Method for predicting robot joint friction based on improved PINN principle and LuGre model

Abstract

The invention belongs to the technical field of six-axis robots, and discloses a method for predicting robot joint friction based on an improved PINN principle and a LuGre model, and the method specifically comprises the following steps: 1, generating a robot excitation track, and collecting the positions, speeds and currents of six joints of a robot; 2, current estimation torque of each joint of the robot is calculated according to the current, and a friction force-speed-displacement mapping of the joints of the robot is obtained; 3, constructing a friction model of the robot based on the improved PINN principle and the LuGre model; and 4, designing a double-neural network learning strategy of the robot friction model. According to the method, the improved physical information neural network PINN and the LuGre model are fused, the multi-joint coupling effect of the six-axis robot and the friction characteristic in the full-speed range can be considered at the same time, accurate prediction of the joint friction force of the six-axis robot is achieved, the prediction precision is improved, and the prediction efficiency is improved. And the problem of physical information loss caused by model simplification is also avoided.

Description

Technical Field

[0001] This invention belongs to the field of six-axis robot technology, specifically a method for predicting robot joint friction based on the improved PINN principle and LuGre model. Background Technology

[0002] With the rapid development of industrial automation and intelligent manufacturing, six-axis robots, as key production equipment, are widely used in precision assembly, material handling and other scenarios. However, the motion accuracy and stability of six-axis robots are easily affected by joint friction, leading to problems such as low-speed crawling, oscillation and positioning deviation, which in turn reduces production efficiency and product quality.

[0003] In the field of industrial robots, friction modeling and identification has always been a key technical challenge. The traditional Coulomb-viscous friction model is widely used due to its simple structure, but it cannot accurately describe the large error problem in the robot's start-up and stop phases. Researchers have proposed ways to improve friction models, among which the LuGre model stands out due to its advantages in describing pre-slip, Stribeck effect, and hysteresis effect. Early studies mostly adopted a two-step identification method: the first step is steady-state parameter identification, which involves conducting multiple sets of experiments at different speeds during steady-state uniform motion to identify steady-state parameters related to the Stribeck curve; the second step is dynamic parameter identification, which uses a driving torque much smaller than the starting resistance to put the system in a pre-slip state and complete the identification of dynamic parameters (i.e., bristle stiffness and damping coefficient). Researchers have designed specific experiments to first obtain steady-state friction parameters by fitting them using the least squares method under uniform motion, and then obtain dynamic parameters by fitting them using the transfer function parameter in the pre-slip state. However, this method is experimentally complex and has high requirements for experimental equipment and operation, making it difficult to apply widely. Summary of the Invention

[0004] The purpose of this invention is to provide a method for predicting robot joint friction based on the improved PINN principle and LuGre model, so as to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for predicting robot joint friction based on the improved PINN principle and LuGre model, the specific steps of which are as follows:

[0006] Step 1:

[0007] Generate the robot's excitation trajectory and collect the position, velocity, and current of the robot's six joints;

[0008] Step Two:

[0009] The torque is estimated by calculating the current of each joint of the robot, and the mapping of robot joint friction force-velocity-displacement is obtained.

[0010] Step 3:

[0011] Construct a friction model for a robot based on the improved PINN principle and the LuGre model;

[0012] Step Four:

[0013] Design a dual neural network learning strategy for a robot friction model;

[0014] Step 5:

[0015] Training and validation of a robot friction model based on the improved PINN principle.

[0016] As a preferred technical solution of the present invention, when collecting the position, speed, and current of the six joints of the robot in step one, the corresponding sampling time, maximum angular displacement, maximum angular velocity, and maximum angular acceleration are set according to the limit requirements of the angular displacement, angular velocity, and angular acceleration of each joint of the robot. A sine curve is selected as the excitation trajectory source of the robot, and its periodic characteristics drive the joint movement, covering different speed and acceleration scenarios. The sine curve function is as follows:

[0017]

[0018] In the formula, t represents the sampling time; q max Indicates the maximum angular displacement; Indicates the maximum angular velocity; This represents the maximum angular acceleration.

