Mechanical analysis method and device of flexible instrument, electronic equipment and storage medium

Abstract

The present application relates to the technical field of mechanical analysis, and provides a mechanical analysis method and device for flexible apparatus, electronic equipment and storage medium, wherein the method models the finite element analysis method by model training to obtain a mechanical analysis model, so that the mechanical analysis model can learn the finite element analysis method, and then through the mechanical analysis model, the requirements of the mechanical analysis on the calculation efficiency and the accuracy can be met, the new configuration information of the flexible apparatus to be analyzed under the action of driving force can be quickly and efficiently obtained, and the accuracy and the calculation efficiency are balanced. Moreover, the current configuration information of the flexible apparatus to be analyzed is taken as the basis of the mechanical analysis, and the new configuration information of the flexible apparatus to be analyzed under the action of the driving force is taken as the mechanical analysis result, so that compared with directly using the node displacement obtained in the finite element analysis process, the representation form of the flexible apparatus to be analyzed can be simplified, and the calculation amount is greatly reduced.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of mechanical analysis, and in particular to a mechanical analysis method and device for a flexible instrument, an electronic device and a storage medium. BACKGROUND

[0002] At present, flexible instruments are widely used in medical examination and surgery. In the application process of the flexible instrument, the flexible instrument usually contacts the application object and is subjected to contact force from the application object. Therefore, mechanical analysis of the flexible instrument plays a crucial role in preoperative navigation of the flexible instrument and virtual surgery training of doctors.

[0003] In the prior art, common means for mechanical analysis include: 1) finite element method. The basic steps of establishing a mechanical model by the finite element method are: three-dimensional digital model establishment of the flexible instrument; three-dimensional finite element meshing of the digital model; mechanical description of the model by using appropriate finite elements; calculation of collision force; solution of the motion equation; display and output. 2) piecewise constant curvature method. The piecewise constant curvature method divides the flexible instrument into a plurality of deformation sections, and each deformation section is approximated as a circular arc section with constant curvature. For each small section, a function relationship is established between the curvature and the radius, the arc length by analyzing the geometric relationship, and finally the kinematic equation of the overall model is obtained. 3) discrete Cosserat rod (DCM) modeling method. The DCM method is usually used to simulate mechanisms with geometric and mechanical properties similar to rods, such as wires and sutures. This method regards the flexible body as a discrete rigid point and only analyzes the center skeleton of tubular objects. Since the coordinates of the model are reduced in dimension, the size of the model can be limited and large-size models in the finite element method are usually not generated.

[0004] For the finite element method, although the calculation is relatively accurate, this method is more commonly used in the field of static mechanical analysis represented by truss analysis, and less consideration is given to the calculation speed. A long calculation time is usually used to obtain accurate mechanical analysis of a structure. Modern real-time finite element technology is first applied in the field of computer animation. This method only has real-time simulation effect for simple models with sparse meshing. If the model structure is complex or the user wants to obtain higher accuracy by using encrypted meshing, the real-time performance of the real-time finite element method will be significantly reduced.

[0005] For the piecewise constant curvature method, only geometric relationships are considered and the mechanical properties of the flexible instrument itself are not considered. Therefore, the accuracy of this method is not high, and when the model is in contact and collision with other models in the environment, the contact cannot be fed back, that is, it cannot solve the shape change problem in the contact environment, which is unacceptable for robot motion problems in the restricted environment in the field of minimally invasive surgery (such as in the trachea).

[0006] For the discrete Cosserat rod modeling method, it is more used for modeling of structures with high flexibility, such as suture modeling, etc. When the model itself has a certain stiffness (such as a flexible robot itself has a certain stiffness to resist external force), the effect of this method is not good. SUMMARY

[0007] The present application provides a mechanical analysis method, device, electronic equipment and storage medium of a flexible instrument, to solve the defects in the prior art that cannot balance accuracy and calculation speed when performing mechanical analysis on a flexible instrument.

[0008] The present application provides a mechanical analysis method of a flexible instrument, comprising:

[0009] Obtaining current configuration information and driving force information of a flexible instrument to be analyzed;

[0010] Inputting the current configuration information and the driving force information into a mechanical analysis model to obtain new configuration information of the flexible instrument to be analyzed under the action of the driving force output by the mechanical analysis model;

[0011] Wherein, the mechanical analysis model is obtained based on the deformation data obtained by finite element analysis of a flexible instrument sample under a known force.

[0012] According to the mechanical analysis method of a flexible instrument provided by the present application, the flexible instrument to be analyzed is a flexible tubular robot, and the skeleton of the flexible tubular robot is characterized based on a target Bezier curve.

[0013] The current configuration information is obtained based on the following steps:

[0014] Obtaining a plurality of skeleton points of the flexible instrument to be analyzed;

[0015] Inputting the plurality of skeleton points into a configuration model to obtain control points of the target Bezier curve output by the configuration model;

[0016] Wherein, the control points of the target Bezier curve are used to represent the current configuration information, and the configuration model is trained based on a plurality of discrete points on a Bezier curve sample in a three-dimensional space and control points of the Bezier curve sample.

[0017] According to the mechanical analysis method of a flexible instrument provided by the present application, before the plurality of skeleton points are input into the configuration model to obtain the control points of the target Bezier curve output by the configuration model, the method further comprises:

[0018] Projecting the plurality of skeleton points from a three-dimensional space to a limited flat space;

[0019] The method further comprises the following steps of:

[0020] Projecting the control points of the target Bezier curve from the limited flat space to the three-dimensional space.

[0021] The method further comprises the following steps of:

[0022] The current configuration information is obtained by the initial configuration of the flexible instrument under the action of a random single-point external force.

[0023] The initial configuration is a new configuration of the flexible instrument obtained in a previous time step, and the driving force information is driving force information of the flexible instrument in a current time step.

[0024] The method further comprises the following steps of:

[0025] Determine the current sample configuration information of the flexible instrument sample, and apply the known force to the flexible instrument sample to make the flexible instrument sample deform;

[0026] Perform finite element analysis on the flexible instrument sample to obtain deformation data of the flexible instrument sample under the action of the known force, and determine new sample configuration information of the flexible instrument sample based on the deformation data.

[0027] Train an initial analysis model based on the current sample configuration information, the new sample configuration information, and the known force to obtain the mechanical analysis model.

