in step 1, construct enhanced feature space;Step 3: build global neural network;Step 4: the global neural network of step 3 is segmented and segmented data are trained two sub-networks;Step 5: based on angle interval design partition corrector carries out statistical correction;Step 6: to the data after correction of step 5, prevent crossing physical model parameter identification, realize the segmented modeling and physical parameter identification of robot joint asymmetric hysteresis characteristics.The application is to solve the problem of symmetry assumption limit, the problem of weak generalization of single model, the problem of physical inconsistency and the problem of unable to extract physical parameters.

Description

Technical Field

[0001] This invention belongs to the field of robot transmission system modeling and parameter identification technology, specifically involving a segmented modeling and physical parameter identification method for the asymmetric hysteresis characteristics of robot joints. Background Technology

[0002] Cycloidal pinwheel reducers are widely used in industrial robots, collaborative robots, and precision rotary table joints due to their high transmission ratio, high torque density, and compact structure. However, due to the contact elasticity of the cycloidal wheel and pin teeth meshing, bearing clearance, lubricating oil film nonlinearity, and manufacturing and assembly errors, the joint exhibits significant asymmetric hysteresis nonlinearity under forward and reverse loading: output torque It depends not only on the current joint angle Also related to the direction of angular velocity This is related to historical paths. More importantly, the asymmetry of the cycloidal pinwheel drive structure (the number of pin tooth contact pairs on both sides of the eccentric shaft is different) causes the hysteresis loop to exhibit asymmetry - the torsional stiffness and hysteresis width are different under forward loading (extension) and reverse loading (buckling).

[0003] Classical models like the Bouc-Wen and Prandtl-Ishlinskii, which assume symmetric hysteresis loops, fail to characterize asymmetric stiffness and width. They are also prone to overfitting to single neural networks and lack precision in characterizing local features such as commutation dead zones and saturation regions. Purely data-driven models may predict reverse torques higher than forward torques (hysteresis loop crossover), contradicting actual physics. Furthermore, they struggle to output interpretable parameters such as forward and reverse stiffness, hysteresis width distribution, and energy consumption, hindering joint health monitoring. Summary of the Invention

[0004] This invention provides a segmented modeling and physical parameter identification method for the asymmetric hysteresis characteristics of robot joints, which solves the problems of symmetry assumption limitations, weak generalization of single models, physical inconsistencies, and inability to extract physical parameters.

[0005] This invention is achieved through the following technical solution: A segmented modeling and physical parameter identification method for the asymmetric hysteresis characteristics of robot joints, the identification method comprising the following steps: Step 1: Determine the direction of movement and initial values; Step 2: Construct an enhanced feature space based on the initial values ​​determined in Step 1; Step 3: Construct a global neural network; Step 4: Segment the global neural network from Step 3 into data segments and train two sub-networks separately; Step 5: Design a partitioned corrector based on the angle interval for statistical correction; Step 6: Identify the anti-crossing physical model parameters of the data corrected in Step 5 to realize the segmented modeling and physical parameter identification of the asymmetric hysteresis characteristics of the robot joints.

[0006] Furthermore, step 1 specifically involves: Joint angle (rad) Joint torque (Nm); Data preprocessing: High-frequency noise is eliminated using moving average filtering. (1) in These are empirical values, adjusted based on the sampling rate. Angular velocity calculation uses central difference: (2) Direction detector: Define direction labels : (3) in The velocity threshold (rad / s) It is a dimensionless hyperparameter, and its physical meaning is the ratio of the threshold to the standard deviation of the velocity. Minimum segment length filtering: Let the length of consecutive segments in the same direction be... ;like Then all points in this segment Forced correction to the dominant direction of the neighborhood; parameters The minimum segment length (dimensionless integer) is used to determine the minimum number of inertia-maintaining points in the direction of joint movement, and is used to eliminate isolated jumps caused by noise. Finally, the parameters output in step 1 are: , and .

