Line-driven soft robot modeling method based on physical information neural network

Abstract

The invention discloses a line-driven soft robot modeling method based on a physical information neural network, and the method comprises the steps: measuring and recording the external force borne by a line-driven soft robot, obtaining the time-space coordinates of the line-driven soft robot, and carrying out the modeling of the line-driven soft robot through a data driving method based on physical information on the premise that the internal stress of a system model is difficult to analyze. A preset physical information neural network model is trained according to the partial differential equation containing model physical information, the borne external force and the space-time coordinate data, and estimated values of the space-time coordinate, the internal force, the internal torque, the speed and the angular speed of the line-driven soft robot are obtained; and obtaining a loss estimation function according to actual values of space-time coordinates, internal force, internal torque, speed, angular speed and unknown parameters obtained by experiments and an estimation value obtained by model training, and detecting the modeling accuracy. The space-time modeling of the line-driven soft robot is realized on the premise that the line-driven soft robot is difficult to measure data such as internal force and the like by utilizing known model physical information.

Description

Technical Field

[0001] The invention belongs to the technical field of robot modeling, and in particular relates to a line-driven soft robot modeling method based on physical information neural network. Background Art

[0002] Wire-driven soft robots are a hot research direction in the current field of robotics research. Wire-driven soft robots are mainly used for operations in limited space environments, which poses a challenge to achieving precise control. In order to achieve the reliability and operability of wire-driven soft robots in complex environments, it is first necessary to model the wire-driven soft robots in space and time, and the model is usually described by partial differential equations. Wire-driven soft robots are deformed by the pulling of multiple external cables, and their dynamic models usually need to consider complex factors such as multiple external forces, cable tension, and elastic response of flexible materials. Due to its highly nonlinear dynamic characteristics, traditional rigid robot modeling methods are difficult to effectively describe its behavior. The use of conventional finite element or numerical simulation technology will result in large amounts of calculation and poor real-time performance, especially in complex tasks with multiple degrees of freedom. It is difficult to achieve fast and precise control. Data-driven modeling methods can theoretically be applied to wire-driven soft robot modeling tasks, but their models are uncertain, have low interpretability, and have difficulty in obtaining high-quality training data. Therefore, it is urgent to develop a wire-driven soft robot modeling method that integrates physical information and data-driven. A schematic diagram of the principle of a wire-driven soft robot is shown in the figure. Figure 1 shown. Summary of the invention

[0003] In view of the above technical problems, the present invention provides a wire-driven soft robot modeling method based on physical information neural network.

[0004] The technical solution adopted by the present invention to solve the technical problem is:

[0005] A method for modeling a wire-driven soft robot based on a physical information neural network, the method comprising the following steps:

[0006] S100: Measure and record the external force data applied to the wire-driven soft robot, obtain the space-time coordinates of the wire-driven soft robot through visual perception or simulation experiments, obtain the actual values ​​of the internal force, internal torque, speed, angular velocity and unknown parameters of the partial differential equation through simulation experiments, and express the external force data and space-time coordinates in the form required by the model;

[0007] S200: Cosserat theory is used to analyze the line-driven soft robot. The kinematic analysis of the soft robot is carried out through Euler description and Lagrangian description, and the motion equation and momentum conservation equation are constructed. The partial differential equation group containing physical information is calculated by combining the constitutive equation;

[0008] S300: using a data-driven method based on physical information, constructing a physical information loss function according to a group of partial differential equations, constructing a data-driven loss function according to the actual values ​​of the spatiotemporal coordinates of the line-driven soft robot, training a preset physical information neural network according to the loss function and external force data, and obtaining estimated values ​​of the spatiotemporal coordinates, internal force, internal torque, velocity, angular velocity, and unknown parameters of the line-driven soft robot;

[0009] S400: Obtain a physical state loss estimation function according to the actual and estimated values ​​of the spatiotemporal coordinates, internal forces, internal torques, speeds, and angular velocities of the wire-driven soft robot; obtain an unknown parameter loss estimation function according to the actual values ​​of the unknown parameters of the equation and the estimated values ​​of the unknown parameters of the equation; and evaluate the trained spatiotemporal model of the wire-driven soft robot according to the physical state loss estimation function and the unknown parameter loss estimation function.

