A flexible body-based surface force solving method, device and equipment

Abstract

The embodiment of the application belongs to the technical field of flexible body mechanics analysis, and relates to a method, device and equipment for solving surface force based on a flexible body. The method for solving surface force based on the flexible body comprises the following steps: obtaining a stiffness matrix corresponding to the flexible body; the stiffness matrix is constructed based on an extended spring-mass model and a tetrahedral mesh corresponding to the flexible body; the extended spring-mass model is a spring-mass model for describing the relationship between force and displacement by using the partial derivative of the element strain energy density; obtaining current displacement information of a measurement node in the tetrahedral mesh corresponding to the flexible body; and solving the surface force of the flexible body based on the stiffness matrix and the displacement information of the measurement node, and combining a static force balance discrete iterative equation of the flexible body. The technical scheme adopted by the application can improve the efficiency of solving the surface force based on the flexible body.

Description

Technical Field

[0001] This application relates to the field of flexible body mechanical analysis technology, and in particular to a method, apparatus and equipment for solving surface forces based on flexible bodies. Background Technology

[0002] Mechanical analysis based on flexible bodies can be applied to various fields to solve corresponding technical problems, such as: force / tactile sensor technology (measuring force), engineering structures (such as the design and analysis of bridges, buildings, ships and aircraft), materials science (studying the mechanical properties and deformation behavior of composite materials and polymer materials), robotics (involving kinematic and dynamic analysis of flexible robotic arms, biomimetic robots, etc.), biomechanics (analyzing the mechanical properties of biological tissues and organs, such as the mechanical behavior of soft tissues and bones), automotive industry (studying the flexible response of automobile suspension systems and body structures), civil engineering (analyzing the interaction between soil and foundation structures), aerospace engineering (flexible structure design and dynamic analysis of satellites and spacecraft), and manufacturing (e.g., flexible fixtures).

[0003] Taking the application of force / tactile sensors as an example, existing force / tactile sensors, including those for flexible bodies, mainly employ data-driven methods and linear elastic finite element methods to calculate the surface force of the flexible body. The advantages and disadvantages of these two methods are as follows:

[0004] 1. Although data-driven methods do not require explicit handling of the nonlinearity of flexible materials and structures, they rely on a large amount of collected data. Each sensor needs to be calibrated during mass production, which is time-consuming and labor-intensive. At the same time, because the actual surface forces cannot be accurately obtained, data-driven methods are difficult to accurately calculate forces with high spatial resolution.

[0005] 2. While linear elastic finite element methods can accelerate computation by calculating the stiffness matrix offline, the relationship between displacement and force is nonlinear for hyperelastic materials such as rubber and silicone under large deformations and dynamic loading. The linear elastic assumption leads to distortion in surface force calculations. Furthermore, employing nonlinear material constitutive relations and denser meshes reduces computational efficiency, making real-time computation on embedded platforms difficult. Summary of the Invention

[0006] The purpose of this application is to provide a method, apparatus, and device for solving surface forces based on flexible bodies, so as to improve the efficiency of force calculation.

[0007] In a first aspect, embodiments of this application provide a method for solving surface forces based on flexible bodies, employing the technical solution described below:

[0008] A method for solving surface forces based on flexible bodies, the method comprising the following steps:

[0009] Obtain the stiffness matrix corresponding to the flexible body; wherein, the stiffness matrix is ​​constructed based on the extended spring-mass model and tetrahedral mesh corresponding to the flexible body; the extended spring-mass model is a spring-mass model that describes the force-displacement relationship using the partial derivative of the element strain energy density;

[0010] Obtain the displacement information of the measurement nodes in the tetrahedral mesh corresponding to the flexible body;

[0011] Based on the stiffness matrix and the displacement information of the measurement nodes, the surface force of the flexible body is solved by combining the static equilibrium discrete iterative equation of the flexible body.

[0012] Furthermore, the stiffness matrix (5) is:

[0013]

[0014] in, Represents the stiffness matrix; V0, M i V j C tr CC tr C 01 C 10 V is a constant; V0 represents the volume of the tetrahedron when it is not deformed; M i It is a constant coefficient matrix; e = {e i {i = 1, 2, 3} is a vector consisting of the three edge vectors corresponding to a node of the tetrahedron after deformation; ll is the square of the side length; x i The spatial coordinates of the node; C tr Represents all matrices C i The vector composed of the traces of the matrix C, where the matrix C is... i It is the component of the Cauchy-Green deformation tensor C with respect to the square of the side length l; CC tr Represents all matrices C i ×C j A matrix composed of traces.

[0015] Furthermore, the static equilibrium discrete iterative equation of the flexible body is:

[0016] K(x)dx=-f ext (x)-f int (x) (8)

[0017] Where K(x) represents the stiffness matrix; dx represents the nodal displacement of the node at position x; f ext (x) represents the surface force; f int (x) represents the internal force acting on the node at position x.

[0018] Furthermore, before obtaining the stiffness matrix corresponding to the flexible body, the method further includes the following steps:

[0019] The stiffness matrix is ​​constructed based on the extended spring-mass model corresponding to the flexible body and the tetrahedral mesh.

[0020] Furthermore, the construction of the stiffness matrix based on the extended spring-mass model corresponding to the flexible body and the tetrahedral mesh includes the following steps:

[0021] Obtain the formula for calculating the internal forces of the nodes of the tetrahedral mesh corresponding to the flexible body;

[0022] Based on the constitutive model of hyperelastic materials, a formula for calculating the strain energy density related to the square of the side length of the tetrahedral element is generated; the tetrahedral element is the element used to construct the tetrahedral mesh.