[0019] As a preferred embodiment of the present invention, in step two, when calculating the torque of each joint of the robot based on the current, the torque of each joint of the robot is estimated by using the motor current and torque constant, and is used as an approximation of the motor torque. The specific calculation formula is as follows:

[0020] T=K T ·I

[0021] In the formula, I represents the motor current; k T T represents the torque constant; T represents the estimated torque of the current at each joint of the robot.

[0022] As a preferred embodiment of the present invention, the method for calculating the robot joint friction force in step two is as follows: based on the robot dynamics equation, the friction torque is separated by subtracting the motor torques of the forward and reverse movements. The expression for the robot dynamics equation is:

[0023]

[0024] In the formula, M(q) represents the inertia matrix; G(q) represents the Coriolis force and centrifugal force matrix; G(q) represents the gravity matrix; F f Indicates frictional torque;

[0025]

[0026] The separated frictional torque F f The angular displacement q and time t at corresponding time points are stored to construct a data mapping relationship. The complete data is divided into two parts: a training set and a validation set. The training set data is specifically used for the training of the PINN neural network, while the validation set is used to test the prediction performance of the PINN neural network.

[0027] As a preferred embodiment of the present invention, the LuGre model described in step three is:

[0028]

[0029] In the formula, F f σ0 represents the joint friction torque; σ0 represents the bristle stiffness coefficient, reflecting the ease with which the bristles deform under stress; σ1 represents the sliding damping coefficient; σ2 represents the viscous friction coefficient, describing the linear relationship between frictional force and relative velocity; z represents the average deformation of the bristles. Indicates the speed of hair deformation;

[0030] The intrinsic relationship between bristle deformation and its velocity is explained by the following differential equation:

[0031]

[0032] It is a key nonlinear function in the LuGre model, responsible for simulating the smooth transition from static to kinetic friction. It mainly describes the Stribeck friction characteristics, and its specific expression is:

[0033]

[0034] In the formula, F C F represents the Coulomb friction force, corresponding to the value of friction force during relative motion; S This represents the maximum static friction force, which is reached at the instant when the object is stationary and about to start. This represents the Stribeck characteristic velocity, which is the key velocity threshold that marks the transition of frictional characteristics from static friction to kinetic friction.

[0035] As a preferred technical solution of the present invention, the dual neural network learning strategy in step four includes a network initialization stage, a data preparation stage, a forward propagation stage, a loss calculation stage, a backpropagation and optimization stage, an iterative training stage, and a symbolic regression module stage.

[0036] As a preferred embodiment of the present invention, the PINN described in steps three and five adopts a dual-network structure, including an auxiliary network u(net) and a main network f(net). The auxiliary network u(net) has two hidden layers, each with 50 neurons and employing a hyperbolic tangent activation function. In addition, a physically customized layer is added, which focuses on training nonlinear functions. And the bristle stiffness coefficient σ0, which outputs the bristle deformation z and joint angular velocity. It not only optimizes parameters through gradient descent, but also ensures they fit the physical model. Therefore, a loss function is established. The output parameters of the auxiliary network u(net) are precisely controlled to ensure that they strictly follow the differential equation of the mane deformation.

[0037] As a preferred embodiment of the present invention, the input of the main network f(net) integrates the output of the auxiliary network u(net) and the mane deformation z and joint angular velocity. In addition, it includes the input variable time t of u(net), and its internal architecture is planned with 3 hidden layers, each containing 50 neurons and using the hyperbolic tangent activation function, and finally outputting the frictional torque F. f The loss of the main network f(net) includes the data loss and the ODE residual loss. It is used as the main loss of the PINN network. The two network parameters are optimized by backpropagation using gradient descent. After entering the iterative training phase, the forward propagation, loss calculation, backpropagation and optimization process are continuously repeated until the network meets the convergence condition.