[0007] Furthermore, step 2 specifically involves constructing a feature vector. Divided into eight groups; Basic variables: (4) Higher-order polynomials, i.e., those that capture stiffness nonlinearity: (5) Periodicity and saturation characteristics, i.e., adaptive joint limitation: normalized angle ,but (6) Describe possible periodic energy distributions; Simulates saturation gradient; Describes a sharp change near the endpoint; Directional coupling characteristics, which directly characterize asymmetry: (7) The characteristics of lag memory, that is, the history that reflects changes in direction: (8) in For indicator functions, , ; Cumulative angular travel, i.e., path-dependent integral effect: (9) Instantaneous stiffness estimation, i.e., local prior: (10) Lag window characteristics, i.e., short-term memory: (11).

[0008] Furthermore, step 3 specifically involves establishing a feature... to torque The global nonlinear mapping is used as a baseline model; The network structure includes an input layer, seven fully connected hidden layers, an output layer, and an activation function. The input layer includes 23 corresponding nodes. The dimensions are as follows: the hidden layer consists of 7 fully connected layers with the number of neurons [60, 50, 40, 35, 30, 25, 20] respectively; the output layer consists of 1 node, namely the predicted moment; the activation function is a hyperbolic tangent applied to the hidden layer and a linear function applied to the output layer. The mathematical expression is: (12) in For all weights and biases to be trained; The loss function is the mean squared error: (13) The training uses the Levenberg-Marquardt algorithm, and finally, the global prediction is output. This model provides a global benchmark for subsequent segmented networks.

[0009] Furthermore, step 4 specifically involves, according to direction Split the data and train two sub-networks separately. Data partitioning specifically refers to forward sets. ,Include Sample; reverse set ,Include sample; The network structure includes an input layer, five fully connected hidden layers, an output layer, and an activation function. The input layer comprises 23 nodes; the hidden layer comprises 5 fully connected layers with a neuron count of [50, 40, 30, 25, 20]; the output layer comprises 1 node; and the activation function is... The output layer is linear; Feature enhancement, to strengthen asymmetric learning, involves reversing the sign of the input features to the inverse subnetwork: (14) That is, the forward subnetwork uses the original features. Reverse subnetwork uses This allows the network to more clearly identify different stiffness characteristics in both forward and reverse directions. Its mathematical expression is: (15) in The weights and biases of the forward subnetwork; The loss function is: (16) The training algorithm is the same as the global network (Levenberg-Marquardt), but each network is trained independently; Predicted fusion is: (17) The segmented network focuses on its own direction of motion, which significantly improves the accuracy of local fitting.

[0010] Furthermore, step 5 specifically involves calculating the correction factor as follows: [Calculate the angle range...] Divided into equal parts 1 small interval; for each interval: Positive: Calculate the median of the true torque and segmented model predicts median Correction factor ; In reverse: Similarly, we get Finally, Loess smoothing is used to obtain a continuous function. and ; The final prediction is: (18) This step will fit the coefficient of determination. Improved to 0.99, RMSE decreased to below 0.1 Nm; Furthermore, from Extracting the smooth point set: (19) These point sets serve as input for subsequent physical model parameter identification.

[0011] Furthermore, the polynomial model parameters in step 6 specifically refer to the forward and backward models: (20) and These are the predicted values ​​(Nm) of the forward and reverse loading torques, respectively. The parameters to be identified are and Similarly, the reverse model identifies parameters. and The meaning is the same as the forward direction, but it corresponds to the reverse path; The PCHIP spline model parameters are specifically: conformal piecewise cubic interpolation (PCHIP) in each subinterval. The above is a cubic polynomial: (twenty one) The parameters to be identified are The PCHIP conformal condition is automatically calculated, and the reverse model is obtained similarly. .

[0012] Furthermore, the anti-crossing consistency constraint specifically means that for all Must meet If the initial identification is violated, perform iterative correction: Calculate the average hysteresis width: (twenty two) Set the safety margin to ; For the set of reverse loading points ,like ,but ; The reverse model parameters are re-identified using the corrected point set, and this process is repeated until there are no intersections, ensuring that the identified parameters meet physical consistency.

