Industrial robot dynamics and friction reconstruction method based on PINN

Abstract

A PINN-based industrial robot dynamics and friction reconstruction method comprises the following steps: constructing a robot excitation track and setting a robot excitation experiment in an off-line stage, and simultaneously collecting robot joint position data, speed data and current data in the process so as to construct a data set; the PINN model is used for carrying out mixed learning on a PINN model of robot dynamics modeling obtained by construction based on a Lagrange method and a PINN model of robot friction modeling obtained by construction based on a Coulomb viscosity model; in the online stage, the trained robot dynamics PINN model and the trained robot friction PINN model are adopted for real-time reasoning prediction, and the dynamics component and the friction component of the robot joint torque are obtained. According to the method, the modeling and prediction process of the joint torque of the industrial robot is remarkably simplified, the high-precision joint torque prediction effect can be achieved, and therefore the whole machine motion control performance of the industrial robot based on a kinetic model is improved.

Description

Technical Field

[0001] The present invention relates to a technology in the field of automated manufacturing, specifically to an industrial robot dynamics and friction reconstruction method based on physical information neural network (PINN). Background Art

[0002] At present, the dynamic model of industrial robots is widely used in specific scenarios such as robot controller design, motion planning with joint force / torque constraints, offline simulation, drag teaching, and disturbance observer design. Existing modeling technologies rely on cumbersome formula derivation and strict optimization constraints, and it is difficult to handle the strong nonlinear parts of joint torque that are difficult to linearize, such as nonlinear joint friction. Summary of the invention

[0003] The present invention aims at the insufficiency that the prior art cannot realize the dynamic modeling of industrial robots in specific task scenarios and cannot optimize the dynamic part and friction part in the dynamics of industrial robots. The present invention proposes a method for dynamic modeling of industrial robots based on physical information neural network, which considers the hybrid learning strategy of the dynamic part and friction part in the dynamics of robots. By constructing a physical information neural network, the Lagrangian dynamic modeling method of the robot is combined with the deep learning method. While introducing the powerful learning ability of the neural network for nonlinear characteristics, the physical constraints of the robot joint dynamics are strictly guaranteed. In addition, the modeling of nonlinear friction of the industrial robot joint is also considered simultaneously. Through the implementation of the present invention, the cumbersome derivation process of the traditional robot dynamic modeling method can be avoided, the modeling and prediction process of the joint torque of the industrial robot is significantly simplified, and the high-precision joint torque prediction effect can be achieved, thereby improving the whole machine motion control performance of the industrial robot based on the dynamic model.

[0004] The present invention is achieved through the following technical solutions:

[0005] The present invention relates to an industrial robot dynamics modeling method based on physical information neural network. In an offline stage, a robot excitation trajectory is constructed and a robot excitation experiment is set. At the same time, robot joint position data, speed data and current data are collected during the process to construct a data set, which is used for hybrid learning of a robot dynamics modeling PINN model constructed based on a Lagrangian method and a robot friction modeling PINN model constructed based on a Coulomb viscosity model. In an online stage, the trained robot dynamics PINN model and robot friction PINN model are used for real-time reasoning and prediction to obtain the dynamic component and friction component of the robot joint torque.

[0006] The present invention relates to a system for implementing the above method, comprising: a model construction unit, a hybrid learning unit and an online reasoning unit, wherein: the model construction unit establishes a robot dynamics model according to the robot Lagrangian dynamics, establishes a robot joint friction model according to the Coulomb viscosity friction model, and constructs a physical information neural network of robot dynamics and friction based on the model to obtain a corresponding network model; the hybrid learning unit designs a cyclic iterative hybrid learning strategy based on the robot dynamics model and the friction model, aiming at the difficult-to-distinguish dynamic components and friction components in the robot joint torque, thereby realizing high-precision learning and prediction of the two torque components; the online reasoning unit deploys the trained PINN network model to the robot control host computer to realize online reasoning and prediction of the robot joint torque. Technical Effects

[0007] The present invention builds a physical information neural network for robot dynamics modeling based on the Lagrangian method, replaces the partial differential derivation process of the Lagrangian method with a deep network layer based on chain calculation, and considers the physical feasibility constraints of the robot dynamics model in the design of the physical information neural network; then, under the unified physical information neural network framework, the modeling prediction of the nonlinear friction of the robot joint is introduced; finally, through a cyclic iterative hybrid learning strategy, the dynamic part and the friction part of the robot joint torque are synchronously learned to realize the overall dynamics modeling of the industrial robot joint torque. Compared with the prior art, the present invention ensures the physical constraints of the robot joint dynamics, can avoid the cumbersome derivation process of the traditional robot dynamics modeling method, greatly simplifies the modeling and prediction process of the industrial robot joint torque, and can achieve a high-precision joint torque prediction effect, thereby improving the whole machine motion control performance of the industrial robot based on the dynamic model. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Figure 1 It is a flow chart of the present invention;

