A physical information neural network-based wire-driven soft robot modeling method

Abstract

The application discloses a kind of line driving soft robot modeling methods based on physical information neural network, measure and record the external force suffered by line driving soft robot, obtain the space-time coordinates of line driving soft robot, under the premise that internal force is difficult to analyze in system model, utilize the data-driven method based on physical information, according to the partial differential equation containing the physical information of model, the external force and the space-time coordinate data of suffered force, the preset physical information neural network model is trained, and the estimated value of the space-time coordinates, internal force, internal moment, velocity, angular velocity of line driving soft robot is obtained;According to the actual value of space-time coordinates, internal force, internal moment, velocity, angular velocity, unknown parameter obtained by experiment and the estimated value obtained by model training, a loss estimation function is obtained, and the accuracy of modeling is detected. Using known model physical information, under the premise that internal force and other data of line driving soft robot are difficult to measure, the space-time modeling of line driving soft robot is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of robot modeling, and in particular relates to a line-driven soft robot modeling method based on a 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 designed for operations in confined 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 perform spatiotemporal modeling of the wire-driven soft robots, and their models are usually described by partial differential equations. Wire-driven soft robots are deformed by the pull 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 body robot modeling methods are difficult to effectively describe its behavior. The use of conventional finite element or numerical simulation techniques will result in large computational complexity 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, there is an urgent need 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 response to 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 spatiotemporal coordinates of the wire-driven soft robot through visual perception or simulation experiments, obtain the actual values ​​of the internal force, internal torque, velocity, angular velocity and unknown parameters of the partial differential equation through simulation experiments, and express the external force data and spatiotemporal coordinates in the form required by the model;

[0007] S200: Analyze the line-driven soft robot using Cosserat theory. Perform kinematic analysis of the soft robot using Euler and Lagrangian descriptions, construct equations of motion and momentum conservation equations, and combine constitutive equations to calculate a set of partial differential equations containing physical information.

[0008] S300: Using a data-driven method based on physical information, constructing a physical information loss function according to a set of partial differential equations, constructing a data-driven loss function according to the actual values ​​of the spatiotemporal coordinates of the wire-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 of the wire-driven soft robot;

[0009] S400: Obtain a physical state loss estimation function based on the actual and estimated values ​​of the spatiotemporal coordinates, internal forces, internal torques, velocities, and angular velocities of the wire-driven soft robot; obtain an unknown parameter loss estimation function based on 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 based on 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 central skeleton spatial position R(t,s) and the external force F(t,s) of the wire-driven soft robot are in the form of:

[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 Represents 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) it receives 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 motion equations and momentum conservation equations of wire-driven soft robots without considering stretching and shearing;

[0020] S220: Based on the Cosserat theory, the constitutive equations are 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, d j is the local coordinate system basis vector, Q is the rotation matrix for converting 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 force and internal moment expressed in the local coordinate system, F and c are the external force and external moment, and I is the second area moment of inertia;

[0027] The partial differential equations in S220 are specifically:

[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 estimates of the space-time coordinates, internal forces, internal torques, velocities, angular velocities, and unknown parameters of the equations;

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

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

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

[0035] S350: Use optimization algorithms in neural network training to minimize the total loss function and gradually adjust model parameters through gradient descent to complete 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 specifically includes:

[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, 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 aforementioned method for spatiotemporal modeling of a wire-driven soft robot based on a physical information neural network measures and records the external forces acting on the wire-driven soft robot. The robot's spatiotemporal coordinates are obtained through visual perception or simulation experiments. Given the difficulty of analyzing the forces acting within the system model, a data-driven approach based on physical information is used to train a pre-set physical information neural network model based on a physical information loss function, a data-driven loss function, and the external forces. This method then generates estimated values ​​for the spatiotemporal coordinates, internal forces, internal torques, velocity, and angular velocity of the wire-driven soft robot. A loss estimation function is then derived based on the actual and estimated values ​​of the spatiotemporal coordinates, internal forces, internal torques, velocity, angular velocity, and unknown parameters, and the accuracy of the modeling is then tested. Leveraging known physical information from the model, the spatiotemporal modeling of the wire-driven soft robot is achieved. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0056] Figure 2 This 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 Schematic diagram of the external force acting on the linearly driven soft robot according to 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 in the simulation experiment;

[0060] Figure 6 : is an error diagram of the x-direction component of the training result of the soft robot spatial position R 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 in 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] Figure 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 in the simulation experiment;

[0064] Figure 10 1 is an error diagram of the y-direction component of the training result of the soft robot spatial position R 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 with reference to the accompanying drawings.

[0066] In one embodiment, Figure 2 As shown, a wire-driven soft robot modeling method 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 spatiotemporal coordinates of the wire-driven soft robot through visual perception or simulation experiments, obtain the actual values ​​of the internal force, internal torque, velocity, angular velocity and unknown parameters of the partial differential equation through simulation experiments, and express the external force data and spatiotemporal coordinates in the form required by the model;

[0068] S200: Analyze the line-driven soft robot using Cosserat theory. Perform kinematic analysis of the soft robot using Euler and Lagrangian descriptions, construct equations of motion and momentum conservation equations, and combine constitutive equations to calculate a set of partial differential equations containing physical information.