[0028] The application further provides a mechanical analysis device for a flexible instrument, which comprises:

[0029] An information acquisition module is configured to acquire current configuration information and driving force information of a flexible instrument to be analyzed.

[0030] A mechanical analysis module is configured to input the current configuration information and the driving force information into a mechanical analysis model to obtain new configuration information of the flexible instrument to be analyzed obtained under the action of the driving force, which is output by the mechanical analysis model.

[0031] The mechanical analysis model is trained based on deformation data obtained by performing finite element analysis on a flexible instrument sample subjected to a known force.

[0032] The application further provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the mechanical analysis method of the flexible instrument according to any one of the above when executing the program.

[0033] The application further provides a non-transitory computer-readable storage medium, which stores a computer program, wherein the computer program is executed by a processor to implement the mechanical analysis method of the flexible instrument according to any one of the above.

[0034] The application further provides a computer program product, comprising a computer program, wherein the computer program is executed by a processor to implement the mechanical analysis method of the flexible instrument according to any one of the above.

[0035] The mechanical analysis method of the flexible instrument, the device, the electronic device and the storage medium provided by the application first acquire current configuration information and driving force information of the flexible instrument to be analyzed, then input the current configuration information and the driving force information into a mechanical analysis model to obtain new configuration information of the flexible instrument to be analyzed under the action of the driving force output by the mechanical analysis model, wherein the mechanical analysis model is obtained based on training of deformation data obtained by finite element analysis on a flexible instrument sample under a known force. The method models the finite element analysis method by model training to obtain the mechanical analysis model, so that the mechanical analysis model can learn the finite element analysis method, and then through the mechanical analysis model, the requirements of the mechanical analysis in the calculation efficiency can be met, and the requirements of the mechanical analysis in the accuracy can also be met, the new configuration information of the flexible instrument to be analyzed under the action of the driving force can be quickly and efficiently and accurately obtained, and the accuracy and the calculation efficiency can be considered. Moreover, the current configuration information of the flexible instrument to be analyzed is taken as the basis of the mechanical analysis, and the new configuration information of the flexible instrument to be analyzed under the action of the driving force is taken as the result of the mechanical analysis, compared with directly using the node displacement obtained in the finite element analysis process, the form of representation of the flexible instrument to be analyzed can be simplified, the calculation amount can be greatly reduced, and the user can more intuitively observe the changes of the flexible instrument to be analyzed before and after the action of the driving force. BRIEF DESCRIPTION OF DRAWINGS

[0036] In order to more clearly illustrate the technical solutions of the present application or the prior art, the following will briefly introduce the drawings needed in the embodiments or prior art description. Obviously, the drawings in the following description can also be obtained by those skilled in the art without creative labor.

[0037] Figure 1 is one of the flowcharts of the mechanical analysis method of the flexible instrument provided by the application;

[0038] Figure 2 is a structural schematic diagram of a mechanical analysis model in a mechanical analysis method of a flexible instrument provided by the present application;

[0039] Figure 3 is a structural schematic diagram of a tetrahedral element in a mechanical analysis method of a flexible instrument provided by the present application;

[0040] Figure 4 is a flowchart of determining a control point of a target Bezier curve by using a configuration model in a mechanical analysis method of a flexible instrument provided by the present application;

[0041] Figure 5 is a target Bezier curve and its control point in a limited flat space in a mechanical analysis method of a flexible instrument provided by the present application;

[0042] Figure 6 is a configuration change schematic diagram of a flexible instrument to be analyzed in a mechanical analysis method of a flexible instrument provided by the present application;

[0043] Figure 7 is a cross-section grid schematic diagram corresponding to a flexible instrument sample in a mechanical analysis method of a flexible instrument provided by the present application;

[0044] Figure 8 is a cross-section grid schematic diagram corresponding to a flexible instrument sample in a mechanical analysis method of a flexible instrument provided by the present application;

[0045] Figure 9 is a mechanical model schematic diagram obtained by using a tetrahedral element finite element algorithm to perform mechanical modeling on a flexible instrument sample in a mechanical analysis method of a flexible instrument provided by the present application;

[0046] Figure 10 is a flowchart of a mechanical analysis method of a flexible instrument provided by the present application;

[0047] Figure 11 is a structural schematic diagram of a mechanical analysis device of a flexible instrument provided by the present application;

[0048] Figure 12 is a structural schematic diagram of an electronic device provided by the present application. DETAILED DESCRIPTION

[0049] To make the objectives, technical solutions and advantages of the present application clearer, the technical solutions in the present application will be described below in connection with the drawings in the present application. Obviously, the described embodiments are some but not all of the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0050] Since the mechanical analysis of flexible instruments should comprehensively consider the accuracy, speed and robustness of the calculation process, this invention provides a mechanical analysis method for flexible instruments.

[0051] Figure 1 This is a flowchart illustrating a mechanical analysis method for a flexible device provided in an embodiment of the present invention, as shown below. Figure 1 As shown, the method includes:

[0052] S1, Obtain the current configuration information and driving force information of the flexible instrument to be analyzed;

[0053] S2, input the current configuration information and the driving force information into the mechanical analysis model to obtain the new configuration information of the flexible device to be analyzed under the action of the driving force, which is output by the mechanical analysis model;

[0054] The mechanical analysis model is trained based on deformation data obtained from finite element analysis of a flexible instrument sample subjected to known forces.

[0055] Specifically, the mechanical analysis method for flexible devices provided in this embodiment of the invention is executed by a mechanical analysis device for flexible devices. This device can be configured in a computer, which can be a local computer or a cloud computer. The local computer can be a computer, tablet, etc., and no specific limitation is made here.

[0056] First, step S1 is executed to obtain the current configuration information and driving force information of the flexible device to be analyzed. The flexible device to be analyzed refers to the flexible device whose configuration change during the force process needs to be analyzed. It can be a flexible tubular device or a flexible device of other shapes, without specific limitations here.

[0057] The current configuration information of the flexible instrument to be analyzed refers to its configuration before being subjected to force. Configuration information refers to shape information, i.e., a numerical representation that characterizes the shape. This current configuration information can be characterized by the displacement information of various points on the flexible instrument, by the edge extreme points of the flexible instrument, or by the control points of the curve model corresponding to the skeleton of the flexible instrument; no specific limitation is made here. Driving force information refers to the magnitude and direction of the driving force acting on the flexible instrument.

