Friction parameter identification method and system based on physical information neural network

Abstract

The invention relates to the technical field of robots and deep learning, and provides a friction parameter identification method and system based on a physical information neural network, and the method comprises the steps: constructing a kinetic equation and a friction model of a mechanical arm; enabling the mechanical arm to move according to a designed track, collecting N groups of related simulation data of the mechanical arm through a sensor, and calculating a corresponding real friction torque; constructing a feedforward neural network for inputting joint speed and outputting predicted friction torque, and completing training of the feedforward neural network by using the obtained data as a training set; adopting typical parameter values to initialize a mechanical arm friction model, and taking the mechanical arm friction model as a regular term of the model; respectively constructing a loss function of the friction model, a loss function of the real friction torque and a total loss function of the model; the total loss function is minimized through an optimization algorithm, a neural network is trained, and friction parameters are identified. Through the method, the accuracy of friction parameter identification is improved.

Description

Technical Field

[0001] This invention relates to the fields of robotics and deep learning technology, specifically to a method and system for identifying friction parameters based on physical information neural networks. Background Technology

[0002] With advancements in science and technology and innovations in engineering, robotics has become an indispensable part of modern industry and science. The applications of robots are constantly expanding, with many used in fields requiring high precision and reliability, such as vehicle manufacturing, surgery, and aerospace engineering.

[0003] Friction, as a fundamental physical phenomenon in mechanical systems, significantly impacts the motion performance and control accuracy of robots. In the coordinated multi-joint motion of robots, friction exists not only in joint actuators and transmission mechanisms but also prevalent in the kinematic pairs and end effectors of robotic arms. Inaccurate modeling of friction can lead to joint oscillations at low speeds, reducing the system's control accuracy. Sudden changes in friction force during joint movement can cause abrupt torque variations, further affecting the robot's overall control performance. Therefore, accurate modeling of friction is beneficial for improving accuracy and stability during actual operation.

[0004] Joint friction exhibits strong nonlinear characteristics; inaccurate description of it can lead to inaccurate robotic arm dynamics models. Many researchers have proposed using various heuristic algorithms and improved heuristic algorithms to identify friction model parameters. For example, Chinese invention patent application CN107918276A, entitled "An Accurate Modeling Method for Friction Pairs in Electromechanical Actuation Systems," discloses an accurate modeling method for friction pairs in electromechanical actuation systems based on the Stribeck friction model and simulated annealing genetic algorithm, improving the accuracy and speed of electromechanical actuation system modeling. Chinese invention patent application CN109940609A, entitled "A Robot Dynamics Modeling Method Based on a Centrally Symmetric Static Friction Model," discloses a method using the WOA optimization algorithm to identify friction model parameters. Chinese invention patent application CN110460277A, entitled "A Friction Nonlinearity Compensation Method for a Single-Motor Servo System Based on Particle Swarm Optimization Algorithm," discloses a friction nonlinearity compensation method for a single-motor servo system based on particle swarm optimization. However, the above heuristic search algorithm has some shortcomings, such as requiring initial values ​​and ranges to be set in advance based on experience as limiting conditions during parameter identification, which places too high demands on the expert's experience and is prone to getting trapped in local optima. For example, Chinese invention patent application CN113051673A, entitled "An Identification Method for an Improved Stribeck Friction Model for Robots," improves the traditional Stribeck friction model, proposing an improved Stribeck friction model and a hybrid genetic algorithm to identify the parameters of the improved friction model. However, this method relies on manual differentiation of the high-speed and low-speed segments of the Stribeck friction curve, resulting in low accuracy of the final identification results. Summary of the Invention

[0005] The technical problem to be solved by this invention is how to introduce a friction model as a regularization term to improve the accuracy of friction parameter identification.

[0006] The present invention solves the above-mentioned technical problems through the following technical means: This invention provides a method for identifying friction parameters based on a physical information neural network, comprising the following steps: S1. Construct the dynamic equations and friction model of the robotic arm; S2. Make the robotic arm move according to the designed trajectory, collect N sets of relevant simulation data of the robotic arm through sensors and calculate the corresponding real friction torque; S3. Construct a feedforward neural network that takes the joint velocity as input and outputs the predicted friction torque. Use the data obtained in step S2 as the training set to complete the training of the feedforward neural network. S4. Initialize the robotic arm friction model using typical parameter values ​​and use them as the model's regularization term; construct the loss function of the friction model, the loss function of the actual friction torque, and the total loss function of the model, respectively. S5. Minimize the total loss function through an optimization algorithm, train the neural network, and identify the friction parameters.