[0038] As a preferred technical solution of the present invention, when training and validating the robot friction model based on the improved PINN principle in step five, the PINN network is iteratively trained using a friction recognition learning strategy driven by dual neural networks until the network converges; the validation set data is input into the well-trained PINN network to comprehensively evaluate the model's generalization ability and the accuracy of its prediction of physical phenomena, ensuring the reliability and effectiveness of the model in practical application scenarios.

[0039] The beneficial effects of this invention are as follows:

[0040] 1. This invention integrates the improved physical information neural network PINN and the LuGre model, which can simultaneously consider the multi-joint coupling effect of a six-axis robot and the friction characteristics across the entire speed range, thereby achieving accurate prediction of the joint friction force of a six-axis robot. This not only improves the prediction accuracy but also avoids the problem of physical information loss caused by model simplification, thus achieving a comprehensive improvement in the prediction accuracy of the joint friction force of a six-axis robot.

[0041] 2. The fusion model proposed in this invention has wider applicability and can adapt to different types of six-axis robots as well as various complex work tasks and motion trajectories. At the same time, the improved PINN can quickly learn and adapt to new data features during the training process, which greatly improves the training efficiency and prediction speed of the model, reduces the computational cost and time cost, and has more advantages in practical industrial applications, and can meet the real-time control and optimization needs of robots in different scenarios.

[0042] 3. By integrating physical information into the training process of the neural network, this invention enables the model to not only have a strong data fitting ability, but also to provide a deep understanding of the physical mechanism of friction. This makes the model more easily accepted and trusted by engineers and researchers in practical applications. In addition, the improved PINN has stronger robustness to data noise and model parameter changes, and can ensure stable friction force prediction in complex and ever-changing real-world environments. Attached Figure Description

[0043] Figure 1 This is a flowchart of the method of the present invention;

[0044] Figure 2 This is a flowchart of the friction identification steps driven by the dual neural network of the present invention;

[0045] Figure 3 This is a schematic diagram of the PINN network architecture of the present invention. Detailed Implementation

[0046] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and 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.

[0047] like Figures 1 to 3 As shown, this embodiment of the invention provides a method for predicting robot joint friction based on the improved PINN principle and the LuGre model. The specific steps are as follows:

[0048] Step 1:

[0049] Generate the robot's excitation trajectory and collect the position, velocity, and current of the robot's six joints;

[0050] Step Two:

[0051] The torque is estimated by calculating the current of each joint of the robot, and the mapping of robot joint friction force-velocity-displacement is obtained.

[0052] Step 3:

[0053] Construct a friction model for a robot based on the improved PINN principle and the LuGre model;

[0054] Step Four:

[0055] Design a dual neural network learning strategy for a robot friction model;

[0056] Step 5:

[0057] Training and validation of a robot friction model based on the improved PINN principle.

[0058] This method leverages the advantages of data-driven and physical models to improve the accuracy and adaptability of joint friction prediction in six-axis robots, while also enhancing the interpretability and robustness of the model, thus providing a more effective technical means to improve robot performance.

[0059] In step one, when collecting the positions, velocities, and currents of the robot's six joints, the sampling time, maximum angular displacement, maximum angular velocity, and maximum angular acceleration are set according to the limit requirements of the robot's angular displacement, angular velocity, and angular acceleration of each joint. A sine curve is selected as the robot's excitation trajectory source, using its periodic characteristics to drive joint motion, covering different speed and acceleration scenarios. The sine curve function is as follows:

[0060]

[0061] In the formula, t represents the sampling time; q max Indicates the maximum angular displacement; Indicates the maximum angular velocity; This represents the maximum angular acceleration.

[0062] By using a sine curve as the excitation trajectory source for the robot, the comprehensiveness and validity of the data can be ensured, thus providing a sound data foundation for subsequent calculations.