[0058] Then, step S2 is executed, inputting the current configuration information and driving force information into the mechanical analysis model to obtain the new configuration information of the flexible device under the driving force, output by the mechanical analysis model. Here, a mechanical analysis model is introduced, whose input can be the current configuration information and driving force information of the flexible device under the driving force, and whose output can be the new configuration information of the flexible device under the driving force.

[0059] The new configuration information refers to the configuration information of the flexible device to be analyzed under the action of driving force. It can be characterized by the edge extreme points of the flexible device to be analyzed after being subjected to force, or by the control points of the curve model corresponding to the skeleton of the flexible device to be analyzed after being subjected to force. No specific limitation is made here.

[0060] The mechanical analysis model can be a trained neural network model, such as... Figure 2 As shown, the mechanical analysis model may include a first normalized layer, a first fully connected module, and a second fully connected module connected in sequence. The first fully connected module may include a 13×256 fully connected layer and a ReLU activation layer, and the second fully connected module may include a 256×128 fully connected layer and a ReLU activation layer. The first normalized layer receives the current configuration information and driving force information of the flexible instrument to be analyzed, and then passes through the first normalized layer, the first fully connected module, and the second fully connected module in sequence to obtain the new configuration information of the flexible instrument to be analyzed under the action of the driving force.

[0061] This mechanical analysis model can be obtained by training an initial analysis model using deformation data obtained from finite element analysis of a flexible device sample subjected to known forces. This initial analysis model can be a neural network model. The material and configuration of the flexible device sample are the same as those of the flexible device sample to be analyzed.

[0062] When training the initial analysis model, training data can be collected first. This involves applying a known force to the flexible device sample and performing finite element analysis on the sample to obtain the deformation data caused by the known force. The flexible device sample can be controlled by multiple stretchable guidewires. The known force can be the guidewire tension acting on the sample, and its magnitude and direction can be randomly selected without specific limitations.

[0063] Finite element analysis (FEM) is the process of analyzing the structure of a flexible instrument sample using the finite element method and obtaining its deformation data under known forces. The finite element method is an effective tool for solving complex differential equations numerically, and its foundation lies in variational principles and the weighted residual method.

[0064] The finite element method can be approximated by dividing the computational domain into a finite number of linear computable elements, each of which is non-overlapping. Within each computable element, linear interpolation is performed on the node configuration, rewriting the differential equation as a linear expression described by the interpolation function of the node configuration. Finally, the variational principle or the weighted residual method is used for discrete solution.

[0065] Following the basic idea of ​​the finite element method, different finite element methods are obtained by adopting different meshing schemes or different interpolation function forms.

[0066] When performing finite element analysis on flexible device samples, the shape of each computable element can be set as needed, such as a tetrahedron, rod, beam, hexahedron, etc. The corresponding computable elements are three-dimensional elements such as tetrahedral elements, rod elements, beam elements, and hexahedral elements.

[0067] For ease of calculation, we will take tetrahedral elements as an example. Figure 3 The diagram shows a schematic of a tetrahedral element. Within each tetrahedral element, the four vertices serve as its four nodes. Each node has three degrees of freedom, representing displacement in three directions within three-dimensional space, denoted by u. i v i w i Represented using the nodal displacement vector q. e and nodal force vector F e To represent the degrees of freedom of each tetrahedral element:

[0068]

[0069] For any point with coordinates x, y, z within each tetrahedral element, there is a displacement set u, v, w. This description is called the displacement field of the tetrahedral element, and a linear relationship is used to describe the displacement field:

[0070]

[0071] in, These are unknown undetermined coefficients, which will be solved in subsequent processes.

[0072] At the four nodes of a tetrahedral element, the displacements are known; this condition is called the boundary condition. For a tetrahedral element, the boundary condition is given by the following equation:

[0073]

[0074] Among them, u i v i wi The displacement group of the ith node. Substitute the boundary condition into formula (2), and the undetermined coefficient can be solved. At this time, the displacement field of the unit is expressed in the form of a matrix:

[0075]

[0076] Wherein:

[0077]

[0078] Wherein, V is the volume of the tetrahedron, a i , b i , c i are coefficients related to the geometric position of the ith node.

[0079] In continuum mechanics, there is a specific mapping relationship between strain and strain. Substitute (4) to have the following relationship:

[0080]

[0081] Wherein, the geometric matrix B is:

[0082]

[0083] Wherein B i is:

[0084]

[0085] The geometric matrix B expresses the relationship between strain and node displacement, and the stress and strain also have a relationship with the elastic matrix D. Substituting it gives the relationship between stress and node displacement:

[0086]

[0087] According to the principle of minimum potential energy in continuum mechanics, when the potential energy of a system is minimized, the system will be in a stable equilibrium state, that is, the system always tends to minimize the potential energy.

[0088] For a tetrahedral unit, the potential energy is as follows:

[0089]

[0090] According to the principle of minimum potential energy, the potential energy of the tetrahedral unit tends to be minimized, that is, taking the first order pole of the formula, the unit stiffness equation is as follows:

[0091]

[0092] Wherein, K e is called the unit stiffness matrix.

[0093] Assemble the element stiffness matrix, i.e. expand q e The total stiffness matrix K is obtained by assembling the element stiffness matrix of all nodes on the flexible instrument sample, i.e. the displacement of all nodes of a flexible instrument sample is linked to the driving force information. The displacement of all nodes, i.e. the position information of all nodes, can represent the configuration information of the flexible instrument sample.

[0094] It can be understood that when performing finite element analysis, the selection of the element can be different, which can lead to different element stiffness matrices K e and different node degrees of freedom, but the equation form of formula (11) remains unchanged.

[0095] In summary, the process of finite element analysis includes: first, meshing. The flexible instrument sample is divided into a finite number of linear calculable elements, which is intuitively abstracted into a large number of nodes, each node has independent node displacement, node velocity and node force. Second, a mechanical model is established by finite element theory, i.e. a linear function relationship between node force and node displacement is established. Given the node position, the node force can be solved. Given the node force and some boundary conditions (such as some points are fixed, the displacement is 0), the displacement of the remaining nodes can also be solved. Macroscopically, it is understood as that the deformation data (i.e. the displacement of each node) of a flexible instrument sample is solved under the known external force.