[0010] Preferably, in S100, the external force data and the time-space coordinates are expressed in the form required by the model, specifically:

[0011] The original data of the spatial position R(t, s) of the central skeleton of the wire-driven soft robot and the external force F(t, s) are as follows:

[0012] t=[t1,…,t l ],s=[s1,…,s m ]

[0013]

[0014] Among them, t is the time coordinate, t∈[0,T], T is the simulation time, and there are l points in total after discretization. s is the arc length coordinate of the central skeleton of the line-driven soft robot, s∈[0,L], L is the total length of the central skeleton, and there are m points in total after discretization. is the spatial position matrix of the central skeleton of the wire-driven soft robot, Represents the component matrices in the three coordinate axis directions, F i 0 is the external force matrix, F1 0 、F2 0 、F3 0 Represent the component matrices in the three coordinate axis directions respectively;

[0015] The spatial position R(t, s) of the central skeleton of the wire-driven soft robot and the external force F(t, s) are expressed in the form required by the model, specifically:

[0016] R i =(R i (t1,s1)…R i (t1,s m ),Ri (t2,s1)…R i (t l ,s m )),i=1,2,3

[0017] F i =(F i (t1,s1)…F i (t1,s m ),F i (t2,s1)…F i (t l ,s m )),i=1,2,3.

[0018] Preferably, S200 includes:

[0019] S210: Based on the Kirchhoff-Love theory, construct the Euler and Lagrangian coordinate systems, and construct the equations of motion and momentum conservation equations of the line-driven soft robot without considering stretching and shearing;

[0020] S220: Based on the Cosserat theory, the constitutive equation is combined with the consideration of tension and shear to obtain a set of partial differential equations containing physical information and unknown parameters.

[0021] Preferably, the motion equation in S210 is specifically:

[0022]

[0023] Among them, R is the spatial position of the central skeleton of the wire-driven soft robot, v is the speed, and d j is the basis vector of the local coordinate system, Q is the rotation matrix for transforming between the local coordinate system and the global coordinate system, specifically Q = (d1, d2, d3) T ,ω L is the angular velocity expressed in the local coordinate system.

[0024] The momentum conservation equation is:

[0025]

[0026] Where ρ is the constant material density, A is the cross-sectional area, and κ L is the generalized curvature expressed in the local coordinate system, n L and τ L are the internal forces and internal moments expressed in the local coordinate system, F and c are the external forces and external moments, and I is the second area moment of inertia;

[0027] The partial differential equations in S220 are as follows:

[0028]

[0029] Where e is the local stretch or compression ratio relative to the initial reference shape, B is the bending stiffness matrix, S is the shear stiffness matrix, and σ L is the shear displacement expressed in the local coordinate system.

[0030] Preferably, S300 includes:

[0031] S310: Using a data-driven method based on physical information, the external force data corresponding to the space-time coordinates are spliced ​​and input into the neural network for training to obtain the space-time coordinates, internal force, internal torque, velocity, angular velocity and estimates of unknown parameters of the equation;

[0032] S320: During the neural network training process, after obtaining the estimated amount, perform corresponding automatic differentiation;

[0033] S330: Use the mean square error to construct the physical information loss function corresponding to the partial differential equation, and use the actual value and estimated value of the space-time coordinates to construct the data-driven loss function;

[0034] S340: Bring the estimated amount and the differential amount into the total loss function for solution;

[0035] S350: An optimization algorithm is used in neural network training to minimize the total loss function and then gradually adjust the model parameters through gradient descent to complete the model training.