[0007] Furthermore, the dynamic equations for constructing the robotic arm described in step S1 are specifically as follows: The dynamic equations of a robotic arm relate to joint torques, joint positions, angular velocities, and angular accelerations, and are expressed mathematically as follows:

[0008] in, These are the vectors of the robotic arm joint angles, joint angular velocity, and joint angular acceleration, respectively. , , ; Here is the inertia matrix of the robotic arm. This is the velocity term matrix related to the centrifugal force and Coriolis force of the robotic arm. For gravity, Let the joint friction torque vector be... This is the joint torque vector.

[0009] Furthermore, the construction of the robotic arm friction model described in step S1 specifically involves: The Stribeck friction model is used to describe the frictional characteristics of the robotic arm joints. The mathematical expression of the Stribeck friction model is as follows:

[0010] in, For joints i Frictional torque, i For joint serial numbers, i =1,2,3,...; ω represents the angular velocity of the robotic arm joints; Coulomb friction; This represents the maximum static friction force. The threshold for Stribeck's velocity; It is the coefficient of viscous friction; Considering the inconsistency of friction model parameters when the robotic arm joints rotate in opposite directions, the friction models for both forward and reverse rotation are as follows:

[0011] The parameters that need to be identified are as follows: .

[0012] Further, step S2 includes the following steps: S21. Design the motion trajectory of the robotic arm, send the desired trajectory motion control command to the controller, and control the robotic arm to run according to the designed trajectory. S22. Collect joint torque information, position information and joint angular velocity information of the robotic arm during operation through sensors, and add 5% Gaussian noise; S23. Calculate the actual friction torque.

[0013] Furthermore, the calculation of the actual frictional torque in step S23 specifically involves: The theoretical joint torque vector of the robotic arm is calculated based on the dynamic equation of the robotic arm. As shown in the following formula:

[0014] The collected joint torque vectors of the robotic arm are Then the true friction torque vector The calculation is as follows: .

[0015] Furthermore, the typical parameter values ​​mentioned in step S4 are specifically as follows: The value is 0.15; The value is 0.60; The value is 0.05; The value is 0.02; The value is 0.20; The value is 0.70; The value is 0.05; The value is 0.03.

[0016] Furthermore, the loss function for constructing the friction model described in step S4 is specifically constructed as follows: The predicted friction torque output by the feedforward neural network The root mean square error between the frictional torque obtained from the Stribeck friction model and the frictional torque is set as the loss function of the friction model. As shown in the following formula:

[0017] in, This is the predicted friction torque vector output by the feedforward neural network.

[0018] Furthermore, the loss function for constructing the actual frictional torque described in step S4 is constructed as follows: The predicted friction torque output by the feedforward neural network Compared with the actual frictional torque The root mean square error between them is set as the loss function of the true friction torque. As shown in the following formula:

[0019] in, This is the predicted friction torque vector output by the feedforward neural network. This is the calculated true frictional torque vector.

[0020] Furthermore, the total loss function of the model described in step S4 is as follows: .

[0021] This invention also provides a friction parameter identification system based on a physical information neural network. The system executes the above-described method during operation and includes the following modules: The physical properties building module is used to construct the dynamic equations and friction models of the robotic arm; The data acquisition module is used to enable the robotic arm to move according to the designed trajectory. It collects N sets of relevant simulation data of the robotic arm through sensors and calculates the corresponding real friction torque. The feedforward neural network module is used to construct a feedforward neural network that takes the joint velocity as input and outputs a predicted friction torque. The data obtained by the data acquisition module is used as the training set to complete the training of the feedforward neural network. The loss function construction module is used to initialize the robotic arm friction model with typical parameter values ​​and use them as the regularization term of the model; it constructs the loss function of the friction model, the loss function of the actual friction torque, and the total loss function of the model, respectively. The parameter identification module is used to train a neural network and identify friction parameters by minimizing the total loss function through an optimization algorithm.

[0022] The advantages of this invention are: (1) This invention uses a physical information neural network to identify the parameters of the friction model. The physical information part is introduced into the friction model as a regularization term and added to the loss function to constrain the network training. The network parameters and the parameters to be identified in the friction model are updated through the gradient descent optimization algorithm of the neural network. Compared with the identification using a heuristic search algorithm, this invention does not need to give the range of parameter variation, does not need to manually divide the high-speed region and low-speed region, and is less likely to get trapped in local optima, thus improving the accuracy of identification.