[0096] Combined with the configuration information of the flexible instrument sample before being subjected to the known force and the deformation data generated by the known force, the configuration information of the flexible instrument sample after deformation under the known force can be obtained. Further, the initial analysis model can be trained by means of machine learning algorithm, i.e. the configuration information of the flexible instrument sample before being subjected to the known force and the known force can be used as the input of the initial analysis model to obtain the output result of the initial analysis model, and then the configuration information of the flexible instrument sample after deformation under the known force is used as a label to calculate the loss function with the output result. The parameter values of the initial analysis model are modified, and the above process is iteratively performed. When the loss function converges, the trained initial analysis model, i.e. the mechanical analysis model, is obtained.

[0097] The above training process can be understood as that the flexible instrument sample is first analyzed by finite element analysis to realize accurate pre-modeling of the flexible instrument sample, and then the machine learning algorithm is used to learn the process of finite element analysis, and finally a mechanical analysis model with both accurate configuration information recognition performance and rapidity in calculation is obtained.

[0098] The method for mechanical analysis of the flexible instrument provided in the embodiment of the present application first acquires current configuration information and driving force information of the flexible instrument to be analyzed; then inputs the current configuration information and the driving force information into a mechanical analysis model to obtain new configuration information of the flexible instrument to be analyzed under the action of the driving force output by the mechanical analysis model; wherein the mechanical analysis model is obtained based on training of deformation data obtained by finite element analysis on a flexible instrument sample under a known force. The method models the finite element analysis method by model training to obtain the mechanical analysis model, so that the mechanical analysis model can learn the finite element analysis method, and then through the mechanical analysis model, not only the requirement of the mechanical analysis in calculation efficiency can be met, but also the requirement of the mechanical analysis in accuracy can be met, the new configuration information of the flexible instrument to be analyzed under the action of the driving force can be quickly and efficiently and accurately obtained, and the accuracy and the calculation efficiency are considered. Moreover, the current configuration information of the flexible instrument to be analyzed is taken as the basis of the mechanical analysis, and the new configuration information of the flexible instrument to be analyzed under the action of the driving force is taken as the result of the mechanical analysis, compared with directly using the node displacement obtained in the finite element analysis process, the representation form of the flexible instrument to be analyzed can be simplified, the calculation amount is greatly reduced, and the user can more intuitively observe the change of the flexible instrument to be analyzed before and after the action of the driving force.

[0099] On the basis of the above-mentioned embodiment, the method for mechanical analysis of the flexible instrument provided in the embodiment of the present application, the flexible instrument to be analyzed is a flexible tubular robot, and the skeleton of the flexible tubular robot is represented based on a target Bezier curve.

[0100] The current configuration information is acquired based on the following steps:

[0101] A plurality of skeleton points of the flexible instrument to be analyzed are acquired.

[0102] The plurality of skeleton points are input into a configuration model to obtain control points of the target Bezier curve output by the configuration model.

[0103] The control points of the target Bezier curve are used to represent the current configuration information, and the configuration model is obtained based on a plurality of discrete points on a Bezier curve sample in a three-dimensional space and control points of the Bezier curve sample.

[0104] Specifically, in the embodiment of the present application, the flexible instrument to be analyzed can be a flexible tubular robot, for example, can be a bronchoscope and a bronchoscope, etc., the bronchoscope can include an electromagnetic navigation bronchoscope (ENB), a virtual bronchoscope (VB) and an ultrasonic bronchoscope (EBUS).

[0105] Further, the skeleton of the flexible tubular robot can be characterized by a target Bezier curve. Since the target Bezier curve can be drawn by its control points, the current configuration information of the flexible tubular robot can be characterized by the control points of the target Bezier curve. The order of the target Bezier curve can be set as needed, for example, it can be set to three orders.

[0106] It can be understood that the target Bezier curve is a parametric curve applied to computer graphics, drawn by a limited number of parameter points, and widely used in computer-aided curve design and drawing. The biggest feature of Bezier curve is that a complete continuous curve can be drawn by using a limited number of discrete points.

[0107] The target Bezier curve is composed of n control points, and the n control points correspond to an n-1 order Bezier curve. The drawing of the target Bezier curve can be in a recursive manner, and each order Bezier curve is a pre-curve of the next order Bezier curve. The formula of the n order target Bezier curve can be expressed as:

[0108]

[0109] Therefore, obtaining the current configuration information of the flexible instrument to be analyzed can be converted into determining the control points of the target Bezier curve corresponding to the skeleton of the flexible instrument to be analyzed.

[0110] Further, when obtaining the current configuration information of the flexible instrument to be analyzed, a plurality of skeleton points of the flexible instrument to be analyzed can be obtained first, and the plurality of skeleton points can be obtained by selecting a plurality of points equidistantly on the skeleton of the flexible instrument to be analyzed. The plurality of skeleton points can be represented by three-dimensional position coordinates. Here, the central axis of the flexible tubular robot can be obtained first, which is the skeleton of the flexible tubular robot, and then a plurality of points equidistantly sampled on the central axis are obtained, that is, a plurality of skeleton points are obtained. The number of skeleton points can be set as needed, for example, it can be set to 10, or other numbers, which are not limited here.

[0111] Thereafter, a configuration model is introduced, and the plurality of skeleton points are input to the configuration model, and the control points of the target Bezier curve corresponding to the skeleton of the flexible instrument to be analyzed are output by the configuration model. The control points can also be represented by three-dimensional position coordinates, and the number of control points is determined by the order of the target Bezier curve.

[0112] The configuration model can be a trained neural network model, and the configuration model can include a second normalization layer, a third full connection module, and a fourth full connection module connected in sequence. The third full connection module can include a full connection layer of 28x256 and a ReLU activation layer, and the fourth full connection module can include a full connection layer of 256x128 and a ReLU activation layer. The plurality of skeleton points are received by the second normalization layer, and sequentially pass through the second normalization module, the third full connection layer, and the fourth full connection module to obtain the control points of the target Bezier curve corresponding to the skeleton of the flexible instrument to be analyzed.

[0113] The configuration model can be trained using a plurality of discrete points on a Bezier curve sample in a three-dimensional space and control points of the Bezier curve sample. The initial configuration model can be a neural network model.

[0114] Here, the plurality of discrete points on the Bezier curve sample and the control points of the Bezier curve sample can be represented by three-dimensional position coordinates.