[0036] Preferably, the input data after splicing in S310 is:

[0037]

[0038] Among them, there are l time sampling points, m spatial sampling points, and the input data C contains a total of l*m rows of data;

[0039] Output estimator of a neural network for:

[0040]

[0041]

[0042] in, is the estimated internal force, is the rotation matrix estimator, is the estimator of the expansion ratio, is the angular velocity estimate, is the internal moment estimator, is the linear velocity estimate, is the center skeleton spatial position estimate, is the generalized curvature estimator;

[0043] The differential obtained after solving in S320 is:

[0044]

[0045] Preferably, S330 is specifically:

[0046]

[0047] Among them, Loss pde1 , Loss pde2 , Loss pde3 , Loss pde4 are the physical information loss functions constructed according to the corresponding partial differential equations, It is a data-driven loss function;

[0048] The total loss function in S340 is specifically:

[0049]

[0050] Among them, Loss total is the total loss function, and a1, a2, a3, a4, and a5 are the weights of the corresponding loss functions.

[0051] Preferably, the physical state loss estimation function and the unknown parameter loss estimation function in S400 are specifically:

[0052]

[0053] Among them, Loss R , Loss v is the physical state loss estimation function, Loss Q 、Loss e , Loss estimation function for unknown parameters.

[0054] The above-mentioned method for spatiotemporal modeling of a wire-driven soft robot based on a physical information neural network measures and records the external force applied to the wire-driven soft robot, obtains the spatiotemporal coordinates of the wire-driven soft robot through visual perception or simulation experiments, and uses a data-driven method based on physical information to train the preset physical information neural network model according to the physical information loss function, the data-driven loss function and the external force applied, and obtains the estimated values ​​of the spatiotemporal coordinates, internal force, internal torque, speed and angular velocity of the wire-driven soft robot; obtains the loss estimation function according to the actual values ​​and estimated values ​​of the spatiotemporal coordinates, internal force, internal torque, speed, angular velocity and unknown parameters, and tests the accuracy of the modeling. The spatiotemporal modeling of the wire-driven soft robot is realized by using the known physical information of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 This is a schematic diagram of the principle of an in-line driven soft robot according to an embodiment of the present invention;

[0056] Figure 2 It is a flow chart of a method for modeling a wire-driven soft robot based on a physical information neural network in one embodiment of the present invention;

[0057] Figure 3 A schematic diagram of a data-driven method based on physical information in one embodiment of the present invention;

[0058] Figure 4 A schematic diagram of the external force acting on the linearly driven soft robot in one embodiment of the present invention;

[0059] Figure 5 The physical information neural network model outputs the spatial position in one embodiment of the present invention. The comparison diagram of the component in the x direction and the component in the x direction of the spatial position R collected by the simulation experiment;

[0060] Figure 6 is an error diagram of the component in the x direction of the training result of the spatial position R of the soft robot in one embodiment of the present invention;

[0061] Figure 7 The physical information neural network model outputs the spatial position in one embodiment of the present invention. The comparison diagram of the component in the z direction and the component in the z direction of the spatial position R collected by the simulation experiment;

[0062] Figure 8 is an error diagram of the component in the z direction of the training result of the spatial position R of the soft robot in one embodiment of the present invention;

[0063] Fig. 9 The physical information neural network model outputs the spatial position in one embodiment of the present invention. The comparison diagram of the component in the y direction and the component in the y direction of the spatial position R collected by the simulation experiment;

[0064] Fig.10 1 is an error diagram of the component in the y direction of the training result of the spatial position R of the soft robot in one embodiment of the present invention. DETAILED DESCRIPTION

[0065] In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings.

