An industrial robot joint digital twin modeling method considering nonlinear friction of harmonic transmission

Abstract

The application discloses a kind of industrial robot joint digital twin modeling methods considering harmonic transmission nonlinear friction, belong to industrial robot digital twin modeling technical field.The method collects industrial robot harmonic joint operation data and obtains joint friction torque data, establishes the joint multi-domain digital twin modeling framework including mechanical domain model, electrical domain model and control domain model;Velocity-dependent steady-state friction component model and position-dependent periodic pulsating friction component model are constructed, and a harmonic transmission two-component nonlinear friction model is obtained by superposition;A physical information neural network residual compensation model is constructed to compensate the prediction residual, and a compensated friction model is obtained;The compensated friction model is embedded in the mechanical domain model, and the mechanical domain model, the electrical domain model and the control domain model are coupled to generate an industrial robot joint digital twin model;The characterization accuracy of the actual joint dynamic response and nonlinear friction characteristics of the industrial robot harmonic joint digital twin model is improved.

Description

Technical Field

[0001] This invention belongs to the field of digital twin modeling technology for industrial robots, specifically relating to a digital twin modeling method for industrial robot joints that considers harmonic drive nonlinear friction. Background Technology

[0002] Industrial robots, with their high reliability and precision, have become a core element of intelligent manufacturing systems. As the requirements for precision, reliability, and safety in robot applications continue to increase, traditional geometric or kinematic models alone are insufficient to accurately describe the dynamic behavior of industrial robots during real-world operation. Digital twin technology, by constructing a high-fidelity mapping model of the physical object in virtual space, can provide a model foundation for state prediction, simulation analysis, motion control, fault diagnosis, and safety monitoring of industrial robots.

[0003] The joints of an industrial robot are the core actuators that determine the overall motion accuracy and dynamic characteristics of the robot. A typical industrial robot joint consists of a servo controller, inverter, permanent magnet synchronous motor, sensors, harmonic reducer, load, and related mechanical structures. Its operation involves coupling between multiple domains, including control, electrical, and mechanical domains. Existing robot digital twin modeling methods often focus on geometric mapping, kinematic simulation, or state visualization at the overall robot level, but they lack sufficient description of the coupling relationships between the control, electrical, and mechanical domains within the joint. This results in the digital twin model failing to accurately reproduce the joint's true dynamic response.

[0004] Furthermore, harmonic reducers are widely used in industrial robot joints due to their advantages such as large transmission ratio, compact structure, and high transmission accuracy. However, harmonic drives rely on the elastic deformation of flexures and gear meshing to transmit motion, which generates complex phenomena such as nonlinear friction, hysteresis, stiffness changes, and position-dependent periodic pulsations during actual operation. Among these, frictional torque not only changes nonlinearly with speed but also exhibits periodic pulsation characteristics with rotor position. Traditional friction models can usually describe speed-dependent steady-state friction changes, but they are difficult to accurately characterize the position-dependent periodic pulsations caused by the harmonic drive structure. Ignoring these periodic pulsations will result in a significant dynamic deviation between the digital twin model and the actual joint.

[0005] On the other hand, while purely data-driven models possess strong nonlinear fitting capabilities, they lack explicit physical information, are prone to overfitting to measurement noise, and may exhibit non-physical oscillations under unseen or extrapolated operating conditions, affecting the reliability and generalization ability of the digital twin model. Therefore, how to simultaneously describe the velocity-related steady-state characteristics, position-related periodic pulsation characteristics, and unmodeled residuals of harmonic drive friction within a multi-domain digital twin modeling framework is a key issue in improving the fidelity of digital twin models for industrial robot joints.

[0006] Therefore, it is necessary to propose a digital twin modeling method for industrial robot joints that considers harmonic drive nonlinear friction, so as to improve the ability of robot joint digital twin models to represent the dynamic behavior, friction characteristics and multi-domain coupling relationships of actual physical joints. Summary of the Invention

[0007] To overcome the shortcomings of existing technologies, this invention aims to provide a digital twin modeling method for industrial robot joints that considers harmonic drive nonlinear friction. This method addresses the difficulty of existing industrial robot joint digital twin models in accurately describing the multi-domain coupling relationships between the mechanical, electrical, and control domains, and in simultaneously characterizing the velocity-dependent steady-state characteristics and position-dependent periodic pulsation characteristics of harmonic drive friction. By constructing a velocity-dependent steady-state friction component model, a position-dependent periodic pulsation friction component model, and a physical information neural network residual compensation model, the accuracy of the industrial robot harmonic joint digital twin model in representing the actual joint dynamic response and nonlinear friction characteristics is improved.

[0008] The present invention adopts the following technical solution: A digital twin modeling method for industrial robot joints considering harmonic drive nonlinear friction includes the following steps: S1. Collect the harmonic joint operation data of the industrial robot. The operation data includes motor rotor position data, motor rotor speed data, joint position data, joint speed data and current feedback data, and obtain joint friction torque data based on the current feedback data. S2. Establish a multi-domain digital twin modeling framework for joints, the modeling framework including a control domain model, an electrical domain model and a mechanical domain model; S3. Construct a speed-related steady-state friction component model based on the aforementioned operating data and joint friction torque data; S4. Construct a position-related periodic pulsating friction component model based on the aforementioned operating data and joint friction torque data; S5. By superimposing the velocity-related steady-state friction component model and the position-related periodic pulsating friction component model, a harmonic drive dual-component nonlinear friction model is obtained. S6. Construct a physical information neural network residual compensation model and perform iterative training and updates; S7. The prediction residual of the harmonic drive dual-component nonlinear friction model is compensated using the updated physical information neural network residual compensation model to obtain the compensated friction model. S8. Embed the friction compensation model into the mechanical domain model, and couple the electrical domain model and the control domain model to generate a digital twin model of the industrial robot joint.