[0115] When training the initial configuration model, training data can be collected first, that is, control points are automatically and randomly generated in a three-dimensional space, and then the control points are used to generate a Bezier curve sample. The randomly generated control points can be in groups of four, and the generated Bezier curve sample can be a third-order Bezier curve. Thereafter, a plurality of discrete points are equally sampled on the Bezier curve sample to express the linearity of the Bezier curve sample.

[0116] Further, the initial configuration model can be trained by means of a machine learning algorithm, that is, the plurality of discrete points on the Bezier curve sample can be used as input of the initial configuration model, and the output result of the initial configuration model is obtained, and then the control points of the Bezier curve sample are used as labels to calculate a loss function with the output result. The parameter values of the initial configuration model are modified, and the above process is iteratively performed, and when the loss function converges, the trained initial configuration model, that is, the configuration model, is obtained.

[0117] In the embodiment of the present application, the control points of the target Bezier curve representing the skeleton of the flexible tubular robot are determined by the configuration model, and the current configuration information of the flexible tubular robot is represented by the control points, so that the current configuration information can be quickly determined, and the efficiency and accuracy of subsequent mechanical analysis can be improved.

[0118] On the basis of the above-mentioned embodiments, the mechanical analysis method of the flexible instrument provided in the embodiment of the present application includes, before the plurality of skeleton points are input into the configuration model to obtain the control points of the target Bezier curve output by the configuration model:

[0119] The plurality of skeleton points are projected from a three-dimensional space to a limited flat space.

[0120] The method comprises the following steps of:

[0121] Projecting the control points of the target Bezier curve from the limited flat space to the three-dimensional space.

[0122] Specifically, in order to reduce the spatial distance of each skeleton point and improve the calculation accuracy, a limited flat space is introduced to limit each skeleton point in the limited flat space, that is, before inputting the plurality of skeleton points into the configuration model to obtain the control points of the target Bezier curve output by the configuration model, each skeleton point is projected from the three-dimensional space to the limited flat space, and then the control points of the target Bezier curve obtained by the configuration model are also in the limited flat space.

[0123] Since the mechanical analysis of the mechanical analysis model is realized in the three-dimensional space, after obtaining the control points of the target Bezier curve, the control points of the target Bezier curve need to be projected from the limited flat space to the three-dimensional space. Here, the projection is a rotation.

[0124] Here, the limited flat space can be set as needed, for example, the x-axis range can be set to 0-10, the y-axis range can be set to 0-10, and the z-axis range can be set to -3-3. The units of the x-axis, the y-axis and the z-axis can be mm or cm, which are determined according to the actual size of the flexible instrument to be analyzed, and are not limited specifically here.

[0125] Figure 4 A flowchart for determining the control points of the target Bezier curve by using the configuration model is shown. As shown in Figure 4 the plurality of skeleton points of the flexible instrument to be analyzed are first projected from the three-dimensional space to the limited flat space, then the plurality of skeleton points in the limited flat space are input into the configuration model to obtain the control points of the target Bezier curve in the limited flat space output by the configuration model, and finally the control points of the target Bezier curve are projected from the limited flat space to the three-dimensional space. Figure 5 The target Bezier curve and its control points in the limited flat space.

[0126] It can be understood that when the initial configuration model is trained, a plurality of discrete points on the Bezier curve sample in the three-dimensional space and the control points of the Bezier curve sample also need to be converted to the limited flat space. Here, in order to further reduce the calculation amount, a plurality of discrete points on the Bezier curve sample in the limited flat space and the control points of the Bezier curve sample can be directly selected.

[0127] For example, taking a cubic Bezier curve sample as an example, a coordinate origin (0, 0, 0) of a limited flat space can be selected as a starting point, and then three control points are randomly generated in the space, including a terminal point and two relay points. The four control points formed by the three points and the coordinate origin determine the shape and position of the cubic Bezier curve sample. Then, a complete Bezier curve sample is determined using the four control points, and 11 discrete points are sampled on the Bezier curve sample at equal distances to represent the shape and position of the Bezier curve sample. The first discrete point and the 11th discrete point coincide with the starting point and the terminal point of the four control points, respectively, that is, the first discrete point is always the coordinate origin and is not used as training data. Then, the above-mentioned 10 non-origin discrete points are used as input of an initial configuration model, and the above-mentioned two relay control points, the coordinate origin and the terminal point are used as labels to form a group of data.

[0128] In the program implementation, the data generator mode is adopted, that is, data is generated once in each training, including training data and verification data, that is, the distribution of the training data and the verification data is the same.

[0129] In the embodiment of the application, since the conversion between the three-dimensional space and the limited flat space is introduced, the space range of the training data of the configuration model can be greatly reduced, and the model training difficulty is reduced, and the accuracy of the control points of the target Bezier curve is improved.

[0130] On the basis of the above-mentioned embodiment, the mechanical analysis method of the flexible instrument provided in the embodiment of the application, the to-be-analyzed flexible instrument is controlled by a plurality of stretchable guide wires, and the driving force is the guide wire tension of the guide wire acting on the to-be-analyzed flexible instrument.

[0131] Specifically, the to-be-analyzed flexible instrument can be controlled by a plurality of stretchable guide wires, and the driving force acting on the to-be-analyzed flexible instrument is the guide wire tension of the guide wire acting on the to-be-analyzed flexible instrument.

[0132] The guide wire can be controlled by a doctor, and then the mechanical analysis of the to-be-analyzed flexible instrument can simulate the intubation process of the virtual surgery of the doctor, pay attention to the stress of each part of the to-be-analyzed flexible instrument, and thus provide analysis and reference basis for whether the intubation process will damage the bronchial wall, better optimize the intubation scheme, and provide safety reference for the intubation scheme.

[0133] On the basis of the above-mentioned embodiment, the mechanical analysis method of the flexible instrument provided in the embodiment of the application, the current configuration information is obtained under the action of a random single-point external force.

[0134] Specifically, the current configuration information of the flexible instrument to be analyzed is obtained by the initial configuration of the flexible instrument to be analyzed under the action of a random single-point external force. Here, the single point does not refer to a node, but a regional force with a certain area. The reason for the random single-point external force is that the flexible instrument to be analyzed generally has only one contact point in the human body, for example, there is only one contact point between the lung and the lung wall, which will cause the flexible instrument to be analyzed to produce a deformation, generate the current configuration G, and in the case of the current configuration G, an external driving force F (linear driving flexible robot controlled by three stretchable guide wires) is added to obtain the final configuration E, so G and F are inputs, and E is output.