[0066] In one embodiment, Figure 2 As shown, a method for modeling a wire-driven soft robot based on a physical information neural network comprises the following steps:

[0067] S100: Measure and record the external force data applied to the wire-driven soft robot, obtain the space-time coordinates of the wire-driven soft robot through visual perception or simulation experiments, obtain the actual values ​​of the internal force, internal torque, speed, angular velocity and unknown parameters of the partial differential equation through simulation experiments, and express the external force data and space-time coordinates in the form required by the model;

[0068] S200: Cosserat theory is used to analyze the line-driven soft robot. The kinematic analysis of the soft robot is carried out through Euler description and Lagrangian description, and the motion equation and momentum conservation equation are constructed. The partial differential equation group containing physical information is calculated by combining the constitutive equation;

[0069] S300: using a data-driven method based on physical information, constructing a physical information loss function according to a group of partial differential equations, constructing a data-driven loss function according to the actual values ​​of the spatiotemporal coordinates of the line-driven soft robot, training a preset physical information neural network according to the loss function and external force data, and obtaining estimated values ​​of the spatiotemporal coordinates, internal force, internal torque, velocity, angular velocity, and unknown parameters of the line-driven soft robot;

[0070] S400: Obtain a physical state loss estimation function according to the actual and estimated values ​​of the spatiotemporal coordinates, internal forces, internal torques, speeds, and angular velocities of the wire-driven soft robot; obtain an unknown parameter loss estimation function according to the actual values ​​of the unknown parameters of the equation and the estimated values ​​of the unknown parameters of the equation; and evaluate the trained spatiotemporal model of the wire-driven soft robot according to the physical state loss estimation function and the unknown parameter loss estimation function.

[0071] Compared with other modeling methods, the method proposed in the present invention uses a data-driven method that integrates physical information. It only needs to know part of the information of the system model and uses visual perception methods or simulation experiments to realize the spatiotemporal modeling of line-driven soft robots under the premise that some model parameters are unknown.

[0072] In one embodiment, in S100, the external force data and the time-space coordinates are expressed in the form required by the model, specifically:

[0073] The original data of the spatial position R(t, s) of the central skeleton of the wire-driven soft robot and the external force F(t, s) are as follows:

[0074] t=[t1,…,t l ],s=[s1,…,s m ]

[0075]

[0076] Among them, t is the time coordinate, t∈[0,T], T is the simulation time, and there are l points in total after discretization. s is the arc length coordinate of the central skeleton of the line-driven soft robot, s∈[0,L], L is the total length of the central skeleton, and there are m points in total after discretization. is the spatial position matrix of the central skeleton of the wire-driven soft robot, Represents the component matrices in the three coordinate axis directions, F i 0 is the external force matrix, F1 0 、F2 0 、F3 0 Represent the component matrices in the three coordinate axis directions respectively;

[0077] The spatial position R(t, s) of the central skeleton of the wire-driven soft robot and the external force F(t, s) are expressed in the form required by the model, specifically:

[0078] R i =(R i (t1,s1)…R i (t1,s m ),R i (t2,s1)…R i (t n ,s m )),i=1,2,3

[0079] F i =(F i (t1,s1)…F i (t1,s m ),F i (t2,s1)…F i (tn ,s m )),i=1,2,3.

[0080] Specifically, the external force data is used as the input of the neural network, and the space-time coordinates, internal force, internal torque, velocity, angular velocity and unknown parameters of the equation are used as the output of the neural network.

[0081] In one embodiment, S200 includes:

[0082] S210: Based on the Kirchhoff-Love theory, construct the Euler and Lagrangian coordinate systems, and construct the equations of motion and momentum conservation equations of the line-driven soft robot without considering stretching and shearing;

[0083] S220: Based on the Cosserat theory, the constitutive equation is combined with the consideration of tension and shear to obtain a set of partial differential equations containing physical information and unknown parameters.

[0084] In one embodiment, the motion equation in S210 is specifically:

[0085]

[0086] Among them, R is the spatial position of the central skeleton of the wire-driven soft robot, v is the speed, and d j is the basis vector of the local coordinate system, Q is the rotation matrix for transforming between the local coordinate system and the global coordinate system, specifically Q = (d1, d2, d3) T ,ω L is the angular velocity expressed in the local coordinate system.