[0023] (2) The present invention uses a physical information neural network to identify the parameters of the friction model, and then substitutes the identified parameters into the friction model. This method of modeling friction force requires less data and has greater generalization ability compared to directly modeling friction force using a neural network. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of the friction parameter identification method based on physical information neural network according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the physical information neural network for identifying friction parameters according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the physical information neural network identification curve in an embodiment of the present invention; Figure 4 This is a schematic diagram comparing the physical information neural network identification value and the true value during forward rotation according to an embodiment of the present invention; Figure 5 This is a schematic diagram showing the comparison between the physical information neural network identification value and the true value during the reversal of an embodiment of the present invention. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0026] Example 1 This embodiment provides a friction parameter identification method based on a physical information neural network. A friction model is introduced into the physical information part of the physical information neural network and added as a regularization term to the loss function to constrain network training. The network parameters and the parameters to be identified in the friction model are updated using the gradient descent optimization algorithm of the neural network, ultimately identifying accurate friction parameters. The specific implementation process is as follows: Figure 1 As shown, it includes the following steps: S1. Construct the dynamic equations and friction model of the robotic arm; The dynamic equations for constructing the robotic arm are as follows: The dynamic equations of a robotic arm relate to joint torques, joint positions, angular velocities, and angular accelerations, and are expressed mathematically as follows:

[0027] in, These are the vectors of the robotic arm joint angles, joint angular velocity, and joint angular acceleration, respectively. , , ; Here is the inertia matrix of the robotic arm. This is the velocity term matrix related to the centrifugal force and Coriolis force of the robotic arm. For gravity, Let the joint friction torque vector be... This is the joint torque vector.

[0028] The construction of the robotic arm friction model specifically involves: The Stribeck friction model is used to describe the frictional characteristics of the robotic arm joints. This model reveals the relationship between frictional force and joint angular velocity, demonstrating the nonlinear characteristics of frictional force as a function of angular velocity. The mathematical expression of the Stribeck friction model is as follows:

[0029] in, For joints i Frictional torque, i For joint serial numbers, i =1,2,3,...; ω represents the angular velocity of the robotic arm joints; Coulomb friction; This represents the maximum static friction force. The threshold for Stribeck's velocity; It is the coefficient of viscous friction; Considering the inconsistency of friction model parameters when the robotic arm joints rotate in opposite directions, the friction models for both forward and reverse rotation are as follows:

[0030] The parameters that need to be identified are as follows: .

[0031] S2. The robotic arm moves along the designed trajectory, and N sets of relevant simulation data of the robotic arm are collected through sensors to calculate the corresponding actual frictional torque; the specific implementation includes the following steps: S21. Design the motion trajectory of the robotic arm, and send the desired trajectory motion control command to the controller to control the robotic arm to run according to the designed trajectory; specifically, first design the motion trajectory of the robotic arm as follows:

[0032] Differentiating the above equation yields the theoretical speed:

[0033] The robotic arm is made to move along the trajectory specified above, and simulation data of the robotic arm is collected.

[0034] S22. Collect joint torque information, position information and joint angular velocity information of the robotic arm during operation through sensors, and add 5% Gaussian noise; S23. Calculate the actual frictional torque; specifically: The theoretical joint torque vector of the robotic arm is calculated based on the dynamic equation of the robotic arm. As shown in the following formula:

[0035] The collected joint torque vectors of the robotic arm are Then the true friction torque vector The calculation is as follows: .

[0036] S3. Construct a feedforward neural network that takes joint velocity as input and outputs predicted friction torque. Use the data obtained in step S2 as the training set to complete the training of the feedforward neural network. The network parameters of the feedforward neural network are set as shown in the table below:

[0037] S4. Initialize the robotic arm friction model using typical parameter values ​​and use them as the model's regularization term; construct the loss function of the friction model, the loss function of the actual friction torque, and the total loss function of the model, respectively. The typical parameter values ​​mentioned are as follows: The value is 0.15; The value is 0.60; The value is 0.05; The value is 0.02; The value is 0.20; The value is 0.70; The value is 0.05; The value is 0.03.

[0038] The loss function for constructing the friction model is specifically constructed as follows: The predicted friction torque output by the feedforward neural network The root mean square error between the frictional torque obtained from the Stribeck friction model and the frictional torque is set as the loss function of the friction model. As shown in the following formula:

[0039] in, This is the predicted friction torque vector output by the feedforward neural network.

[0040] The loss function for constructing the actual friction torque is specifically constructed as follows: The predicted friction torque output by the feedforward neural network Compared with the actual frictional torque The root mean square error between them is set as the loss function of the true friction torque. As shown in the following formula:

[0041] in, This is the predicted friction torque vector output by the feedforward neural network. This is the calculated true frictional torque vector.