[0135] In the doctor virtual surgery training scene, the random single-point external force can be derived from the resistance received by the flexible instrument to be analyzed. Thus, the random single-point external force can be collected as the input of the force feedback touch device, and the doctor can feel the realistic intubation resistance in the simulation training, greatly reducing the gap in training effect between virtual surgery training and entity surgery training.

[0136] As shown in Figure 6 , it is a configuration change diagram of the flexible instrument to be analyzed. The initial configuration of the flexible instrument to be analyzed obtains the current configuration under the action of the random single-point external force, and the current configuration obtains the new configuration under the action of the random guide wire tension F.

[0137] The traditional static finite element method is mostly used for the analysis of static structures, and a long calculation time is used to obtain a one-time accurate mechanical analysis of the structure. The optimization scope is mostly in how to improve the accuracy of simulation and the reliability of results, and the consumption of calculation time is ignored. In fact, this practice has no problem in the traditional application field of static finite element, because the traditional static finite element application field only needs to obtain the static mechanical description of a structure, and the calculation time is only a kind of consumable resource. Compared with the traditional static finite element, the real-time finite element method can achieve the speed of 30-40 frames per second by large-scale approximation and simplification of the structure, so as to be widely used in the field of computer animation. However, in the application field of computer animation, developers pay more attention to visual effects rather than approximation to real situations, and all non-physical methods such as PBD (Position Based Dynamics) can basically achieve the effect of confusing the false with the true in vision, so that the application of real-time finite element is greatly limited. The method of real-time finite element is only used to simulate a small amount of micro-elastic objects, or even only used for rigid body motion.

[0138] In the field of modeling and simulation of flexible apparatus to be analyzed, the research on real-time finite element method is increasing year by year. The biggest difference between computer animation in this field and traditional computer animation for visual effects is that the modeling and simulation of flexible apparatus to be analyzed needs to greatly approximate the real situation, and even many model-based control methods of flexible apparatus to be analyzed need to use the robot model at each moment. Therefore, the modeling method of flexible apparatus to be analyzed has a very high requirement of balancing the calculation speed and the calculation accuracy.

[0139] In the above embodiment, the initial configuration is the new configuration of the flexible apparatus to be analyzed obtained at the previous time step, and the driving force information is the driving force information of the flexible apparatus to be analyzed at the current time step.

[0140] Specifically, in the embodiment of the application, the initial configuration of the flexible apparatus to be analyzed is the new configuration of the flexible apparatus to be analyzed obtained at the previous time step, and the driving force information is the driving force information of the flexible apparatus to be analyzed at the current time step. Therefore, the mechanical analysis of the flexible apparatus to be analyzed is real-time.

[0141] For the real-time finite element method, it is assumed that a system includes n rigid body points, each rigid body point includes 6 degrees of freedom (three translations and three rotations), and the system satisfies the linear momentum conservation:

[0142]

[0143] In the finite element theory, force and displacement are related, that is, force can be expressed as a function of displacement, and the momentum conservation can be expressed as the following formula:

[0144] MΔv=dt·f(x)(14)

[0145] Euler method is a numerical solution method of ordinary differential equations, and the basic idea is iteration. The formats of explicit Euler method and implicit Euler method are as follows:

[0146]

[0147] In the explicit Euler method, the value at each time is calculated only from the previous time, so the solution is very fast, but in the case of large step size, the solution may diverge. In the implicit Euler method, the value at each time is determined by the previous time and the current time, and a complex equation needs to be solved, which is slow, but it is unconditionally stable in the numerical solution process.

[0148] The implicit Euler method is used to solve formula (14), and the following formula is obtained:

[0149]

[0150] In finite element, force is expressed as a function of displacement, and the mapping relationship between force and displacement is called constitutive relation, which is expressed by stiffness matrix K in numerical value. In problem modeling, if the influence of velocity on force is added, force is expressed as a function of displacement and velocity, the mapping relationship between force and velocity is introduced, and it is expressed by damping matrix B. The form of the above formula is as follows:

[0151]

[0152] The equation is a linear equation, in the actual solving process, the Rayleigh damping method is used to optimize the above equation, so that the convergence of the equation is better, and the correction of Rayleigh damping and the linear form of the equation are as follows:

[0153]

[0154] The coefficient in formula (18) has no actual physical and mathematical meaning, and is only a numerical skill used for correcting the equation.

[0155] The linear solving method (such as conjugate gradient method, Runge-Kutta method, etc.) is used to solve the above formula, so that the solution v is obtained, and then the original equation is substituted, so that all degrees of freedom in the physical system at this moment are obtained.

[0156] The above process can be trained on the initial analysis model by a machine learning method, so that the mechanical analysis model learns.

[0157] On the basis of the above embodiment, the mechanical analysis method of the flexible instrument provided in the embodiment of the application is trained based on the following steps:

[0158] Determine the current sample configuration information of the flexible instrument sample, and apply the known force to the flexible instrument sample to make the flexible instrument sample deform;

[0159] Perform finite element analysis on the flexible instrument sample to obtain deformation data of the flexible instrument sample under the action of the known force, and determine new sample configuration information of the flexible instrument sample based on the deformation data;

[0160] Train the initial analysis model based on the current sample configuration information, the new sample configuration information and the known force to obtain the mechanical analysis model.

[0161] Specifically, in the process of training the initial analysis model to obtain the mechanical analysis model, the current sample configuration information of the flexible instrument sample can be determined first, which can be obtained by the flexible instrument sample under the action of random single-point external force, and the control points of the Bezier curve used to characterize the current sample configuration information can be obtained by inputting a plurality of skeleton points of the flexible instrument sample into the configuration model.

[0162] Then a known force is applied to the flexible instrument sample to make the flexible instrument sample produce deformation under the action of the known force.

[0163] Then finite element analysis is performed on the flexible instrument sample to obtain deformation data of the flexible instrument sample under the action of the known force.

[0164] Wherein, the Frontal-Denaunay meshing technology can be used to mesh the initial configuration of the flexible instrument sample, and the meshing is to define the number and position of the finite nodes, and in the subsequent deformation, the physical information (position, velocity, and applied force) of the finite nodes represents different configurations of the flexible instrument sample.