[0063] In step two, when calculating the torque of each joint of the robot based on the current, the estimated torque of each joint is calculated using the motor current and torque constant. This estimated torque is then used as an approximation of the motor torque. The specific calculation formula is as follows:

[0064] T=K T ·I

[0065] In the formula, I represents the motor current; K T T represents the torque constant; T represents the estimated torque of the current at each joint of the robot.

[0066] By calculating the torque of each joint of the robot using the motor current and torque constant, the ease of calculation can be improved.

[0067] The calculation method for robot joint friction in step two is as follows: Based on the robot dynamics equations, the friction torque is separated by subtracting the motor torques of the forward and reverse movements. The expression for the robot dynamics equations is:

[0068]

[0069] In the formula, M(q) represents the inertia matrix; G(q) represents the Coriolis force and centrifugal force matrix; G(q) represents the gravity matrix; F f Indicates frictional torque;

[0070]

[0071] The separated frictional torque F f The angular displacement q and time t at corresponding time points are stored to construct a data mapping relationship. The complete data is divided into two parts: a training set and a validation set. The training set data is specifically used for the training of the PINN neural network, while the validation set is used to test the prediction performance of the PINN neural network.

[0072] The inertia matrix only reflects the physical properties of the link, such as its mass, center of mass position, and moment of inertia, while the gravity matrix depends on the joint position and gravitational acceleration and is independent of the direction of motion. Therefore, the inertia matrix and gravity matrix will not change with the change of the direction of motion. Thus, by subtracting the joint torque of the reverse motion from the joint torque of the forward motion, the inertia matrix and gravity matrix will cancel each other out. However, the Coriolis force and centrifugal force matrices usually have nonlinear characteristics and cannot guarantee strict symmetrical cancellation when the velocities are reversed. However, they can be approximately ignored in cases of low speed and low precision requirements.

[0073] The LuGre model in step three is as follows:

[0074]

[0075] In the formula, F f σ0 represents the joint friction torque; σ0 represents the bristle stiffness coefficient, reflecting the ease with which the bristles deform under stress; σ1 represents the sliding damping coefficient; σ2 represents the viscous friction coefficient, describing the linear relationship between frictional force and relative velocity; z represents the average deformation of the bristles. Indicates the speed of hair deformation;

[0076] The intrinsic relationship between bristle deformation and its velocity is explained by the following differential equation:

[0077]

[0078] It is a key nonlinear function in the LuGre model, responsible for simulating the smooth transition from static to kinetic friction. It mainly describes the Stribeck friction characteristics, and its specific expression is:

[0079]

[0080] In the formula, F C F represents the Coulomb friction force, corresponding to the value of friction force during relative motion; S This represents the maximum static friction force, which is reached at the instant when the object is stationary and about to start. This represents the Stribeck characteristic velocity, which is the key velocity threshold that marks the transition of frictional characteristics from static friction to kinetic friction.

[0081] The LuGre model is a dynamic friction model that captures static friction, dynamic friction, and the transition between them by simulating the behavior of microscopic bristles. It can describe complex friction phenomena such as pre-slip, Stribeck effect, and hysteresis effect.

[0082] The dual neural network learning strategy in step four includes the network initialization stage, data preparation stage, forward propagation stage, loss calculation stage, backpropagation and optimization stage, iterative training stage, and symbolic regression module stage.

[0083] The dual neural network learning strategy is a learning method based on two neural networks (an auxiliary network and a main network). This strategy can make full use of the advantages of the two networks to achieve more accurate capture of physical phenomena.

[0084] In steps three and five, PINN employs a dual-network structure, consisting of an auxiliary network u(net) and a main network f(net). The auxiliary network u(net) has two hidden layers, each with 50 neurons and using a hyperbolic tangent activation function. Additionally, a physically customized layer is added, focusing on training the nonlinear function. And the bristle stiffness coefficient σ0, which outputs the bristle deformation z and joint angular velocity. It not only optimizes parameters through gradient descent, but also ensures they fit the physical model. Therefore, a loss function is established. The output parameters of the auxiliary network u(net) are precisely controlled to ensure that they strictly follow the differential equation of the mane deformation.