[0009] Furthermore, during the collection of industrial robot harmonic joint operation data, the robot harmonic joint is under constant speed, no-load, or near-no-load conditions; the electromagnetic torque on the motor side is calculated using motor current feedback data and motor torque constant, thereby obtaining joint friction torque data.

[0010] Furthermore, the control domain model in S2 includes a trajectory planning module, a coordinate transformation module, a speed closed-loop control module, and a current closed-loop control module, used to generate voltage commands, current commands, or pulse width modulation signals based on joint position commands or joint speed commands, and send them to the electrical domain model; the electrical domain model includes a drive modulation module, an inverter module, a permanent magnet synchronous motor electromagnetic model, and a sensor feedback module, used to receive the voltage commands, current commands, or pulse width modulation signals output by the control domain model, generate motor electromagnetic torque, and send it to the mechanical domain model; the mechanical domain model includes a transmission chain structure description module, an equivalent inertia module, a load torque module, and a friction torque module, used to model the joint transmission chain composed of the motor mechanical end, harmonic reducer, and load, and receive the motor electromagnetic torque output by the electrical domain model, calculate the dynamic response of the joint transmission chain based on the motor electromagnetic torque, equivalent moment of inertia, load torque, and friction torque, and generate the joint motion response.

[0011] Furthermore, the velocity-dependent steady-state friction component model is constructed using the Stribeck friction model to characterize the nonlinear steady-state characteristics of the harmonic joint friction torque of the industrial robot as a function of joint velocity; the Stribeck friction model is expressed as: in, This represents the velocity-dependent steady-state friction component. Indicates joint speed or motor rotor speed. Represents the velocity sign function, Represents the Coulomb friction parameter. Represents static friction parameters. This represents the Stribeck characteristic velocity parameters. This represents the empirical index parameter. This represents the viscous friction parameter.

[0012] Furthermore, the specific process of S4 is as follows: first, the steady-state friction component is removed from the joint friction torque data to obtain periodic pulsating friction data; based on the correspondence between the periodic pulsating friction data and the motor rotor position, a position-related periodic pulsating friction component model is constructed using Fourier series; the position-related periodic pulsating friction component model includes at least a fundamental term and a second harmonic term, expressed as: in, This represents the position-dependent periodic pulsating friction component. Indicates the position of the motor rotor. This represents the amplitude parameter of the fundamental term. This represents the amplitude parameter of the second harmonic term. Represents the phase parameter of the fundamental term. This represents the phase parameter of the second harmonic term.

[0013] Furthermore, the harmonic drive dual-component nonlinear friction model superimposes the velocity-related steady-state friction component and the position-related periodic pulsating friction component to obtain the mechanism prediction value of the harmonic joint friction torque. The velocity-dependent steady-state friction component is used to characterize the macroscopic velocity-dependent nonlinear change of the friction torque, and the position-dependent periodic pulsating friction component is used to characterize the microscopic periodic pulsation caused by the harmonic drive structure.

[0014] Furthermore, the physical information neural network residual compensation model in S6 adopts a fully connected multilayer perceptron structure, including an input layer, at least one hidden layer, and an output layer. Information is transmitted between adjacent layers using a fully connected method. The input layer includes four input nodes, which are used to receive the sine term of the motor rotor position, the cosine term of the motor rotor position, the normalized velocity, and the velocity sign, respectively. Each hidden layer includes 128 neurons, all of which use the hyperbolic tangent function as the activation function. The output layer includes one output node, which is used to output the residual compensation value.

[0015] Furthermore, the iterative training steps for the physical information neural network residual compensation model include: constructing a training sample set based on the motor rotor position, motor rotor speed, current feedback data collected in S1, and the mechanism prediction values ​​of the harmonic drive dual-component nonlinear friction model in S5; for each sampling time, obtaining the measured friction torque from the current feedback, calculating the sample prediction residuals in combination with the mechanism prediction values, and constructing an input feature vector containing the sine term, cosine term, normalized velocity, and velocity sign based on the motor rotor position and motor rotor speed, with each set of input feature vectors and the corresponding prediction residuals constituting a single training sample; iteratively updating the network parameters using Adam or other gradient optimization algorithms, inputting the training sample input feature vector into the model to obtain the residual compensation value in each iteration, substituting it into a preset loss function to calculate the loss value, and updating the model parameters through backpropagation based on the loss function; iterating repeatedly until training is completed to obtain the trained physical information neural network residual compensation model.

[0016] Furthermore, the loss function of the physical information neural network residual compensation model includes a data fitting term and a physical constraint term. The data fitting term employs a velocity adaptive weighting strategy to increase the weight of samples in low-speed regions in the loss function. The physical constraint term is constructed based on the derivative of the residual compensation value output by the physical information neural network residual compensation model with respect to velocity, and is used to constrain the smoothness of the residual compensation value as it changes with velocity, thereby reducing the risk of overfitting the physical information neural network residual compensation model to high-frequency measurement noise. This is expressed as... ; in , , In the formula, L represents the total loss function. Represents the data fitting term. Represents physical constraint terms. The weights of the physical constraint terms are represented by N, the number of samples is N, and the training sample index is i. Indicates speed adaptive weights, This represents the residual compensation value output by the neural network residual compensation model corresponding to the i-th training sample. This represents the prediction residual for the corresponding sample. This represents the motor rotor speed corresponding to the i-th training sample. This represents the derivative of the residual compensation value with respect to velocity.

[0017] Furthermore, the compensation friction model is embedded into the mechanical domain model as a friction torque module.