[0009] Figure 2 It is a hardware framework diagram of an embodiment;

[0010] Figure 3 It is a schematic diagram of the network of the embodiment;

[0011] Figure 4 It is a flowchart of the algorithm of the embodiment;

[0012] Figures 5 to 10 This is a model verification diagram for the embodiment. DETAILED DESCRIPTION

[0013] like Figure 1 As shown, this embodiment relates to a dynamic modeling method of an industrial robot based on a physical information neural network, comprising:

[0014] Step 1: Construct and optimize the robot motion excitation trajectory, including:

[0015] 1.1) The fifth-order Fourier series form is used to generate the excitation trajectory of the robot motion, specifically: Where: N = 5 is the order of the selected Fourier series, i = 1, 2, ..., 6, a i,k and b i,k is the coefficient of the kth trigonometric function of the ith joint, q i,0 is a constant term to ensure that the trajectory can satisfy the initial position and velocity constraints. f is the fundamental frequency of the excitation trajectory. t is the time.

[0016] The excitation trajectory in the form of a fifth-order Fourier series is multi-order differentiable, and it is easy to obtain analytical expressions for velocity and acceleration, and the flexibility effect of the robot can be avoided by designing the frequency range.

[0017] 1.2) Using the Patternsearch toolbox in MATLAB, the robot motion trajectory is further optimized through the method of constraint condition number to cover more motion states. Specifically, under the constraints of the robot joint's extreme position constraints, velocity constraints, acceleration constraints, and the initial velocity being zero, the optimization algorithm in Patternsearch is used to obtain the excitation trajectory with the minimum observation matrix condition number. This shows that the trajectory is more general and covers more motion states.

[0018] Step 2: Conduct a robot excitation experiment to collect the robot joint position, speed and current data, and calculate the current estimated torque of each joint of the robot based on the current, including:

[0019] 2.1) Setup Figure 2 The robot shown executes the excitation trajectory generated in step 1, uses the robot joint end encoder to collect the position and speed information of each joint of the robot, and uses the robot joint driver feedback to obtain the driving current signal of each joint of the robot.

[0020] 2.2) Calculate the current estimated torque τ of each joint of the robot est_j =k j r j I j , where: I j is the driving current of each joint of the robot, k j is the motor torque constant of each joint, r j is the transmission ratio coefficient of each joint, τ est_j Estimate the torque for each joint current. k j and r j The value is provided by the robot manufacturer or identified by the robot itself.

[0021] Step 3: filter the data collected in step 2 and divide the data set, including:

[0022] 3.1) First, the robot joint position data, velocity data and current estimated torque collected in step 2 are processed by mean filtering, and then the robot joint velocity data is further filtered by a fifth-order Butterworth low-pass filter and differentiated to obtain the acceleration information of each joint.

[0023] 3.2) The robot joint position, velocity, acceleration and current estimated torque after two filtering are used as the data set for robot dynamics modeling and PINN network training, and are divided into training set, validation set and test set according to the ratio of 6:2:2.

[0024] Step 4: Based on the Lagrangian method, construct Figure 3 The PINN model of robot dynamics modeling shown in the figure specifically includes:

[0025] 4.1) According to the Lagrangian method, the second-order ordinary differential equation of the robot rigid body dynamics model can be derived: Where: q, are the robot joint angles, velocities and accelerations respectively, M(q) is the robot’s mass matrix, is the force generated by the centripetal force and the Coriolis force, G(q) = dV / dq is the gravity, τ dyn is the dynamic torque of each joint of the robot.

[0026] 4.2) Use PINN to learn the various parts of the dynamic model: decompose the robot's mass matrix M(q) into M(q) = L(q)L T (q), where L(q) is a lower triangular matrix, and the network calculates M(q) and G(q) as in: represents the network prediction value of L(q), θ is the corresponding network parameter, represents the network prediction value of G(q), ψ is the corresponding network parameter, represents the network prediction value of M(q); the optimization problem of the PINN network training in the dynamics part is: in: The constraints are Represents the inverse dynamics model of the robot, that is, through the joint angle, velocity and acceleration q, And network parameters θ, ψ calculate the predicted value of dynamic torque Represents the loss function of the PINN network. The lower triangular matrix can be further decomposed into L(q)=Lo (q)+L d (q), where L o (q) represents the off-diagonal elements, L d (q) represents the diagonal elements. In order to ensure the positive diagonal of L(q) and the positive eigenvalue of M(q), L d The network output layer of (q) uses a non-negative activation layer (such as ReLu), while L o The network output layer of (q) can use a linear activation layer.