[0023] Based on the strain energy density calculation formula related to the square of the side length, the internal force calculation formula is converted into an internal force calculation formula related to the square of the side length.

[0024] Based on the formula for calculating internal forces related to the square of the side length, the stiffness matrix is ​​derived.

[0025] Furthermore, after obtaining the displacement information of the measurement nodes in the tetrahedral mesh corresponding to the flexible body, the method further includes the following steps:

[0026] Interpolation is set between the displacement information of the measurement node to obtain the interpolated displacement information of the measurement node.

[0027] Furthermore, before solving for the surface force of the flexible body based on the stiffness matrix and the displacement information of the measurement nodes, combined with the static equilibrium discrete iterative equation of the flexible body, the method further includes:

[0028] The static equilibrium discrete iterative equation is constructed based on the static equilibrium equation;

[0029] Set the boundary conditions for the static equilibrium discrete iterative equation.

[0030] Secondly, embodiments of this application provide a surface force solving device based on a flexible body, the device comprising:

[0031] The matrix acquisition module is used to acquire the stiffness matrix corresponding to the flexible body; wherein, the stiffness matrix is ​​constructed based on the extended spring-mass model and tetrahedral mesh corresponding to the flexible body; the extended spring-mass model is a spring-mass model that describes the force-displacement relationship using the partial derivative of the element strain energy density;

[0032] The displacement acquisition module is used to acquire displacement information of the measurement nodes in the tetrahedral mesh corresponding to the flexible body;

[0033] The force-solving module is used to solve the surface force of the flexible body based on the stiffness matrix and the displacement information of the measurement node, combined with the static equilibrium discrete iterative equation of the flexible body.

[0034] Thirdly, embodiments of this application provide a controller, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the surface force solution method based on flexible bodies described above.

[0035] Fourthly, embodiments of this application provide a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the surface force solution method based on flexible bodies described above.

[0036] Compared with the prior art, the embodiments of this application have the following main advantages:

[0037] The embodiments of this application reduce the computational load of the stiffness matrix by using a stiffness matrix constructed based on an extended spring-mass model, and some constant terms can be calculated offline, thereby improving the computational efficiency of solving surface forces based on flexible bodies. Attached Figure Description

[0038] To more clearly illustrate the solutions in this application, the accompanying drawings used in the description of the embodiments of this application will be briefly introduced below. Obviously, the accompanying drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0039] Figure 1 This is an exemplary system architecture diagram in which this application can be applied.

[0040] Figure 2 This is a schematic diagram of the structure of one embodiment of the tetrahedral unit of this application;

[0041] Figure 3 This is a flowchart illustrating an embodiment of the surface force solution method based on flexible bodies according to this application;

[0042] Figure 4 This is a schematic diagram of the structure of one embodiment of the surface force solving device based on flexible bodies of this application;

[0043] Figure 5 This is a schematic diagram of the structure of one embodiment of the computer device of this application. Detailed Implementation

[0044] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains; the terminology used herein in the specification of the application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application; the terms "comprising" and "having," and any variations thereof, in the specification, claims, and foregoing drawings of this application, are intended to cover non-exclusive inclusion. The terms "first," "second," etc., in the specification, claims, or foregoing drawings of this application are used to distinguish different objects, not to describe a particular order.

[0045] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0046] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings.

[0047] For ease of understanding, some basic concepts involved in the embodiments of this application will be described below first.

[0048] "Flexible bodies" are typically made from natural rubber, synthetic rubber, thermoplastic elastomers (TPE), special elastomers, foam elastomers, and bio-based elastomers using solid-state or liquid-state molding processes. Based on a node displacement measuring device, displacement signals of some nodes of the flexible body can be obtained (i.e., the measurement node displacement signals described in the following embodiments), and the surface forces of the flexible body can be determined based on these partial node displacement signals.

[0049] "Measurement node" refers to a portion of the nodes in the finite element model of a flexible body. "Displacement information of measurement node" can be obtained directly or indirectly based on the node displacement measuring device set for the corresponding measurement node.

[0050] A "node" refers to the connection point between finite element units in the finite element model of a flexible body. Specifically, the 3D model of the flexible body can be discretized into multiple virtual finite element units (e.g., tetrahedral units, hexahedral units, etc.), thereby forming a virtual mesh corresponding to the flexible body, composed of multiple unit units. The connection points between the unit units within the mesh can be used as the aforementioned "nodes". For example, taking tetrahedral units as an example, the 3D model of the flexible body to be measured can be pre-meshed offline to obtain a tetrahedral mesh formed by multiple tetrahedral units.

[0051] A "tetrahedral mesh" refers to the mesh obtained by meshing a 3D model of a flexible body using tetrahedral elements. This mesh consists of multiple tetrahedral elements, each containing four nodes. Specifically, meshing can be performed using various existing or future meshing tools / software, such as Code_aster and Gmsh. Figure 2 As shown, for a certain tetrahedral element (denoted as T) after the above meshing... k The unit number is denoted as k), and the spatial coordinates of the four vertices of the tetrahedron are represented by x. a (a = 1, 2, 3, 4) represents the tetrahedron, and the six edges of the tetrahedron are represented by e. a (a = 1, 2, ..., 6) represents this.