[0018] Compared with the prior art, the present invention has the following beneficial effects: First, this invention establishes a multi-domain digital twin modeling framework for industrial robot joints, including mechanical domain model, electrical domain model and control domain model. It can describe the coupling relationship between joint motion commands, servo drives, motor output, harmonic transmission and mechanical response, and improve the ability of the joint digital twin model to represent the actual physical system.

[0019] Second, this invention decomposes harmonic drive friction into velocity-dependent steady-state friction components and position-dependent periodic pulsating friction components, which can simultaneously describe the macroscopic velocity-dependent nonlinear change of friction torque and the microscopic periodic pulsating characteristics caused by the harmonic drive structure, thereby improving the modeling accuracy of friction torque.

[0020] Third, this invention uses Fourier series to construct a position-related periodic pulsating friction component model, and selects either the forward rotation parameter set or the reverse rotation parameter set according to the joint motion direction. This can characterize the directional dependence of harmonic drive friction pulsation under different motion directions and improve the model's adaptability to bidirectional motion conditions.

[0021] Fourth, this invention constructs a physical information neural network residual compensation model to compensate for the prediction residual of the two-component nonlinear friction model, thereby improving the ability to represent unmodeled high-order nonlinear features while maintaining the physical interpretability of the mechanism model.

[0022] Fifth, by introducing sine, cosine, normalized speed, and speed sign of the motor rotor position into the neural network input, and by introducing a speed adaptive weighting strategy and a smoothness physical constraint term for the residual compensation value into the loss function, this invention can enhance the ability of the physical information neural network residual compensation model to express periodic continuity, low-speed nonlinearity, and changes in motion direction, and reduce the risk of overfitting to high-frequency measurement noise.

[0023] Sixth, this invention sets the compensation friction model as the friction torque module in the mechanical domain model, so that the friction torque output by the model acts as a resistance torque on the joint transmission chain described by the mechanical domain model; and couples the improved mechanical domain model with the electrical domain model and the control domain model to generate a digital twin model of the industrial robot joint, providing a model basis for joint state prediction, motion control compensation, fault diagnosis, assembly jamming identification and safety monitoring. Attached Figure Description

[0024] Figure 1 This is a flowchart illustrating a digital twin modeling method for industrial robot joints that considers harmonic drive nonlinear friction, as described in this invention. Figure 2 This is a schematic diagram of the multi-domain digital twin modeling framework for industrial robot joints according to the present invention; Figure 3 This is a schematic diagram of the structure of the harmonic drive nonlinear friction model and the physical information neural network residual compensation model of the present invention; Figure 4 This is a comparison chart of the friction torque predictions of the Stribeck friction model, the harmonic drive dual-component nonlinear friction model, and the compensated friction model of this invention. Figure 5 This is a comparison diagram showing the virtual and real results of the digital twin model of the industrial robot joint and the physical joint, as presented in this invention. Figure 5 (a) is a comparison chart of motor speed response. Figure 5 (b) is a comparison of the q-axis current response. Detailed Implementation

[0025] The technical solution of the present invention will be further described below with reference to the accompanying drawings and specific embodiments. It should be understood that the following embodiments are for illustrative purposes only and are not intended to limit the scope of protection of the present invention. Equivalent substitutions, modifications, or combinations made by those skilled in the art without departing from the concept of the present invention should all fall within the scope of protection of the present invention.

[0026] like Figure 1 As shown, this embodiment provides a digital twin modeling method for industrial robot joints considering harmonic drive nonlinear friction, including the following steps: S1: Collects harmonic joint operation data of industrial robots. The operation data includes joint position data, joint speed data and current feedback data, and obtains joint friction torque data based on the current feedback data.

[0027] In this embodiment, the industrial robot harmonic joint includes a motor, a harmonic reducer, sensors, and a load component. The motor is a permanent magnet synchronous motor, and the harmonic reducer is used to achieve speed reduction transmission from the motor side to the joint output side. The collected operating data includes motor rotor position, motor rotor speed, joint position, joint speed, motor q-axis current feedback data, and driver feedback data.

[0028] During data acquisition, the harmonic joints of the industrial robot can be left unloaded, or the influence of gravity on the target joint can be effectively eliminated by adjusting the robot's configuration. Furthermore, the target joint can be controlled to operate under multiple constant speed conditions to reduce the influence of acceleration and inertia terms on friction torque identification.

[0029] Under constant speed, no-load, or near-no-load conditions, the joint drive torque is primarily used to overcome the frictional torque during harmonic drive. Therefore, the electromagnetic torque on the motor side can be calculated based on the motor's q-axis current feedback data and the motor torque constant, and further, the joint frictional torque data can be obtained. For example, it can be calculated based on the following relationship: ,in, Indicates the electromagnetic torque on the motor side. Represents the motor torque constant. This represents the q-axis current feedback value of the motor. Under constant speed and no-load conditions, the electromagnetic torque on the motor side obtained from the current feedback data can be used as an approximate representation of the friction torque. If it is necessary to convert it to the joint output side, it can be done by combining the transmission ratio of the harmonic reducer.

[0030] The above methods can provide the data foundation required for subsequent steady-state friction component models, periodic pulsating friction component models, and physical information neural network residual compensation models.

[0031] S2: Establish a multi-domain digital twin modeling framework for joints, such as Figure 2 As shown, the multi-domain digital twin modeling framework for joints includes a control domain model, an electrical domain model, and a mechanical domain model, which are coupled through control commands, motor electromagnetic torque, joint motion state, and sensor feedback signals.