[0165] Figure 7 The cross-sectional meshing diagram corresponding to the flexible instrument sample is shown in Figure 8 The cross-sectional meshing diagram corresponding to the flexible instrument sample is shown in

[0166] Based on the meshing, the finite element algorithm of tetrahedral element is used to perform mechanical modeling on the flexible instrument sample. Figure 9 As shown in the mechanical model, the deformation data (i.e., node displacement) under the configuration can be solved by the known force (i.e., node force) and the node position at the present moment (i.e., current sample configuration information), and the next moment node position can be obtained by adding the deformation data and the node position at the present moment, i.e., the new sample configuration information of the flexible instrument sample is obtained.

[0167] Finally, the current sample configuration information and the known force are used as inputs, and the new sample configuration information is used as a label to train the initial analysis model to obtain the final mechanical analysis model.

[0168] In the embodiment of the application, the deformation data obtained by the finite element analysis and the conversion of the configuration information can simplify the training data, reduce the training difficulty of the initial analysis model, and simplify the complex process of finite element analysis.

[0169] Figure 10 The complete diagram of the mechanical analysis method of the flexible instrument is shown in Figure 10 The method comprises the following steps.

[0170] The related parameters of the flexible instrument sample include the elastic modulus E, the polar moment of inertia I, and the cross-sectional radius R.

[0171] The random single-point external force is applied to the initial configuration of the flexible instrument sample to generate a pre-bend, and a known force is applied to generate a deformation, the tetrahedral element finite element analysis is performed on the flexible instrument sample, training data for training the initial analysis model is obtained, and the initial analysis model is trained by using the training data to obtain the mechanical analysis model.

[0172] In the mechanical analysis of the flexible instrument to be analyzed, in the current time step, the driving force information and the current configuration information of the flexible instrument to be analyzed are obtained, and the current configuration information can be obtained by applying a random single-point external force to the initial configuration of the flexible instrument to be analyzed.

[0173] The current configuration information and the driving force information are input into the mechanical analysis model to obtain new configuration information output by the mechanical analysis model, that is, the new configuration of the flexible instrument to be analyzed is obtained.

[0174] At this point, the current time step ends.

[0175] As shown in Figure 11 on the basis of the above embodiment, the embodiment of the present application provides a mechanical analysis device for flexible instrument, comprising:

[0176] The information acquisition module 111 is configured to acquire the current configuration information and the driving force information of the flexible instrument to be analyzed.

[0177] The mechanical analysis module 112 is configured to input the current configuration information and the driving force information into the mechanical analysis model to obtain the new configuration information of the flexible instrument to be analyzed output by the mechanical analysis model under the action of the driving force.

[0178] The mechanical analysis model is trained based on the deformation data obtained by performing finite element analysis on the flexible instrument sample under the known force.

[0179] On the basis of the above embodiment, the mechanical analysis device for flexible instrument provided in the embodiment of the present application, the flexible instrument to be analyzed is a flexible tubular robot, and the skeleton of the flexible tubular robot is characterized based on a target Bezier curve.

[0180] The information acquisition module is specifically configured to:

[0181] Obtain a plurality of skeleton points of the flexible instrument to be analyzed.

[0182] Input the plurality of skeleton points into the configuration model to obtain the control points of the target Bezier curve output by the configuration model.

[0183] The control point of the target Bezier curve is used to represent the current configuration information, and the configuration model is trained based on a plurality of discrete points on a Bezier curve sample in a three-dimensional space and a control point of the Bezier curve sample.

[0184] On the basis of the above-mentioned embodiments, the mechanical analysis device of the flexible instrument provided in the embodiments of the present application further comprises a space conversion module, which is configured to:

[0185] Before the plurality of skeleton points are input into the configuration model to obtain the control point of the target Bezier curve output by the configuration model, the plurality of skeleton points are projected from a three-dimensional space to a limited flat space;

[0186] After the plurality of skeleton points are input into the configuration model to obtain the control point of the target Bezier curve output by the configuration model, the control point of the target Bezier curve is projected from the limited flat space to the three-dimensional space.

[0187] On the basis of the above-mentioned embodiments, the mechanical analysis device of the flexible instrument provided in the embodiments of the present application, the flexible instrument to be analyzed is controlled by a plurality of stretchable guide wires, and the driving force is a guide wire tension force of the guide wire acting on the flexible instrument to be analyzed.

[0188] On the basis of the above-mentioned embodiments, the mechanical analysis device of the flexible instrument provided in the embodiments of the present application, the current configuration information is obtained under the action of a random single-point external force on an initial configuration of the flexible instrument to be analyzed.

[0189] On the basis of the above-mentioned embodiments, the mechanical analysis device of the flexible instrument provided in the embodiments of the present application, the initial configuration is a new configuration of the flexible instrument to be analyzed obtained in a previous time step, and the driving force information is driving force information of the flexible instrument to be analyzed in a current time step.

[0190] On the basis of the above-mentioned embodiments, the mechanical analysis device of the flexible instrument provided in the embodiments of the present application further comprises a training module, which is configured to:

[0191] Determine current sample configuration information of the flexible instrument sample, and apply the known force to the flexible instrument sample to make the flexible instrument sample deform;

[0192] Perform finite element analysis on the flexible instrument sample to obtain deformation data of the flexible instrument sample under the action of the known force, and determine new sample configuration information of the flexible instrument sample based on the deformation data;

[0193] Train an initial analysis model based on the current sample configuration information, the new sample configuration information and the known force to obtain the mechanical analysis model.

[0194] Specifically, the functions of each module in the mechanical analysis device for flexible instruments provided in this embodiment of the invention correspond one-to-one with the operation flow of each step in the above-mentioned method-like embodiments, and the achieved effects are also the same. For details, please refer to the above embodiments, and this will not be repeated in this embodiment of the invention.

[0195] Figure 12 An example is a schematic diagram of the physical structure of an electronic device, such as... Figure 12 As shown, the electronic device may include: a processor 1210, a communication interface 1220, a memory 1230, and a communication bus 1240, wherein the processor 1210, the communication interface 1220, and the memory 1230 communicate with each other through the communication bus 1240. The processor 1210 can call logical instructions in the memory 1230 to execute the mechanical analysis method of the flexible device provided in the above embodiments. The method includes: acquiring the current configuration information and driving force information of the flexible device to be analyzed; inputting the current configuration information and the driving force information into the mechanical analysis model to obtain the new configuration information of the flexible device to be analyzed under the action of the driving force, output by the mechanical analysis model; wherein the mechanical analysis model is trained based on the deformation data obtained by finite element analysis of a flexible device sample subjected to known forces.