[0042] The total loss function of the model is as follows: .

[0043] S5. Minimize the total loss function through an optimization algorithm, train the neural network, and identify the friction parameters.

[0044] Specifically, the structure of the physical information neural network for identifying friction parameters is as follows: Figure 2 As shown, the training iterations are set to 50,000 and the learning rate to 0.001, using the Xaiver initialization method and the Adam iterative optimization method. To illustrate the training process of the neural network, the computation process of a single neuron is taken as an example. For example, the first neuron... The first layer of a neural network The output of each neuron can be denoted as: , It can be calculated using the following formula:

[0045]

[0046] In the formula, Represents the input to the current neuron. The activation function representing the current neuron is, in this embodiment, the Tanh activation function is mainly selected. It represents from The -1st layer of the neural network The first neuron to the second The first layer of a neural network The transmission weights between neurons It represents the first The first layer of a neural network The deviation of each neuron. During the forward computation of the neural network, it is necessary to continuously adjust the weights and deviations in the neural network to continuously reduce the error between the output result and the target value.

[0047] Automatic differentiation techniques are used to calculate the derivative of the neural network output with respect to the input variables to satisfy the differential constraints in the Stribeck friction model. The corresponding weights and biases are then updated as follows:

[0048]

[0049] Finally, the loss function is minimized using optimization algorithms such as Adam or L-BFGS. This allows the neural network to be trained and the parameters of the friction model to be identified.

[0050] This embodiment integrates data-driven approaches with prior knowledge of physical laws. Its core lies in embedding constraints from physical equations into the structure of the neural network, which are embodied in the loss function during network training. Compared to traditional neural networks, this method not only learns the model from data but also ensures that the learned model obeys physical laws. During training, the symmetry, invariance, and conservation properties of the physical equations are automatically taken into account, thereby improving the model's accuracy and reliability.

[0051] In this embodiment, the identified parameters are compared with the set parameters to illustrate the identification effect.

[0052] This method is compared with Particle Swarm Optimization (PSO) and Genetic Algorithm (GA). When using PSO to identify parameters, the population size is set to 100, the number of iterations to 50,000, the learning factor to 1, the minimum values ​​to 0, and the maximum values ​​to [1, 1, 0.1, 0.1, 1, 1, 0.1, 0.1]. When using GA, the population size is set to 100, the number of iterations to 50,000, and the search boundary is the same as in PSO. The identification results are shown in the table below:

[0053] Among them, the identification curve is as follows Figure 3 As shown, Figure 4 , Figure 5 These represent the comparison between the physical information neural network's identified values ​​and the true values ​​during forward and reverse rotation, respectively. To quantitatively demonstrate the effectiveness of this method, the comparison results of three parameter identification methods are shown in the table above. The table shows that the maximum error rate of this method is 8.6233%, while the maximum error rates of the genetic algorithm and particle swarm optimization algorithm are 15.9732% and 17.2978%, respectively. Furthermore, the average error rate of this method is approximately 50% lower than that of the particle swarm optimization algorithm and the genetic algorithm, indicating that this method can accurately identify noisy data.

[0054] Example 2 It should be further explained that, based on the same inventive concept, this embodiment provides a friction parameter identification system based on a physical information neural network. When the system runs, it executes the method described in Embodiment 1, including the following modules: The physical properties building module is used to construct the dynamic equations and friction models of the robotic arm; The data acquisition module is used to enable the robotic arm to move according to the designed trajectory. It collects N sets of relevant simulation data of the robotic arm through sensors and calculates the corresponding real friction torque. The feedforward neural network module is used to construct a feedforward neural network that takes the joint velocity as input and outputs a predicted friction torque. The data obtained by the data acquisition module is used as the training set to complete the training of the feedforward neural network. The loss function construction module is used to initialize the robotic arm friction model with typical parameter values ​​and use them as the regularization term of the model; it constructs the loss function of the friction model, the loss function of the actual friction torque, and the total loss function of the model, respectively. The parameter identification module is used to train a neural network and identify friction parameters by minimizing the total loss function through an optimization algorithm.

[0055] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for identifying friction parameters based on a physical information neural network, characterized in that, Includes the following steps: S1. Construct the dynamic equations and friction model of the robotic arm; S2. Make the robotic arm move according to the designed trajectory, collect N sets of relevant simulation data of the robotic arm through sensors and calculate the corresponding real friction torque; S3. Construct a feedforward neural network that takes the joint velocity as input and outputs the predicted friction torque. Use the data obtained in step S2 as the training set to complete the training of the feedforward neural network. S4. Initialize the robotic arm friction model using typical parameter values ​​and use them as regularization terms for the model; The loss functions for the friction model and the actual friction torque, as well as the total loss function of the model, are constructed separately. S5. Minimize the total loss function through an optimization algorithm, train the neural network, and identify the friction parameters.