[0087] The momentum conservation equation is:

[0088]

[0089] Where ρ is the constant material density, A is the cross-sectional area, and κ L is the generalized curvature expressed in the local coordinate system, n L and τ L are the internal forces and internal moments expressed in the local coordinate system, F and c are the external forces and external moments, and I is the second area moment of inertia;

[0090] The partial differential equations in S220 are as follows:

[0091]

[0092] Where e is the local stretch or compression ratio relative to the initial reference shape, B is the bending stiffness matrix, S is the shear stiffness matrix, and σ L is the shear displacement expressed in the local coordinate system.

[0093] In one embodiment, S300 includes:

[0094] S310: Using a data-driven method based on physical information, the external force data corresponding to the space-time coordinates are spliced ​​and input into the neural network for training to obtain the space-time coordinates, internal force, internal torque, velocity, angular velocity and estimates of unknown parameters of the equation;

[0095] S320: During the neural network training process, after obtaining the estimated amount, perform corresponding automatic differentiation;

[0096] S330: Use mean square error to construct the physical information loss function corresponding to the partial differential equation, and the actual value of the space-time coordinates to construct the data-driven loss function;

[0097] S340: Bring the estimated amount and the differential amount into the total loss function for solution;

[0098] S350: An optimization algorithm is used in neural network training to minimize the total loss function and then gradually adjust the model parameters through gradient descent to complete the model training.

[0099] In one embodiment, the input data after splicing in S310 is:

[0100]

[0101] Among them, there are l time sampling points, m spatial sampling points, and the input data C contains a total of l*m rows of data;

[0102] Output estimator of a neural network for:

[0103]

[0104]

[0105] in, is the estimated internal force, is the rotation matrix estimator, is the estimator of the expansion ratio, is the angular velocity estimate, is the internal moment estimator, is the linear velocity estimate, is the center skeleton spatial position estimate, is the generalized curvature estimator;

[0106] The differential obtained after solving in S320 is:

[0107]

[0108] In one embodiment, S330 specifically includes:

[0109]

[0110] Among them, Loss pde1 , Loss pde2 , Loss pde3 , Loss pde4 are the physical information loss functions constructed according to the corresponding partial differential equations, It is a data-driven loss function;

[0111] The total loss function in S340 is specifically:

[0112]

[0113] Among them, Loss total is the total loss function, and a1, a2, a3, a4, and a5 are the weights of the corresponding loss functions.

[0114] Specifically, considering the characteristics of some state quantities of wire-driven soft robots that are difficult to measure and some model parameters that are unknown, a new data-driven method that integrates physical information is proposed for model training. The schematic diagram of this method is shown in the figure. Figure 3 shown.

[0115] In one embodiment, the physical state loss estimation function and the unknown parameter loss estimation function in S400 are specifically:

[0116]

[0117] Among them, Loss R , Loss v is the physical state loss estimation function, Loss Q 、Loss e , Loss estimation function for unknown parameters.

[0118] Specifically, the physical state loss estimation function and the unknown parameter loss estimation function are calculated by the mean squared error (MSE) to evaluate the spatiotemporal model of the wire-driven soft robot.

[0119] In a detailed embodiment, the present invention builds a wire-driven soft robot simulation experimental platform to collect spatial position data of the wire-driven soft robot. The experimental object is a wire-driven soft robot with one end fixed, whose length and cross-sectional radius are 3 meters and 0.25 meters respectively, and the density is 1000kg*m -3 , Young's modulus of elasticity is 10 6Pa, shear modulus is 10 4 Pa, in the experiment, the free end of the line-driven soft robot is subjected to a downward force of 10N, as shown in the schematic diagram Figure 4 shown.