[0032] The control domain model is used to generate voltage commands, current commands, or pulse width modulation signals based on joint position commands or joint speed commands, and sends the voltage commands, current commands, or pulse width modulation signals to the electrical domain model. The control domain model includes a trajectory planning module, a coordinate transformation module, a speed closed-loop control module, and a current closed-loop control module; wherein, the trajectory planning module is used to generate joint position commands or joint speed commands, the coordinate transformation module is used to perform Clarke transformation, Park transformation, inverse Park transformation, and inverse Clarke transformation, the speed closed-loop control module is used to generate torque current commands based on the deviation between the speed command and the feedback speed, and the current closed-loop control module is used to generate voltage commands based on the deviation between the current command and the feedback current.

[0033] The electrical domain model receives voltage commands, current commands, or pulse width modulation (PWM) signals output by the control domain model and generates motor electromagnetic torque based on these commands. The electrical domain model includes a drive modulation module, an inverter module, a permanent magnet synchronous motor electromagnetic model, and a sensor feedback module. The drive modulation module generates PWM signals based on voltage commands, the inverter module converts DC voltage to three-phase AC voltage based on the PWM signals, the permanent magnet synchronous motor electromagnetic model generates motor electromagnetic torque based on the three-phase AC voltage, motor parameters, and motor current, and the sensor feedback module feeds back motor current, rotor position, and rotor speed to the control domain model.

[0034] The mechanical domain model is used to model the joint transmission chain consisting of the motor mechanical end, harmonic reducer, and load. It receives the motor electromagnetic torque output from the electrical domain model and calculates the dynamic response of the joint transmission chain based on the motor electromagnetic torque, equivalent moment of inertia, load torque, and friction torque, generating the joint motion response. The mechanical domain model includes a transmission chain structure description module, an equivalent inertia module, a load torque module, and a friction torque module. The transmission chain structure description module describes the power transmission path consisting of the motor mechanical end, harmonic reducer, and load. The equivalent inertia module describes the equivalent moment of inertia on the motor side or joint side. The load torque module describes the external load torque acting on the joint transmission chain. The friction torque module calculates the friction torque based on the friction torque model and applies the friction torque as a resistance torque to the joint transmission chain described by the mechanical domain model. In step S8, the compensated friction model obtained in step S7 is set as the friction torque module.

[0035] In the above framework, the control domain model sends voltage commands, current commands, or pulse width modulation signals to the electrical domain model, the electrical domain model sends the motor electromagnetic torque to the mechanical domain model, the mechanical domain model feeds back the joint position and joint speed to the control domain model, and the electrical domain model feeds back the motor current to the control domain model, thus forming a closed-loop digital twin model in which the control domain model, electrical domain model, and mechanical domain model work together.

[0036] For a single-joint system, its dynamic relationship can be expressed as: Where J represents the equivalent moment of inertia, Indicates the acceleration of a motor or joint. Indicates the electromagnetic torque of the motor. Indicates load torque. This represents the friction torque. The friction torque is calculated by outputting the compensated friction model. Introducing this dynamic relationship allows us to characterize the influence of harmonic drive nonlinear friction on the dynamic response of joints in the mechanical domain model.

[0037] S3: Constructing a velocity-dependent steady-state friction component model in the mechanical domain model based on harmonic joint operation data and joint friction torque data of industrial robots; specifically, firstly, based on the joint friction torque data collected under different constant speed conditions, extracting data segments of the stable operation phase, and calculating the steady-state representative value of the friction torque under each constant speed condition. Then, based on the relationship between friction torque and joint speed, constructing a velocity-dependent steady-state friction component model.

[0038] The velocity-dependent steady-state friction component model is constructed using the Stribeck friction model to characterize the nonlinear steady-state characteristics of harmonic joint friction torque in industrial robots as a function of joint velocity. The Stribeck friction model is expressed as: in, This represents the velocity-dependent steady-state friction component. Indicates joint speed or motor rotor speed. Represents the velocity sign function, Represents the Coulomb friction parameter. Represents static friction parameters. This represents the Stribeck characteristic velocity parameters. This represents the empirical index parameter. This represents the viscous friction parameter.

[0039] By identifying nonlinear parameters from steady-state friction torque data that includes low-speed or near-zero-speed operating conditions, the Coulomb friction parameters, static friction parameters, Stribeck characteristic velocity parameters, empirical exponent parameters, and viscous friction parameters in the Stribeck model can be jointly estimated.

[0040] This speed-dependent steady-state friction component model is used to describe the macroscopic nonlinear trend of friction torque as a function of speed, especially to characterize the Stribeck effect in the low-speed region and the viscous friction variation in the high-speed region.

[0041] S4: Construct a position-related periodic pulsating friction component model in the mechanical domain model based on industrial robot harmonic joint operation data and joint friction torque data; During harmonic drive, due to factors such as the elastic deformation of the flexspline, gear meshing, and structural periodicity, the frictional torque not only varies with speed but also exhibits periodic pulsations depending on the position of the motor rotor or joint. To characterize this type of position-dependent periodic pulsation characteristic, this embodiment constructs a position-dependent periodic pulsation friction component model.

[0042] Specifically, the steady-state friction component is first removed from the friction torque data to obtain periodic pulsating friction data. Then, based on the correspondence between the periodic pulsating friction data and the motor rotor position, a position-dependent periodic pulsating friction component model is constructed using Fourier series.

[0043] The position-dependent periodic pulsating friction component model includes at least a fundamental term and a second harmonic term, which can be expressed as: in, This represents the position-dependent periodic pulsating friction component. Indicates the position of the motor rotor. This represents the amplitude parameter of the fundamental term. This represents the amplitude parameter of the second harmonic term. Represents the phase parameter of the fundamental term. This represents the phase parameter of the second harmonic term.