[0013] A segmented modeling and physical parameter identification system for asymmetric hysteresis characteristics of robot joints, wherein the identification system uses the segmented modeling and physical parameter identification method for asymmetric hysteresis characteristics of robot joints as described above, and the identification system includes: Data acquisition and preprocessing module: realizes synchronous acquisition of angle and torque, smoothing filtering, and resampling; Motion direction recognition module: performs hysteresis threshold direction detection and minimum segment length filtering; Feature engineering module: Constructs 23-dimensional enhanced feature vectors; Global Neural Network Module: Constructs a 7-layer network, trains it, and makes predictions; Segmented neural network module: Constructs forward and reverse subnetworks, performs sign inversion enhancement, trains and merges them; Physical model parameter identification module: Select the model form, fit polynomial coefficients or spline coefficients, and apply anti-crossing constraints.

[0014] A segmented modeling and physical parameter identification method using the asymmetric hysteresis characteristics of robot joints as described above is applied to the cycloidal pinwheel reducer joint of a robot.

[0015] The beneficial effects of this invention are: This invention realizes a high-precision forward and reverse model with physical consistency, and outputs joint physical parameters with clear engineering significance.

[0016] This invention uses a global-segmented hybrid intelligent model combined with statistical correction, achieving an accuracy of 0.99, providing a high-fidelity foundation for parameter identification.

[0017] This invention automatically selects the optimal polynomial from the PCHIP. This selection mechanism improves adaptability to different joint data characteristics.

[0018] The hysteresis threshold, segment length filtering, and safety margin design in the direction recognition of this invention are insensitive to low-speed jitter and noise.

[0019] This invention provides a high-precision, physically consistent, and parameter-interpretable modeling and identification solution for asymmetric hysteresis systems such as cycloidal pinwheel joints, which has significant industrial practical value. Attached Figure Description

[0020] Figure 1 This is a simplified structural diagram of the present invention.

[0021] Figure 2 These are experimental data on the torsion angle and corresponding velocity collected by the cycloidal joint of the robot of the present invention, wherein (a) is a graph of torsion angle variation and (b) is a graph of corresponding velocity variation.

[0022] Figure 3 These are the results of fitting experimental data to the hysteresis model of the present invention, where (a) is the result of the full neural network characterizing the hysteresis loop, and (b) is the result of the piecewise hysteresis model characterizing the hysteresis loop.

[0023] Figure 4 The diagram shows the residuals of the hysteresis loop fitting position and the actual torque of the present invention. (a) is a residual variation diagram of the hysteresis torsion angle fitted by the neural network and the piecewise model, and (b) is a residual variation diagram of the actual hysteresis torque fitted by the neural network and the piecewise model. Detailed Implementation

[0024] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of this application with unnecessary detail.

[0025] It should be understood that, when used in this specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0026] It should also be understood that the terminology used in this application specification is for the purpose of describing particular embodiments only and is not intended to limit the application. As used in this application specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0027] The following is in conjunction with the appendix to this application specification. Figure 1-4 The technical solutions in the embodiments of this application are clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0028] Many specific details are set forth in the following description in order to provide a full understanding of this application. However, this application may also be implemented in other ways different from those described herein. Those skilled in the art can make similar extensions without departing from the spirit of this application. Therefore, this application is not limited to the specific embodiments disclosed below.

[0029] Implementation Method 1 This embodiment provides a segmented modeling and physical parameter identification method for the asymmetric hysteresis characteristics of robot joints. The identification method includes the following steps: Step 1: Determine the direction of movement and initial values; Step 2: Construct an enhanced feature space based on the initial values ​​determined in Step 1; Step 3: Construct a global neural network; Step 4: Segment the global neural network from Step 3 into data segments and train two sub-networks separately; Step 5: Design a partitioned corrector based on the angle interval for statistical correction; Step 6: Identify the anti-crossing physical model parameters of the data corrected in Step 5 to realize the segmented modeling and physical parameter identification of the asymmetric hysteresis characteristics of the robot joints.

[0030] Furthermore, step 1 specifically involves: Joint angle (rad) Joint torque (Nm).