[0027] 4.3) For the robot dynamics model that requires partial differential solutions Item, then the PINN network is used for chain calculation to obtain: in: Can be Therefore, the robot inverse dynamics model All derivatives contained in can be calculated in closed form, so the dynamic torque of the robot can be obtained

[0028] Step 5: Construct a PINN model for robot friction modeling based on the Coulomb viscosity model, specifically: Where: τ fri represents the friction component of the robot's joint torque, f ci , f vi and f bi They represent the Coulomb friction coefficient, viscous friction coefficient and friction bias constant of the robot's i-th joint. sign(·) represents the sign function and represents the O zero matrix. K f represents the friction coefficient matrix, W f represents the friction model matrix.

[0029] Step 6: Figure 4 The hybrid learning strategy of the robot dynamics model and friction model shown in the figure includes:

[0030] 6.1 Train the dynamics part and the friction part at the same time to obtain the dynamic torque And the friction torque prediction value in: and Represent the prediction results of the dynamic model and friction model, PINN dyn (·) and PINN fri (·) represents the PINN network model of the robot dynamics part and the friction part respectively; the loss function of the network

[0031] 6.2 Error back propagation, and update the network parameters of the dynamics and friction models. Repeat multiple times until the loss function converges.

[0032] 6.3 Freeze the friction network parameters and only train the dynamics part to obtain the dynamic torque And the friction torque prediction value Among them: PINN fri_frozen (·) represents the PINN network friction model where the robot is frozen and its network parameters are no longer updated; the network loss function is

[0033] 6.4 Error is propagated backwards and the network parameters of the dynamic model are updated. Repeat multiple times until the Loss function converges.

[0034] 6.5 Alternately execute steps 6.1 to 6.4 to form the inner loop of the hybrid learning strategy of the robot dynamics model and friction model, training N E generation.

[0035] 6.6 After the inner loop training is completed, continue to freeze the friction parameters and only train the dynamics part. The training method is consistent with the inner loop until the Loss function converges and the entire PINN network training is completed.

[0036] Step 7: Train the PINN model for hybrid modeling of robot dynamics and friction. Specifically, the data set required for network training is obtained based on step 3. The network input is the joint angle q, the joint velocity Joint acceleration and the joint current estimated torque τ est The network output is the prediction result based on the dynamic model and friction model based on the PINN network. and Get the total joint torque The loss function for training is: Where: N is the number of samples in the data set, τ est_ij is the current estimated torque value of the robot's ith joint at the jth time point, is the PINN network prediction value of the dynamic torque of the robot's ith joint at the jth time point, is the PINN network prediction value of the friction torque of the robot's i-th joint after compensation at the j-th time point. This loss function reflects the mean of the symmetric mean absolute percentage error (SMAPE) of the torque of each joint of the robot.

[0037] Step 8: Verify the effectiveness of the robot PINN modeling method on the test track: Select the validation set from the data set generated in step 3, and use the trained PINN dynamics and friction hybrid model to predict the joint torque of the robot. The prediction results and residual values ​​are shown in Figure 5-Figure 10The verification results show that the torque values ​​of the six joints of the robot are predicted with high accuracy, which is better than the existing methods based on dynamic parameter identification and data-driven dynamic modeling methods.

[0038] like Figure 2 As shown, the environment setting of this embodiment includes: a system control module and a robot body execution module, wherein: the system control module includes a host computer, a Beckhoff industrial PC, an EtherCAT communication bus and a robot control cabinet. The host computer designs the robot motion trajectory and imports it into the Beckhoff industrial PC, and then sends it to the robot control cabinet through the EtherCAT communication bus to control the robot body to move according to the command trajectory; the robot body execution module includes a servo motor and a robot body. The robot selected in this embodiment is an independently developed industrial robot, and its six joints are all rotary joints. The servo motor and the driver are selected from the Panasonic MINAS A6 series. Based on the real-time PLC kernel of the Beckhoff industrial PC, the system can collect the status information of the servo motor at a maximum frequency of 20Khz. During the movement of the robot body, the joint data is collected at the same time, fed back to the host computer and stored as the training trajectory data for robot dynamics modeling and PINN network learning.