[0044] Because industrial robot harmonic joints may exhibit differences in periodic pulsation amplitude and phase during forward and reverse rotation, this embodiment classifies the periodic pulsation friction data according to the sign of the joint speed or motor rotor speed. When the joint speed or motor rotor speed is greater than zero, the corresponding motor rotor position data and periodic pulsation friction data are classified as a forward-rotating periodic pulsation friction dataset; when the joint speed or motor rotor speed is less than zero, the corresponding data are classified as a reverse-rotating periodic pulsation friction dataset.

[0045] The position-related periodic pulsating friction component model is parameterized using the forward-rotating periodic pulsating friction dataset and the reverse-rotating periodic pulsating friction dataset, respectively. In this embodiment, a nonlinear least squares method is used, with the objective of minimizing the sum of squared errors between the predicted values ​​of the periodic pulsating friction model and the corresponding periodic pulsating friction data, to identify the forward-rotating parameter set and the reverse-rotating parameter set, respectively. The forward-rotating parameter set can be expressed as: The inverted parameter set can be represented as: }.in, These are the fundamental term amplitude parameters, second harmonic term amplitude parameters, fundamental term phase parameters, and second harmonic term phase parameters under forward rotation conditions, respectively. These are the parameters corresponding to the reverse operation condition.

[0046] During model execution, when the joint movement direction is positive, the forward rotation parameter set is called. Calculate the position-dependent periodic pulsating friction components; when the joint movement direction is reversed, call the inverted parameter set. Calculations are performed. Through the aforementioned direction-related data division, parameter identification, and parameter switching methods, the amplitude and phase differences of harmonic drive friction pulsation under different motion directions can be characterized.

[0047] S5: By superimposing the velocity-dependent steady-state friction component model and the position-dependent periodic pulsating friction component model, a harmonic drive dual-component nonlinear friction model is obtained. The harmonic drive dual-component nonlinear friction model can be expressed as: .

[0048] in, This represents the mechanistic prediction value of harmonic joint friction torque. Represents the velocity-dependent steady-state friction components This represents the position-dependent periodic pulsating friction component.

[0049] Among them, the velocity-dependent steady-state friction component is used to characterize the macroscopic velocity-dependent nonlinear change of friction torque; the position-dependent periodic pulsating friction component is used to characterize the microscopic periodic pulsation caused by the harmonic drive structure.

[0050] In this embodiment, the harmonic joint friction torque is decoupled into a velocity-dependent steady-state component and a position-dependent periodic pulsation component through the above method, so that the model can simultaneously describe the macroscopic changes of the friction torque in the velocity dimension and the periodic pulsation in the position dimension.

[0051] S6: Construct a physical information neural network residual compensation model and train it.

[0052] S6.1 Constructing a physical information neural network residual compensation model. In this embodiment, the physical information neural network residual compensation model adopts a fully connected multilayer perceptron structure, including an input layer, at least one hidden layer, and an output layer. Information is transmitted between adjacent layers using a fully connected method. The input layer includes four input nodes, which are used to receive the sine term of the motor rotor position, the cosine term of the motor rotor position, the normalized speed, and the speed sign, respectively.

[0053] The multilayer perceptron has three hidden layers, each containing 128 neurons. The hyperbolic tangent function is used as the activation function to perform nonlinear mapping on the input features, extract the high-order nonlinear residual features that the harmonic drive dual-component nonlinear friction model fails to represent, and ensure the differentiability of the neural network output with respect to the input velocity. This allows for the automatic differentiation calculation of the derivative of the residual compensation value with respect to the velocity, and the construction of smoothness physical constraint terms.

[0054] The output layer includes an output node for outputting residual compensation values. The output layer can employ a linear mapping, allowing the residual compensation value to be positive or negative based on the actual predicted residual.

[0055] The physical information neural network residual compensation model is not used to replace the harmonic drive dual-component nonlinear friction model, but rather to learn and compensate for the residual parts that the harmonic drive dual-component nonlinear friction model fails to represent.

[0056] S6.2. Based on the motor rotor position data, motor rotor speed data, and current feedback data collected in step S1, and the mechanism prediction values ​​output by the harmonic drive dual-component nonlinear friction model constructed in step S5 under the corresponding motion state, a training sample is constructed.

[0057] Specifically, this involves mapping the motor rotor position data, motor rotor speed data, and current feedback data at each sampling time. For the first... i At each sampling time, the measured friction torque is obtained based on the current feedback data and the motor torque constant. The motor rotor position corresponding to the sampling time and motor rotor speed Input a two-component nonlinear friction model of harmonic drive to obtain mechanism prediction values. .

[0058] Based on the measured friction torque and mechanism prediction value Calculate the first i The prediction residuals corresponding to each sample : in, Indicates by the first i The measured friction torque was obtained from the current feedback data of the training samples. The two-component nonlinear friction model of harmonic drive is represented in the first... i Each training sample corresponds to a predicted value of the mechanism output under motion conditions.

[0059] At the same time, according to the first i Motor rotor position corresponding to each training sample and motor rotor speed Construct the input feature vector of the physical information neural network residual compensation model: in, Indicates the first i The normalized velocity corresponding to each training sample is used to characterize the joint velocity state; The velocity symbol is used to characterize the direction of joint movement; Indicates the position of the motor rotor. The sine and cosine terms are used to map the angle variable to a continuous periodic space to characterize the periodic continuity of the rotor position.

[0060] From the input feature vector and the corresponding predicted residuals This constitutes a training sample, which in turn forms a training sample set. D , is represented as: in, N This represents the number of training samples. Input feature vector. As input to the physical information neural network residual compensation model, the predicted residual is... As the supervised training target for the corresponding samples.

[0061] S6.3 The loss function of the physical information neural network residual compensation model includes a data fitting term and a physical constraint term: Where L represents the total loss function, Represents the data fitting term. Represents physical constraint terms. This represents the weighting coefficient of the physical constraint term.