[0031] Data preprocessing: High-frequency noise is eliminated using moving average filtering. (1) in These are empirical values, adjusted based on the sampling rate.

[0032] Angular velocity calculation uses central difference: (2) Direction detector: Define direction labels : (3) in The velocity threshold (rad / s) It is a dimensionless hyperparameter, and its physical meaning is the ratio of the threshold to the standard deviation of the velocity.

[0033] Minimum segment length filtering: Let the length of consecutive segments in the same direction be... .like Then all points in this segment Forced correction to the neighborhood-dominant direction. Parameters The minimum segment length (dimensionless integer) is used to determine the minimum number of inertia-maintaining points in the direction of joint movement, and is used to eliminate isolated jumps caused by noise.

[0034] Finally, the parameters output in step 1 are: , and .

[0035] Furthermore, step 2 specifically involves constructing feature vectors to achieve high-precision fitting. These features are divided into eight groups and serve as the input to the neural network. Basic variables: (4) Higher-order polynomials, i.e., those that capture stiffness nonlinearity: (5) Periodicity and saturation characteristics, i.e., adaptive joint limitation: normalized angle ,but (6) Describe possible periodic energy distributions; Simulates saturation gradient; Describes a sharp change near the endpoint.

[0036] Directional coupling characteristics, which directly characterize asymmetry: (7) The characteristics of lag memory, that is, the history that reflects changes in direction: (8) in For indicator functions, , .

[0037] Cumulative angular travel, i.e., path-dependent integral effect: (9) Instantaneous stiffness estimation, i.e., local prior: (10) Lag window characteristics, i.e., short-term memory: (11) Furthermore, step 3 specifically involves establishing a feature... to torque The global nonlinear mapping is used as a baseline model; The network structure includes an input layer, seven fully connected hidden layers, an output layer, and an activation function. The input layer includes 23 corresponding nodes. The dimensions are as follows: the hidden layer consists of 7 fully connected layers with the number of neurons [60, 50, 40, 35, 30, 25, 20] respectively; the output layer consists of 1 node, namely the predicted moment; the activation function is a hyperbolic tangent applied to the hidden layer and a linear function applied to the output layer. The mathematical expression is: (12) in For all weights and biases to be trained.

[0038] The loss function is the mean squared error: (13) The training uses the Levenberg-Marquardt algorithm, and finally, the global prediction is output. This model provides a global benchmark for subsequent segmented networks.

[0039] Furthermore, step 4 specifically involves addressing the difficulty of accurately capturing the local differences between forward and reverse paths using a global model. Therefore, according to direction... Split the data and train two sub-networks separately. Data partitioning specifically refers to forward sets. ,Include Sample; reverse set ,Include sample; The network structure (the forward and reverse subnetworks have the same structure but independent parameters) includes an input layer, five fully connected hidden layers, an output layer, and an activation function. The input layer comprises 23 nodes; the hidden layer comprises 5 fully connected layers with a neuron count of [50, 40, 30, 25, 20]; the output layer comprises 1 node; and the activation function is... The output layer is linear.

[0040] Feature enhancement, to strengthen asymmetric learning, involves reversing the sign of the input features to the inverse subnetwork: (14) That is, the forward subnetwork uses the original features. Reverse subnetwork uses This allows the network to more clearly identify the different stiffness characteristics in the forward and reverse directions.

[0041] Its mathematical expression is: (15) in These represent the weights and biases of the forward subnetwork.

[0042] The loss function is: (16) The training algorithm is the same as the global network (Levenberg-Marquardt), but each network is trained independently.

[0043] Predicted fusion is: (17) Each segmented network focuses on its own direction of motion, avoiding the averaging effect of the global model in the direction-changing region and significantly improving local fitting accuracy.

[0044] Furthermore, step 5 specifically involves designing a partition corrector to further eliminate residuals, even though the segmented network has improved accuracy.

[0045] The correction factor is calculated as follows: (The angular range is not specified in the original text.) Divided into equal parts There are several small intervals. For each interval: Positive: Calculate the median of the true torque and segmented model predicts median Correction factor ; In reverse: Similarly, we get Finally, Loess smoothing is used to obtain a continuous function. and .