[0085] The auxiliary network u(net) is used to learn the nonlinear function and physical parameters, while the main network f(net) combines the output of the auxiliary network u(net) with other input variables to predict the friction torque.

[0086] The input of the main network f(net) integrates the output of the auxiliary network u(net) and the mane deformation z and joint angular velocity. In addition, it includes the input variable time t of u(net), and its internal architecture is planned with 3 hidden layers, each containing 50 neurons and using the hyperbolic tangent activation function, and finally outputting the frictional torque F. f The loss of the main network f(net) includes the data loss and the ODE residual loss. It is used as the main loss of the PINN network. The two network parameters are optimized by backpropagation using gradient descent. After entering the iterative training phase, the forward propagation, loss calculation, backpropagation and optimization process are continuously repeated until the network meets the convergence condition.

[0087] If the loss function value drops below a preset threshold or reaches the upper limit of the predetermined number of iterations, the friction torque F, which is well-trained by the PINN network, is eventually approximated by jointly learning physical data and constraining the LuGre equation. f The subsequent symbolic regression module utilizes the F output of the PINN network. f Data points are intelligently searched for potential mathematical structures and operator combinations to generate refined and accurate LuGre parsing expressions.

[0088] In step five, when training and validating the robot friction model based on the improved PINN principle, the PINN network is iteratively trained using a friction recognition learning strategy driven by dual neural networks until the network converges. The validation set data is then input into the well-trained PINN network to comprehensively evaluate the model's generalization ability and the accuracy of its predictions of physical phenomena, ensuring the model's reliability and effectiveness in real-world application scenarios.

[0089] During training, it is necessary to closely monitor the dynamics of the loss value on the training data in order to prevent potential problems such as overfitting in advance.

[0090] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0091] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for predicting robot joint friction based on the improved PINN principle and LuGre model, characterized in that, The specific steps are as follows: Step 1: Generate the robot's excitation trajectory and collect the position, velocity, and current of the robot's six joints; Step Two: The torque is estimated by calculating the current of each joint of the robot, and the mapping of robot joint friction force-velocity-displacement is obtained. Step 3: Construct a friction model for a robot based on the improved PINN principle and the LuGre model; Step Four: Design a dual neural network learning strategy for a robot friction model; Step 5: Training and validation of a robot friction model based on the improved PINN principle.

2. The method for predicting robot joint friction based on the improved PINN principle and LuGre model according to claim 1, characterized in that: In step one, when collecting the position, velocity, and current of the robot's six joints, the sampling time, maximum angular displacement, maximum angular velocity, and maximum angular acceleration are set according to the limit requirements of the robot's angular displacement, angular velocity, and angular acceleration of each joint. A sine curve is selected as the robot's excitation trajectory source, using its periodic characteristics to drive joint movement, covering different speed and acceleration scenarios. The sine curve function is as follows: In the formula, t represents the sampling time; q max Indicates the maximum angular displacement; Indicates the maximum angular velocity; This represents the maximum angular acceleration.

3. The method for predicting robot joint friction based on the improved PINN principle and LuGre model according to claim 1, characterized in that: In step two, when calculating the torque of each joint of the robot based on the current, the estimated torque of each joint is calculated using the motor current and torque constant. This estimated torque is then used as an approximation of the motor torque. The specific calculation formula is as follows: T=K T ·I In the formula, I represents the motor current; K T T represents the torque constant; T represents the estimated torque of the current at each joint of the robot.