[0062] The data fitting term employs a velocity-adaptive weighting strategy to increase the weight of samples in low-velocity regions in the loss function. This can be expressed as: Where N represents the number of samples, Indicates speed adaptive weights, This represents the residual compensation value output by the neural network. This represents the prediction residual for the corresponding sample. The data fitting term is minimized... and The difference between the two components allows the residual compensation value to approximate the actual predicted residual of the harmonic drive dual-component nonlinear friction model, thereby enabling the physical information neural network residual compensation model to learn the residual characteristics that the harmonic drive dual-component nonlinear friction model failed to represent. The speed adaptive weight can be set as a monotonically decreasing function of the absolute value of the speed, so that the smaller the absolute value of the speed, the larger the corresponding weight, thereby enhancing the model's ability to fit low-speed nonlinear friction characteristics.

[0063] The physical constraint term is constructed based on the derivative of the residual compensation value output by the physical information neural network residual compensation model with respect to velocity. It is used to constrain the smoothness of the residual compensation value as a function of velocity, and can be expressed as: .in, This represents the physical constraint term, and N represents the number of training samples. i Indicates the training sample number. Indicates the first i The residual compensation value output by the neural network residual compensation model corresponding to each training sample. Indicates the first i The motor rotor speed corresponding to each training sample This represents the derivative of the residual compensation value with respect to velocity. By introducing physical constraint terms, the drastic fluctuations in the output of the physical information neural network residual compensation model with velocity can be limited, reducing the risk of overfitting the neural network to high-frequency measurement noise and improving the model's generalization ability under unseen operating conditions.

[0064] S6.4 Model Training: The training process uses the Adam optimization algorithm or other gradient optimization algorithms to iteratively update the neural network parameters. During each iteration, the input feature vectors of the training samples are... Input physical information into a neural network residual compensation model to obtain residual compensation values. Based on residual compensation value With corresponding predicted residuals Calculate the data fitting term and, based on the residual compensation value... Relative to speed The derivative is used to calculate the physical constraint term; the total loss function is calculated based on the data fitting term and the physical constraint term, and the neural network parameters Θ are updated in reverse according to the total loss function. This process is iterated until training is complete, resulting in a trained physical information neural network residual compensation model.

[0065] S7: The prediction residual of the harmonic drive dual-component nonlinear friction model is compensated using the trained physical information neural network residual compensation model to obtain the compensated friction model, such as... Figure 3 As shown.

[0066] For any joint motion state, the corresponding motor rotor position and motor rotor speed are constructed into an input feature vector. and the input feature vector Input the trained physical information into the neural network residual compensation model to obtain the residual compensation value: in, This represents the neural network parameters determined after training.

[0067] The residual compensation value Mechanism predictions from the output of the harmonic drive two-component nonlinear friction model By superimposing these values, we obtain the friction torque output by the compensated friction model: in, This represents the friction torque output by the friction compensation model. Because the physical information neural network residual compensation model predicts the residual during training... As a supervised training objective, when the residual compensation value When the friction torque output by the compensated friction model can approximate the predicted residual under the corresponding motion state, it can be closer to the measured friction torque.

[0068] S8: Set the compensation friction model as the friction torque module in the mechanical domain model, and couple the mechanical domain model, electrical domain model and control domain model to generate a digital twin model of the industrial robot joint.

[0069] Specifically, the compensated friction model obtained in step S7 is set as the friction torque module in the mechanical domain model established in step S2. The friction torque module takes the motor rotor position, motor rotor speed or joint speed, and direction of motion as inputs, and outputs the compensated friction torque. and the frictional torque The joint transmission chain described by the mechanical domain model acts as a resistance torque.

[0070] The mechanical domain model receives the motor electromagnetic torque output from the electrical domain model and calculates the joint motion response based on the motor electromagnetic torque, load torque, friction torque output from the compensated friction model, and equivalent moment of inertia, according to the dynamic relationship of the joint transmission chain. For a single-joint system, the dynamic relationship can be expressed as: Where J represents the equivalent moment of inertia, Indicates the acceleration of a motor or joint. Indicates the electromagnetic torque of the motor. Indicates load torque. This represents the friction torque output by the compensated friction model.

[0071] Through the above settings, the compensation friction model obtained in step S7 is integrated into the mechanical domain model in the joint multi-domain digital twin modeling framework established in step S2. This allows the mechanical domain model to further characterize the velocity-related steady-state friction, position-related periodic pulsating friction, and residual characteristics that the dual-component nonlinear friction model fails to characterize, in addition to describing the conventional dynamic relationship of the joint transmission chain.

[0072] Specifically, within the same simulation time step or control cycle, the control domain model generates voltage commands, current commands, or pulse width modulation signals based on joint motion commands, joint position feedback, joint velocity feedback, and current feedback, and sends the voltage commands, current commands, or pulse width modulation signals to the electrical domain model.

[0073] The electrical domain model generates the motor electromagnetic torque based on the voltage command, current command, or pulse width modulation signal through drive modulation, inverter power conversion, and permanent magnet synchronous motor electromagnetic conversion, and sends the motor electromagnetic torque to the mechanical domain model; at the same time, the electrical domain model sends the motor current feedback signal to the control domain model.

[0074] The mechanical domain model generates joint motion response based on the motor electromagnetic torque, load torque, equivalent moment of inertia, and friction torque output by the compensation friction model, and outputs joint position and joint velocity. The joint position and joint velocity are fed back to the control domain model via the sensor feedback module to form a closed-loop digital twin model in which the control domain model, electrical domain model, and mechanical domain model work together.