[0046] The final prediction is: (18) This step will fit the coefficient of determination. The value was increased to 0.99, and the RMSE dropped to below 0.1 Nm.

[0047] Furthermore, from Extracting the smooth point set: (19) These point sets serve as input for subsequent physical model parameter identification.

[0048] Furthermore, the polynomial model parameters in step 6 specifically refer to the forward and backward models: (20) and These are the predicted values ​​(Nm) of the forward and reverse loading torques, respectively. The parameters to be identified are and Similarly, the reverse model identifies parameters. and The meaning is the same as the forward direction, but it corresponds to the reverse path.

[0049] The PCHIP spline model parameters are specifically: conformal piecewise cubic interpolation (PCHIP) in each subinterval. The above is a cubic polynomial: (twenty one) The parameters to be identified are The PCHIP conformal condition is automatically calculated, and the reverse model is obtained similarly. .

[0050] Model selection: Compare the root mean square error (RMSE) of cross-validation between the polynomial model and the PCHIP model, and select the one with the smaller error as the final model.

[0051] Furthermore, the anti-crossing consistency constraint specifically means that for all Must meet If the initial identification is violated, perform iterative correction: Calculate the average hysteresis width: (twenty two) Set the safety margin to ; For the set of reverse loading points ,like ,but ; The reverse model parameters are re-identified using the corrected point set, and this process is repeated until there are no intersections, ensuring that the identified parameters meet physical consistency.

[0052] 1. Experimental Data Acquisition and Preprocessing High-precision torque sensors and angle encoders are used to synchronously collect torque and rotation data of the robot's cycloidal joint (equipped with a load-bearing load) during quasi-static reciprocating motion (e.g., ...). Figure 2 (As shown). The acquisition frequency was set to 1 kHz to ensure that subtle changes in the hysteresis loop could be captured. To avoid the influence of sensor noise and quantization errors on subsequent modeling, the original torque and angle signals were smoothed and filtered separately. The torque signal was smoothed using a 5-point moving average, and the angle signal was smoothed using a 7-point moving average, in order to remove high-frequency noise while retaining the main characteristics of the hysteresis loop.

[0053] Furthermore, by analyzing the smoothed corner signal, the position range was found to be approximately -0.148 rad to 0.148 rad, and the torque range was approximately -1.25 Nm to 1.90 Nm. The data includes multiple reciprocating cycles, covering approximately 2730 data points each in the rising and falling segments, with a ratio close to 1:1, providing a sufficient data foundation for subsequent asymmetric modeling.

[0054] 2. Motion Direction Recognition and Feature Engineering The asymmetry of the hysteresis loop depends on the direction of motion, therefore it is essential to accurately distinguish between the rising and falling segments. This method employs a three-step direction identification strategy: The first step is to calculate an adaptive threshold based on the smoothed velocity signal. The velocity is obtained by performing gradient calculation on the turning angle and dividing by the sampling interval. Points with velocities greater than the positive threshold are marked as upward (+1), points with velocities less than the negative threshold are marked as downward (-1), and the remaining points are marked as uncertain (0).

[0055] The second step is to fill in the uncertain points. For each point marked as 0, check the directions of its preceding and following points and determine the direction based on the trend of position increases or decreases. Through two iterations, all points obtain a valid direction.

[0056] The third step is to remove isolated directional segments. Traverse the direction sequence and count the lengths of segments with consecutive identical directions. If a segment length is less than 5 points and the preceding and following directions of that segment are consistent, modify the segment to follow the preceding and following directions; otherwise, keep the original direction. Ultimately, ensure that the direction sequence is continuous and consistent with the physical motion.

[0057] Based on direction recognition, a 23-dimensional feature vector is constructed, including: position and its 2nd to 4th powers, velocity, acceleration, trigonometric functions (sine, cosine), hyperbolic tangent, and exponentially decaying function after position normalization; direction indication signal; hysteresis memory factor (increases when direction changes, otherwise decays exponentially); cumulative displacement effect; stiffness estimation and its separated rise / fall stiffness; asymmetric functions constructed based on position and direction; inflection point markers and strength; interaction terms between position and direction (product, square product, cube product); interaction terms between velocity and direction; and the mean position, mean velocity, position difference, torque, direction, and asymmetric factor of the previous 5 time steps. These features fully capture the nonlinearity, historical dependence, and direction dependence of asymmetric hysteresis.