[0052] The "Extended Spring-Particle Model" is a method that uses Newton's laws of motion to simulate the deformation of flexible bodies in force / tactile sensors. The flexible body is considered as multiple discrete point masses connected by springs. The motion of the flexible body is divided into tensile and compressive deformation, shear deformation between adjacent springs, and bending deformation. Different types of springs are used to constrain the force states of the point masses in various directions. A point mass can be considered as an object without size or shape, possessing only mass and position. Typically, in a general spring-particle model, the relationship between force and displacement is linear, and the force between point mass i and point mass j is described by the spring constant k: f i =k(x i -x j In this embodiment, the relationship between force and displacement is described by the partial derivative of the element k strain energy density W, i.e.: Therefore, the embodiments of this application are referred to as "extended spring-mass model".

[0053] "Constitutive model of hyperelastic materials" is a hyperelastic model commonly used in materials science and engineering to describe the stress-strain relationship of polymer materials.

[0054] The "static equilibrium discrete iterative equation" is constructed based on the static equilibrium equation of a flexible body. It discretizes the continuous solution space (time or space) into finite points through methods such as gridding while the body remains stationary or relatively stationary under the action of internal and external forces. This allows the equation to be solved numerically. Furthermore, the equation needs to be iteratively calculated so that it can approximate the solution to the problem.

[0055] like Figure 1 As shown, Figure 1 This is an exemplary system architecture diagram in which this application can be applied.

[0056] This application provides a surface force solving system 100 based on flexible bodies, which includes a nodal displacement measuring device 110 and a controller 120.

[0057] The controller communicates with the nodal displacement measuring device to calculate the surface force based on the displacement information of the measuring nodes obtained by the nodal displacement measuring device.

[0058] The node displacement measuring device 110 is used to directly or indirectly measure the displacement information of the measuring nodes of the flexible body 200.

[0059] It should be noted that, in the embodiments of this application, the nodal displacement measuring device can directly measure the current displacement information of the measuring nodes of the flexible body; in addition, some intermediate data (such as sensing signals) can also be collected by the nodal displacement measuring device, and then the intermediate data can be processed by the controller to obtain the displacement information described in the embodiments of this application.

[0060] It should be noted that the surface force solution method and system based on flexible bodies described in this application embodiment can be applied to various fields. For ease of understanding, this application embodiment mainly uses the application of the surface force solution method and system based on flexible bodies in the field of force / tactile sensors as an example for detailed description. In this case, the force / tactile sensor includes a flexible body, and the aforementioned "nodal displacement measuring device 110" can be the "nodal displacement measuring device" of the force / tactile sensor.

[0061] Specifically, force sensors can be, but are not limited to, one-dimensional or multi-dimensional force sensors used to measure pressure or three-dimensional force data, etc.

[0062] Tactile sensors can measure contact force information with objects. This contact force information includes, but is not limited to, array-based multidimensional contact force information, surface deformation information, temperature information, and / or texture information. The contact surface between the tactile sensor and the object is typically made of a flexible material, which is flexible and has good resilience. The implementation of a tactile sensor includes a flexible material, sensing circuitry, computing devices, and contact force information parsing algorithms. Compared to traditional force sensors, tactile sensors can more sensitively sense various forces from multiple dimensions; for example, they can sense dense tangential frictional forces. Tactile sensors can be applied in various fields as needed. For example, a tactile sensor can be placed in a dexterous hand or other grasping actuator to measure contact force information while working with the dexterous hand to perform grasping functions, thereby enabling the grasping of objects of different shapes and softness.

[0063] Specifically, the nodal displacement measuring device can adopt measuring devices based on different principles (such as magnetic field induction, resistance induction, voltage induction, capacitance induction or optical induction) according to the actual situation. Then, the force / tactile sensor can use devices based on the principles of magnetic field induction, resistance induction, voltage induction, capacitance induction or optical induction to solve the surface force.

[0064] In an optional embodiment of this application, the nodal displacement measuring device may refer to an array-type nodal displacement measuring device. An array-type nodal displacement measuring device typically includes multiple sensor units arranged in an array.

[0065] In an optional embodiment of this application, continuing to use a force / tactile sensor as an example, each sensing unit of the node displacement measuring device may include a data acquisition unit and a sensing unit that are correspondingly arranged. The data acquisition unit is used to acquire force / tactile related signals. For example, electrodes, magnetic sources, or pressure-sensitive materials can be embedded within the flexible body. When the flexible body deforms under external force, it can cause the magnetic source, etc., to displace. The sensing unit is used to generate current displacement information of the measuring node based on the acquired signals or to obtain intermediate data for displacement information. For example, the current displacement information of the flexible body measuring node can be calculated based on the changes in resistance, voltage, magnetic field, and other signals generated by the internal material due to the deformation of the flexible body.

[0066] For example, continue as follows Figure 1As shown, continuing with the force / tactile sensor as an example, the acquisition unit of the node displacement measuring device includes a magnetic source embedded in the flexible body 200 (not shown in the figure due to obstruction), and the sensing unit 111 includes a chip corresponding to the magnetic source. This chip is mounted on a circuit board. The sensing unit senses the current displacement information of the measuring node based on the change value of the magnetic source. The subsequent controller can obtain the surface force based on the current displacement information of the measuring node. Continuing with the example of the force / tactile sensor 110 being mounted on the surface of a dexterous hand (omitted in the figure) (for example, forming a mounting surface on the surface of the circuit board corresponding to the force / tactile sensor, and mounting the force / tactile sensor on the contact surface of the dexterous hand through the mounting surface), during the process of the dexterous hand grasping an object, the reaction force exerted by the object on the dexterous hand acts on the surface of the flexible body 200, and then the current displacement information of the measuring node is obtained by the sensing unit. The subsequent controller can obtain the surface force acting on the flexible body (i.e., obtain the surface force of the dexterous hand acting on the object) based on the displacement information.