[0039] After specific actual experiments, under the above hardware environment settings, the training batch size of the network of the present invention is set to 50, the learning rate is set to 5e-4, and Adam is used as the optimizer. Finally, the RMSE values ​​of the torque prediction errors of each joint of the robot are: 6.4048N·m, 12.7397N·m, 3.911N·m, 1.5428N·m, 0.8337N·m, and 0.5016N·m. Among them, RMSE is the root mean square error.

[0040] Compared with the prior art, this method reduces the torque prediction error of each joint of the above-mentioned robot, achieves a higher-precision joint torque prediction effect, and thus improves the overall motion control performance of the industrial robot based on the dynamics model.

[0041] The above-mentioned specific implementation can be partially adjusted in different ways by those skilled in the art without departing from the principle and purpose of the present invention. The protection scope of the present invention shall be based on the claims and shall not be limited by the above-mentioned specific implementation. Each implementation scheme within its scope shall be subject to the constraints of the present invention.

Claims

1. A PINN-based industrial robot dynamics and friction reconstruction method, characterized in that: In the offline stage, the robot excitation trajectory is constructed and the robot excitation experiment is set up. At the same time, the robot joint position data, velocity data and current data are collected during the process to construct a data set for hybrid learning of the PINN model of robot dynamics modeling constructed based on the Lagrangian method and the PINN model of robot friction modeling constructed based on the Coulomb viscosity model. In the online stage, the trained robot dynamics PINN model and robot friction PINN model are used for real-time reasoning and prediction to obtain the dynamic component and friction component of the robot joint torque.

2. The PINN-based industrial robot dynamics and friction reconstruction method according to claim 1 is characterized in that: The construction and optimization of the excitation trajectory of the robot movement specifically includes: 1.1) The fifth-order Fourier series form is used to generate the excitation trajectory of the robot motion, specifically: Where: N = 5 is the order of the selected Fourier series, i = 1, 2, ..., 6, a i,k and b i,k is the coefficient of the kth trigonometric function of the ith joint, q i,0 is a constant term to ensure that the trajectory can satisfy the initial position and velocity constraints, w f is the fundamental frequency of the excitation trajectory, t is the time; 1.2) Using the Patternsearch toolbox in MATLAB, the robot motion trajectory is further optimized through the method of constraint condition number to cover more motion states. Specifically, under the constraints of the robot joint's extreme position constraints, velocity constraints, acceleration constraints, and the initial velocity of zero, the optimization algorithm in Patternsearch is used to obtain the excitation trajectory with the minimum observation matrix condition number.

3. The PINN-based industrial robot dynamics and friction reconstruction method according to claim 1 is characterized in that: The current estimated torque of each joint of the robot is obtained by the following method: 2.1) Set the robot to execute the excitation trajectory generated in step 1, use the robot joint end encoder to collect the position and speed information of each joint of the robot, and use the robot joint driver feedback to obtain the driving current signal of each joint of the robot; 2.2) Calculate the current estimated torque τ of each joint of the robot est_j =k j r j I j , where: I j is the driving current of each joint of the robot, k j is the motor torque constant of each joint, r j is the transmission ratio coefficient of each joint, τ est_j The current estimated torque for each joint, k j and r j The value is provided by the robot manufacturer or identified by the robot itself.

4. The PINN-based industrial robot dynamics and friction reconstruction method according to claim 1 is characterized in that: The data set is obtained in the following way: 3.1) First, the collected robot joint position data, velocity data and current estimated torque are processed by mean filtering, and then the robot joint velocity data is further filtered by a fifth-order Butterworth low-pass filter and differentiated to obtain the acceleration information of each joint; 3.2) The robot joint position, velocity, acceleration and current estimated torque after two filtering are used as the data set for robot dynamics modeling and PINN network training, and are divided into training set, validation set and test set.