[0058] 3. High-precision neural network fitting A cascaded neural network structure was used for initial fitting. The network had seven hidden layers with centered feature inputs, containing 60, 50, 40, 35, 30, 25, and 20 neurons respectively, using hyperbolic tangent activation functions, and a linear output layer. The Levenberg-Marquardt algorithm was used for training, with a training objective of a mean squared error less than 10⁻⁴ and a maximum of 10 iterations to avoid overfitting. After training, predictions were made on the entire dataset to obtain the initial fitted torque.

[0059] To further improve accuracy, separate neural networks were trained for the ascending and descending segments. The feature matrices of the ascending and descending segments were inverted and then fused to enhance sensitivity to directional differences. Both sub-networks had 5 hidden layers (50, 40, 30, 25, 20), and the training parameters were the same as the global network. The segmented prediction results were combined with the global prediction results to obtain the segmented model prediction values. Experiments show that the R² of the segmented model is improved to 0.99, achieving high-precision fitting results. Figure 3 and Figure 4 As shown.

[0060] 4. Intelligent correction of hysteresis loop Since piecewise neural networks may still exhibit local biases, a proportional correction method based on binning statistics was designed. First, the entire position range was divided into 25 equal intervals. Within each interval, the median of the experimental torque and the actual torque in the ascending and descending segments were statistically analyzed. A correction factor was calculated and smoothed using LOESS. Then, the correction factor at each point was obtained through linear interpolation, and the predicted torque was multiplied to obtain a further refined fitted value.

[0061] 5. Enhanced physical constraints To ensure the physical validity of the hysteresis loop (the torque in the rising segment is always greater than that in the falling segment), a slight adjustment is applied using the binning median comparison method. This constraint not only eliminates the crossover phenomenon but also maintains the smoothness of the predicted curve without significantly reducing the fitting accuracy.

[0062] 6. Parameter identification of physical models based on best fit The final fitting results described above are used as ideal experimental data to identify physical models that are easy to apply in engineering. This invention constructs both anti-crossing spline models and bipolynomial models, and selects the optimal one.

[0063] 6.1 Anti-Crossing Spline Model (PCHIP) The position-torque pairs for the ascending and descending segments are extracted from the fitted data, sorted by position, and duplicate points are removed. The system checks for intersections (descending segment torque greater than ascending segment torque) within a common position range. If an intersection exists, the average hysteresis loop width is calculated, and a safety margin of 1% of the average width is set. Each descending segment data point is checked; if the descending segment torque at a point is greater than the corresponding ascending segment linear interpolation minus the safety margin, the torque at that point is adjusted down to the ascending segment value minus the safety margin. Then, PCHIP is used to construct ascending and descending segment splines respectively. Anti-crossing measures ensure that the spline model satisfies the condition that the ascending segment torque is higher than the descending segment torque. Therefore, as a numerical model, PCHIP can be directly used for torque prediction.

[0064] 6.2 Bipolynomial Model Polynomial fitting was performed on the position-torque data for both the ascending and descending segments, with the order automatically selected and an upper limit of 6. In the experiment, both the ascending and descending segments were fitted with 6th-order polynomials. Polynomial models have fewer parameters, making them easier to express analytically, but their fitting accuracy is much lower than that of spline models (R²=0.85, RMSE=0.196). This is because global polynomials cannot accurately describe subtle local nonlinear characteristics.

[0065] 6.3 Model Selection Comparing the R² values ​​of the spline model and the polynomial model, the model with the higher R² is selected as the optimal physical model. In this embodiment, the spline model (R²=0.99, RMSE=0.011) is significantly better than the polynomial model; therefore, the anti-crossing spline model is selected as the final physical model.