[0067] The controller is used to execute the steps of the surface force solution method based on flexible bodies described in the embodiments of this application.

[0068] The surface force solution method based on flexible bodies provided in this invention can be applied to computer terminals (PCs); industrial personal computers (IPCs); mobile terminals; servers; systems including terminals and servers, implemented through interaction between terminals and servers; programmable logic controllers (PLCs); field-programmable gate arrays (FPGAs); digital signal processors (DSPs) or microcontroller units (MCUs) and similar controllers. The controller generates program instructions based on a pre-set program and / or incorporating displacement information of some nodes of the flexible body measured by a node displacement measuring device. Specifically, it can be applied to, for example... Figure 5 The computer equipment shown.

[0069] It should be noted that the controller described in the embodiments of this application can be set up separately, or it can be partially or wholly integrated into devices such as nodal displacement measuring instruments, all of which fall within the scope of protection of this application.

[0070] like Figure 3 As shown, Figure 3 This is a flowchart illustrating an embodiment of the surface force solution method based on flexible bodies according to this application.

[0071] Based on the system of the above embodiments, this application provides a method for solving surface forces based on flexible bodies, which is generally executed by controller 130. The above method may include the following steps:

[0072] Step 210 obtains the stiffness matrix corresponding to the flexible body; wherein, the stiffness matrix is ​​constructed based on the extended spring-mass model and tetrahedral mesh corresponding to the flexible body; the extended spring-mass model is a spring-mass model that describes the relationship between force and displacement using the partial derivative of the element strain energy density.

[0073] Step 220: Obtain the displacement information of the measurement nodes in the tetrahedral mesh corresponding to the flexible body.

[0074] Step 230 combines the stiffness matrix, the current displacement information of the measured nodes, and the static discrete iterative equation of the flexible body to solve for the current surface force of the flexible body.

[0075] The embodiments of this application reduce the computational load of the stiffness matrix by using a stiffness matrix constructed based on an extended spring-mass model, and some constant terms can be calculated offline, thereby improving the computational efficiency of solving surface forces based on flexible bodies.

[0076] To facilitate understanding, the above methods and steps will be explained in further detail below.

[0077] Step 210 obtains the stiffness matrix corresponding to the flexible body; wherein, the stiffness matrix is ​​constructed based on the extended spring-mass model and tetrahedral mesh corresponding to the flexible body; the extended spring-mass model is a spring-mass model that describes the relationship between force and displacement using the partial derivative of the element strain energy density.

[0078] In one embodiment, the controller retrieves the stiffness matrix corresponding to the flexible body, either preset or generated in real time, from a memory or server according to a preset address.

[0079] In one embodiment, before obtaining the stiffness matrix corresponding to the flexible body in step 210, the surface force solution method based on the flexible body in this application embodiment may further include the following method steps:

[0080] Step 240 constructs the stiffness matrix based on the extended spring-mass model and tetrahedral mesh corresponding to the flexible body.

[0081] In one embodiment, the stiffness matrix of the flexible body can be constructed in advance, either manually or automatically based on program code. Taking the automatic construction of the stiffness matrix of the flexible body as an example, the controller of the surface force solving system or other controllers can construct the stiffness matrix in advance based on the extended spring-mass model and tetrahedral mesh of the flexible body.

[0082] The embodiments of this application reduce the computational load of the stiffness matrix by using a stiffness matrix constructed based on an extended spring-mass model, and some constant terms can be calculated offline, thereby improving the computational efficiency of solving surface forces based on flexible bodies.

[0083] In one embodiment, step 240 may include the following method steps:

[0084] Step 241 Obtain the formula for calculating the internal forces of the nodes in the tetrahedral mesh of the flexible body.

[0085] like Figure 2 As shown, for a tetrahedral element k of the flexible body after meshing, a node of this tetrahedral element k (i.e., the "mass" in the extended spring-mass model, denoted as a, a = 1, 2, 3, 4) is related to the internal force acting on that node, the strain energy density w of element k, and the node coordinate x. a The relation (1) is as follows:

[0086]

[0087] Among them, f int (x a ) represents the internal force acting on each particle; x a The position of the particle is indicated by ; w represents the strain energy density of element k.

[0088] Step 242 generates a formula for calculating strain energy density based on the constitutive model of the hyperelastic material, which is related to the square of the side length of the tetrahedral element.

[0089] Since the relationship between the total strain energy and strain energy density of a hyperelastic material is as follows:

[0090] W=V0·w(I1,I2,I3)=V0·w(ll)=V0·w(x a (1.1)

[0091] Where V0 is the volume of the tetrahedron when it is not deformed, W is the total strain energy, w is the strain energy density, and I1, I2, I3 are the first, second, and third invariants of the Cauchy-Green deformation tensor C.

[0092] The Cauchy-Green deformation tensor C can also be expressed as... A linear combination, therefore:

[0093] W=V0·w(I1,I2,I3)=V0·w(ll)=V0·w(x a (1.2)

[0094] That is, the strain energy density w is only related to the square of the tetrahedron's side length. It is related only to the spatial coordinates x of the four nodes of the tetrahedron. a related.