[0196] Furthermore, the logical instructions in the aforementioned memory 1230 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, essentially, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0197] In another aspect, the present application also provides a computer program product comprising a computer program, which can be stored on a non-transitory computer readable storage medium, and the computer program, when executed by a processor, enables a computer to perform the method for mechanical analysis of a flexible instrument provided in the above embodiments, which comprises: obtaining current configuration information and driving force information of a flexible instrument to be analyzed; inputting the current configuration information and the driving force information into a mechanical analysis model to obtain new configuration information of the flexible instrument to be analyzed under the action of the driving force output by the mechanical analysis model; wherein the mechanical analysis model is obtained based on deformation data obtained by performing finite element analysis on a flexible instrument sample subjected to a known force.

[0198] In another aspect, the present application also provides a non-transitory computer readable storage medium having a computer program stored thereon, and the computer program, when executed by a processor, enables a computer to perform the method for mechanical analysis of a flexible instrument provided in the above embodiments, which comprises: obtaining current configuration information and driving force information of a flexible instrument to be analyzed; inputting the current configuration information and the driving force information into a mechanical analysis model to obtain new configuration information of the flexible instrument to be analyzed under the action of the driving force output by the mechanical analysis model; wherein the mechanical analysis model is obtained based on deformation data obtained by performing finite element analysis on a flexible instrument sample subjected to a known force.

[0199] The device embodiments described above are merely illustrative, wherein the units described as separate components can or can not be physically separate, and the components displayed as units can or can not be physical units, i.e., they can be located in one place, or distributed on multiple network units. Part or all of the modules can be selected to achieve the purpose of the embodiment scheme according to actual needs. Those skilled in the art can understand and implement it without creative labor.

[0200] From the above description of the embodiments, those skilled in the art can clearly understand that the embodiments can be realized by means of software plus necessary universal hardware platforms, and of course, can also be realized by hardware. Based on such understanding, the above technical solutions, essentially or in other words, the part that contributes to the prior art, can be embodied in the form of a software product, which can be stored in a computer readable storage medium, such as a ROM / RAM, a magnetic disk, an optical disk, etc., and includes a number of instructions to make a computer device (which can be a personal computer, a server, or a network device, etc.) execute the methods described in the various embodiments or some parts of the embodiments.

[0201] It should be pointed out finally that the above embodiments are only used to illustrate the technical solutions of the present application, but not to limit the same; and although the present application has been described in detail with reference to the foregoing embodiments, it should be appreciated by those skilled in the art that the technical solutions recorded in the foregoing embodiments can be modified, or some technical features thereof can be replaced equivalently; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A mechanical analysis method for a flexible device, characterized in that, include: Obtain the current configuration information and driving force information of the flexible instrument to be analyzed; The current configuration information and the driving force information are input into the mechanical analysis model to obtain the new configuration information of the flexible instrument under the driving force output by the mechanical analysis model. The mechanical analysis model is trained based on deformation data obtained from finite element analysis of a flexible device sample subjected to known forces. The flexible device to be analyzed is a flexible tubular robot, and the skeleton of the flexible tubular robot is characterized based on the target Bézier curve. The current configuration information is obtained based on the following steps: Obtain multiple skeleton points of the flexible device to be analyzed; The multiple skeleton points are input into the configuration model to obtain the control points of the target Bézier curve output by the configuration model; The control points of the target Bézier curve are used to characterize the current configuration information, and the configuration model is trained based on several discrete points on the Bézier curve sample in three-dimensional space and the control points of the Bézier curve sample.

2. The mechanical analysis method for flexible instruments according to claim 1, characterized in that, The step of inputting the plurality of skeleton points into the configuration model to obtain the control points of the target Bézier curve output by the configuration model includes: Project the multiple skeleton points from three-dimensional space to a finite flat space; The process of inputting the plurality of skeleton points into the configuration model to obtain the control points of the target Bézier curve output by the configuration model includes: The control points of the target Bézier curve are projected from the finite flat space to the three-dimensional space.

3. The mechanical analysis method for flexible instruments according to claim 1, characterized in that, The flexible instrument to be analyzed is controlled by multiple stretchable guidewires, and the driving force is the guidewire tension acting on the flexible instrument to be analyzed.

4. The mechanical analysis method for flexible instruments according to claim 1, characterized in that, The current configuration information is obtained from the initial configuration of the flexible instrument to be analyzed under the action of a random single-point external force.

5. The mechanical analysis method for flexible instruments according to claim 4, characterized in that, The initial configuration is the new configuration of the flexible instrument to be analyzed obtained in the previous time step, and the driving force information is the driving force information of the flexible instrument to be analyzed in the current time step.

6. The mechanical analysis method for a flexible device according to any one of claims 1-5, characterized in that, The mechanical analysis model was trained based on the following steps: The current sample configuration information of the flexible device sample is determined, and the known force is applied to the flexible device sample to cause deformation of the flexible device sample; Finite element analysis is performed on the flexible device sample to obtain the deformation data of the flexible device sample under the action of the known force, and the new sample configuration information of the flexible device sample is determined based on the deformation data. Based on the current sample configuration information, the new sample configuration information, and the known forces, the initial analysis model is trained to obtain the mechanical analysis model.

7. A mechanical analysis device for a flexible instrument, characterized in that, include: The information acquisition module is used to acquire the current configuration information and driving force information of the flexible instrument to be analyzed; The mechanical analysis module is used to input the current configuration information and the driving force information into the mechanical analysis model to obtain the new configuration information of the flexible device to be analyzed under the action of the driving force, which is output by the mechanical analysis model. The mechanical analysis model is trained based on deformation data obtained from finite element analysis of a flexible device sample subjected to known forces. The flexible device to be analyzed is a flexible tubular robot, and the skeleton of the flexible tubular robot is characterized based on the target Bézier curve. The information acquisition module is specifically used for: Obtain multiple skeleton points of the flexible device to be analyzed; The multiple skeleton points are input into the configuration model to obtain the control points of the target Bézier curve output by the configuration model; The control points of the target Bézier curve are used to characterize the current configuration information, and the configuration model is trained based on several discrete points on the Bézier curve sample in three-dimensional space and the control points of the Bézier curve sample.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the mechanical analysis method for the flexible device as described in any one of claims 1-6.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the mechanical analysis method for the flexible device as described in any one of claims 1-6.

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