[0066] 6.4 Results of Physical Parameter Identification In this example, the spline model was selected as the final model through optimal selection, and the identification results are shown in Table 1: Table 1 Spline model identification results

[0067] Implementation Method 2 This embodiment provides a segmented modeling and physical parameter identification system for the asymmetric hysteresis characteristics of robot joints. The identification system uses the segmented modeling and physical parameter identification method for the asymmetric hysteresis characteristics of robot joints as described in Embodiment 1. The identification system includes: Data acquisition and preprocessing module: realizes synchronous acquisition of angle and torque, smoothing filtering, and resampling; Motion direction recognition module: performs hysteresis threshold direction detection and minimum segment length filtering; Feature engineering module: Constructs 23-dimensional enhanced feature vectors; Global Neural Network Module: Constructs a 7-layer network, trains it, and makes predictions; Segmented neural network module: Construct forward and reverse subnetworks (5 layers), perform sign inversion enhancement, train and fuse them; Physical model parameter identification module: Select the model form, fit polynomial coefficients or spline coefficients, and apply anti-crossing constraints.

[0068] Implementation Method 3 This embodiment provides a segmented modeling and physical parameter identification method for robot joints using the asymmetric hysteresis characteristics of robot joints as described in Embodiment 1, which is applied to the cycloidal pinwheel reducer joint of a robot.

Claims

1. A method for segmented modeling and physical parameter identification of asymmetric hysteresis characteristics of robot joints, characterized in that, The identification method includes the following steps: Step 1: Determine the direction of movement and initial values; Step 2: Construct an enhanced feature space based on the initial values ​​determined in Step 1; Step 3: Construct a global neural network; Step 4: Segment the global neural network from Step 3 into data segments and train two sub-networks separately; Step 5: Design a partitioned corrector based on the angle interval for statistical correction; Step 6: Identify the anti-crossing physical model parameters of the data corrected in Step 5 to realize the segmented modeling and physical parameter identification of the asymmetric hysteresis characteristics of the robot joints.

2. The identification method according to claim 1, characterized in that, Specifically, step 1 is as follows: Joint angle (rad), Joint torque (Nm); Data preprocessing: High-frequency noise is eliminated using moving average filtering. (1) in These are empirical values, adjusted based on the sampling rate. Angular velocity calculation uses central difference: (2) Direction detector: Define direction labels : (3) in The velocity threshold (rad / s) It is a dimensionless hyperparameter, and its physical meaning is the ratio of the threshold to the standard deviation of the velocity. Minimum segment length filtering: Let the length of consecutive segments in the same direction be... ;like Then all points in this segment Forced correction to the dominant direction of the neighborhood; parameters The minimum segment length (dimensionless integer) is used to determine the minimum number of inertia-maintaining points in the direction of joint movement, and is used to eliminate isolated jumps caused by noise. Finally, the parameters output in step 1 are: , and .

3. The identification method according to claim 1, characterized in that, Step 2 specifically involves constructing a feature vector. Divided into eight groups; Basic variables: (4) Higher-order polynomials, i.e., those that capture stiffness nonlinearity: (5) Periodicity and saturation characteristics, i.e., adaptive joint limitation: normalized angle ,but (6) Describe possible periodic energy distributions; Simulates saturation gradient; Describes a sharp change near the endpoint; Directional coupling characteristics, which directly characterize asymmetry: (7) The characteristics of lag memory, that is, the history that reflects changes in direction: (8) in For indicator functions, , ; Cumulative angular travel, i.e., path-dependent integral effect: (9) Instantaneous stiffness estimation, i.e., local prior: (10) Lag window characteristics, i.e., short-term memory: (11)。 4. The identification method according to claim 1, characterized in that, Step 3 specifically involves establishing features... to torque The global nonlinear mapping is used as a baseline model; The network structure includes an input layer, seven fully connected hidden layers, an output layer, and an activation function. The input layer includes 23 corresponding nodes. The dimensions are as follows: the hidden layer consists of 7 fully connected layers with the number of neurons [60, 50, 40, 35, 30, 25, 20] respectively; the output layer consists of 1 node, namely the predicted moment; the activation function is a hyperbolic tangent applied to the hidden layer and a linear function applied to the output layer. The mathematical expression is: (12) in For all weights and biases to be trained; The loss function is the mean squared error: (13) The training uses the Levenberg-Marquardt algorithm, and finally, the global prediction is output. This model provides a global benchmark for subsequent segmented networks.