[0095] For example, taking the Mooney-Rivlin model in the constitutive model of a hyperelastic body as an example, the strain energy density w can be expressed as formula (2):

[0096] w(I1,I2)=C 01 (I1-3)+C 10 (I0-3) (2)

[0097] Where I1 and I2 are the first and second invariants, respectively, and C 01 and C 10 This is a material-related constant that can be obtained experimentally or, generally, directly by querying a materials database.

[0098] Therefore, the internal forces acting on each node can be expressed as formula (3):

[0099]

[0100] in addition,

[0101] e = {e i {i = 1, 2, 3} is a vector consisting of the three edge vectors corresponding to a node of the tetrahedron after deformation; M i It is a matrix with constant coefficients.

[0102] The derivation of formula (3.3) is as follows:

[0103] Using the Mooney-Rivlin model formula (2), we can conclude that:

[0104]

[0105] because,

[0106] Define trace(C a ) is C tr,a All C tr,a The vector formed is C tr Therefore:

[0107] I1=C tr ×ll (2.4)

[0108] because,

[0109] Define trace(C i ×Cj ) for CC tr,ij All CC tr,ij The resulting matrix is ​​CC tr Therefore,

[0110] trace(C 2 ) = ll T ×CC tr ×ll (2.7)

[0111] therefore,

[0112] According to formulas (2) and (3),

[0113]

[0114] because Therefore, for the i-th node

[0115]

[0116] Among them, for example,

[0117]

[0118] Step 243 transforms the internal force calculation formula into a formula related to the square of the side length based on the strain energy density calculation formula.

[0119] Since the strain energy density w is only related to the square of the tetrahedron's side length... Related, combined with formula Formula (3) is expressed as the square of the side lengths of the tetrahedron. The relationship is as follows:

[0120]

[0121] In the above formula, C tr M a CC tr All are constant matrices / vectors. Where e = {e i ,i=1,2,3} is a vector consisting of the three edge vectors corresponding to a node after the tetrahedron is deformed.

[0122] Step 244 derives the stiffness matrix based on the formula for calculating internal forces related to the square of the side length.

[0123] The formula (5) for the stiffness matrix can then be derived as follows:

[0124]

[0125] For a given initial tetrahedral mesh and material type, V0, Mi V j C tr CC tr V is a constant; V0 represents the volume of the tetrahedron when it is not deformed; M i It is a constant coefficient matrix; e = {e i {i = 1, 2, 3} is a vector consisting of the three edge vectors corresponding to a node of the tetrahedron after deformation; ll is the square of the side length; x i The spatial coordinates of the node; C tr Represents all matrices C i The vector composed of the traces of the matrix C, where the matrix C is... i It is the component of the Cauchy-Green deformation tensor C with respect to the square of the side length l; CC tr Represents all matrices C i ×C j A matrix composed of traces.

[0126] Right now

[0127]

[0128] This application embodiment generates a strain energy density calculation formula that is related to the square of the side length of the tetrahedral element by the constitutive model of the hyperelastic material. Then, based on the strain energy density calculation formula related to the square of the side length, the internal force calculation formula is converted into an internal force calculation formula related to the square of the side length. Then, based on the internal force calculation formula related to the square of the side length, the stiffness matrix is ​​derived, so that the stiffness matrix is ​​mainly related to the square of the side length and the spatial coordinates of the nodes, and the matrix includes multiple constant terms, thereby improving the efficiency of subsequent surface force solution.

[0129] Step 220: Obtain the displacement information of the measurement nodes in the tetrahedral mesh corresponding to the flexible body.

[0130] In one embodiment, the controller can retrieve the displacement information of the measured nodes at the current moment, directly or indirectly measured by the node displacement measuring device described in the previous embodiment, from a memory or server according to a preset address. The surface force at the current moment can then be calculated based on this information. Typically, as described in the previous embodiments, the measured nodes are a subset of nodes in the tetrahedral mesh corresponding to the flexible body.

[0131] In one embodiment, prior to step 220, the displacement information of the measurement node can be obtained based on various existing or future methods. For example, the displacement information of the nodes near the signal change location of the flexible body can be calculated by acquiring the changes in resistance, voltage, magnetic field, and other signals generated by the deformation of the flexible body due to external force measured by the node displacement measuring device 110 described in the above embodiment. For example, the displacement information obtained from the signal change location can be directly used as the displacement information of the measurement node, or the displacement information of the measurement node can be obtained by interpolation / extrapolation based on the spatial location.

[0132] In one embodiment, after obtaining the displacement information of the measurement nodes in the tetrahedral mesh in step 220, the method described in this embodiment may further include the following method steps:

[0133] Interpolation is set between the displacement information of the measurement nodes to obtain the interpolated displacement information of the measurement nodes.

[0134] This application embodiment obtains more node displacement information by setting interpolation at some nodes, which can reduce the density of the tetrahedral mesh, thereby reducing the overall computational load and improving computational efficiency.

[0135] Step 230 combines the stiffness matrix, the displacement information of the measured nodes, and the static equilibrium discrete iterative equation of the flexible body to solve for the surface force of the flexible body.