2. The friction parameter identification method based on physical information neural network according to claim 1, characterized in that, The construction of the dynamic equations for the robotic arm described in step S1 is specifically as follows: The dynamic equations of a robotic arm relate to joint torques, joint positions, angular velocities, and angular accelerations, and are expressed mathematically as follows: in, These are the vectors of the robotic arm joint angles, joint angular velocity, and joint angular acceleration, respectively. , , ; Here is the inertia matrix of the robotic arm. This is the velocity term matrix related to the centrifugal force and Coriolis force of the robotic arm. For gravity, Let the joint friction torque vector be... This is the joint torque vector.

3. The friction parameter identification method based on physical information neural network according to claim 2, characterized in that, Step S1, which involves constructing the friction model of the robotic arm, specifically includes: The Stribeck friction model is used to describe the frictional characteristics of the robotic arm joints. The mathematical expression of the Stribeck friction model is as follows: in, For joints i Frictional torque, i For joint serial numbers, i =1,2,3,...; ω represents the angular velocity of the robotic arm joints; Coulomb friction; This is the maximum static friction force; The threshold for Stribeck's velocity; It is the coefficient of viscous friction; Considering the inconsistency of friction model parameters when the robotic arm joints rotate in opposite directions, the forward and reverse friction models are as follows: The parameters that need to be identified are as follows: .

4. The friction parameter identification method based on physical information neural network according to claim 1, characterized in that, Step S2 includes the following steps: S21. Design the motion trajectory of the robotic arm, send the desired trajectory motion control command to the controller, and control the robotic arm to run according to the designed trajectory. S22. Collect joint torque information, position information and joint angular velocity information of the robotic arm during operation through sensors, and add 5% Gaussian noise; S23. Calculate the actual friction torque.

5. The friction parameter identification method based on physical information neural network according to claim 3, characterized in that, The calculation of the actual friction torque in step S23 specifically involves: The theoretical joint torque vector of the robotic arm is calculated based on the dynamic equation of the robotic arm. As shown in the following formula: The collected joint torque vectors of the robotic arm are Then the true friction torque vector The calculation is as follows: 。 6. The friction parameter identification method based on physical information neural network according to claim 3, characterized in that, The typical parameter values ​​mentioned in step S4 are as follows: The value is 0.15; The value is 0.60; The value is 0.05; The value is 0.02; The value is 0.20; The value is 0.70; The value is 0.05; The value is 0.

03.

7. The friction parameter identification method based on physical information neural network according to claim 6, characterized in that, The loss function for constructing the friction model described in step S4 is constructed as follows: The predicted friction torque output by the feedforward neural network The root mean square error between the frictional torque obtained from the Stribeck friction model and the frictional torque is set as the loss function of the friction model. As shown in the following formula: in, This is the predicted friction torque vector output by the feedforward neural network.

8. The friction parameter identification method based on a physical information neural network according to claim 6, characterized in that, The loss function for constructing the actual friction torque in step S4 is constructed as follows: The predicted friction torque output by the feedforward neural network Compared with the actual frictional torque The root mean square error between them is set as the loss function of the true friction torque. As shown in the following formula: in, This is the predicted friction torque vector output by the feedforward neural network. This is the calculated true frictional torque vector.

9. The friction parameter identification method based on a physical information neural network according to claim 8, characterized in that, The total loss function of the model described in step S4 is as follows: 。 10. A friction parameter identification system based on a physical information neural network, characterized in that, Includes the following modules: The physical properties building module is used to construct the dynamic equations and friction models of the robotic arm; The data acquisition module is used to enable the robotic arm to move according to the designed trajectory. It collects N sets of relevant simulation data of the robotic arm through sensors and calculates the corresponding real friction torque. The feedforward neural network module is used to construct a feedforward neural network that takes the joint velocity as input and outputs a predicted friction torque. The data obtained by the data acquisition module is used as the training set to complete the training of the feedforward neural network. The loss function building module is used to initialize the robotic arm friction model with typical parameter values ​​and use them as the regularization term of the model; The loss functions for the friction model and the actual friction torque, as well as the total loss function of the model, are constructed separately. The parameter identification module is used to train a neural network and identify friction parameters by minimizing the total loss function through an optimization algorithm.

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