[0069] S300: Using a data-driven method based on physical information, constructing a physical information loss function according to a set of partial differential equations, constructing a data-driven loss function according to the actual values ​​of the spatiotemporal coordinates of the wire-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 of the wire-driven soft robot;

[0070] S400: Obtain a physical state loss estimation function based on the actual and estimated values ​​of the spatiotemporal coordinates, internal forces, internal torques, velocities, and angular velocities of the wire-driven soft robot; obtain an unknown parameter loss estimation function based on 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 based on 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. It 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 central skeleton spatial position R(t,s) and the external force F(t,s) of the wire-driven soft robot are in the form of:

[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 Represents 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) it receives 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 motion equations and momentum conservation equations of wire-driven soft robots without considering stretching and shearing;

[0083] S220: Based on the Cosserat theory, the constitutive equations are 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, d j is the local coordinate system basis vector, Q is the rotation matrix for converting 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 force and internal moment expressed in the local coordinate system, F and c are the external force and external moment, and I is the second area moment of inertia;

[0090] The partial differential equations in S220 are specifically:

[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 estimates of the space-time coordinates, internal forces, internal torques, velocities, angular velocities, and unknown parameters of the equations;

[0095] S320: During the neural network training process, after obtaining the estimated value, 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 values ​​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: Use optimization algorithms in neural network training to minimize the total loss function and gradually adjust model parameters through gradient descent to complete 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, 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 wire-driven soft robots where some state quantities are difficult to measure and some model parameters are unknown, a new data-driven method integrating 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 Loss is the physical state loss estimation function. 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 using 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 a fixed end, a length and a cross-sectional radius of 3 meters and 0.25 meters respectively, and a density of 1000 kg*m -3 , Young's modulus of elasticity is 10 6Pa, shear modulus is 10 4 Pa, in the experiment, the free end of the linear drive soft robot is subjected to a downward force of 10N, as shown in the schematic diagram. Figure 4 shown.

[0120] Figure 5 、 Figure 7 、 Figure 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 by the simulation experiment, Figure 6 、 Figure 8 、 Figure 10 They respectively represent the errors of the components of the training results of the spatial position R of the central skeleton of the line-driven soft robot in three directions. It can be seen that the data-driven method of integrating physical information proposed in the present invention can better fit the model characteristics and establish a spatiotemporal model of the line-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 were performed respectively and the calculation results were averaged. The modeling method proposed in the present invention shortened the computational 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 to other modeling methods, the spatiotemporal modeling method for wire-driven soft robots proposed in this invention utilizes a data-driven approach that integrates physical information, requiring only position data and partial information about the system model. Compared to improved finite-difference simulation-based modeling methods, the modeling method based on physical information neural networks proposed in this invention can effectively shorten computational time. By utilizing visual perception methods or simulation experiments to obtain spatiotemporal coordinates, spatiotemporal modeling of wire-driven soft robots is achieved even when some model parameters are unknown.

[0125] The above is a detailed introduction to the 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, several improvements and modifications can be made to the present invention, and these improvements and modifications also fall within the scope of protection of the claims of the present invention.

Claims

1. A wire-driven soft robot modeling method based on 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 spatiotemporal coordinates of the wire-driven soft robot through visual perception or simulation experiments, obtain the actual values ​​of the internal force, internal torque, velocity, angular velocity and unknown parameters of the partial differential equation through simulation experiments, and express the external force data and spatiotemporal coordinates in the form required by the model; S200: Analyze the line-driven soft robot using Cosserat theory. Perform kinematic analysis of the soft robot using Euler and Lagrangian descriptions, construct equations of motion and momentum conservation equations, and calculate a set of partial differential equations containing physical information using constitutive equations. S200 includes: S210: Based on the Kirchhoff-Love theory, construct the Euler and Lagrangian coordinate systems, and construct the motion equations and momentum conservation equations of wire-driven soft robots without considering stretching and shearing; S220: Based on the Cosserat theory, a system of partial differential equations containing physical information and unknown parameters is obtained by combining the constitutive equations while considering tension and shear. S300: Using a data-driven method based on physical information, a physical information loss function is constructed based on a set of partial differential equations. A data-driven loss function is constructed based on the actual values ​​of the spatiotemporal coordinates of the line-driven soft robot. A preset physical information neural network is trained based on the loss function and external force data to obtain estimated values ​​of the spatiotemporal coordinates, internal forces, internal torques, velocities, angular velocities, and unknown parameters of the equations. 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 estimates of the space-time coordinates, internal forces, internal torques, velocities, angular velocities, and unknown parameters of the equations; S320: During the neural network training process, after obtaining the estimated value, perform corresponding automatic differentiation; S330: Use mean square error to construct the physical information loss function corresponding to the partial differential equation, and use the actual and estimated values ​​of the space-time coordinates to construct a data-driven loss function; S340: Bring the estimated amount and the differential amount into the total loss function for solution; S350: Use optimization algorithms in neural network training to minimize the total loss function and gradually adjust model parameters through gradient descent to complete model training; S400: Obtain a physical state loss estimation function based on the actual and estimated values ​​of the spatiotemporal coordinates, internal forces, internal torques, velocities, and angular velocities of the wire-driven soft robot; obtain an unknown parameter loss estimation function based on 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 based on 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 central skeleton spatial position R(t,s) and the external force F(t,s) of the wire-driven soft robot are in the form of: 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, Represents the component matrices in the three coordinate axis directions, F i 0 is the external force matrix, F1 0 、 F3 0 Represents 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) it receives 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 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, d j is the local coordinate system basis vector, Q is the rotation matrix for converting between the local coordinate system and the global coordinate system, specifically Q = (d1, d2, d3) T , 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, is the generalized curvature expressed in the local coordinate system, and are the internal force and internal moment expressed in the local coordinate system, F and c are the external force and external moment, and I is the second area moment of inertia; The partial differential equations in S220 are specifically: 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, is the shear displacement expressed in the local coordinate system.

4. The method according to claim 3, 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:

5. The method according to claim 4, characterized in that S330 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, 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.

6. The method according to claim 5, 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 Loss is the physical state loss estimation function. Q 、Loss e 、 Loss estimation function for unknown parameters.

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