[0136] Specifically, various existing or future methods can be used to combine the stiffness matrix, displacement information of the measured nodes, and the static equilibrium discrete iterative equations of the flexible body to solve for the surface force. For example, the displacement information and stiffness matrix of the measured nodes can be directly substituted into the aforementioned static equilibrium discrete iterative equations to iteratively solve the equations and obtain the surface force of the flexible body; or, based on a quadratic programming method, the static equilibrium discrete iterative equations can be transformed into an optimization objective function, and the surface force can be obtained by solving the optimization objective function. For example, the static equilibrium discrete iterative equations can be transformed into the following minimization problem:

[0137]

[0138] Where M = K(x)dx + f ext (x)+f int (x) is the residual matrix of the discrete iterative equations for static equilibrium. The above minimization problem can be solved using methods such as L-BFGS, Levenberg-Marquardt, and quadratic programming.

[0139] In one embodiment, prior to step 230, the force-solving method described in this application embodiment may further include the following method steps:

[0140] Step 240: Construct a static equilibrium discrete iterative equation based on the static equilibrium equation of the flexible body.

[0141] When a flexible body reaches static equilibrium, the internal forces and external forces acting on it are equal. After discretizing it into tetrahedral elements in space, and considering the nodes of the elements (whose spatial coordinates are denoted as x) as mass points, its static equilibrium equation (6) is as follows:

[0142] f int (x)+f ext (x)=0 (6)

[0143] For nonlinear materials, the internal force f int The relationship with position x is non-linear, and the above equation can be solved by any exact or approximate solution method, such as Newton iteration, NR iteration, etc.

[0144] For example, using the NR iteration method, the internal forces can be expanded into equation (7):

[0145]

[0146] in, This is the stiffness matrix obtained in step 230 (hereinafter referred to as K(x)), and thus the original static equilibrium equation (6) can be expressed as the following static equilibrium discrete iterative equation (8):

[0147] K(x)dx=-f ext (x)-f int (x) (8)

[0148] Where K represents the stiffness matrix; f int (x) represents the internal force acting on node x; f ext (x) represents the external force acting on node x, which is a variable that needs to be determined in this embodiment of the application.

[0149] The internal force and stiffness matrices can be expressed as follows:

[0150]

[0151]

[0152] Among them W k x represents the strain energy density of element k; i Represents the spatial coordinates of node i; x j This represents the spatial coordinates of node j, which is adjacent to node i.

[0153] For example, continuing with the Mooney-Rivlin incompressible two-parameter model, W k (I1,I2)=C01 (I1-3)+C 10 (I2-3).

[0154] Where I1 and I2 are the first and second invariants, respectively, and C 01 and C 10 W is a material-related constant, which can be obtained experimentally or generally directly from a materials database. Based on the above material constitutive relations, W can be calculated. k .

[0155] The unknowns in the above static equilibrium discrete iterative equation (8) include the displacements of the discrete nodes of the flexible body and the forces acting on the surface nodes. Since the flexible body is generally installed on the support, the nodes on the surface in contact with the support are fixed. Therefore, the displacements of the discrete nodes only need to consider the displacements of the free nodes (i.e., nodes that can move under external forces). The variables to be solved in the above equation (the external forces acting on the surface nodes and the displacements of the free nodes) are greater than the known variables (the displacements of the measurement nodes measured by the sensors). It is an underdetermined equation and needs to be solved by a quadratic programming method, that is, the static equilibrium discrete iterative equation is converted into an optimization objective function, and the optimization objective function is solved to obtain the surface forces.

[0156] Step 250 sets the boundary conditions for the static equilibrium discrete iterative equation.

[0157] In one embodiment, the boundary conditions may include: a sensing surface boundary and a support boundary; wherein, the sensing surface boundary is the surface of the flexible body used for sensing, and the discrete nodes of the sensing surface boundary are freely movable; the support boundary is the surface of the flexible body in contact with a support (for example, taking the measurement of the force on the surface of a dexterous hand by a tactile sensor as an example, the flexible body needs to be fixed to the interaction surface of the fingers of the dexterous hand, and the interaction surface of the fingers forms a support to fix the flexible body), and the discrete nodes of the support boundary are subject to fixed constraints.

[0158] Specifically, the boundary of a flexible body mainly consists of two parts: first, the sensing surface boundary, which is the surface on which the flexible body is used for sensing, i.e., the surface that bears force / sensors tactile sensation. Discrete nodes on this surface can move freely, and the force (i.e., f) at the nodes... ext One boundary is to be solved; the other boundary is the support boundary, which is the surface where the flexible body contacts the support. The nodes on this surface are fixed and cannot move.

[0159] By setting boundary conditions for the static equilibrium discrete iterative equations, the range of surface forces to be solved can be limited, thereby improving the accuracy of surface force determination.

[0160] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. This computer program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the methods described above. The aforementioned storage medium can be a non-volatile storage medium such as a magnetic disk, optical disk, or read-only memory (ROM), or random access memory (RAM).

[0161] It should be understood that although the steps in the flowcharts of the accompanying figures are shown sequentially as indicated by the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the accompanying figures may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times, and their execution order is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the sub-steps or stages of other steps.

[0162] Further reference Figure 4 As a response to the above Figure 3 To implement the method shown, this application provides an embodiment of a surface force solving device based on a flexible body. This device embodiment is similar to... Figure 3 Corresponding to the method embodiment shown, the device can be specifically applied to a controller.