[0075] Therefore, the digital twin model of an industrial robot joint can output predicted joint position, joint speed, current, and torque. Furthermore, it can also output intermediate state quantities such as predicted voltage, pulse width modulation signal, motor electromagnetic torque, friction torque, motor rotor position, and motor rotor speed based on the simulation model. Further, in scenarios involving hole-shaft assembly, contact detection, or assembly jamming identification, the predicted torque output by the industrial robot joint digital twin model can be compared with the feedback torque of the physical joint to obtain the torque residual. An adaptive judgment threshold is then set based on the residual noise floor during normal operation. When the real-time torque residual exceeds the adaptive judgment threshold, external contact, jamming, or collision is determined, triggering an alarm or control command. Because this invention improves the prediction accuracy of the digital twin model for harmonic drive nonlinear friction and reduces the residual noise floor during normal operation, it enhances the sensitivity of contact anomaly detection under unsensitized conditions.

[0076] To verify the effectiveness of the method of the present invention, the method was verified from two aspects: the prediction accuracy of the friction model and the consistency between the virtual and real aspects of the multi-domain digital twin model.

[0077] First, the friction model was validated step by step. The target industrial robot's harmonic joints were controlled to operate at a constant speed. Motor rotor position, motor rotor speed, and current feedback data were collected, and the measured friction torque was obtained based on the current feedback data. The Stribeck friction model, the harmonic drive two-component nonlinear friction model, and the compensated friction model were used to predict the friction torque of the same set of operating data, and the prediction results of each model were compared with the measured friction torque.

[0078] like Figure 4 As shown, the Stribeck friction model can characterize the steady-state variation trend of friction torque, but it is difficult to reconstruct the periodic pulsations related to the rotor position of the motor. The harmonic drive dual-component nonlinear friction model introduces a position-related periodic pulsating friction component on the basis of the velocity-related steady-state friction component, which can reconstruct the main periodic pulsation characteristics. The compensated friction model further superimposes the residual compensation value output by the physical information neural network residual compensation model, making the friction torque prediction result closer to the measured friction torque. This shows that the harmonic drive dual-component nonlinear friction model in this invention can improve the characterization ability of position-related periodic pulsating friction, and the physical information neural network residual compensation model can further compensate for the unmodeled residuals, thereby improving the accuracy of friction torque prediction.

[0079] Secondly, the consistency between the virtual and real systems in the multi-domain digital twin model is verified. The compensated friction model is set as the friction torque module in the mechanical domain model, so that its output friction torque acts as a resistance torque on the joint transmission chain described by the mechanical domain model. Then, the mechanical domain model is coupled with the control domain model and the electrical domain model to generate a digital twin model of the industrial robot joint. Under a given typical motion command, the physical joint and the industrial robot joint digital twin model are run respectively, and the motor speed and q-axis current response of the physical joint are collected and compared with the corresponding prediction results output by the industrial robot joint digital twin model.

[0080] like Figure 5 As shown, Figure 5 (a) shows the comparison results of motor speed response. Figure 5 (b) shows the comparison results of the q-axis current response. Figure 5 (a) It can be seen that the digital twin model of an industrial robot joint can reproduce the motor speed response of the physical joint quite well; from Figure 5(b) It can be seen that the digital twin model of the industrial robot joint can reproduce the periodic fluctuation characteristics in the q-axis current quite well. The above results show that the constructed control domain model, electrical domain model, and mechanical domain model can achieve effective coupling, and the compensation friction model can characterize the influence of harmonic drive nonlinear friction on the joint dynamic response in the mechanical domain model, thereby improving the consistency between the virtual and real aspects of the industrial robot joint digital twin model. The industrial robot joint digital twin model constructed through the above steps in this embodiment can not only describe the multi-domain coupling process of joint control, electrical, and mechanical aspects, but also accurately characterize the nonlinear friction characteristics of harmonic drive, thereby improving the dynamic consistency and prediction accuracy of the industrial robot joint digital twin model.

Claims

1. A digital twin modeling method for industrial robot joints considering harmonic drive nonlinear friction, characterized in that, Includes the following steps: S1. Collect the harmonic joint operation data of the industrial robot. The operation data includes motor rotor position data, motor rotor speed data, joint position data, joint speed data and current feedback data, and obtain joint friction torque data based on the current feedback data. S2. Establish a multi-domain digital twin modeling framework for joints, the modeling framework including a control domain model, an electrical domain model and a mechanical domain model; S3. Construct a speed-related steady-state friction component model based on the aforementioned operating data and joint friction torque data; S4. Construct a position-related periodic pulsating friction component model based on the aforementioned operating data and joint friction torque data; S5. By superimposing the velocity-related steady-state friction component model and the position-related periodic pulsating friction component model, a harmonic drive dual-component nonlinear friction model is obtained. S6. Construct a physical information neural network residual compensation model and perform iterative training and updates; S7. The prediction residual of the harmonic drive dual-component nonlinear friction model is compensated using the updated physical information neural network residual compensation model to obtain the compensated friction model. S8. Embed the friction compensation model into the mechanical domain model, and couple the electrical domain model and the control domain model to generate a digital twin model of the industrial robot joint.

2. The digital twin modeling method for industrial robot joints considering harmonic drive nonlinear friction according to claim 1, characterized in that, During the collection of operating data of the harmonic joint of the industrial robot, the robot's harmonic joint is under constant speed, no load or near no load conditions; the electromagnetic torque on the motor side is calculated using motor current feedback data and motor torque constant, and then the joint friction torque data is obtained.