4. The method for predicting robot joint friction based on the improved PINN principle and LuGre model according to claim 1, characterized in that: The method for calculating the robot joint friction force described in step two is as follows: Based on the robot dynamics equations, the friction torque is separated by subtracting the motor torques of the forward and reverse movements. The expression for the robot dynamics equations is: In the formula, M(q) represents the inertia matrix; G(q) represents the Coriolis force and centrifugal force matrix; G(q) represents the gravity matrix. F f Indicates frictional torque; The separated frictional torque F f The angular displacement q and time t at corresponding time points are stored to construct a data mapping relationship. The complete data is divided into two parts: a training set and a validation set. The training set data is specifically used for the training of the PINN neural network, while the validation set is used to test the prediction performance of the PINN neural network.

5. The method for predicting robot joint friction based on the improved PINN principle and LuGre model according to claim 1, characterized in that: The LuGre model mentioned in step three is: In the formula, F f σ0 represents the joint friction torque; σ0 represents the bristle stiffness coefficient, reflecting the ease with which the bristles deform under stress; σ1 represents the sliding damping coefficient; σ2 represents the viscous friction coefficient, describing the linear relationship between frictional force and relative velocity; z represents the average deformation of the bristles. Indicates the speed of hair deformation; The intrinsic relationship between bristle deformation and its velocity is explained by the following differential equation: It is a key nonlinear function in the LuGre model, responsible for simulating the smooth transition from static to kinetic friction. It mainly describes the Stribeck friction characteristics, and its specific expression is: In the formula, F C F represents the Coulomb friction force, corresponding to the value of friction force during relative motion; S This represents the maximum static friction force, which is reached at the instant when the object is stationary and about to start. This represents the Stribeck characteristic velocity, which is the key velocity threshold that marks the transition of frictional characteristics from static friction to kinetic friction.

6. The method for predicting robot joint friction based on the improved PINN principle and LuGre model according to claim 1, characterized in that: The dual neural network learning strategy described in step four includes the network initialization stage, data preparation stage, forward propagation stage, loss calculation stage, backpropagation and optimization stage, iterative training stage, and symbolic regression module stage.

7. The method for predicting robot joint friction based on the improved PINN principle and LuGre model according to claim 1, characterized in that: The PINN described in steps three and five employs a dual-network structure, consisting of an auxiliary network u(net) and a main network f(net). The auxiliary network u(net) has two hidden layers, each with 50 neurons and using a hyperbolic tangent activation function. In addition, a physically customized layer is added, focusing on training nonlinear functions. And the bristle stiffness coefficient σ0, its output bristle deformation z and joint angular velocity It not only optimizes parameters through gradient descent, but also ensures they fit the physical model. Therefore, a loss function is established. The output parameters of the auxiliary network u(net) are precisely controlled to ensure that they strictly follow the differential equation of the mane deformation.

8. The method for predicting robot joint friction based on the improved PINN principle and LuGre model according to claim 7, characterized in that: The input of the main network f(net) integrates the output of the auxiliary network u(net) and the mane deformation z and joint angular velocity. In addition, it includes the input variable time t of u(net), and the internal architecture is planned with 3 hidden layers, each containing 50 neurons and using the hyperbolic tangent activation function, and finally outputting the frictional torque F. f The loss of the main network f(net) includes the data loss and the ODE residual loss. It is used as the main loss of the PINN network. The two network parameters are optimized by backpropagation using gradient descent. After entering the iterative training phase, the forward propagation, loss calculation, backpropagation and optimization process are continuously repeated until the network meets the convergence condition.

9. The method for predicting robot joint friction based on the improved PINN principle and LuGre model according to claim 1, characterized in that: In step five, when training and validating the robot friction model based on the improved PINN principle, the PINN network is iteratively trained using a friction recognition learning strategy driven by dual neural networks until the network converges. The validation set data is then input into the well-trained PINN network to comprehensively evaluate the model's generalization ability and the accuracy of its predictions of physical phenomena, ensuring the model's reliability and effectiveness in real-world application scenarios.

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