[0163] like Figure 4 As shown, the surface force solving device 300 based on a flexible body according to an embodiment of this application includes:

[0164] The matrix acquisition module is used to obtain the stiffness matrix corresponding to the flexible body; wherein, the stiffness matrix is ​​constructed based on the extended spring-mass model and tetrahedral mesh corresponding to the flexible body; the extended spring-mass model is a spring-mass model that describes the force-displacement relationship using the partial derivative of the element strain energy density;

[0165] The displacement acquisition module is used to acquire displacement information of the measurement nodes in the tetrahedral mesh corresponding to the flexible body;

[0166] The force solution module is used to solve the surface forces of a flexible body based on the stiffness matrix and displacement information of the measured nodes, combined with the static equilibrium discrete iterative equations of the flexible body.

[0167] In one embodiment, the surface force solving device 300 may further include:

[0168] The matrix construction module is used to construct the stiffness matrix based on the extended spring-mass model and tetrahedral mesh corresponding to the flexible body.

[0169] In one embodiment, the matrix construction module may include:

[0170] The internal force acquisition submodule is used to obtain the formulas for calculating the internal forces of the nodes in the tetrahedral mesh of a flexible body.

[0171] The strain energy density calculation submodule is used to generate a strain energy density calculation formula that is related to the square of the side length of the tetrahedral element based on the constitutive model of the hyperelastic material.

[0172] The internal force conversion submodule is used to convert the internal force calculation formula based on the strain energy density related to the square of the side length into an internal force calculation formula related to the square of the side length.

[0173] The stiffness matrix derivation submodule is used to derive the stiffness matrix based on the formula for calculating internal forces related to the square of the side length.

[0174] In one embodiment, the stiffness matrix is:

[0175]

[0176] in, Represents the stiffness matrix; V0, M i V j C tr CC tr C 01 C 10 V is a constant; V0 represents the volume of the tetrahedron when it is not deformed; M i It is a constant coefficient matrix; e = {e i {i = 1, 2, 3} is a vector consisting of the three edge vectors corresponding to a node of the tetrahedron after deformation; ll is the square of the side length; x i The spatial coordinates of the node; C tr Represents all matrices C i The vector composed of the traces of the matrix C, where the matrix C is... i It is the component of the Cauchy-Green deformation tensor C with respect to the square of the side length l; CC tr Represents all matrices C i ×C j A matrix composed of traces.

[0177] In one embodiment, the surface force solving device 300 may further include:

[0178] Discrete building module, used to construct discrete iterative equations for static equilibrium based on static equilibrium equations;

[0179] The boundary setting module is used to set the boundary conditions for the static equilibrium discrete iterative equations. The boundary conditions include: sensing surface boundary and support boundary. The sensing surface boundary is the surface of the flexible body used for sensing, and the discrete nodes of the sensing surface boundary can move freely. The support boundary is the surface of the flexible body in contact with the support, and the discrete nodes of the support boundary are subject to fixed constraints.

[0180] In one embodiment, the discrete iterative equation for the static equilibrium of the flexible body is:

[0181] K(x)dx=-f ext (x)-f int (x) (8)

[0182] Where K(x) represents the stiffness matrix; dx represents the nodal displacement of the node at position x; f ext (x) represents the surface force; f int (x) represents the internal force acting on the node at position x.

[0183] In one embodiment, the surface force solving device 300 may further include:

[0184] The displacement interpolation module is used to set interpolation between the displacement information of nodes to obtain the displacement information of the nodes after the difference.

[0185] To address the aforementioned technical problems, embodiments of this application also provide a method such as... Figure 5 The computer equipment shown.

[0186] The computer device can be a terminal or a server.

[0187] The server can be a standalone physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server providing basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, CDN (Content Delivery Network), and big data and artificial intelligence platforms. The terminal can be a smartphone, tablet, laptop, desktop computer, smart speaker, smartwatch, etc., but is not limited to these. The terminal and server can be directly or indirectly connected via wired or wireless communication, which is not limited herein.

[0188] The computer device 6 includes a memory 61, a processor 62, and a network interface 63 that are interconnected via a system bus. It should be noted that only the computer device 6 with components 61-63 is shown in the figure; however, it should be understood that it is not required to implement all the shown components, and more or fewer components can be implemented alternatively. Those skilled in the art will understand that the computer device described here is a device capable of automatically performing numerical calculations and / or information processing according to pre-set or stored instructions, and its hardware includes, but is not limited to, microprocessors, application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), digital signal processors (DSPs), embedded devices, etc.

[0189] The memory 61 includes at least one type of readable storage medium, including flash memory, hard disk, multimedia card, card-type memory (e.g., SD or DX memory), random access memory (RAM), static random access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic memory, magnetic disk, optical disk, etc. In some embodiments, the memory 61 may be an internal storage unit of the computer device 6, such as the hard disk or memory of the computer device 6. In other embodiments, the memory 61 may also be an external storage device of the computer device 6, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc., equipped on the computer device 6. Of course, the memory 61 may include both the internal storage unit and its external storage device of the computer device 6. In this embodiment, the memory 61 is typically used to store the operating system and various application software installed on the computer device 6, such as program code for a surface force solution method based on flexible bodies. In addition, the memory 61 can also be used to temporarily store various types of data that have been output or will be output.

[0190] In some embodiments, the processor 62 may be a central processing unit (CPU), controller, microcontroller, microprocessor, or other data processing chip. The processor 62 is typically used to control the overall operation of the computer device 6. In this embodiment, the processor 62 is used to run program code stored in the memory 61 or process data, for example, to run program code for a surface force solution method based on flexible bodies.