3. The digital twin modeling method for industrial robot joints considering harmonic drive nonlinear friction according to claim 2, characterized in that, The control domain model in S2 includes a trajectory planning module, a coordinate transformation module, a speed closed-loop control module, and a current closed-loop control module. These modules generate voltage commands, current commands, or pulse width modulation (PWM) signals based on joint position or speed commands and send them to the electrical domain model. The electrical domain model includes a drive modulation module, an inverter module, a permanent magnet synchronous motor electromagnetic model, and a sensor feedback module. These modules receive the voltage commands, current commands, or PWM signals output from the control domain model, generate the motor electromagnetic torque, and send it to the mechanical domain model. The mechanical domain model includes a transmission chain structure description module, an equivalent inertia module, a load torque module, and a friction torque module. These modules model the joint transmission chain consisting of the motor's mechanical end, a harmonic reducer, and the load. They receive the motor electromagnetic torque output from the electrical domain model, calculate the dynamic response of the joint transmission chain based on the motor electromagnetic torque, equivalent moment of inertia, load torque, and friction torque, and generate the joint motion response.

4. The method for digital twin modeling of industrial robot joints considering harmonic drive nonlinear friction according to claim 3, characterized in that, The velocity-dependent steady-state friction component model is constructed using the Stribeck friction model to characterize the nonlinear steady-state characteristics of harmonic joint friction torque in industrial robots as a function of joint velocity; the Stribeck friction model is expressed as: in, This represents the velocity-dependent steady-state friction component. Indicates joint speed or motor rotor speed. Represents the velocity sign function, Represents the Coulomb friction parameter. Represents static friction parameters. This represents the Stribeck characteristic velocity parameters. This represents the empirical index parameter. This represents the viscous friction parameter.

5. The digital twin modeling method for industrial robot joints considering harmonic drive nonlinear friction according to claim 4, characterized in that, The specific process of S4 is as follows: First, the steady-state friction component is removed from the joint friction torque data to obtain periodic pulsating friction data; based on the correspondence between the periodic pulsating friction data and the motor rotor position, a position-related periodic pulsating friction component model is constructed using Fourier series; the position-related periodic pulsating friction component model includes at least a fundamental term and a second harmonic term, expressed as: in, This represents the position-dependent periodic pulsating friction component. Indicates the position of the motor rotor. This represents the amplitude parameter of the fundamental term. This represents the amplitude parameter of the second harmonic term. Represents the phase parameter of the fundamental term. This represents the phase parameter of the second harmonic term.

6. The digital twin modeling method for industrial robot joints considering harmonic drive nonlinear friction according to claim 5, characterized in that, The harmonic drive dual-component nonlinear friction model superimposes the velocity-related steady-state friction component and the position-related periodic pulsating friction component to obtain the mechanism prediction value of the harmonic joint friction torque. The velocity-dependent steady-state friction component is used to characterize the macroscopic velocity-dependent nonlinear change of the friction torque, and the position-dependent periodic pulsating friction component is used to characterize the microscopic periodic pulsation caused by the harmonic drive structure.

7. A digital twin modeling method for industrial robot joints considering harmonic drive nonlinear friction according to any one of claims 1-6, characterized in that, The physical information neural network residual compensation model in S6 adopts a fully connected multilayer perceptron structure, including an input layer, at least one hidden layer, and an output layer. Information is transmitted between adjacent layers using a fully connected method. The input layer includes four input nodes, which are used to receive the sine term of the motor rotor position, the cosine term of the motor rotor position, the normalized velocity, and the velocity sign, respectively. Each hidden layer includes 128 neurons, all of which use the hyperbolic tangent function as the activation function. The output layer includes one output node, which is used to output the residual compensation value.

8. The method for digital twin modeling of industrial robot joints considering harmonic drive nonlinear friction according to claim 7, characterized in that, The iterative training steps for the physical information neural network residual compensation model include: constructing a training sample set based on the motor rotor position, motor rotor speed, current feedback data collected by S1, and the mechanism prediction values ​​of the harmonic drive dual-component nonlinear friction model of S5; for each sampling time, obtaining the measured friction torque from the current feedback, calculating the sample prediction residuals by combining the mechanism prediction values, and constructing an input feature vector containing the sine term, cosine term, normalized velocity, and velocity sign based on the motor rotor position and motor rotor speed, with each set of input feature vectors and the corresponding prediction residuals constituting a single training sample; iteratively updating the network parameters using Adam or other gradient optimization algorithms, inputting the training sample input feature vector into the model to obtain the residual compensation value in each iteration, substituting it into a preset loss function to calculate the loss value, and updating the model parameters through backpropagation based on the loss function; iterating repeatedly until training is completed to obtain the trained physical information neural network residual compensation model.

9. A digital twin modeling method for industrial robot joints considering harmonic drive nonlinear friction according to claim 8, characterized in that, The loss function of the physical information neural network residual compensation model includes a data fitting term and a physical constraint term. The data fitting term employs a velocity-adaptive weighting strategy to increase the weight of samples in low-speed regions in the loss function. The physical constraint term is constructed based on the derivative of the residual compensation value output by the physical information neural network residual compensation model with respect to velocity, and is used to constrain the smoothness of the residual compensation value as it changes with velocity, thereby reducing the risk of overfitting the physical information neural network residual compensation model to high-frequency measurement noise. This is expressed as... ； in , , In the formula, L represents the total loss function. Represents the data fitting term. Represents physical constraint terms. The represents the weight coefficient of the physical constraint term, N represents the number of samples, and i represents the training sample index. Indicates speed adaptive weights, This represents the residual compensation value output by the neural network residual compensation model corresponding to the i-th training sample. This represents the prediction residual for the corresponding sample. This represents the motor rotor speed corresponding to the i-th training sample. This represents the derivative of the residual compensation value with respect to velocity.

10. A digital twin modeling method for industrial robot joints considering harmonic drive nonlinear friction according to claim 9, characterized in that, The compensation friction model is embedded into the mechanical domain model as a friction torque module.

Images