[0120] Figure 5 , Figure 7 , Fig. 9 They respectively represent the comparison of the components of the training results of the spatial position R of the center skeleton of the wire-driven soft robot in the x, z, and y directions with the data collected from the simulation experiment. Figure 6 , Figure 8 , Fig.10 They respectively represent the errors of the components of the spatial position R of the central skeleton of the wire-driven soft robot in three directions. It can be seen that the data-driven method integrating physical information proposed in the present invention can better fit the model characteristics and establish the spatiotemporal model of the wire-driven soft robot.

[0121] Table 1 shows the comparison of the computational time of the line-driven soft robot modeling method based on the physical information neural network and the computational time of the improved finite difference simulation modeling method after the model training is completed. Five calculations are performed respectively and the calculation results are averaged. The modeling method proposed in the present invention shortens the calculation time by 30 times compared with the improved finite difference simulation modeling method.

[0122] Table 1 Comparison of calculation time of different modeling methods

[0123]

[0124] Compared with other modeling methods, the spatiotemporal modeling method of the wire-driven soft robot proposed in the present invention uses a data-driven method that integrates physical information, and only needs to know part of the position data and system model information. Compared with the improved finite difference simulation modeling method, the modeling method based on physical information neural network proposed in the present invention can effectively shorten the calculation time. The spatiotemporal coordinates are obtained by visual perception methods or simulation experiments, and the spatiotemporal modeling of the wire-driven soft robot is realized under the premise that some model parameters are unknown.

[0125] The above is a detailed introduction to a wire-driven soft robot modeling method based on a physical information neural network provided by the present invention. This article uses specific examples to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the core idea of ​​the present invention. It should be pointed out that for ordinary technicians in this technical field, without departing from the principles of the present invention, the present invention can also be improved and modified, and these improvements and modifications also fall within the scope of protection of the claims of the present invention.

Claims

1. A method for modeling a wire-driven soft robot based on a physical information neural network, characterized in that: The method comprises the following steps: S100: Measure and record the external force data applied to the wire-driven soft robot, obtain the space-time coordinates of the wire-driven soft robot through visual perception or simulation experiments, obtain the actual values ​​of the internal force, internal torque, speed, angular velocity and unknown parameters of the partial differential equation through simulation experiments, and express the external force data and space-time coordinates in the form required by the model; S200: Cosserat theory is used to analyze the line-driven soft robot. The kinematic analysis of the soft robot is carried out through Euler description and Lagrangian description, and the motion equation and momentum conservation equation are constructed. The partial differential equation group containing physical information is calculated by combining the constitutive equation; S300: using a data-driven method based on physical information, constructing a physical information loss function according to a group of partial differential equations, constructing a data-driven loss function according to the actual values ​​of the spatiotemporal coordinates of the line-driven soft robot, training a preset physical information neural network according to the loss function and external force data, and obtaining estimated values ​​of the spatiotemporal coordinates, internal forces, internal torques, velocities, angular velocities, and unknown parameters of the equations; S400: Obtain a physical state loss estimation function according to the actual and estimated values ​​of the spatiotemporal coordinates, internal forces, internal torques, speeds, and angular velocities of the wire-driven soft robot; obtain an unknown parameter loss estimation function according to the actual values ​​of the unknown parameters of the equation and the estimated values ​​of the unknown parameters of the equation; and evaluate the trained spatiotemporal model of the wire-driven soft robot according to the physical state loss estimation function and the unknown parameter loss estimation function.