[0191] The network interface 63 may include a wireless network interface or a wired network interface, which is typically used to establish communication connections between the computer device 6 and other electronic devices.

[0192] This application also provides another embodiment, namely, providing a computer-readable storage medium storing a surface force solving program based on a flexible body, the surface force solving program based on a flexible body being executable by at least one processor to cause the at least one processor to perform the steps of the surface force solving method based on a flexible body as described above.

[0193] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk), and includes several instructions to cause a terminal device (which may be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in the various embodiments of this application.

[0194] Obviously, the embodiments described above are only some embodiments of this application, not all embodiments. The accompanying drawings show preferred embodiments of this application, but do not limit the patent scope of this application. This application can be implemented in many different forms; rather, the purpose of providing these embodiments is to provide a more thorough and comprehensive understanding of the disclosure of this application. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing specific embodiments, or make equivalent substitutions for some of the technical features. Any equivalent structures made using the content of this application's specification and drawings, directly or indirectly applied to other related technical fields, are similarly within the scope of patent protection of this application.

Claims

1. A method for solving surface forces based on flexible bodies, characterized in that, The method includes the following steps: Obtain the stiffness matrix corresponding to the flexible body; wherein, the stiffness matrix is ​​constructed based on the extended spring-mass model and tetrahedral mesh corresponding to the flexible body; the extended spring-mass model is a spring-mass model that describes the force-displacement relationship using the partial derivative of the element strain energy density; Obtain the displacement information of the measurement nodes in the tetrahedral mesh corresponding to the flexible body; Based on the stiffness matrix and the displacement information of the measurement nodes, the surface force of the flexible body is solved by combining the static equilibrium discrete iterative equation of the flexible body.

2. The surface force solution method based on flexible bodies according to claim 1, characterized in that, The stiffness matrix (5) is: in, Represents the stiffness matrix; V0, M i V j C tr CC tr C 01 C 10 V is a constant; V0 represents the volume of the tetrahedron when it is not deformed; M i It is a constant coefficient matrix; e = {e i {i = 1, 2, 3} is a vector consisting of the three edge vectors corresponding to a node of the tetrahedron after deformation; ll is the square of the side length; x i The spatial coordinates of the node; C tr Represents all matrices C i The vector composed of the traces of the matrix C, where the matrix C is... i It is the component of the Cauchy-Green deformation tensor C with respect to the square of the side length l; CC tr Represents all matrices C i ×C j A matrix composed of traces.

3. The surface force solution method based on flexible bodies according to claim 1 or 2, characterized in that, The static equilibrium discrete iterative equation of the flexible body is: K(x)dx=-f ext (x)- f int (x) (8) Where K(x) represents the stiffness matrix; dx represents the nodal displacement of the node at position x; f ext (x) represents the surface force; f int (x) represents the internal force acting on the node at position x.

4. The surface force solution method based on flexible bodies according to claim 1 or 2, characterized in that, Before obtaining the stiffness matrix corresponding to the flexible body, the method further includes the following steps: The stiffness matrix is ​​constructed based on the extended spring-mass model corresponding to the flexible body and the tetrahedral mesh.

5. The surface force solution method based on flexible bodies according to claim 4, characterized in that, The process of constructing the stiffness matrix based on the extended spring-mass model corresponding to the flexible body and the tetrahedral mesh includes the following steps: Obtain the formula for calculating the internal forces of the nodes of the tetrahedral mesh corresponding to the flexible body; Based on the constitutive model of hyperelastic materials, a formula for calculating the strain energy density related to the square of the side length of the tetrahedral element is generated; the tetrahedral element is the element used to construct the tetrahedral mesh. Based on the strain energy density calculation formula related to the square of the side length, the internal force calculation formula is converted into an internal force calculation formula related to the square of the side length. Based on the formula for calculating internal forces related to the square of the side length, the stiffness matrix is ​​derived.

6. The surface force solution method based on flexible bodies according to claim 1 or 2, characterized in that, After obtaining the displacement information of the measurement nodes in the tetrahedral mesh corresponding to the flexible body, the method further includes the following steps: Interpolation is set between the displacement information of the measurement node to obtain the interpolated displacement information of the measurement node.

7. The surface force solution method based on flexible bodies according to claim 1 or 2, characterized in that, Before solving for the surface force of the flexible body based on the stiffness matrix and the displacement information of the measurement nodes, combined with the static equilibrium discrete iterative equation of the flexible body, the method further includes: The static equilibrium discrete iterative equation is constructed based on the static equilibrium equation; Set the boundary conditions for the static equilibrium discrete iterative equation.

8. A surface force solving device based on a flexible body, characterized in that, The device includes: The matrix acquisition module is used to acquire the stiffness matrix corresponding to the flexible body; wherein, the stiffness matrix is ​​constructed based on the extended spring-mass model and tetrahedral mesh corresponding to the flexible body; the extended spring-mass model is a spring-mass model that describes the force-displacement relationship using the partial derivative of the element strain energy density; The displacement acquisition module is used to acquire displacement information of the measurement nodes in the tetrahedral mesh corresponding to the flexible body; The force-solving module is used to solve the surface force of the flexible body based on the stiffness matrix and the displacement information of the measurement node, combined with the static equilibrium discrete iterative equation of the flexible body.

9. A controller comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the surface force solution method based on flexible bodies as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the surface force solution method based on flexible bodies as described in any one of claims 1 to 7.

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