5. The PINN-based industrial robot dynamics and friction reconstruction method according to claim 1 is characterized in that: The PINN model of the robot dynamics modeling is obtained in the following way: 4.1) The second-order ordinary differential equation of the robot rigid body dynamics model is derived according to the Lagrangian method Where: q, are the robot joint angles, velocities and accelerations respectively, M(q) is the robot’s mass matrix, is the force generated by the centripetal force and the Coriolis force, G(q) = dV / dq is the gravity, τ dyn is the dynamic torque of each joint of the robot; 4.2) Use PINN to learn the various parts of the dynamic model: decompose the robot's mass matrix M(q) into M(q) = L(q)L T (q), where L(q) is a lower triangular matrix, and the network calculates M(q) and G(q) as in: represents the network prediction value of L(q), θ is the corresponding network parameter, represents the network prediction value of G(q), ψ is the corresponding network parameter, represents the network prediction value of M(q); the optimization problem of the PINN network training in the dynamics part is: in: The constraints are Represents the inverse dynamics model of the robot, that is, through the joint angle, velocity and acceleration q, And network parameters θ, ψ calculate the predicted value of dynamic torque l represents the loss function of the PINN network, which is further decomposed into L(q)=L for the lower triangular matrix o (q)+L d (q), where L o (q) represents the off-diagonal elements, L d (q) represents the diagonal elements. In order to ensure the positive diagonal of L(q) and the positive eigenvalue of M(q), L d The network output layer of (q) uses a non-negative activation layer (such as ReLu), while L o (q) The network output layer can use a linear activation layer; 4.3) For the robot dynamics model that requires solving partial differentials Item, then the PINN network is used for chain calculation to obtain: in: Depend on The result is that, therefore, the robot inverse dynamics model All derivatives contained in are calculated in closed form, so the dynamic torque of the robot is obtained 6. The PINN-based industrial robot dynamics and friction reconstruction method according to claim 1 is characterized in that: The PINN model for robot friction modeling based on the Coulomb viscosity model is obtained by the following method: Where: τ fri represents the friction component of the robot's joint torque, f ci , f vi and f bi denote the Coulomb friction coefficient, viscous friction coefficient and friction bias constant of the robot's ith joint, sign(·) denotes a sign function, O denotes a zero matrix, K f represents the friction coefficient matrix, W f represents the friction model matrix.

7. The PINN-based industrial robot dynamics and friction reconstruction method according to claim 1 is characterized in that: The hybrid learning strategy specifically includes: 6.1 Train the dynamics part and the friction part at the same time to obtain the dynamic torque And the friction torque prediction value in: and Represent the prediction results of the dynamic model and the friction model, PINN dyn (·) and PINN fri (·) represents the PINN network model of the robot dynamics part and the friction part respectively; the loss function of the network 6.2 Error back propagation, and update the network parameters of the dynamics and friction models, multiple iterations until the Loss function converges; 6.3 Freeze the friction network parameters and only train the dynamics part to obtain the dynamic torque And the friction torque prediction value Among them: PINN fri_frozen (·) represents the PINN network friction model where the robot is frozen and its network parameters are no longer updated; the network loss function is 6.4 Error is propagated backwards and the network parameters of the dynamic model are updated, and multiple iterations are performed until the Loss function converges; 6.5 Alternately execute steps 6.1 to 6.4 to form the inner loop of the hybrid learning strategy of the robot dynamics model and friction model, training N E generation; 6.6 After the inner loop training is completed, continue to freeze the friction parameters and only train the dynamics part. The training method is consistent with the inner loop until the Loss function converges and the entire PINN network training is completed.

8. The PINN-based industrial robot dynamics and friction reconstruction method according to claim 1 or 7, characterized in that: Based on the data set required for network training, the network input is the joint angle q, joint velocity Joint acceleration and the joint current estimated torque τ est The network output is the prediction result based on the dynamic model and friction model based on the PINN network. and Get the total joint torque The loss function for training is: Where: N is the number of samples in the data set, τ est_ij is the current estimated torque value of the robot's ith joint at the jth time point, is the PINN network prediction value of the dynamic torque of the robot's ith joint at the jth time point, is the PINN network predicted value of the compensated friction torque of the i-th joint of the robot at the j-th time point. The loss function reflects the mean of the symmetric mean absolute percentage error (SMAPE) of the torque of each joint of the robot.

9. A PINN-based industrial robot dynamics and friction reconstruction system for implementing any of the methods described in claims 1-8, characterized in that: include: Model building unit, hybrid learning unit and online reasoning unit, among which: the model building unit establishes the robot dynamics model according to the robot Lagrangian dynamics, establishes the robot joint friction model according to the Coulomb viscosity friction model, and builds the physical information neural network of the robot dynamics and friction based on the model to obtain the corresponding network model; the hybrid learning unit, based on the robot dynamics model and friction model, designs a cyclic iterative hybrid learning strategy for the difficult-to-distinguish dynamic components and friction components in the robot joint torque, and realizes high-precision learning and prediction of the two torque components; The online reasoning unit deploys the trained PINN network model to the robot control host computer to realize the online reasoning and prediction of the robot's joint torque.

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