2. The method according to claim 1, characterized in that In S100, the external force data and space-time coordinates are expressed in the form required by the model, specifically: The original data of the spatial position R(t, s) of the central skeleton of the wire-driven soft robot and the external force F(t, s) are as follows: t=[t1,…,t n ],s=[s1,…,s m ] Among them, t is the time coordinate, t∈[0,T], T is the simulation time, and there are l points in total after discretization. s is the arc length coordinate of the central skeleton of the line-driven soft robot, s∈[0,L], L is the total length of the central skeleton, and there are m points in total after discretization. is the spatial position matrix of the central skeleton of the wire-driven soft robot, Represent the component matrices in the three coordinate axis directions respectively, is the external force matrix, Represent the component matrices in the three coordinate axis directions respectively; The spatial position R(t, s) of the central skeleton of the wire-driven soft robot and the external force F(t, s) are expressed in the form required by the model, specifically: R i =(R i (t1,s1)…R i (t1,s m ),R i (t2,s1)…R i (t l ,s m )),i=1,2,3 F i =(F i (t1,s1)…F i (t1,s m ),F i (t2,s1)…F i (t l ,s m )),i=1,2,3。 3. The method according to claim 2, characterized in that S200 includes: S210: Based on the Kirchhoff-Love theory, construct the Euler and Lagrangian coordinate systems, and construct the equations of motion and momentum conservation equations of the line-driven soft robot without considering stretching and shearing; S220: Based on the Cosserat theory, the constitutive equation is combined with the consideration of tension and shear to obtain a set of partial differential equations containing physical information and unknown parameters.

4. The method according to claim 3, characterized in that The specific motion equation in S210 is: Among them, R is the spatial position of the central skeleton of the wire-driven soft robot, v is the speed, and d j is the basis vector of the local coordinate system, Q is the rotation matrix for transforming between the local coordinate system and the global coordinate system, specifically Q = (d1, d2, d3) T ,ω L is the angular velocity expressed in the local coordinate system. The momentum conservation equation is: Where ρ is the constant material density, A is the cross-sectional area, and κ L is the generalized curvature expressed in the local coordinate system, n L and τ L are the internal forces and internal moments expressed in the local coordinate system, F and c are the external forces and external moments, and I is the second area moment of inertia; The partial differential equations in S220 are as follows: Where e is the local stretch or compression ratio relative to the initial reference shape, B is the bending stiffness matrix, S is the shear stiffness matrix, and σ L is the shear displacement expressed in the local coordinate system.

5. The method according to claim 4, characterized in that S300 includes: S310: Using a data-driven method based on physical information, the external force data corresponding to the space-time coordinates are spliced ​​and input into the neural network for training to obtain the space-time coordinates, internal force, internal torque, velocity, angular velocity and estimates of unknown parameters of the equation; S320: During the neural network training process, after obtaining the estimated amount, perform corresponding automatic differentiation; S330: Use the mean square error to construct the physical information loss function corresponding to the partial differential equation, and use the actual value and estimated value of the space-time coordinates to construct the data-driven loss function; S340: Bring the estimated amount and the differential amount into the total loss function for solution; S350: An optimization algorithm is used in neural network training to minimize the total loss function and then gradually adjust the model parameters through gradient descent to complete the model training.

6. The method according to claim 5, characterized in that The input data after splicing in S310 is: Among them, there are l time sampling points, m spatial sampling points, and the input data C contains a total of l*m rows of data; Output estimator of a neural network for: in, is the estimated internal force, is the rotation matrix estimator, is the estimator of the expansion ratio, is the angular velocity estimate, is the internal moment estimator, is the linear velocity estimate, is the center skeleton spatial position estimate, is the generalized curvature estimator; The differential obtained after solving in S320 is:

7. The method according to claim 6, characterized in that S330 is specifically: Among them, Loss pde1 , Loss pde2 , Loss pde3 , Loss pde4 are the physical information loss functions constructed according to the corresponding partial differential equations, It is a data-driven loss function; The total loss function in S340 is specifically: Among them, Loss total is the total loss function, and a1, a2, a3, a4, and a5 are the weights of the corresponding loss functions.

8. The method according to claim 7, characterized in that The physical state loss estimation function and unknown parameter loss estimation function in S400 are specifically: Among them, Loss R , Loss v is the physical state loss estimation function, Loss Q 、Loss e , Loss estimation function for unknown parameters.

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