5. The identification method according to claim 1, characterized in that, Step 4 specifically involves, according to direction Split the data and train two sub-networks separately. Data partitioning specifically refers to forward sets. ,Include Sample; reverse set ,Include sample; The network structure includes an input layer, five fully connected hidden layers, an output layer, and an activation function. The input layer comprises 23 nodes; the hidden layer comprises 5 fully connected layers with a neuron count of [50, 40, 30, 25, 20]; the output layer comprises 1 node; and the activation function is... The output layer is linear; Feature enhancement, to strengthen asymmetric learning, involves reversing the sign of the input features to the inverse subnetwork: (14) That is, the forward subnetwork uses the original features. Reverse subnetwork uses This allows the network to more clearly identify different stiffness characteristics in both forward and reverse directions. Its mathematical expression is: (15) in The weights and biases of the forward subnetwork; The loss function is: (16) The training algorithm is the same as the global network (Levenberg-Marquardt), but each network is trained independently; Predicted fusion is: (17) The segmented network focuses on its own direction of motion, which significantly improves the accuracy of local fitting.

6. The identification method according to claim 1, characterized in that, Step 5 specifically involves calculating the correction factor as follows: [The angle range is then considered.] Divided into equal parts 1 small interval; for each interval: Positive: Calculate the median of the true torque and segmented model predicts median Correction factor ; In reverse: Similarly, we get Finally, Loess smoothing is used to obtain a continuous function. and ; The final prediction is: (18) This step will fit the coefficient of determination. Improved to 0.99, RMSE decreased to below 0.1 Nm; Furthermore, from Extracting the smooth point set: (19) These point sets serve as input for subsequent physical model parameter identification.

7. The identification method according to claim 1, characterized in that, The polynomial model parameters in step 6 specifically refer to the forward and backward models: (20) and These are the predicted values ​​(Nm) of the forward and reverse loading torques, respectively. The parameters to be identified are and Similarly, the reverse model identifies parameters. and The meaning is the same as the forward direction, but it corresponds to the reverse path; The PCHIP spline model parameters are specifically: conformal piecewise cubic interpolation (PCHIP) in each subinterval. The above is a cubic polynomial: (21) The parameters to be identified are The results are automatically calculated using the PCHIP conformal condition, and the reverse model is similarly obtained. .

8. The identification method according to claim 7, characterized in that, The anti-cross consistency constraint specifically means that for all Must meet ; If the initial identification is violated, perform iterative correction: Calculate the average hysteresis width: (22) Set the safety margin to ; For the set of reverse loading points ,like ,but ; The reverse model parameters are re-identified using the corrected point set, and this process is repeated until there are no intersections, ensuring that the identified parameters meet physical consistency.

9. A segmented modeling and physical parameter identification system for the asymmetric hysteresis characteristics of robot joints, characterized in that, The identification system uses a segmented modeling and physical parameter identification method for asymmetric hysteresis characteristics of robot joints as described in any one of claims 1-8. The identification system includes: Data acquisition and preprocessing module: realizes synchronous acquisition of angle and torque, smoothing filtering, and resampling; Motion direction recognition module: performs hysteresis threshold direction detection and minimum segment length filtering; Feature engineering module: Constructs 23-dimensional enhanced feature vectors; Global Neural Network Module: Constructs a 7-layer network, trains it, and makes predictions; Segmented neural network module: Constructs forward and reverse subnetworks, performs sign inversion enhancement, trains and merges them; Physical model parameter identification module: Select the model form, fit polynomial coefficients or spline coefficients, and apply anti-crossing constraints.

10. A segmented modeling and physical parameter identification method using the asymmetric hysteresis characteristics of robot joints as described in any one of claims 1-8, applied to the cycloidal pinwheel reducer joint of a robot.

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